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Piaget’s Theory of Intellectual Development
Third Edition
Herbert P. Ginsburg and Sylvia Opper
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e-Book2016InternationalPsychotherapyInstitute
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Copyright©1988HerbertP.GinsburgandSylviaOpper
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Table of Contents
1 Biography and Basic Ideas
2 Infancy
3 The Years 2 through 11: The Semiotic Function and Piaget’s Early Work
4 The Years 2 through 11: Piaget’s Later Work
5 Adolescence
6 Learning, Development, and Education
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Foreword
TodayPiagetseemstobethechildpsychologistintheeyesoftheAmericanpublic.Hisnamecrops
up in countless publications, and his ideas are discussed in many different circles—psychological,
educational,philosophical,psychiatric.Inspiteofhispopularity,however,heremainsadifficultauthor,
especiallyforanEnglish-speakingreader.Piaget’sTheoryofIntellectualDevelopment is thereforevery
welcome.Thanks to the joint effortsof aPiagetian-trainedpsychologist andanAmericanprofessorof
developmentalpsychology,wenowhave abook thatbringsout andexplains thedifficulties sooften
encounteredbystudentsofPiaget.Nottofeeldisturbedatanymisinterpretationofhisthoughtisarare
pleasurewhenreadingabookaboutPiaget,andIwasdelightedtofindthattheauthorshavenotfallen
intothetwomostcommonpitfalls:theyhavenotoversimplified,norhavetheybeencontenttoadoptthe
difficultPiagetianterminologywithoutadequateexplanation.
The undergraduate students of Piagetian theory, for whom this book is intended, are really
fortunate to have this book to help them understand some of the more abstruse concepts; even our
Genevanstudentsdonotfindhistheoryeasytograsp.EachtimePiagetcomesacrossabehavior,however
trivial itmay seem, he seeks to explain itwith reference to his theoretical framework,which is thus
continuously being refined and enriched; with Piaget, the empirical is never separated from the
theoretical.Itisthiscontinuingdevelopmentthatstudentsfinddifficult,andthatissoclearlybroughtto
light in thisbook.The authors in fact adopt this technique, passing from theory to example, andvice
versa,inawaywhichisbothclearandcomprehensible.Theirexamplesofchildren’sbehaviorhavebeen
most carefully selected, and I particularly like the use of various aspects of one example to illustrate
differenttheoreticalpoints.Ialsothinkitusefulthattheauthorshaveincludedotherinterpretationsof
somePiagetianconcepts,thusgivingthereaderanideaofPiaget’spositionincontemporarypsychology.
Infact,althoughthiswell-writtenbookisprimarilydestinedforstudents,itisquiteclearthatitwill
enablemanyreadersalreadywellacquaintedwithPiaget’stheorytoexplorehisreasoningmoredeeply.
It is not concernedwith lengthydiscussionor criticism,butprovides, as itwas intended to, a concise
descriptionandclearanalysisofPiaget’sthoughtandwork.
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BärbelInhelder
Geneva,Switzerland
ProfessorofDevelopmentalPsychology
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Preface
Sincetheearly1950s,Piaget’stheoryhasdominatedthefieldof intellectualdevelopment.From
1920until his death in1980, Piaget andhis collaboratorsproducedmoreworthwhile research and
theory than any other individual or group of investigators in child psychology. The sheer volume of
Piaget’soutputisstaggering.Hepublishedmorethanfortyfull-lengthbooksandmorethanahundred
articlesinthefieldofchildpsychology.
Butnumbersalonedonottellthestory.Piagetcapturedtheinterestofmodernpsychologistsand
educators for several important reasons.First,he introduceda scoreofnewand interestingproblems
whichpreviouslywentunnoticed.Forexample,itwasPiagetwhodiscoveredtheprofoundlycomplex
problemofconservation,whichhascaughttheimaginationofmanyinvestigators.Thisproblemtapsone
aspectofthechild’sabilitytoconstructarealitywhichtranscendsthemereappearanceofthings.Second,
Piaget’s theorieshave reorientedcurrent conceptionsof the child’sdevelopment.His ideasarenovel,
imaginative,andcomprehensive.Theyhavesubstantiallysupplantedthestimulus-responsebehaviorist
theoryasthemostinfluentialpointofviewindevelopmentalpsychology.Andfinally,ofalltheoriesof
development, Piaget’s is the one most securely founded upon the study of the child. None of the
investigatorswhose theories have beenused to explain the development of children—Freud, Lewin,
Hull,Miller andDollard, Skinner,Werner—has studied childrenas extensively ashasPiaget. In fact,
someof these figures— for example, Freud,Hull, Skinner—hardly studied children at all. Gesell did
studychildren,butdidnotproduceaviabletheory.Bycontrast,fornearlysixtyyearsPiagetobserved,
interviewed,andtestedchildrenofallages,andthisenormoussetofempiricaldataisthefoundationof
histheory.
Clearly, then, persons interested in human development should at the least be familiar with
Piaget’swork.Unfortunately, this is no simple task. For themost part, Piaget is an extremely difficult
writer:hisideasarenovelandhardtoassimilate;hisstyleofwritingisnottheultimateinlucidity;many
of his theoretical terms sound strange to the ears of the professional psychologist or educator, and
certainlytothenovice;andhislatercontributionsarestatedintermsofsymboliclogicandmathematics.
Thesedifficultieshaveseveralunfortunateconsequences.OneisthatthejoboflearningaboutPiagetis
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veryonerousindeed.TheinterestedreaderseemstorequireatextintroducingPiaget’sideasbeforehe
orsheisabletoprofitfromtheprimarysourcesthemselves.
Wehavewritten this book in the hope of assisting the beginning student of Piaget. It is a brief
introductiontohisbasic ideasand findingsconcerningthechild’s intellectualdevelopment.Wehope
that the book will be useful to students, particularly undergraduates, in psychology, education, and
alliedfields.Thebookmaybeusedassupplementaryreading, inwholeorinpart, incoursesdealing
withchildpsychology,cognition,educationalpsychology,andsoon.Wehope,too,thatthebookmaybe
readwithprofitbythegeneralreader.
Despitethefactthatthebookisanintroduction,andabriefoneatthat,wehavetriedtopresentthe
material in some depth. That is, we have assumed that the reader, although knowing little about
psychologyandPiaget,isintelligentandwillingtoworkabittounderstandPiaget’sideas.Second,we
haveassumedthatthereadershouldnotbeshieldedfromdifficultaspectsofPiaget’stheory,liketheuse
ofsymboliclogic.
Naturally,inabookofthistype,wehavehadtobeselective.NodoubtreadersfamiliarwithPiaget
willnoticethatwehaveomittedanumberofimportanttopics.Forexample,wedonotdescribethework
on perception, or the research on concepts of geometry. We make no pretense at offering a
comprehensive treatment of Piaget’s work. Rather, we have tried to present, as lucidly as possible,
Piaget’smajortheoreticalnotionsconcerningintellectualdevelopment,aswellassomeoftheresearch
onwhichtheyarebased.SincetheaimofthisbookistopresentclearlythebasicsofPiaget’sideas,we
havekeptourowncritiquetoaminimum.Forthesamereason,andalsotoavoidavery longbook,we
havenot referredextensively to independent investigators’ researchonPiaget’s ideas. So thisbook is
neitheracritiquenorareviewoftheliterature;itisanintroductiontoPiaget.
Theaimofthisthirdeditionistoupdatethesecond.Sincethewritingofthesecondedition,Piaget
and his collaborators produced new research and theory on a variety of topics, mainly concerning
developmentandlearning.Itisquiteremarkablethatduringthelasttenyearsofhislife—whenhewas
inhisseventiesandearlyeighties—Piagetwasengagedinamajorexpansionandevenrevisionofhis
theory. In this edition,we outline thesemajor changes and thereby complete our account of Piaget’s
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theory.(ForadetailedexpositionoflatedevelopmentsinPiaget’stheory,seeGallagherandReid,1981.)
Whileintroducingthisnewmaterial,wehaveattemptedtoretainfeaturesthatwethinkmadethebook
valuabletomanyreaders,namely,anexpositionwhichissimpleandclearandyetfaithfultothedepth
ofPiaget’sideas.
Chapter1beginswithabriefbiographyofPiagetandoutlinessomeofhisbasicideas.Chapter2
dealswithhisaccountofdevelopmentininfancy.Thefocusisonanaspectofthetheorywhichhasnot
beensufficientlystressed,namely,theaccountoflearningandmotivation.Chapter3describesPiaget’s
earlyresearchandtheoryconcerningthechildfromabout2to11yearsofage.Amongthetopicscovered
arethedevelopmentofsymbolism,thechild’smethodsofcommunication,andmoraljudgment.Chapter
4presentsPiaget’sresearchonchildrenfromabout2or3to11or12yearsofageandcoverstheclassic
workonclasses,relations,number,andconservation,aswellasnewerresearchonfunctions,imagery,
andmemory.Weincludecross-culturalwork,wherepertinent.Chapter5discussesadolescentthought,
describing Piaget’s use of logic as a model for adolescent thought and his notion of adolescent
competence.Chapter6presentsadiscussionof learninganddevelopmentandcoversmaterials from
Piaget’slastworks,publishedduringtheperiodfromthemid-1970sonward.Itincludesdescriptionsof
hisrevisedmodelof theequilibrationprocess, theroleofdisturbancesanddisequilibria, thespiralof
knowing, and possibility and necessity. We have followed this with an expanded discussion of the
implicationsofPiaget’sworkforeducation.Wehopethatbytheendofthebookstudentswillhavesome
insightintoPiaget’sviewsandwillappreciatethemagnitudeofhiscontribution.
Finally, we have employed several bibliographic conventions. If a book of Piaget’s has been
translatedintoEnglish,weuseitsEnglishtitleandpublicationdate;otherwise,weusetheFrench.Ifa
bookisfrequentlycited,werefertoitbyitsinitials.Thus,foreasyreference,TheOriginsofIntelligencein
Childrenbecomes01.
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Acknowledgments
Theauthorswishtothankthefollowingpublishersforpermissiontoreprintinthisbookcopyrighted
materialsbyPiaget:
Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique et Phénocopie (Paris:
Hermann,1974),Figureofthespiralofknowing,reprintedbypermissionofHermann.
The Child’s Conception of Number (with Alina Szeminska), translated by C. Gattegno and F. M.
Hodgson(London:Routledge&KeganPaulLtd.,1952),pp.45,50,75,79,82,124-125,reprintedby
permissionofRoutledge&KeganPaulLtd.andW.W.Norton&Co.,Inc.
TheChild’sConceptionoftheWorld,translatedbyJ.andA.Tomlinson(NewYork:Harcourt,Brace&
World, Inc., 1929), pp. 258-259, 274, reprinted by permission of Routledge & Kegan Paul Ltd. and
HumanitiesPress,Inc.
The Construction of Reality in the Child, translated by M. Cook (New York: Basic Books, Inc.,
Publishers,1954),pp.14,25,51,76,77,79-80,reprintedbypermissionofRoutledge&KeganPaulLtd.
andBasicBooks,Inc.,Publishers.
TheEarlyGrowthofLogicintheChild,translatedbyE.A.LunzerandD.Papert(London:Routledge
&KeganPaulLtd.,1964),pp.21,102,109,reprintedbypermissionofRoutledge&KeganPaulLtd.and
Harper&Row,Publishers.
“EquilibrationandtheDevelopmentofLogicalStructures,”inDiscussionsonChildDevelopment:The
FourthMeetingoftheWorldHealthOrganization,StudyGrouponthePsychobiologicalDevelopmentofthe
Child, edited by J. M. Tanner and B. Inhelder (London: Tavistock Publications Ltd., 1956), p. 102,
reprintedbypermissionoftheWorldHealthOrganization.TheGrowthofLogical
ThinkingfromChildhoodtoAdolescence, translatedbyA.ParsonsandS.Seagrin(NewYork:Basic
Books,Inc.,Publishers,1958),pp.56,60,70-71,75,103,116-17,129,130,reprintedbypermissionof
Routledge&KeganPaulLtd.andBasicBooks,Inc.,Publishers.
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JudgmentandReasoningintheChild,translatedbyM.Warden(NewYork:Harcourt,Brace&World,
Inc., 1926), pp. 17-18, 87, 88, 123, reprinted by permission of Routledge & Kegan Paul Ltd. and
HumanitiesPress,Inc.
TheLanguageandThoughtoftheChild,translatedbyM.Gabain(London:Routledge&KeganPaul
Ltd.,1926),pp.35,37,41,126,130,149,reprintedbypermissionofRoutledge&KeganPaulLtd.and
HumanitiesPress,Inc.
TheMoralJudgmentoftheChild,translatedbyM.Gabain(NewYork:Harcourt,Brace&World,Inc.,
1932),pp.55,60,122,126,141,reprintedbypermissionofRoutledge&KeganPaulLtd.andCrowell-
Collier,Inc.
TheOriginsof Intelligence inChildren, translatedbyM.Cook (NewYork: InternationalUniversity
Press,1952),reprintedbypermissionofDelachaux&Niestlé.
Play,Dreams,andImitationinChildhood,translatedbyC.GattegnoandF.M.Hodgson(NewYork:W.
W.Norton&Co.,Inc.,1951,1962),pp.10,30,31,46-47,55-56,63,65,96,218,222,224,225,231,
232,bypermissionofRoutledge&KeganPaulLtd.andW.W.Norton&Co.,Inc.
The Psychology of Intelligence, translated by M. Percy and D. E. Berlyne (London: Routledge &
KeganPaulLtd.,1950),pp.6,7,reprintedbypermissionofRoutledge&KeganPaulLtd.andHumanities
Press,Inc.
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Biography and Basic Ideas
WeshallbeginbyreviewingJeanPiaget’slifetogivethereaderanideaoftheinfluencesaffecting
hisworkandofthewidescopeofhisactivities;thenweshalldiscussinapreliminarywaysomebasic
ideasandthemesthatunderliehistheoryofintellectualdevelopment.
BIOGRAPHY1
JeanPiagetwasbornonAugust9,1896,inthesmalluniversitytownofNeuchatel,Switzerland.
His father was a historian who specialized in medieval literature, and his mother was a dynamic,
intelligent,andreligiouswoman.Piagetshowedanearlyinterestinnature;heenjoyedobservingbirds,
fish,andanimalsintheirnaturalhabitat.Atschool,too,hisleaningsweretowardthebiologicalsciences.
But his was no ordinary schoolboy enthusiasm: when he was only 10 years old, a natural history
magazinepublishedhisfirstarticle,describinganalbinosparrowseeninthepark.Soonhewasableto
help the director of the natural history museum of Neuchatel, where his task was to assist in the
classificationofthemuseum’szoologycollection.Atthistime,hebegantostudymollusksand,from15to
18yearsofage,publishedaseriesofarticlesontheseshellfish.Oneofthepapers,writtenwhenPiaget
wasonly15yearsold,resultedintheofferofthepostofcuratorofthemolluskcollectionattheGeneva
naturalhistorymuseum.Piagethadtodeclinethepositiontocompletehishighschoolstudies.
Asanadolescenthespentavacationwithhisgodfather,SamuelCornut,aSwissscholar,whowasto
haveaconsiderableinfluenceonhisintellectualdevelopment.CornutfeltthatPiaget’shorizonswere
too restricted in the direction of the biological sciences and decided to introduce the young man to
philosophy,particularlytotheworkofBergson.Consequently,Piaget,whountilthenhadgivenhismain
attentiontothestudyofbiologyandthenaturalbehavioroforganisms,nowturnedhisthoughtstoother
pursuits.Hisreadingsbroadenedtoincludephilosophy,religion,andlogic.Contactwiththesesubjects
ledeventuallytoaspecialinterestinepistemology,thebranchofphilosophyconcernedwiththestudyof
knowledge.Hebecamecurioustodiscovertheanswerstosomeofthebasicquestionsofthediscipline:
Whatisknowledge?Howisitacquired?Canonegainanobjectiveunderstandingofexternalreality,oris
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one’sknowledgeof theworld coloredanddistortedby internal factors?Although fascinatedby these
issues, Piaget felt that their solution could not be provided solely by philosophy. In comparing the
attributesofphilosophyandscience,Piaget’sconclusionwasthat“anideaisonlyanidea,whileafactis
only a fact” (Insights and Illusions in Philosophy, 1971b). In other words, he was convinced that the
philosophicalapproachistoospeculative,andthescientificapproachissometimestoofactual.Whatis
neededisalinkagebetweenthetwo:anexperimentalphilosophy,asitwere.
Wesee,then,thatduringhisadolescencePiagetconcentratedontwomajorintellectualpursuits:
biologyandepistemology.Thereis,ofcourse,agreatgapbetweenthetwodisciplines.Oneisconcerned
with life and the other with knowledge. One employs scientific methods and the other relies on
speculation.Piagetbegantowonderwhetheritmightnotbepossibletobridgethisgapbetweenthetwo
disciplinesandtofindsomewayofintegratinghisbiologicalandepistemologicalinterests.Howcould
oneinvestigatetheveryfascinatingproblemsofknowledge,andatthesametimeutilizethescientific
frameworkofbiology?
Although interested in epistemological questions, Piaget put his major efforts into the study of
biology. In 1916he completedhis undergraduate studies in natural sciences at theuniversity of his
hometown,Neuchatel.Only twoyears later, at theageof21,he submitted to the sameuniversityhis
dissertationon themollusksof theValais regionof Switzerlandand received thedegreeofDoctorof
Philosophy.
After finishing his formal studies, Piaget decided to explore psychology. He left Neuchatel for
ZurichtoworkintwopsychologicallaboratoriesandatBleuler’spsychiatricclinic.Hethendiscovered
psychoanalysisandtheideasofFreud,Jung,andothersandlaterpublishedanarticleontherelations
betweenpsychoanalysisandchildpsychology.In1919heleftZurichforParis,wherehespenttwoyears
at the Sorbonne University, studying clinical psychology as well as logic, epistemology, and the
philosophyofscience.Hisencounterwithphilosophyoncemoreconvincedhimthat it isnecessaryto
supplementpurespeculationwiththescientificapproach.
ItwasduringhisstayinParisthatanopportunityarosewhichwastoshapethedirectionofhis
futurework.In1920heacceptedapostwithDr.TheophileSimonintheBinetLaboratoryinParis.(With
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Alfred Binet, Simon had earlier constructed the first successful intelligence test.) Piaget’s taskwas to
develop a standardized French version of certain English reasoning tests. In a standardized test the
wordingofthequestionsandtheirorderofpresentationarepreciselydefined,andtheexaminermust
notdeviatefromthepre-establishedprocedure.Theaimofastandardizedtestistopresenteachsubject
with the same problems so that the subsequent differences in performance can be attributed not to
variations in the questions, but to differences in the subjects’ intelligence (or other traits being
measured).
Attheoutset,Piagetwasnotveryenthusiasticaboutthework.Standardizingatestcanbeavery
mechanical and tedious process. But then three major events occurred. First, although intelligence
testingusuallyfocusesonthechild’sabilitytoproducecorrectresponses,Piagetfeltthat,onthecontrary,
thechild’sincorrectanswerswerefarmorefascinating.Whenquestioningthechildren,Piagetfoundthat
thesamewronganswersoccurredfrequentlyinchildrenofaboutthesameage.Moreover,therewere
different kinds of commonwrong answers at different ages. Piaget puzzled on themeaning of these
mistakes. He came to the conclusion that older children are not just “brighter” than younger ones;
instead,thethoughtofyoungerchildrenisqualitativelydifferentfromthatofolderones.Inotherwords,
Piaget came to reject a quantitative definition of intelligence—a definition based on the number of
correct responseson a test. The real problemof intelligence, Piaget felt,was todiscover thedifferent
methodsofthinkingusedbychildrenofvariousages.
Second,Piagetsoughtadifferentmethodforthestudyofintelligence.Heimmediatelyrejectedthe
standardized testprocedure. Suchanapproach,he felt,was too rigid: for example, itmight lead toa
considerablelossofinformationifthechilddidnotunderstandthequestions.Consequently,hesoughta
lessstructuredmethodwhichwouldgivehimmorefreedomtoquestionthechild.Hissolutionwasto
apply to the task his previous experience in clinical psychology: he modified psychiatric interview
techniquestomakethemsuitable for thestudyofchildren’s thought.Thenewmethodwasextremely
flexible.Itinvolvedlettingthechild’sanswers(andnotsomepreconceivedplan)determinethecourseof
questioning. If the child said something interesting, then it would immediately be pursued, without
regardforastandardizedprocedure.Theaimofthis“clinicalmethod”wastofollowthechild’sownline
of thought,without imposing anydirectionon it, to comprehend theunderlying causesof the child’s
responses.
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At about the same time as hiswork in theBinet Laboratory, Piagetwas also studying abnormal
childrenattheSalpetrièreHospitalinParis.Hefelt,likeFreud,thatknowledgeofabnormalfunctioning
might provide insight into the normal working of the mind. Piaget therefore applied the “clinical
method”developedattheBinetLaboratorytohisstudyofabnormalchildren.However,hefoundthatthe
methodwasnot adequate since abnormal children’s verbal abilitiesweredeficient. Consequently, for
thesechildrenheaddedanimportantprocedure:thechildwasrequirednotonlytoanswerquestions,
but also to manipulate certain materials. Unfortunately, Piaget did not immediately apply the
supplementedclinicalmethod—freeverbalquestioningplusmaterialsformanipulation—tothetesting
ofnormalchildren.ItwasonlyaftertheexclusivelyverbalprocedureprovedinadequatethatPiagetlater
madeuseofhisexperienceatSalpetrière.
Third,whileusingtheclinicalmethodtostudychildren’sthought,Piagetwasreadingextensively
inlogic.Itoccurredtohimthatabstractlogicmightberelevantinseveralwaystochildren’sthinking.He
noticed, for instance, that children younger than about 11 years were unable to carry out certain
elementary logical operations. The possibility of extensively investigating this apparent deficiency
immediatelypresenteditself.Also,Piagetfeltthatthoughtprocessesformanintegratedstructure(nota
conglomerationofisolatedunits)whosebasicpropertiescanbedescribedinlogicalterms.Forexample,
thelogicaloperationsinvolvedindeductionseemedtocorrespondtocertainmentalstructuresinolder
children. He set himself the goal of discovering how closely thought approximates logic. This was a
distinctiveconceptionofthepsychologyofintelligence.
The years at the Binet Laboratory were very fruitful. Piaget published several accounts of his
psychologicalresearchonchildren.But,moreimportant,thestayinParistaughtPiagetthattheproblem
of intelligencemust be defined in terms of discovering children’s ways of thinking, that the clinical
method isuseful for the studyof thought, and that logic, rather than the imprecisenatural language,
mightbeanefficientwayofdescribingthought.Furthermore,Piagethadnowdiscoveredawayinwhich
hemightintegratehisbiologicalandepistemologicalinterests.Ashesawit,thefirststepwastopursue
thepsychologyofhumanintelligence.Asapsychologist,hecouldstudytheinpidual’sknowledgeofthe
world,hisattemptstocomprehendreality.Thiskindofpsychology,inotherwords,wouldbedirectedat
epistemologicalissues.Also,itwouldbebiologicallyoriented.ForPiaget,thismeantseveralthings.First,
psychologicaltheorymightmakeuseofbiologicalconcepts.Forinstance,intelligencecouldbeviewedin
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termsofanorganism’sadaptationtoitsenvironment.Second,psychologymightfocusontheprocessof
intellectualgrowthintheinpidual.Hebelievedthatafullunderstandingofhumanknowledgecouldbe
gainedonlythroughthestudyofitsformationandevolutioninchildhood.Howcouldonecomprehend
thefinalproductwithoutknowinghowitdeveloped?Forthesereasons,then,Piagetdecidedtoengage
firstinthepsychologicalstudyofthechild’sunderstandingofreality.Hisinitialintentionwastospenda
fewyearsinexperimentedstudiesofthechild’sintelligenceandthenturntoasecondproject,namely,
theapplicationofhispsychologicaldiscoveriestothetheoreticalproblemsofepistemology.Hefeltthat
hecouldclarifyepistemologicalissuesonlyafterhehaddevelopedanunderstandingoftheinpidual’s
cognitivegrowth.Asweshallsee,Piagetspentmorethana“fewyears”athisfirsttask.Itwasonlyafter
somethirtyyearsofpsychologicalstudythatPiagetwasabletoturnhisattentiontotheoreticalquestions
ofepistemology.
In1921, thedirectorof theJean-JacquesRousseauInstitute inGeneva,EdouardClaparède,who
hadbeenimpressedbyPiaget’searlyarticlesonchildren,offeredhimthepostofdirectorofresearchat
theInstitute.Piagetacceptedtheoffer,whichgavehimanexcellentopportunitytocarryonhisstudyof
child thought.Theoutcomeofhis researchwas a seriesof articles and thepublication, from1923 to
1932, of his first five books on children. The first one, Language and Thought in the Child (1926b),
provides naturalistic and experimental observations on the child’s use of language. Piaget found, for
instance, that the young child’s speech is substantially egocentric and that this tendency decreases
graduallyasthechildgrowsolder.JudgmentandReasoningintheChild(1926a)dealswiththechanges
incertaintypesofreasoningfromearlytolatechildhood.TheChild’sConceptionoftheWorld(1929)uses
theexclusivelyverbalclinicalmethodtoprovidedataonhowthechildviewsthesurroundingworld,
and onwhat he believes to be the origins of dreams, of trees, the sun, and themoon. InThe Child’s
Conception of Physical Causality (1960a), Piaget describes the child’s ideas on the causes of certain
naturalphenomena,suchasthemovementofthecloudsandofrivers,theproblemofshadows,orthe
displacement ofwaterwhen an object is immersed. Finally,The Moral Judgment of the Child (1932)
providesinformationonthedevelopmentofmoralbehaviorandjudgment.HerePiagetmaintainsthat
children show two typesofmoral judgment: theyoung childholds to apredominantly authoritarian
moralcode,whereastheolderchilddevelopsamoralityofsocialconcernandcooperation.
Contactwithpsychoanalysisisevidentintheearlyworks:Piaget’stheoriesmakeuseofFreudian
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ideasandaresometimesevenstatedinFreudianterms.Thebooksalsogiveabrief indicationofwhat
Piagetwaslatertoexpandupon:aviewofintellectualdevelopmentasconsistingofaseriesofstages.
Throughhis research,Piagetwasbecoming increasinglyawareof thedifferencesbetween the child’s
and the adult’s thoughtprocesses.He realized that the child isnotmerely aminiature replicaof the
adult:notonlydoesthechildthinklessefficientlythantheadult,buthealsothinksdifferently.Thus,
Piagetbecame convinced that itwasnecessary to conceiveof intellectualdevelopment in termsof an
evolutionthroughqualitativelydifferentstagesofthought.
Piagetalsoattemptedtodiscover thecausesof this intellectualevolution.His first interpretation
was that intellectual development resulted particularly from social factors, like language and contact
withparentsandpeers.Later, afterhis studyof infancy,where the roleof language isnegligiblebut
whereonthecontrarythechild’sownactivityisparamount,hechangedhisinterpretationofthenature
ofintellectualdevelopment:hedeemphasizedtheinfluenceofsocialfactorsandstressedactionasthe
sourceofthought.
MuchtoPiaget’sastonishment,thefirstfivebooks,whichhehimselfcallshis“adolescent”works,
gainedhimconsiderablefame,particularlyamongchildpsychologists.Piaget,whohadneverinhislife
passedanexaminationinpsychology,suddenlybecameanauthorityonthesubject.Thestircausedby
thebooksdisturbedhimsomewhatsinceheconsideredthemtobeonlypreliminaryandtentative,and
notanexpressionofhisdefinitiveviewsonthenatureofintelligence.Hewaswellawareofthebooks’
deficiencies. Nevertheless, he agreed to publish the volumes,mainly because he felt theymight lead
otherstofurtherresearcheventuallyresultinginafullerunderstandingofchildthought.
IntheUnitedStates, thebookswereat firstreceivedenthusiastically,andduringthe1920sand
1930s, Piaget’sworkwas highly regarded in this country. Then followed a period, lasting until the
middle 1950s, when his views, as expressed in the early books, came under much criticism. Some
investigators felt that Piaget’s findings could not be replicated. Butwith the publication in the early
1950sofEnglishtranslationsofseveralofPiaget’slaterbooks,interestinhisworkrevived.
Duringtheperiodfrom1920to1930,Piaget’stimewasfullyoccupied.Heperformedagreatdeal
of research and at the same time also taught various courses in psychology, sociology, and scientific
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thoughtatGenevaandNeuchatel.Histhreechildrenwerebornduringtheseyears:adaughterin1925,
aseconddaughterin1927,andasonin1931.Piagetandhiswife,oneofhisformerstudents,became
closeobserversoftheirchildren’sbehavior.Theresultsoftheirstudy,whichcoveredthe“sensorimotor
period”frombirthuntilabouttheageof2,werepublishedintwovolumes:TheOriginsofIntelligencein
Children(1952c)andTheConstructionofRealityintheChild(1954).Piaget’sstudyofinfancyconvinced
himthatthoughtderivedfromthechild’saction,andnotfromhislanguage.Thisincreasedemphasison
actionledPiagettomodifyhistestingtechniqueforolderchildren.Herememberedhispastexperience
at the Salpetrière Hospital and his solution to the difficulties encountered in trying to apply an
exclusivelyverbalmethodtoabnormalchildren.Consequently,hemadethemanipulationofconcrete
materialsanessentialaspectoftheclinicalmethodforchildrenofallages.Theemphasiswasnolonger
onlanguagealone,butonmanipulationsupplementedbylanguage.
From1929to1939Piaget’sprofessionallifebecameevenmoreactive.Hewasappointedprofessor
ofhistoryofscientificthoughtatGenevaUniversity.Hebecameassistantdirector,andshortlyafterward
co-director, of the Jean-Jacques Rousseau Institute, which he helped to reorganize when it became
attachedtoGenevaUniversity.HetaughtexperimentalpsychologyatLausanneUniversity.Also,Piaget
becameinvolvedininternationalaffairsandacceptedthechairmanshipoftheInternationalBureauof
Education,latertobecomeaffiliatedwithUNESCO.
Piaget’sexperiencesledtoseveralchangesinhisthinking.Thestudiesofinfancyinfluencedhimto
modifyhistechniquesofresearch,andtoplacegreateremphasisontheroleofthechild’sactivityinthe
formationofthought.Also,histeachingopenedupnewareasforresearchandexperiment.Thecourse
onthehistoryofscientificthoughtdirectedhimtowardthestudyofthechild’sunderstandingofcertain
scientificnotions.Withtwoimportantcollaborators,BärbelInhelderandAlinaSzeminska,hesetoutto
explorethisfield,andin1941publishedtwobooksontheirresearch.Thefirst,writtenwithB.Inhelder
wasTheChild’sConstructionofQuantities (1974). Itshowshowthechildgraduallycomestorecognize
that certain physical attributes of an object, like its substance orweight, do not varywhen the object
merelychangesshape.Surprisingly,youngchildrenfailtoconservetheseinvariants.Thesecondbook,
written with A. Szeminska was The Child’s Conception of Number (1952). Here Piaget describes the
evolutionofthechild’seffortstomasterthenotionofnumber.
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Thenextbook,publishedin1942,Classes,Relations,etNombres,dealswith thecorrespondence
betweencertainoperationsofformallogicandmentaloperations.Piagetuseslogictodescribethemental
operationsavailabletothechild from7to11 inthestageof“concreteoperations.”Thebookis thusa
fulfillment of Piaget’s early intention at the Binet Laboratory in Paris to use a formal language for
psychologicalpurposes.
Piagetthenbecameinterestedintheperceptualresearchofthe“Gestalt”psychologists.Hislackof
agreementwith some of their theories, however, led him and his collaborators to a lengthy series of
experiments into the nature of perception. At first Piaget replicated the experiments of the Gestalt
psychologists.Laterhisstudieswereextendedtocoverperceptionnotonlyasanisolatedprocess,but
also its relation to intelligence. For some twenty years, from 1943 onward, Piaget and his associates
producedanumberofarticlesandmonographsonperception.Theculminationwasthepublicationin
1961 of his book, The Mechanisms of Perception (1969), which describes perceptual structures and
processesandrelatesthemtointellectualones.
Intheearly1940s,AlbertEinsteinsuggestedtoPiagetthatitmightbeofinteresttoepistemologyif
hewere to investigate thechild’sunderstandingof time,velocity,andmovement.Piaget followedthe
suggestionandin1946publishedtwobooksonthesematters:TheChild’sConceptionofTime(1970b)
andTheChild’sConceptionofMovementandSpeed(1970a).Inthesameyear,1946,Piagetalsopublished
hisbookon symbolic thought,Play,Dreams,and Imitation (1951),which contains observationsonhis
ownchildren,from2to4yearsofage.
AftertheSecondWorldWar,appreciationofPiaget’sworkbegantospreadthroughouttheworld.
He received honorary degrees from several universities, including Harvard, the Sorbonne in Paris,
Brussels,andtheUniversityofBrazil. In theUnitedStates,however,Piagetwashonoredbutnot fully
understood;onlyhisfirstfivebookshadbeentranslated.Duringthe1940s,hecontinuedhisactivitiesin
theInternationalBureauofEducationandwasappointedheadoftheSwissdelegationtoUNESCO.In
1947PiagetpublishedasmallvolumeentitledThePsychologyof Intelligence (1950b). The book is a
collectionoflecturesPiagethadgivenin1942totheCollegedeFranceinParisandsetsout,forthefirst
timeatanylength,anoverviewofPiaget’stheoryofmentaldevelopment.
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During this time, Piaget continued his research into various aspects of cognition. From the
experimentsonperceptiongrewthestudyoftwocloselyalliedfields:thechild’sunderstandingofspace
and of geometry. In collaboration with Inhelder and Szeminska, he published in 1948 The Child’s
ConceptionofSpace(1956)andTheChild’sConceptionofGeometry(1960).In1949PiagetwroteTraité
deLogique,abookdealingwiththebasicoperationsinvolvedinlogic.Thebookisthefirstfullsummary
of his logical system: it expands upon the logical models already used in previous research and
introducesadditionallogicalmodelswhichhewaslatertoapplytoadolescentthought.
Fromabout1920 to1950,Piagethadbeenengaged in experimentalworkwith children in an
attempttounderstandtheevolutionofhumanintelligence.Nowhefeltpreparedtoapplytheresultsof
hispsychologicalresearchtotheepistemologicalproblemswhichhadoriginallymotivatedhisinterestin
psychology.In1950hepublishedathree-volumeserieson“geneticepistemology”entitledIntroductiona
l’Epistémologie Génétique (1950a). The books are a synthesis of his thinking on various aspects of
knowledge, includingmathematics, physics, psychology, sociology, biology, and logic. Piaget analyzes
thesefacetsofknowledgeintermsoftherelationbetweentheinpidualandhisenvironment—between
theknowerand theknown.He tries todeterminewhether this relationship isaffectedby the typeof
knowledge involved, for instance, whether mathematical knowledge involves a different kind of
interactionwiththeenvironmentfromthatofphysicalknowledge.Piagetalsodrawsaparallelbetween
the historical and inpidual development of knowledge, and he finds that the evolution of inpidual
thoughtsometimesfollowsthesameprogressionasthehistoryofscientificthought.
NextPiagetturnedtothestudyofchanceandtheelementaryconceptsofprobability.In1951,he
andInhelderpublishedabookentitledTheOriginoftheIdeaofChanceintheChild(1975),whichdeals
with the child’s understandingof randomevents inhis environment. In1952Piagetwas appointed
ProfessorofGeneticPsychologyattheUniversityofParis(Sorbonne),whereheremaineduntil1962.At
the same time he continued to teach at Geneva University and to head the Jean-Jacques Rousseau
Institute.Healsopursuedhisresearchintobothperceptionandlogicalthought.In1952hepublisheda
bookcalledEssai sur lesTransformationsdesOpérationsLogiques (1952b), dealingwithprepositional
logicandvariouslogicalstructures,likethegroupandlattice,whichheusedasmodelsforadolescent
andadultthought.Afterhavingstudiedtheperiodofearlyandmiddlechildhood,Piagetturnedtothe
nextphaseofintellectualdevelopment:thethoughtoftheadolescentandtheadult.In1955Piagetand
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Inhelderpublishedabookonthissubject,TheGrowthofLogicalThinkingfromChildhoodtoAdolescence
(1958),whichcompared,againinlogicalterms,thethoughtprocessesoftheadolescentwiththoseofthe
youngerchild.
The year 1956was important for Piaget, for hewas able to initiate a project that he had been
contemplating for some time. With his broad scope of interests, including biology, zoology, logic,
mathematics,psychology,philosophy,andepistemology,Piagethadalwaysdreamedofthepossibilityof
an interdisciplinary approach to basic problems of cognition. The idea had initially encountered a
certain amount of skepticism, but Piaget finally managed to establish an institution where such
interdisciplinary cooperation was possible. An international Center for Genetic Epistemology was
createdwithintheFacultyofScienceofGenevaUniversity.TheaimoftheCenterwastogathertogether
eachyearanumberofeminentscholarsinvariousfields—biologists,psychologists,mathematicians,and
others—whowouldcombinetheireffortstostudyagivenproblem.Eachpersonwouldtreattheproblem
from the point of view of his specialty, but the research was to be coordinated through regular
discussions. At the end of the year, a symposiumwould be held,where the researchers’ conclusions
wouldbediscussed.Thedeliberationsofeachsymposiumwouldbepublishedinaseriesofmonographs,
entitledStudiesinGeneticEpistemology.Overthepastthirtyyears,approximatelyfortyofthesevolumes
havealreadybeenpublished,andhavedealtwithavarietyofsubjectssuchasthenotionofcausality,the
learningprocesses,andmathematicalthinking.
In1959PiagetpublishedwithInhelderTheEarlyGrowthofLogic intheChild (1964).Thebook
againuseslogicalmodelstodescribethementaloperationsofthechildfrom7to11years.Ittreatsin
particularthechild’smethodofclassifyingandoforderingobjects.In1964asmallbookcontainingsix
short essays on various psychological topicswas published (Six Psychological Studies, 1967) and the
following year, 1965, Piaget published Insights and Illusions of Philosophy (1971b). In this book he
discussestheessentialdifferencesbetweenphilosophy,whichleadstosubjective“wisdom,”andscience,
whichleadstoobjectiveknowledge.Healsoexplainswhyheturnedawayfromhisearlypreferencefor
theformertowardthelatter.Inthesameyear,1965,healsopublishedabookoffoursociologicalstudies
entitledEtudesSociologiques,whichisacollectionofsomeofthelectureshehadgiveninhiscourseson
sociology.
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ThetitlesofPiaget’sbooksindicatethatthecontentsdealingeneralwithhighlyspecializedaspects
ofthinkingorcognition.Eachbooktreatsaparticulartopic,likegeometryornumber,inasimilarmanner.
That is, the notion is studied from its origins in the child to the point, usually in late childhood or
adolescence,whereitreachesamaturestatus.Althoughsuchanapproachisofinteresttopsychologists
andeducators,difficultiesarepresentedforthepersonwhowishesonlytogetageneralunderstanding
ofPiaget’soverallsystem.In1966,therefore,recognizingtheneedforashortintroductoryworkonhis
system,PiagetandInhelderpublishedashortbookentitledThePsychologyoftheChild(1969),which
was intended for thegeneralpublic.Thebookgivesabrief summaryofPiaget’s theoryof intellectual
developmentandalsodealswithrelatedmatterssuchasperception.Inthesameyear,1966,thesetwo
authorsalsopublishedabookonmentalimagery,MentalImageryintheChild(1971),whichdescribes
thedevelopmentofmental imagesand relates it to thegrowthof intelligence. In1967hepublished
Biology and Knowledge (1971a), which deals with the relations between biological factors and the
cognitive processes. He then turned his interests in another direction and in 1968 with Inhelder
publishedMemoryandIntelligence(1973).Inthisbook,Piagetintroducesanewapproachtothestudyof
memory:heexaminestherelationsbetweenmemoryandthedevelopmentof intellectualfunctioning.
He finds, forexample, thatmemorydoesnotalwaysdeteriorateovertime;paradoxically,memorycan
improveasaresultofthedevelopmentofcertainrelatedintellectualskills.Anotherbookpublishedin
1968,Structuralism(1970d),reflectsPiaget’scontinuinginterestintheapplicationofstructuralmodels
tomanydifferentdisciplines,andinparticulartotheoperationsofintelligence.
In the1960s and1970sPiaget’s fame continued to spread, andhis bookswere translated into
many languages. In America, where his work had at first been received with a certain amount of
skepticism,hewasnowrecognizedasa leader inhis field. In1969hewashonoredbytheAmerican
PsychologicalAssociation.In1971,attheageof75,PiagetretiredasdirectoroftheRousseauInstitute,
althoughhestillactivelypursuedhisresearchactivitiesasheadoftheCenterforGeneticEpistemology.
Hecontinuedtobeprolificinhiswritingsandpublications.Agreatmanynewbooksandarticles,aswell
asreeditionsofearlierworks,werepublishedinthe1970s.Someofthemajortitlesincludetwobooks
dealingwitheducation,ScienceofEducationandthePsychologyoftheChild(1970c)andToUnderstandIs
to Invent: The Future of Education (1973b) and two books on genetic psychology, Psychology and
Epistemology:TowardsaTheoryofKnowledge(1972b)andTheChildandReality:ProblemsofGenetic
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Psychology (1973a). In Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique et
Phénocopie(1974a),Piagetreturnedtohisearlyinterestinbiologyandtriedtorelateabiologicalmodel
ofdevelopmenttotheintellectualprocesses.
Piaget also conducted studies with Garcia into the notion of causality (Understanding Causality,
1974). Stemming from this research has been Piaget’swork on the child’s growing awareness of his
actions.Studiesinthisareahavebeenpublishedinthreebooks,TheGraspofConsciousness:Actionand
Concept in theYoungChild (1976b),Réussir et Comprendre (1974b), andLe Comportement, Moteur de
I’Evolution(1976a).Attheendofhislife,Piagetpublishedseveralimportantbooksdealingwithissues
ofdevelopmentandlearning.TheseincludeTheEquilibrationofCognitiveStructures(1985),Successand
Understanding(1978),Experiments in Contradiction (1981a),andLePossible et leNecessaire (1981b,
1983).
TheevolutionofPiaget’sinterestsisclearlyillustratedbythetitlesandcontentsofhisbooksand
other publications. From his early work in biology, particularly the study of mollusks, he gradually
turned to the psychological development of the child. His intention was to find a link between the
biological study of life and the philosophical study of knowledge. His first few books on children’s
thought were exploratory, setting forth his preliminary theory of intellectual development. Later,
however,hebegan tostatehis theories in termsofa formal language: logic.Thesubjectmatterofhis
booksalsobegantochange;hebecameattractedtothestudyofthechild’sunderstandingofscientificand
mathematicalnotions,aswellastootheraspectsofthecognitiveprocesses:perception,mentalimagery,
memory, consciousness. Once he had achieved a good measure of understanding of the child’s
intellectualprocesses,Piagetthenwishedtoplacehispsychologicaltheorieswithinalargerframework.
Hereturned,aftermorethanfortyyearsofpsychologicalresearch,tohisoriginalinterests—theoretical
problemsinepistemologyandbiology—andattemptedtoviewthedevelopmentof intelligenceasthe
linkbetweenthetwo.Towardtheendofhislife,Piagetbecameinvolvedintheproblemoftherelations
among reality, necessity, and possibility and in the issues of development and learning. It is quite
remarkable that, intohis eighties, Piaget pursuedhis professionalworkwith great vigor.Hedied on
September16,1980.
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BASIC IDEAS
Inthepresentsection,wewillintroduceseveralbasicideasthathaveshapedPiaget’sapproachto
the study of intellectual development. A scientist usually employs a theoretical framework to guide
experimentationandtheorizing.Theframeworkisnotadetailedtheorybutapointofvieworasetof
attitudeswhichorientsthescientist’sactivities.Apsychologist,forexample,maybebasicallycommitted
bothtoFreudian ideasandtothepersonalitytestapproach,whicharethen likelytogivedirectionto
researchandanalysis.Forexample, this frameworkmay influence thescientist tochoose tostudy the
familialcausesofneurosisratherthanpossiblephysicalbasesofthedisorder.Further,thisorientation
mightleadthescientisttoinvestigatethematterbygivingpaper-and-penciltests,whichmightproduce
resultsdifferentfromthosewhichcouldbeobtainedbythedirectobservationofthechildinthehome.
Thisisnottodeny,ofcourse,thatscientistsdochangetheiropinionsasaresultofconflictingresearch
evidence.Itisneverthelesstruethatorientingattitudescanbeinfluential;thescientistdoesnotbegin
workwithoutpreconceptions,andthesethenorganizetheinterpretationofresearchdata.2
Piaget’sorientingattitudes, statedquiteexplicitly, areconcernedwith thenatureof intelligence
andwithitsstructureandfunctions.
Intelligence
First,howdoesPiagetdefinethenatureof intelligence?ThereadershouldbeawarethatPiaget
hadalmostcompletefreedominthisregard.Previoustothe1920s,whenhebeganhisinvestigations,
there had been little research or theorizing on intelligence. The mental testing approach was in
evidence, as exemplified by the Binet-Simon IQ test, and there were also scattered experimental
investigationsofintellectualprocesseslikememoryintheadult.However,neitheroftheseapproaches
hadbeendevelopedextensively,andpsychologistshadhardlyagreed,anddonotconcureventoday,on
thepropersubjectmatterforthepsychologyofintelligence.3Doesintelligencerefertorotememory,to
creativity,toIQtestperformance,tothechild’sreasoning,ortoothermatters?BecausePiagetbeganhis
studies during a pioneering era, he was free to conceive of intelligence in terms of his unique
perspective.Hewascarefulnot tobeginbyproposing too rigidorpreciseadefinitionof intelligence.
Piagetdidnotwanttofallintothetrapoftoonarrowlycircumscribingthesubjectmatterwhensolittle
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wasknownaboutit.Tolaydownanoverlyrestrictivedefinitionattheoutsetwouldhavebeentocurtail
investigation and impede discovery. In fact, themajor aim of Piaget’s researchwas to discoverwhat
actuallyconstitutesintelligence.
Desiring to avoid premature restrictions, Piaget offered several definitions of intelligence, all
couched in general terms. These definitions reflect Piaget’s biological orientation. For example,
“intelligenceisaparticularinstanceofbiologicaladaptation. . .”(OriginsofIntelligence,pp.3-4).This
states quite clearly that human intelligence is one kind of biological achievement, which allows the
inpidualtointeracteffectivelywiththeenvironmentatapsychologicallevel.Anotherdefinitionstates
that intelligence “is the formofequilibriumtowardswhich thesuccessiveadaptationsandexchanges
betweentheorganismandhisenvironmentaredirected”{PsychologyofIntelligence,p.6).Theuseofthe
term “equilibrium,” borrowed fromphysics, suggests a balance, a harmonious adjustment between at
least two factors—in this case between the person or his cognitive structures and his environment.
Althoughthebalancemaybedisturbed,theinpidualcanperformactionstorestoreit.Intelligenceisthe
“instrument”which enables the inpidual to achieve this equilibriumor to adapt bymeans of certain
actionscarriedoutontheenvironment.Thedefinitionalsoimpliesthatequilibriumisnotimmediately
achieved:asthechilddevelops,thetypeofactionsthatheisabletocarryoutontheenvironmentwill
change and so, too, will the resulting equilibrium. Thus, for Piaget, there is no single and final
intelligence,butratherasuccessionof intellectualstages. It isofspecial interest to thepsychologist to
studytheevolutionofattemptsatequilibriumandthedynamicprocessesunderlyingit.Piaget’sprimary
goal,then,couldbedefinedasthestudyofchildren’sgradualattainmentofintellectualstructureswhich
allowforincreasinglyeffectiveinteractionswiththeenvironment.
Another definition stresses that intelligence is “a system of living and acting operations”
(PsychologyofIntelligence,1950b,p.7).Piagetisinterestedinmentalactivity,inwhattheinpidualdoes
in his interactionwith theworld. Piaget believes that knowledge is not given to a passive observer;
rather,knowledgeofrealitymustbediscoveredandconstructedbytheactivityofthechild.Asweshall
seelater,thispositionisatoddswiththebehavioristviewwhichforalongtimedominatedAmerican
psychology.
Finally,Piaget’sdefinitionofintelligenceinvolvesintellectualcompetence.Heisinterestedinthe
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inpidual’soptimumleveloffunctioningathiscurrentdevelopmentalstage.ForPiaget,intelligencedoes
notnecessarilyrefertotheinpidual’sordinaryorhabitualactivities,buttothebestthathecando.This
competencemayofcoursebeobscuredbyallkindsofconditions,bothtemporaryandlong-lasting—for
example,fatigue,boredom,illness.Factorslikethesemayproduceperformancethatfallsshortofpossible
competence.Whileitisimportanttounderstandhowandwhythishappens,Piaget’smaininterestisin
whattheinpidualcando,whetherornotthisiswhatheordinarilydoes.
Thusfar,wehaveseenthat intelligence involvesbiologicaladaptation,equilibriumbetweenthe
inpidualandtheenvironment,gradualevolution,mentalactivity,andcompetence.Thesedefinitionsare
intentionallyquitegeneral.Itisalsoinstructivetotakenoteofwhatthedefinitionsdonotstress.Theydo
notemphasizeinpidualdifferencesinintelligence.Whilesuchanemphasiswouldbequiteconsonant
withabiologicalapproach,Piagetisnotconcernedwithwhetheronepersonismoreintelligentormore
cleverthananother,orwhy.Piaget,ofcourse,recognizesthatdifferencesinintellectualabilitydoexist,
but he is not particularly interested in their analysis; instead, he seeks to abstract from the various
idiosyncraticmanifestationsofbehavioradescriptionofthegeneralformofthought.Thus,forPiaget,the
issueisnotwhyonebabystartstotalkat18monthsandanotherat22months;theissueisratherwhat
wordsmeantobothbabiesoncetheydotalk.Similarly,forPiaget,thequestionisnotwhyonechildcan
rememberthenamesoftwenty-fourstateswhileanotherchildrememberstwenty-eight;itisratherwhat
mental processes allow each child to remember whatever he does. So Piaget is less concerned with
explainingintellectualdifferencesthanunderstandingthementalprocesseswhichweallshare.
Itisimportanttonotethatthedefinitionsplacelittleemphasisontheemotions.Piaget,ofcourse,
recognizes that the emotions influence thought, and in fact, he repeatedly states that no act of
intelligence is complete without emotions. They represent the energetic or motivational aspect of
intellectual activity.Nevertheless,Piaget’s empirical investigationsanddetailed theories substantially
ignoretheemotionsinfavorofthestructureofintellect.
Piagethaschosenoneofseveralavailablestrategieswithwhichto investigate thepsychologyof
intelligence.Hedeemphasizesinpidualdifferencesandtheeffectsofemotionsonthoughtand,instead,
focusesontheoptimumleveloffunctioning.Manypsychologists,particularlyBritishandAmerican,have
concentratedon inpidualdifferencesbymeansof the testapproachto investigate intellectualactivity.
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Othershaveattemptedfromtheoutsettoconsidertheinfluenceoftheemotions,especiallyanxiety,on
intellectualperformance.Whichstrategyisbest?Theanswerseemstobethatallareofinterest.Allview
theproblemof intelligence fromdifferent angles anddealwith somewhatdifferent issues.Unable to
studyeverything,thescientistusuallysettlesononeapproachtoaccomplishanythingatall.Asweshall
seeinthepagesthatfollow,Piaget’sapproachseemstohaveamplydemonstrateditsmerits.
Inadditiontoproposinggeneraldefinitions,Piagethasstructuredthepsychologyofintelligenceby
theselectionoftheparticularsubjectmatterhehasinvestigated.Aswesawinthebiographicalreview,
Piaget’searlyworkswereconcernedwithsuchmattersasverbalcommunicationandmoral judgment.
With thepassageof timePiagethas come to stress thechild’sunderstandingofvarious scientific and
mathematical ideaslikevelocityandone-to-onecorrespondence.TounderstandPiaget’sconceptionof
intelligence,therefore,wemustnotonlyconsiderhisdefinitions,butthenatureofhisresearchactivities.
Thelatter,especiallyinrecentyears,revealratheruniquescientificandepistemologicalconcerns.
Inconclusion,wehaveseenhowPiaget’s twomajor interests—biologyandepistemology—have
shapedhisapproachtothepsychologyofintelligence.Thebiologicalconcernresultedindefinitionsof
intelligence in general terms of growth, stages, adaptation, equilibrium, and similar factors. The
epistemologicalfocushasresultedintheempiricalinvestigationofthechild’sunderstandingofspace,
time, causality, and similar notions. Piaget looks at intelligence in terms of content, structure, and
function.Wewillconsideraspectsoftheseinthefollowingsections.
Content
Onesimpleaspectofthought is itsmanifestcontent.Thisreferstowhattheinpidual isthinking
about,what interestshimat themoment,or the terms inwhichhecontemplatesagivenproblem.For
instance,whenaskedwhatmakesacargo,themechanicgivesananswerintermsoftheexplosionofgas,
themovementofpistons,thetransferofpowerfromonepointtoanother.Thesestatementsreflectthe
contentsof his thought. If a young childwereposed the samequestion, the responsewouldbequite
different.Ignorantoftheworkingsofthemotor,hemightsupposethatthecar’smovementresultsfrom
allthehorsesinside.Obviously,thecontentofhisthoughtisquitedifferentfromthatoftheadult.
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During the early portion of his career, Piaget’s research focused on the contents of the child’s
thought.TheChild’sConceptionoftheWorldandTheChild’sConceptionofPhysicalCausality,bothwritten
inthe1920s,paidparticularattentiontothechild’sviewsofthephysicalworld.Theclinicalmethodwas
used to obtain the child’s answers to such questions as:Where do shadows come from?What causes
rivers to flow or the clouds tomove?Despite these initial investigations, Piaget felt that the study of
contentwasonlyaminorgoalforthepsychologyofintelligence.Whiledescriptionsofcontentmayhave
someinterest,theydonotgetattheheartofthematter;theydonotexplainwhythoughttakestheformit
does.ForPiaget,therefore,theprimarygoalofthepsychologyofintelligenceisnotthemeredescription
of the content of thought but the understanding of basic processes underlying and determining the
content. Piaget has therefore devoted the greater part of his career in psychology to the study of the
structuresandfunctionsofintelligence.
Specific Heredity
ItshouldcomeasnosurprisethatPiaget’stheoreticalframeworkdealswiththeroleofbiological
factorsinthedevelopmentofintelligence.Thesefactorsoperateinseveralways:oneofthemisdefined
asthehereditarytransmissionofphysicalstructures,orspecificheredity.Differentspeciesare,ofcourse,
endowed by heredity with different physical structures. The nervous system, for example, varies
considerablyfromwormtohuman,andtheeffectsofthisvariationareobvious.Theinheritedphysical
structuresbothpermitcertainintellectualachievementsandprohibitothers.Theeyeisoneexampleof
suchastructure.Gibson(1966)pointsoutthatpredatoryanimalsaregenerallyendowedbyheredity
with frontal eyeswhichallow them to see clearlywhat is aheadand thereforewhat canbepounced
upon. By contrast, preyed-upon animals are generally endowed by hereditywith lateral eyeswhich
allowwideperipheralvisionsothatpotentialenemiescanbeidentified.Indeed,therabbitcanevensee
behinditsownhead.Thephysicalstructureoftheorganismquiteliterallydeterminesitsbasicviewofthe
world.
Another form of specific heredity is theautomatic behavioral reaction.For example, members of
manyspeciespossessvariousreflexesfrombirth.Whenaspecifiedeventintheenvironment(astimulus)
occurs,theorganismautomaticallyrespondswithaparticularbehavior.Nolearningortrainingorother
experiencewith the environment is usually necessary for the reflex response to occur.Moreover, all
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members of the species, unless they are in someway defective, possess the reflex. The basis for this
automatic behavior is an inherited physical mechanism. When the stimulus occurs it activates this
mechanism which produces the response. One example of automatic behavior is the sucking reflex,
whichisnecessaryforsurvival.Whenanyobject(thestimulus)touchesaninfant’s lips, theautomatic
responseistosuck.Thenewborndoesnotneedtobetaughttomakeanelementarysuckingresponse.A
furtherexampleistheabilitytocry.
Thenewborn’s physical structure is such thatwhenhungryhe automatically signalsdiscomfort
with a wail. Often the reflexes are adaptive: they help the organism in its interaction with the
environment.
Piaget feels that in the case of human intelligence, reflexes and other automatic patterns of
behaviorplayonlyaminorrole.Itisonlytheinfant,andmorespecificallythenewborn,whosebehavior
isheavilydependentontheelementarybehavioralreactionsofthetypedescribed.Piaget’sresearchhas
shownthatafterthefirstfewdaysof life,thereflexesaremodifiedbytheinfant’sexperienceandare
transformed into a new type of mechanism—the psychological structure—which is not directly and
simply provided by heredity. Aswe shall see, psychological structures form the basis for intellectual
activityandaretheproductofacomplexinteractionbetweenbiologicalandexperientialfactors.
Athirdaspectofspecificheredityisphysicalmaturation.Thegeneticcodeprovidesthebasisforthe
growthofphysicalstructuresalongcertainpaths.Forexample,asthechildgrowsolder,thebraingrows
larger,andthemusclesof the legsbecomestronger.Suchphysicalmaturation isoftenassociatedwith
various psychological activities: as the brain grows, speech emerges; as the leg muscles strengthen,
permitting greatermobility, the child expands his exploration of the world. Maturation alone is not
sufficienttocausethedevelopmentoftheseandotheractivities,butappearstobenecessaryformany,if
not all, of them. We shall see shortly that, in Piaget’s view, experience and other factors are also
necessary.
General Heredity
We have seen that specific heredity affects intelligence in three ways: (1) inherited physical
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structures set broad limits on intellectual functioning, (2) inherited behavioral reactions have an
influenceduringthefirstfewdaysofhumanlifebutafterwardareextensivelymodifiedastheinfant
interactswithhisenvironment,and(3) thematurationofphysical structuresmayhavepsychological
correlates.Piaget’stheoreticalframeworkpostulatesthatbiologicalfactorsaffectintelligenceinafourth
way:allspeciesinherittwobasictendenciesor“invariantfunctions”:organizationandadaptation.Thisis
generalheredity.
Letusfirstconsiderorganization.Thistermreferstothetendencyforallspeciestosystematizeor
organize their processes into coherent systemswhichmay be either physical or psychological. In the
formercase,fishpossessanumberofstructureswhichallowfunctioninginthewater,forexample,gills,a
particular circulatory system, and temperature mechanisms. All these structures interact and are
coordinated into an efficient system. This coordination is the result of the organization tendency. It
shouldbeemphasizedthatorganizationrefersnottogillsorthecirculatorystructureinparticular,butto
thetendencyobservedinall lifeto integratetheirstructures intoacompositesystem(orhigher-order
structure).
Atapsychologicallevel,too,thetendencytoorganizeispresent.Inhisinteractionwiththeworld,
theinpidualtendstointegratehispsychologicalstructuresintocoherentsystems.Forexample,thevery
younginfanthasavailabletheseparatebehavioralstructuresofeitherlookingatobjectsorofgrasping
them. He does not initially combine the two. After a period of development, he organizes these two
separatestructuresintoahigher-orderstructurewhichenableshimtograspsomethingwhilelookingat
it.Organization,then, isthetendencycommontoall formsof lifeto integratestructures,bothphysical
andpsychological,intohigher-ordersystemsorstructures.
Thesecondgeneralprincipleoffunctioningisadaptation.Allorganismsarebornwithatendencyto
adapt to the environment. Theways in which adaptation occurs differ from species to species, from
inpidualtoinpidualwithinaspecies,orfromstagetostagewithinanyoneinpidual.Nevertheless,the
tendencytoadaptinsomewayoranotherisaninvariantfunctionandthereforeconsideredanaspectof
biology. Adaptation may be considered in terms of two complementary processes: assimilation and
accommodation.
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We will illustrate these processes first by means of a simple physiological example, namely,
digestion.Whenapersoneatssomethinghisdigestivesystemreactstothesubstancesincorporated.To
dealwith the foreign substance, themuscles of the stomach contract in variousways, certain organs
release acids, and so on. Putting thematter in general terms,wemay say that the person’s physical
structures(thestomachandrelatedorgans)accommodatetotheenvironmentalevent(thefood).Inother
words, the process of accommodation describes the inpidual’s tendency to change in response to
environmentaldemands.Thefunctionalinvariantofassimilationisthecomplementaryprocessbywhich
theinpidualdealswithanenvironmentaleventintermsofcurrentstructures.Inthecaseofdigestion,
theacidstransformthefood intoa formwhichthebodycanuse.Thusthe inpidualnotonlymodifies
structuresinreactiontoexternaldemands(accommodation),healsouseshisstructurestoincorporate
elementsoftheexternalworld(assimilation).
ForPiaget,intellectualadaptationisalsoaninteraction,oranexchange,betweenapersonandhis
environmentandinvolvesthesametwoprocesses—assimilationandaccommodation—asarefoundin
biology.Ontheonehand,thepersonincorporatesorassimilatesfeaturesofexternalrealityintohisown
psychologicalstructures;ontheotherhand,hemodifiesoraccommodateshispsychologicalstructuresto
meetthepressuresoftheenvironment.Consideranexampleofadaptationininfancy.Supposeaninfant
of4monthsispresentedwitharattle.Hehasneverbeforehadtheopportunitytoplaywithrattlesor
similartoys.Therattle,then,isafeatureoftheenvironmenttowhichheneedstoadapt.Hissubsequent
behaviorrevealsthetendenciesofassimilationandaccommodation.Theinfanttriestograsptherattle.
Todothissuccessfullyhemustaccommodateinmorewaysthanareimmediatelyapparent.First,hemust
accommodatehisvisualactivitiestoperceivetherattlecorrectly,forexample,bylocatingitinspace.Then
he must reach out, adjusting his armmovements to the distance between himself and the rattle. In
graspingtherattle,hemustmoldhisfingerstoitsshape;inliftingtherattlehemustaccommodatehis
muscular exertion to its weight. In sum, the grasping of the rattle involves a series of acts of
accommodation, or modifications of the infant’s behavioral structures, to suit the demands of the
environment.
Atthesametime,graspingtherattlealsoinvolvesassimilation.Inthepasttheinfanthasalready
graspedthings;forhim,graspingisawell-formedstructureofbehavior.Whenheseestherattleforthe
firsttime,hetriestodealwiththenovelobjectbyincorporatingitintoahabitualpatternofbehavior.Ina
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sensehetriestotransformthenovelobjecttosomethingwithwhichheisfamiliar,namely,athingtobe
grasped.Wecansay,therefore,thatheassimilatestheobjectintohisframeworkandtherebyassignsthe
objecta“meaning.”
Adaptation, then, is a basic tendency of the organism and consists of the two processes of
assimilationandaccommodation.Howdo the tworelate tooneanother?First, it is clear that theyare
complementaryprocesses.Assimilationinvolvestheperson’sdealingwiththeenvironmentintermsof
his structures, while accommodation involves the transformation of his structures in response to the
environment.Moreover,theprocessesaresimultaneouslypresentineveryact.Whentheinfantgrasps
the rattle,his fingersaccommodate to its shape; at the same timehe is assimilating the rattle intohis
framework,thegraspingstructure.
In sum, Piaget postulates that there are two general principles of functioning which affect
intelligence: organization and adaptation (assimilation and accommodation). These biological factors,
aspectsofgeneralheredity,arecommontoallspecies.Whileorganizationandadaptationareinherited,
theyarenotstructures(likereflexes)buttendencies.Theparticularwaysinwhichanorganismadapts
andorganizes itsprocessesdependalsoon itsenvironmentand its learninghistory. InPiaget’sview,
humanbeingsinheritfewparticularintellectualreactions;rather,theyinheritatendencytoorganize
theirintellectualprocessesandtodevelopparticularadaptationstotheirenvironment.
Psychological Structures
Wehaveseen that the inpidual tends toorganizehisbehaviorand thoughtand toadapt to the
environment.Thesetendenciesresultinanumberofpsychologicalstructureswhichtakedifferentforms
at different ages. The child progresses through a series of stages, each characterized by different
psychological structures, before attaining adult intelligence. Frombirth to about 2 years, the infant is
unabletothinkandcanonlyperformovertaction.Forexample,ifatoyfallsaparthecannotfirstthink
how it might best be put together again; instead, he might immediately act on the toy and try to
reassemble it. His activities, however, are not random, but display order and coherence. Almost
immediatelyafterbirththeinfantshowsorganizedbehavior.As-wehaveseen,someofthesepatternsof
action,likethereflex,areduemainlytohereditaryfactors.However,specifichereditycannotexplainall
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theorderlinessintheinfant’sbehavior.Forexample,the2-month-oldinfantusuallysuckshisthumbora
finger.Whenputinthecribheregularlybringshishandtothemouthinarelativelyquickandefficient
way.Inthecommonlanguagewewouldprobablysaythattheinfanthasacquiredthe“habit”ofthumb-
sucking.Theword“habit”impliesaregularity,acoherence,intheinfant’sactions.Itisclearthatthumb-
suckingisnotbasedentirelyoninheritedphysicalstructures.Whilethereisareflextosuckanyobject
touching the lips, there is no innate tendency to bring the hand to themouth; this activitymust be
learned.InPiaget’stheory,suchanorganizedpatternofbehavioristermedascheme,4Theconceptof
schemeisusedinaverybroadway.Itcanrefertothereflexesandotherkindsofinnatebehavioralready
discussed.ItisinthiswaythatPiagetspeaksofthe“suckingscheme.”Butthevastmajorityofschemesare
not innate; instead, they are in someway based on experience, as in the case of the thumb-sucking
scheme.
Thusfarwehavespokenoftheschemeonlyasapatternofbehavior,orasanactionwhichdisplays
coherenceandorder.However,thereareanumberofadditionalaspectsofthescheme.First,itinvolves
activityonthepartofthechild;theconceptisusedtodescribethingshedoes.Mostoften,useoftheterm
inthiswaypresentsnodifficulties.Occasionally,however,schemeisusedtodescribeactionswhichare
notimmediatelyobvious.Forexample,Piagetspeaksofthe“lookingscheme.”Theuseof“scheme”hereis
quitedeliberatesincehemeanstoimplythatvisionisanactiveprocess;thechild’seyesmoveasthey
activelysearchtheenvironment.Second,schemereferstothebasicstructureunderlyingthechild’sovert
actions.Schemeisusedtodesignatetheessenceofthechild’sbehavior.Letustakethumb-suckingasan
example. Ifweexamine the infant’sbehavior indetail,wewill see thatno twoactsof thumb-sucking
performedbyonechildarepreciselythesame.Ononeoccasiontheactivitystartswhenthethumbis10
inchesfromthemouth,onanotherwhenitis11inchesaway.Atonetimethethumbtravelsinalmosta
straightlinetothemouth;atanothertimeitstrajectoryisquiteirregular.Inshort,ifwedescribebehavior
insufficientdetail,wefindthattherearenotwoidenticalactions.Thereisnooneactofthumb-sucking,
butmany;infactthereareasmanyasthenumberoftimesthechildbringsthethumbtothemouth.At
firstglancethissituationmightseemtoposeinsurmountabledifficultiesforthepsychologist.Howcan
shedescribeandexplainbehaviorifeachactisdifferentfromeveryother?Fortunately,thedifficultyis
onlyapparent,sincemostpsychologistsarenotreallyinterestedinthefinedetailsofbehavior.Whatis
important,especiallyforPiaget,isthestructureofbehavior,thatis,anabstractionofthefeaturescommon
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toawidevarietyofactswhichdifferindetail.Inthecaseofthumb-sucking,whetherornottheactstarts
fromadistanceof10or11inchesisofnosignificance.Whatiscrucialisthattheinfanthasacquireda
regularwayofgettingthethumbintothemouth.This“regularway”isanabstractionfurnishedbythe
psychologist.Theinfantputsthehandintohismouthinmanyparticularways,notwobeingidentical,
andthepsychologistdetectsinthesespecificactionsacertainregularitywhichshethencallsascheme.
Letusnowconsideranothertypeofpsychologicalstructure:thatoftheclassifyingoperationsofthe
olderchildfromabout7to11years.Supposeanexaminerpresentsthechildwithacollectionofredand
bluebeadsmixed together.Confrontedwith this situation theolderchild first thinksof theobjectsas
beingmembersofclasses.Thereistheclassofredbeadsandtheclassofblueones.Further,unlikethe
youngerchild,herealizesthattheclassofredbeadsisincludedinalargerclass,thatofbeadsingeneral.
Anotherwayofputtingthematteristosaythathegroupstheredbeadsintooneclassandconceivesofit
asbeingapartofahierarchyofclasses.Theclassimmediately“above”theredbeads(thatis,themore
inclusiveclass)isthatofbeads-in-general.Ofcourse,theclassofbeads-in-generalmayalsobelocatedin
aclassificationhierarchy.Theclassofsolidobjectscontainstheclassofbeads.
Obviously, theolder child’s operational schemes arequitedifferent from the infant’s behavioral
schemes.Thelatterinvolvepatternsofbehavior;theinfantactsovertlyontheworld.Althoughtheolder
child’sschemesalsoinvolveactingontheworld,thisisdoneintellectually.Heconsiders,forexample,the
relativelyabstractproblemofwhethergivenclassesarecontainedinothers.Piagetdescribesthisaspect
oftheolderchild’sthoughtintermsoftheoperationsofclassification.WhatisimportantforPiagetisnot
thatthechildcananswerquestionsaboutbeads(that,ofcourse,istrivial),butthathisactivitiesreveal
theexistenceofabasicthoughtstructure,namely,theoperationsofputtingthingstogether,ofplacing
theminclasses,offorminghierarchiesofclasses,andsoon.Classification,then,iscomposedofaseriesof
intellectualactivitieswhichconstituteapsychologicalstructure.Ofcourse,thechilddoesnotrealizethat
hehassuchastructureandmaynotevenknowwhattheword“classification”means.Theclassification
structure and “schemes”bothdescribe anobserver’s conceptionof thebasicprocessesunderlying the
child’sactivities;thechildhimselfiscertainlynotawareofthesestructures.
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The Description of Structures
HowcanwedescribethepsychologicalstructuressobasictoPiaget’stheory?Onewayisbyusing
commonlanguage.Wecansaythatthechildclassifiesobjectsorthathismoraljudgmentis“objective,”
andsoforth.Sometimesthecommonlanguageadequatelyconveysmeaning,butsometimesitdoesnot.
Unfortunately, thereareoccasionswhenanordinarywordmeansdifferentthingstodifferentpeople.
When this occurs the scientist is in danger of beingmisunderstood. Consequently, the sciences have
tendedtodevelopvariousformallanguagestoguaranteeprecisecommunication.Thephysicistdoesnot
saythatobjects“fallveryfast”or“pickupspeedastheygoalong.”Instead,hewritesaformulainwhich
eachtermispreciselydefinedandinwhichtherelationsamongthetermsarecompletelyspecifiedby
the formal language of mathematics. If the reader of the formula knows what the terms mean and
understands the requisite mathematics, then the physicist’s meaning can be accurately transmitted
withoutthedangerofmisinterpretation.
Piaget feels that psychology, too, should attempt to use formal languages in describing the
structuresunderlyingthought.Psychologicalwordsinparticulararequiteambiguous.Whilethetheorist
mayintendaparticularmeaningforwordslike“habit,”or“thought,”or“classification,”itisextremely
probable that these terms will signify to others a wide variety of alternative interpretations.
Consequently, Piaget has attempted to use formal languages—particularly aspects of logic and of
mathematics—to describe the structures underlying the child’s activities. In later chapters we shall
considerindetailboththeformaldescriptionofthestructuresandPiaget’srationaleforusingit.
Functions, Structures, and Equilibrium
WecannotemphasizesufficientlytheextenttowhichPiagetbelievesthatthefunctionalinvariants
—organizationandadaptation(assimilationandaccommodation)—andthepsychologicalstructuresare
inextricablyintertwined.Aswehaveseen,assimilationandaccommodation,althoughcomplementary,
nevertheless occur simultaneously. A balance between the two is necessary for adaptation.Moreover,
adaptation is not separate from organization. In the process of organizing his activities the inpidual
assimilates novel events into preexisting structures, and at the same time accommodates preexisting
structurestomeetthedemandsofthenewsituation.
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Furthermore, the functional invariants (organization and adaptation) are closely related to the
structures of intelligence. As a result of the tendencies toward adaptation and organization, new
structuresarecontinuallybeingcreatedoutoftheoldonesandareemployedtoassisttheinpidualin
interactionwiththeworld.Lookingatthematteranotherway,structuresarenecessaryforadaptation
andorganization.Onecouldneitheradapttotheenvironmentnororganizeone’sprocessesiftherewere
nobasicstructuresavailableattheoutset.Ontheotherhand,theveryexistenceofastructure,whichby
Piaget’sdefinitionisanorganizedtotality,entailsthenecessityfororganizationandadaptation.
Thereare,however,importantdifferencesbetweentheinvariantfunctionsandthestructures.As
theinpidualprogressesthroughthelifespan,thefunctionsremainthesamebutthestructuresvary,and
appearinafairlyregularsequence.Anotherwayofsayingthisisthatintellectualdevelopmentproceeds
throughaseriesofstageswitheachstagecharacterizedbyadifferentkindofpsychologicalstructureand
adifferenttypeofinteractionbetweentheinpidualandtheenvironment.Aninpidualofanyagemust
adapttotheenvironmentandmustorganizehisresponsescontinually,buttheinstrumentsbywhichthe
personaccomplishesthis—thepsychologicalstructures—changefromoneageleveltoanother.Boththe
infantandadultorganizeandadapt,buttheresultingpsychologicalstructuresarequitedifferentforthe
twoperiods.
Piaget further proposes that organisms tend toward equilibrium with the environment. The
organism—whether a human being or some other form of life—tends to organize structures into
coherentandstablepatterns.Thesewaysofdealingwiththeworldtendtowardacertainbalance.The
organismtriestodevelopstructureswhichareeffectiveininteractionwithreality.Thismeansthatwhen
aneweventoccurs theorganismcanapply to it the lessonsof thepast (or assimilate theevents into
already existing structures) and easily modify current patterns of behavior to respond to the
requirementsof thenewsituation.With increasingexperience theorganismacquiresmoreandmore
structuresandthereforeadaptsmorereadilytoanincreasingnumberofsituations.
SUMMARY AND CONCLUSIONS
Early inhis lifePiagetdeveloped twomajor intellectual interests:biology, thestudyof life, and
epistemology, the study of knowledge. After devoting a number of years to each of these disciplines,
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Piagetsoughtawaytointegratethem.InthecourseofhisworkattheBinetLaboratoryinParis,hecame
to the conclusion that psychology might provide the link between biology and epistemology. Piaget
decidedtospendafewyearsstudyingtheevolutionofknowledgeinthechildandthenapplythefruits
ofthisresearchtothesolutionofthetheoreticalproblemswhichinitiallymotivatedhim.Fortunatelyfor
child psychology, the few years became many, and in their course Piaget has produced over forty
volumes reporting his investigations into such matters as the child’s moral judgment, the infant’s
patternsofbehavior,andtheadolescent’ssolutionofscientificproblems.Onlyinthe1950swasPiaget
able to return to theoretical issues in epistemology. Late in life, Piaget continued his contributions to
psychology,andpublishedworksoncausality,consciousness,anddevelopmentandlearning.Hediedin
1980.
Piaget’sresearchandtheoryhavebeenguidedbya frameworkwhichcanbedefinedasasetof
orientingattitudes.Hisdefinitionof intelligence isnot restrictive,but states that intelligence involves
biological adaptation, equilibrium between the inpidual and his environment, and a set of mental
operationswhichpermitthisbalance.Piaget’sresearchactivitiesalsohaveincreasinglycometofocuson
the growth of the child’s understanding of the basic concepts of science, mathematics, and similar
disciplines. Piaget is less interested in studying the contents of the child’s thought than the basic
organizationunderlyingit.
Theinpidualinheritsphysicalstructureswhichsetbroadlimitsonintellectualfunctioning.Many
of theseare influencedbyphysicalmaturation.The inpidualalso inheritsa fewautomaticbehavioral
reactionsorreflexeswhichhavetheirgreatestinfluenceonfunctioninginthefirstfewdaysoflife.These
reflexes are rapidly transformed into structureswhich incorporate the results of experience.Another
aspectofinheritanceinvolvesthegeneralprinciplesoffunctioning.Onegeneralprincipleoffunctioning
isorganization;allspecieshavethetendencytoorganizetheirprocesses.
A second aspect of general functioning is adaptation, which may be further subpided into
assimilation and accommodation. Accommodation refers to the organism’s tendency to modify its
structures according to the pressures of the environment, while assimilation involves using current
structures to deal with the environment. The result of the principles of functioning is a series of
psychologicalstructureswhichdifferqualitativelyfromoneanotherthroughoutaperson’slifetime.For
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example,theinfantemploysbehavioralschemesorpatternsofaction,whilethechildfromabout7to11
usesmentaloperations.WhatisimportantforPiagetisnotthechild’sbehaviorinall itsdetailbutthe
structureunderlyinghis activities. For thepurposeof clarity, Piagethasmadean attempt todescribe
these structures in terms of formal languages—logic and mathematics. The general tendencies—
adaptationandorganization—andthestructuresareallrelatedtooneanother.
Assimilation and accommodation are complementary,whereas organization and adaptation are
interwoven. For instance, one assimilates an environmental event into a structure, and one
accommodatesa structure to thedemandsof theenvironment.Eventually theorganism tends toward
equilibrium,aimingatabalancebetweenexistingstructuresandtherequirementsoftheworld.Inthis
balance thestructuresaresufficientlydevelopedso that theorganismneedexert littleefforteither to
accommodatethemtorealityortoassimilateeventsintothem.
Piaget’sframeworkisquitegeneral,andatthispointthereadermustfindithardtoevaluate.Inthe
followingpageswewillseethefruitfulnessofPiaget’sorientingattitudes.Wewillreview,forexample,
the evolutionof thepsychological structuresunderlying the child’s intelligence,wewill examine the
waysinwhichassimilationandaccommodationaffectthechild’sinteractionwiththeworld,andwewill
considerPiaget’stheoryofequilibration.
Notes
1Piagethaswrittenshortautobiographiesinseveralvolumes.One,althoughoutdated,appearsinEnglish:J.Piaget,“Autobiography,”inE.G.Boring et al., eds.,HistoryofPsychology inAutobiography, Vol. IV (Worcester,Mass.: ClarkUniversity Press, 1952), pp.237-56.SeealsoChapter1inJ.Piaget,InsightsandIllusionsinPhilosophy,trans.W.Mays(NewYork:WorldPublishingCo.,1971).
2For a discussion of these and related matters, see T. S. Kuhn, The Structure of Scientific Revolutions, 2nd ed. (Chicago: University ofChicagoPress,1970).
3In this connection, it is interesting to compare two sources. One is a 1921 symposium inwhich leading psychologists attempted,withconsiderabledifficulty, todefine intelligence:L.E.Tyler, ed., Intelligence:SomeRecurring Issues (New York: VanNostrandReinhold Company, 1969). A second is a similar symposium, held in 1974: L. B. Resnick, ed., The Nature of Intelligence(Hillsdale, N.J.: L. Erlbaum Associates, 1976). Howmuch progress in defining intelligence has beenmade in the past fiftyyears?
4Piaget’sFrench termschemehasusuallybeen translated intoEnglishasschema (plural,schemata).Wedonot follow this practice sincePiagethadbeenusingtheFrenchwordschema foranotherpurpose.Also,thereadershouldbeawarethatschemeneednotreferonlytobehavior;therearementalschemestoo.
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Infancy
Piaget’s theorypides intellectual development into fourmajorperiods: sensorimotor (birth to2
years), preoperational (2 years to 7 years), concrete operational (7 years to 11 years), and formal
operational(11yearsandabove).(Asweshallseeshortly,theseagesareonlyroughestimates;theyvary
frominpidualtoinpidual,andfromculturetoculture.)Thischaptertreatsthefirstoftheseperiods,the
sensorimotor,whichoccursduringinfancy.
Theaccountof infancyisnovelandsometimessurprising.Thesurprisesusuallytakeoneoftwo
forms:caseswhere,accordingtoPiaget,theinfantiscapableofmuchmoresophisticatedandelaborate
forms of behavior than we would have expected and, conversely, cases where the infant shows
unexpecteddeficiencies.Consideranexampleofthefirstcase.
The untrained observer of an infant in the first few months of life usually reports several
impressions. The baby, who is much smaller than anticipated, appears weak and fragile, and
extraordinarilypassive.Hedoesnotseemtodomuchofanything.Thenewbornspendsmostofthetime
insleep,andusuallywakesonlytobefed.Evenduringthefeeding,hedoesnotseemveryalert,and
sometimes,infact,fallsasleepduringthemeal.Sincetheinfantseemstoshowlittlereactiontopeopleor
things, our observer may even suspect that the newborn does not see the world clearly, if at all.
Apparentlysuchaninfantiscapableoflearningalmostnothing.
Piaget’sviewoffersastrongcontrasttothisconceptionofthenewbornasapredominantlyhelpless
and inactive creature, forhe characterizes thenewbornas active andas an initiatorofbehavior.The
infantquicklylearnstodistinguishamongvariousfeaturesoftheimmediateenvironmentandtomodify
hisbehaviorinaccordancewiththeirdemands.Infact,hisactivityrevealstheoriginsofintelligence.
One of the first questions we should ask about these surprising findings (or indeed about any
findings) is, how does he know?What are themethodswhich allow Piaget to penetrate beyond the
commonly held assumptions and to propose a new and startling view of infancy? The question is
particularly germane in the case of Piaget since he ismethodologically unorthodox, at least by some
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standards.
METHOD
In the courseofhispsychological investigations,Piagethasemployedavarietyofmethods.The
assumptionhasbeenthatmethodsmustbetailoredtomeettherequirementsofdifferentproblemsand
agegroups.Inthecaseofinfancy,themethodologyemployedispartlynaturalisticandpartlyinformal-
experimental.
Formuchofthetime,Piagetcarefullyobservedthebehaviorofhisownthreeinfants—Lucienne,
Laurent,andJacqueline—asitoccurrednaturally.Forinstance,hewouldsitbythecribandmakecareful
notes of the infant’s play, or he would direct his attention to the infant’s eyemovements and try to
determine the direction of the infant’s gaze. In these instances Piaget did not make use of special
scientificinstrumentsorexperimentalapparatus.Hedidnotuseanotherobservertocheckthereliability
of the observations. In general, the intention was to employ careful observation, unaided by
instrumentation,tolearnasmuchaspossibleaboutthebehavioroftheinfantinthenaturalhabitat.The
procedureisobviouslydifferentfromtheusualexperimentalapproachinwhichthechild’sbehavioror
physiological reactions are observed, often with special instruments, under carefully controlled
conditionsinthelaboratory.ButPiaget’sapproachishardlyuniqueorscientificallytaboo.Naturalistic
methodsareusedinzoology,forexample,byethologistsinterestedinthebehaviorofanimalsintheir
naturalsurroundings.Ithasbeenused,too,inchildpsychology,bythe“babybiographers”whoobserved
theirownchildrenandwhoincludedsuchnotablefiguresasCharlesDarwin.
Piaget’s procedure has its unique advantages and disadvantages. The latter have often been
stressedattheexpenseoftheformer.Forexample,Piagetbasedhisconclusionsonasampleofonlythree
children,hardlyasufficientnumbertoensurethegeneralityoftheresults.Piagetandhiswifemadeall
the observations themselves. Although both Piaget and his wife were trained psychologists, it is the
generalfeelingthatparentsarenotoriouslypoorevaluatorsoftheirownchildren’sperformance.Also,
when naturalistic observation is used, it is impossible to identify cause-and-effect relations with
certainty.Whilesomeeventmayhaveseemedtobethecause,otheruncontrolledeventsmayinfacthave
beeninvolvedtoo.Further,thestandardstatisticaltestswerenotused,althoughtodaytheyareusually
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seenasindispensabletoolsofresearch.
Despite these apparent deficiencies, Piaget’s methods offer a number of advantages. First and
foremost,Piaget is anexceedingly sensitiveobserverof children. Somepeople,probably regardlessof
formaltraining,havethisabilityandsomepeopledonot;Piagetdoes.TheacuityofPiaget’sobservations
is confirmed by their generally successful replication by independent investigators.1 Second, Piaget’s
intimate contact with his subjects allowed him to discover phenomena which might have gone
unobservedorunnoticedinthelaboratory.Thecontrolledexperimenttendstofocustheinvestigator’s
attentiononthelimitedclassofbehaviorofinterest,andindeed,oftenmakesitimpossibleforotherkinds
ofbehavior tooccurorbenoticed.Theseotherevents,ofcourse,maybeofgreater interest thanthose
whichtheexperimenterisstudying.Third,Piaget’sgreatfamiliaritywithhischildrenoftengavehimthe
insighttoresolvecertaindelicateissuesofinterpretation.If,forexample,oneofhischildrenwasunable
towindupatoy,Piaget’sextensiveknowledgeofthechildwaslikelytogivegoodgroundsfordeciding
whetherthefailurewasduetolackofinterest,orfatigue,orrealinability.Anexperimenter,ontheother
hand,notknowingthesubjectswell,oftenisunabletomakesuchreasonabledecisions.
Fourth,Piagetwasabletoobservehissubjectsoveralongperiodoftime.Suchlongitudinalstudies
are rare in psychology and provide a perspective which is notably absent from most experimental
designs. Fifth, Piaget feels that at the initial stagesof research theuseof statisticsmaybepremature.
One’saimattheoutsetistoexploreanddescribe.Theintentionistodiscoverandidentifythesignificant
processesandproblemswhichatalaterstageofinvestigationmaybesubjecttorigorousstatisticaltest.
Sixth, Piaget attempted to compensate for the obvious deficiencies of the naturalistic procedure by
performinginformalexperiments.If,forexample,observationsuggeststhatthechildcannotdeedwith
certain kinds of obstacles, Piaget may intervene in the natural course of events by imposing these
obstaclesonthechildandthenobservetheresults.Theseexperimentsare,ofcourse,informal,sincea
verysmallnumberofsubjects—threeatmost—isinvolved,andsincethecontrolsareoftenincomplete.
Nevertheless,Piagetissensitivetothelimitationsofnaturalisticobservationandwheneverpossibletries
to supplement itwith experimental techniques.We see then that Piaget’s unorthodox procedure for
studyinginfantshasagooddealtorecommenditandcannotbesummarilydismissed.2
Theresultoftheseinvestigationsisanaccountof infancyintermsofsix“sensorimotor”stages.It
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should be emphasized that the age limits of each stage are only approximate, and subject to wide
inpidual variations. Piaget stresses the flexibility of the age normswhich are probably influenced by
inpidual differences in physical and social environment, physiological factors, and so on. What is
importantistheregularorderofsuccessionofthestages,regardlessoftheparticularagesatwhichthey
appear.
STAGE 1: BIRTH TO 1 MONTH
Thenewbornisnotacompletelyhelplesscreature,butarrivesintheworldwithcertainabilities
which are provided by heredity. (In fact, over the past several years research has shown that the
newbornisfarmoreskilled,visually,forexample,thanwaseversupposed.3)Oneinnateskillthatthe
newbornpossessesisthesuckingreflex.Whenthelipsaretouched,thenewborninallculturesresponds
automaticallywithunlearnedsuckingmovements.Indescribingthenewborn’sbehavior,Piaget’scentral
themes are, first, that the sucking reflex, and others too, are not simply activated by external stimuli;
instead,thenewbornofteninitiatesactivityhimself.Second,althoughthephysicalstructureoftheinfant
provides ready-mademechanisms, like the sucking reflexwhich functions frombirthandwhich isof
obvious utility, these furnish only a basis for future development. Even in the first month of life
experienceplaysanimportantroleinmodifyingandsupplementingtheinheritedmechanisms.
Considerthefollowingobservation.
DuringtheseconddayalsoLaurentagainbeginstomakesucking-movementsbetweenmeals....Hislipsopenand close as if to receive a real nippleful butwithout having an object. This behavior subsequently became
morefrequent....(OriginsofIntelligence,OI,pp.25-26)4
The observationmay at first seem quite pedestrian. But let us review it.Why did Laurent suck
betweenmeals?Thereareseveralpossibleinterpretations.Sometimesreflexactivitymaybesaidtobe
involved.Thatis,an“externalexcitant”or“unconditionedstimulus,”likeafinger,mayautomaticallyset
off thereflexof suckingby touching the lips.But in thecaseofLaurent, a reflex interpretationseems
untenable, since no external excitant appears to have been involved. Another explanation might
attribute Laurent’s sucking to hunger, but this interpretation too seems implausible, since Laurent’s
suckingsometimesoccurredsoonafterhislastfeeding(when,presumably,hewasnothungry)andnot
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just immediatelyprecedingthenext feeding(whenheprobablywashungry).Athirdpossibility,also
rejectedbyPiaget,involvestwosteps:(1)Weassumethatinthepastthechild’snutritivesuckinghad
beenassociatedwithpleasure;thatis,whenhesuckshegetsmilk,whichreduceshishungerpangsand
is therefore pleasurable. (2) Because of this previous association between sucking and pleasure, it
graduallyoccursthatsuckingaloneintheabsenceofmilkacquiresthepowertoelicitfeelingsofpleasure
intheinfant.Consequently,itmaybethatintheobservationcited,Laurentsuckedbecausesuckingitself
had become rewarding through its past association with pleasure. But this explanation also seems
implausiblesincetheextentoftheassociationbetweenpleasureandsuckingwaslimitedtosuchashort
periodoftime.
Since thesevarious explanations—external excitant, hunger, andassociationwithpleasure—do
notseemabletoaccountfornonnutritivesucking,Piagetinvokesoneformofassimilationtoexplainthe
results.RecallthatinChapter1wedefinedassimilationasafunctionalinvariant,atendencycommonto
all forms of life. In itsmost general form assimilation involves the organism’s tendency to deal with
environmentaleventsintermsofcurrentstructures.Piagethasfurtherproposedthatassimilationtakes
threeparticularforms.Inthepresentinstance,theprincipleoffunctionalassimilationapplies.(Theother
twotypesarerecognitoryassimilationandgeneralizingassimilation,whichwewill discuss later.) The
principleof functionalassimilationassertsthatwhenanorganismhasastructureavailable, there isa
basictendencytoexercisethestructure,tomakeitfunction.Thisisparticularlytruewhenthestructureis
notwellformedorisincompleteinsomeway.Also,theprincipleapplieswhetherthestructureisinnate,
asinthecaseofthesuckingreflex,orlearned,asinotherinstanceswewillreviewshortly.Whenapplied
to thepresentobservation, theprincipleof functionedassimilationasserts thatLaurent’snonnutritive
suckingsimplyrepresentsthetendencyofthesuckingreflextoexerciseitselfortofunction.Thissimple
behavioral scheme is not yetwell formed and requires exercise to consolidate itself. In otherwords,
Laurentdidnotsuckbecausehewashungry,orbecauseanexternalexcitantsetoffthereflex,orbecause
he had associated the sucking with pleasure. He sucked because there is a tendency for available
schemeslikesuckingtofunction.
Acloselyrelatedtendencyisgeneralizingassimilation.Sinceschemesneedexerciseandrepetition,
theyalsorequireobjectstobeusedinsatisfyingthisneed.Thesuckingscheme,therefore,tendstoextend
itself,togeneralize,toavarietyofobjects.Whilethenewbornatfirstsucksonlythenipple,orperhapsa
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fingerthataccidentallycomesintocontactwiththelips,theinfantlaterexercisessuckingonnewobjects
likeablanketorvarioustoys.Thus,Piagetstressesactivityonthepartoftheinfant.Thesuckingreflexis
not simply activated by a series of excitants; rather, the infant, in seeking to exercise this scheme
(functionalassimilation),activelysearchesoutobjectswhichwillallowittofunction.Theobjectsserveas
nourishment,or“aliments,”fortheneedtosuck.
The first two principles—functional and generalizing assimilation—are energetic: they get the
newborn’sbehaviorstarted.Inthecourseofhisactivities,thenewbornhastheoccasiontolearnaboutthe
environment. The reflex of sucking becomes “differentiated.” Consider this observation concerning
Laurent:
At0;0(20)[zeroyears,zeromonths,and20days]hebitesthebreastwhichisgivenhim5cm.fromthenipple.Foramomenthesuckstheskinwhichhethenletsgoinordertomovehismouthabout2cm.Assoonashebeginssuckingagainhestops. . . .Whenhissearchsubsequentlyleadshimaccidentlytotouchthenipplewiththemucosaoftheupperlip(hismouthbeingwideopen),heatonceadjustshislipsandbeginstosuck.(OI, p.26)
Fromthisandothersimilarobservations,Piagetconcludesthattheinfantinthefirstmonthoflife
showsaprimitiverecognitioncalledrecognitoryassimilation.Whentheinfantisnottoohungry,hemay
suckanything—thefingers,theblanket,whatever—toexercisehisscheme.Butwhenhungerisstrong,
the infant shows selectivity or discrimination in choosing objects to suck. While rejecting the skin
surroundingthenipple, the infantseizes immediatelyuponthenipple itselfanddoesthissorapidly
thatwemayreasonablycallthebehavioracrudeformofrecognition.Onecautionhere:Piagetdoesnot
proposethattheinfant“recognizes”thenippleinthesamesensethatanadultdoes.(Wewillseelater
thattheinfant’sconceptofobjectsisimmature.)Inthepresentcasetheinfantmerelyshowsthatwhenit
isnecessaryhecanperceivethedifferencebetweenthenippleandotherthings.
Howdoestheinfantlearntorecognizethenipple?Learningmustbeinvolvedsincethenewborn
doesnotimmediatelydisplaythiskindofrecognition;experienceiscertainlyrequiredforittodevelop.
Piaget’spositionisthatinthecourseofexercisingandgeneralizingthesuckingscheme,theinfantcomes
intocontactwithavarietyofstimulation.Someofthestimulationisvisual(thesightofthebreast,etc.).
Some is tactual-kinesthetic (touches on the lips, the feeling of swallowing milk, etc.). And some
stimulationispostural(theinfantisgenerallylyingdowninacertainposition).Whileaccumulatingthis
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experience,theinfantcomestodifferentiateamongmanyaspects.Hefindsthatsomeareasofthebreast
lookdifferentfromothers;somefeeldifferentfromothers;andthatoneareayieldsmilkwhileothersdo
not.Theinfantcomestomakethesediscriminationsthroughrepetitiousexperiencewhichistheresultof
functional and generalizing assimilation. Then,when hungry the infant shows evidence of previous
perceptuallearning5bychoosingthatareawhichhasproducedmilkinthepastandbyrejectingother
areas. To put the matter in another way, the infant learns about the world in the course of many
explorations; when properly motivated, he manifests this learning by the performance of certain
distinctivereactions.
Finally,anevenmorecomplicatedkindoflearningoccursduringthefirststage.Theprincipleof
accommodation—of modification of the scheme to suit the demands of the environment—is also
operative,andoneresult is that the infant learns tosearch for thenipple inan increasinglyeffective
manner.Considertheseobservations:
At first, when put to the breast, Laurent does not show a particularly systematic search for the
nipple.Heobviouslyhasnothadsufficientexperienceeithertorecognizethenippleorlocateit.Buton
thethirddayLaurentmakesnewprogressinhisadjustmenttothebreast.Allheneedsinordertogropewithopenmouthtowardfinedsuccessistohavetouchedthebreastorthesurroundingtegumentswithhislips.Buthehuntsonthewrongsideaswellasontherightside. . . .Assoonashischeekcomes intocontactwiththebreast, Laurent at 0;0(12) applies himself to seeking until he finds drink. His search takes its bearings:immediately from the correct side, that is to say, the side where he experienced contact. . . . At 0;0(26)Laurent. . . feelsthenippleinthemiddleofhisrightcheek.Butashetriestograspit, it iswithdrawn10cm.Hethen turnshishead in therightdirectionandsearches. . . .This timehegoeson to touch thenipple, firstwithhisnoseandthenwiththeregionbetweenhisnostrilsandlips....Heraiseshisheadinordertograspthenipple.(OI,pp.26,29)
Wequotetheseobservationsinsomedetailtodocumenttheextentoftheinfant’slearningduring
thefirstmonth.Theinfantlearnsnotonlytorecognizethenipple,butalsowheretolookforit.Thus,in
response to therequirementsof thesituation,heaccommodates—hedevelopsnewpatternsofaction,
whichresult infairlysystematicsearch.Howarethesepatternsofbehavior learned?Attheoutsetthe
child’sheadmovementsare“desultory,”that is,essentiallywithoutorder inrelationtothenipple.By
chance,someofthemovementsleadtograspingthenippleandsomeareunsuccessful.Astimegoeson,
the infant learnsthroughthisprocessof trialanderrorthata turnof thehead in thedirectionof the
touch on the cheek provided by the nipple leads to the reward of swallowingmilk.With increased
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experiencetheinfantbecomesrelativelyproficientandflexibleinthissearchandnowcanproceednot
onlyinasidewaysdirectiontowardthecheek,butinanupwardordownwarddirectionaswell.This
last observation is important since some head movements at birth are reflexive. When the infant is
touchedonthecheeknearthemouth,heautomaticallyturnstheheadinthatdirection.Thesideways
movement is the “rooting reflex.” Consequently, a learning explanationmay not be required for the
sidewaysmovement,butdoesseemnecessaryfortheupwardanddownwardmotions.
Such,then,isthefirststage.Theapparentlyprimitivebehavioroftheinfantinthefirstmonthoflife
in fact involves considerable complexity, and the extent of the learning achieved is not immediately
obvious.Theresultisthatthehereditarysuckingschemebecomesprogressivelymodifiedandelaborated
asafunctionofexperience.Attheendofstage1,suckingisnolongeranautomaticpatternofbehavior
providedbyheredity.Inaccordancewiththeprincipleoforganization,thesuckingschemehasbecome
elaboratedandhasdevelopedintoafairlycomplexpsychologicalstructurewhichnowincorporatesthe
resultsoftheinfant’sexperiences.
While stage 1 involves significant learning, there are also limitations on the infant’s
accomplishments.Learningisconfinedtothesphereofthereflexesanddoesnotgofarbeyondthem;the
effectsofexperiencearecenteredonthemechanismsprovidedbyheredity.Weshallseehowtheinfant
instage2beginstoovercometheselimitations.
Atthetimeitwasproposed,Piaget’sviewofinfancywasnovelinseveralrespects.Thetwomost
influential theoriesof theday—Freud’spersonalitypsychologyandHull’sexperimentalpsychology—
bothemphasizedthattheorganismseeksescapefromstimulationandexcitation.Allmotiveswereseen
asanalogoustothesexualorhungerdrives;whenthesedrivesintensify,theorganismtakesactionsto
reducethemandtoreturntoaquiescentstate.Piaget’semphasis,ontheotherhand,isthateveninthe
firstfewdaysoflifetheinfantoftenseeksstimulation.Whencapableofactivity,hetendstoperformit
(functional assimilation); when a structure is available, he tends to generalize it to new objects
(generalizingassimilation).InPiaget’sview,allbehaviorcannotbeexplainedbytheinfant’sreactingtoa
noxiousstateofaffairs;instead,theinfantsometimesactivelyseeksthestimulationwhichhisbehavior
provides.ItseemsfairtosaythatrecentpsychologicalresearchhasshownthattheHullianandFreudian
conceptsarenotfullyadequateandthatalternativeviewsdesignedtoexplaintheinpidual’spreference
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foractivityandstimulationmustbedeveloped(Hunt,1961).
STAGE 2: 1 TO 4 MONTHS
Inthesecondstageofsensorimotordevelopmenttheinfantacquirescertainhabits,which,although
fairlysimpleandcenteredabouthisownbody,neverthelesssurpasstheacquisitionsofthefirststage.
Nowthehistoricaldevelopmentofsucking,forexample,extendsbeyondthefeedingsituation.
Primary Circular Reaction
Piaget’s theory involves the notion ofprimary circular reaction. The infant’s behavior by chance
leads toanadvantageousor interestingresult;he immediatelyattempts toreinstateorrediscover the
effectivebehaviorand,afteraprocessoftrialanderror,issuccessfulindoingso.Thereafter,thebehavior
andtheresultmayberepeated;thesequencehasbecomea“habit.”Considertheseexamples:
At0;1(1)Laurentisheldbyhisnurseinanalmostverticalposition....Heisveryhungry....Twice,whenhishandwaslaidonhisrightcheek,Laurentturnedhisheadandtriedtograsphisfingerswithhismouth.Thefirsttimehefailedandsucceededthesecond.Butthemovementsofhisarmsarenotcoordinatedwiththoseofhishead:thehandescapeswhilethemouthtriestomaintaincontact....
At0;1(3)...afterameal...hisarms,insteadofgesticulatingaimlessly,constantlymovetowardhismouth...ithasoccurredtomeseveraltimesthatthechancecontactofhandandmouthsetinmotionthedirectingofthelattertowardtheformerandthatthen(butonlythen),thehandtriestoreturntothemouth. . . . [Later,though] it is no longer themouth that seeks the hand, but the handwhich reaches for themouth. ThirteentimesinsuccessionIhavebeenabletoobservethehandgobackintothemouth.Thereisnolongeranydoubtthatcoordinationexists....
At0;1(4). . .hisrighthandmaybeseenapproachinghismouth. . . .Butasonlytheindexfingerwasgrasped,thehandfelloutagain.Shortlyafter itreturned.Thistimethethumbwasinthemouth ... I thenremovethehandandplaceitnearhiswaist. . . .Aftera fewminutesthe lipsmoveandthehandapproachesthemagain.Thistimethereisaseriesofsetbacks....[Butfinally]thehandentersthemouth,thethumbaloneisretainedand sucking continues. I again remove the hand. Again lipmovements cease, new attempts ensue, successresultsfortheninthandtenthtime,afterwhichtheexperimentisinterrupted.(OI,pp.51-53)
These observations nicely illustrate Piaget’s dual role of observer and experimenter. Note how
Piagetaspatientobserverrecordsthattheinfantspontaneouslyplacesthehandinthemouththirteen
timesinsuccession.Then,Piagetasexperimenterintervenesinthenaturalcourseofeventsbyplacing
the infant’shandnearhiswaist todeterminewhether,underthesemodifiedconditions, the infant is
abletodirectthehandtothemouth.
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The observations also display the gradual and steady development of thumb-sucking. First, the
infantcannotconsistentlygetthehandintothemouthandthenslowlylearnstodoso;nexthelearnsto
suckthethumbalone,notthewholehand;and,finally,afteralongandcontinuousprocessoflearning,
theinfantisabletoperformwithrapiditytheentiresequenceofactions.
Piaget’s explanation of thumb-sucking again involves principles of assimilation and of
accommodation.However,thesequencebeginswithanunplannedorunintentionaloccurrence.Recall
thatanotherpersoninitiallyplacedLaurent’shandonhischeek;hedidnotdosohimself.Afterthehand
wasputthere,Laurenttooktheinitiativebyattemptingtograspthehandwiththemouth.Thisaction
was,ofcourse,apreviously learnedscheme:Laurenthadearlieracquiredbehaviorpatternsenabling
himtosearchforthenipple.Otherobservationsnotdescribedhererevealthatinsomecasestheinitial
behaviorisachanceoccurrence,andnotcausedbytheinterventionofanotherperson.Ineitherevent,
theunplannedbehaviorleadstoaresultwhichhasvaluefortheinfant.InthecaseofLaurentthehand
inthemouthenablesthesuckingschemetofunction.Thisisrewardingsince,accordingtotheprinciple
offunctionalassimilation,thesuckingschemeneedstofunction.Inotherwords,afortuitousoccurrence
hasgiventheinfantachancetoexerciseoneofhispreviouslyestablishedschemes,andthisactivity,in
itself,isasatisfyingevent.ButLaurent’smovementsarenotyetfullycoordinated;itoccursthatthehand
falls from themouth and interrupts the functioningof the sucking scheme.The child thendesires to
reinstate the pleasurable activity and resume sucking the thumb. This desire, stemming from the
interruption,thendirectsthechild’sbehavior.Laurentactivelytriestoinsertthehandinthemouth.In
twosenses,then,theinfant’slearningisactive:hisdesiresetsinmotionthesequenceofevents,andhe
initiatesbehaviortofulfillthisdesire.
The principle of accommodation is now operative. The infant modifies the previously aimless
movementsof thehand tomake themeffective inbringing it to themouth. Initially,Laurent ison the
wrongtrack;he tries tobring themouth to thehand. It isonlyaftersome failure thathereverses the
procedure.Thelearningisslowandseemstoinvolvetwofactors—muscularadjustmentsanddirection
bythepropercues.The infantmust learn tomakecertainnewandprecisemuscularmovementsand
mustlearntobringthesemovementsunderthedirectionofthepropercues.Whentouchingtheblanket,
thehandmustbemovedincertainways;whentouchingthecheek,itmustbemovedinotherways.The
infant learns thatparticularcuesandmovementsareusefulwhileothersarenot.Theusefulones,of
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course, are thosewhich lead to placing the hand in themouth. Thus, success “confirms” some of the
movements and cues,while failure eliminates other attempts at accommodation. Yet the observations
showthattheinfant’slearningisnotcomplete.Heapparentlyfindsitmoresatisfyingtosuckthethumb
thantheotherfingers,andthroughaprocessoflearningsimilartothatjustdescribedbecomesableto
place the thumb alone in the mouth. Further, the infant’s behavior shows the ability to distinguish
(recognitoryassimilation)thethumbfromtherestofthehand.Theresultofallthislearningisfinallya
smoothly organized and directed series of movements, a new scheme or structure, which can be
exercisedrepeatedly.
In summary, the primary circular reaction involves an action on the part of the infant which
fortuitouslyleadstoaneventwhichhasvalueforhimandwhichiscenteredabouthisownbody.The
infant then learns to repeat thebehavior to reinstate the event. The culminationof theprocess is an
organizedscheme.
Primitive Anticipations
Whilethenewborninthefeedingsituationsucksonlywhenhislipsareincontactwiththebreast,
the older infant shows a different pattern of behavior. This observation concerns Laurent at the
beginningofthesecondmonth.
assoonasheis inapositiontoeat(inhismother’sarmsoronthebed,etc.)hishandsloseinterest, leavehismouth,and itbecomesobvious that thechildno longerseeksanythingbut thebreast, that is tosay,contactwithfood...attheendofthemonth,Laurentonlytriestonursewhenheisinhismother’sarmsandnolongerwhenonthedressingtable.(OI,p.58)
. . .between0;3(15)and0;4 . . . [whenLaurent] isput inmyarmsinpositionfornursing,he looksatmeandthensearchesallaround...buthedoesnotattempttonurse.WhenIplacehiminhismother’sarmswithouthistouchingthebreast,helooksatherandimmediatelyopenshismouthwide.(OI,p.60)
Theinfant initiallysucks, then,onlywhenthenipple is inserted inhismouth.Thenipple isan
externalexcitantwhichautomaticallyelicitssucking.Afteraperiodofexperiencewithfeeding,hemakes
sucking-likemovementsbefore the external excitant can operate. During the secondmonth, Laurent
showssuckingassoonasheisplacedinhismother’sarmsoronthebed.Later,Laurent’ssucking-like
movementsarearousedonlybybeinginthemother’sarms.Onewayoflookingatthesefactsistosaythat,
whileatfirstonlythenippleservedasacueorsignalforsucking,latertheinfant’sbeinginthemother’s
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armsreplacedthenippleasasignalforsucking.Anotherwayofphrasingthematteristomaintainthat
theinfantseemstoshowaprimitiveanticipationoffeedingandthatthisexpectancy,astimegoeson,is
evokedbyfewerandmoreappropriateeventsthanformerly.Ineitherevent,thephenomenonissimilar
towhathasbeencalled“classicalconditioning,”althoughPiaget’sexplanationofthefactsdiffersfrom
thetraditionalone.
Piagetemphasizesthattheassociationbetweensuckingandthevarioussignals(e.g.,positionin
themother’sarms)thatprecedeitisnotacquiredinamechanicalway.Whathappensisthis:thesucking
schemecomestoconsistofmorethansuckingalone.Italsoinvolvesasetofposturalkinestheticcues.That
is,whentheinfantnursesinthefirstfewmonthsheisalmostinvariablyheldinthesameposition,and
theinternalbodysensationsassociatedwiththispositionbecomeapartoftheactofsucking.Thebody
sensationsandthemovementsofthelipsformawhole.Then,whentheinfantisplacedintheposition
fornursingandtheposturalandkinestheticsensationsareactivated,thewholecycleofthesuckingactis
released.Becausethetwoaspectsofthecycle—bodilysensationsandlipmovements—formawhole,the
occurrenceofoneaspectusuallyevokestheother.Piaget feelsthatthisprocessdoesnot involvemere
“passiverecording”onthepartofthechild,sincetheinfanthimselfenlargestheinitiallylimitedscheme
of sucking to include other components such as bodily cues. Furthermore, the association cannot be
maintainedifitisnotconsistently“confirmed”bytheenvironment.Thatis,forposturalcuestoprovoke
the child’s anticipatory sucking, the suckingmust ordinarily be followed by drinkingmilk. Thus, the
associationbetweenposturalcuesandsuckingderivesitsmeaningonlyfromalargersetofrelationships
existingbetweentheschemeofsuckinganditssatisfaction.Thereflexmusthaveachancetofunction
effectively (todrinkmilk)beforeanyassociations canbe formed.Thus, the sequencebodilycues—►
sucking—►satisfactionofneedformsawhole,andtoisolatethefirsttwotermsinthissequenceandcall
themaconditionedreflexomitsmuchthatisrelevant.
Curiosity
InthediscussionofthesecondstagePiagetintroducesamotivationalprincipleofgreatimportance.
Thefollowingisapreliminaryobservationinconnectionwiththeproblemofvision:
Laurent at 0;0(24) watches the back of my hand, which is motionless, with such attention and so markedprotrusionofthelipsthatIexpecthimtosuckit.Butitisonlyvisualinterest....At0;0(25)hespendsnearlyan
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hourinhiscradlewithoutcrying,hiseyeswideopen....Hestaresatapieceoffringeonhiscradle.(OI,p.64)
Whydoestheinfantattendtothesemundanefeaturesoftheenvironment?Heisnotrewardedfor
doingsoand isnot inanyotherwayencouragedtodirectattention toanobject like the fringeof the
cradle.Again,Piagetinvokestheprincipleoffunctionalassimilationtoaccountforthesefacts.Theeyes
arestructures,givenbyspecificheredity,andrequireexercise.Inthepresentinstanceexercisemeans
lookingatthing,andthethingslookedatarenecessaryforthefunctioningoftheeyes.
Thusfar,theprincipleoffunctionalassimilationhasbeenappliedtothecaseofvisioninmuchthe
samewayasitwasusedtoexplainsomefeaturesofsucking:bothschemesneedtofunction.Oneresultof
repetitiouslookingatthingsisthattheybecomefamiliartotheinfant.Throughaprocessofperceptual
learning, the infant becomes acquaintedwith the environment and comes to recognize things. These
observationsaremadenext:
At0;1(15)hesystematicallyexplores thehoodofhisbassinetwhich I shookslightly.Hebeginsby theedge,then little by little looks backward at the lowest part of the roof. . . . Four days later he resumes thisexploration in the opposite direction. . . . Subsequently, he constantly resumes examining the cradle, but,duringthethirdmonth,heonlylooksatthetoyshangingfromthehoodoratthehooditselfwhenanunwontedmovementexciteshiscuriosityorwhenhediscoversaparticularnewpoint(apleatinthematerial,etc.).(OI,p.68)
Noticehowatfirsttheinfantthoroughlyexaminesthecradleuntilheisapparentlyfamiliarwithit.
Then,duringthethirdmonthhisattentionbecomesmoreselectivethanwaspreviouslythecase.Heno
longer seems to explore the cradle and instead directs his attention to novel objects or movements
connected with the cradle. For example, he stares at toys hanging from the hood or at a previously
unnoticedpleatinthematerial.
Piaget’sexplanationoftheinfant’scuriosityinvolvesanextension—reallyafurtherspecification—
oftheprincipleofgeneralizingassimilation.Theinfant’s lookingscheme,accordingtoPiaget,tendsto
extendtherangeofobjects it“uses.”Buttheinfantdoesnotsimplylookatmoreandmorethings.His
visualpreferencesbecomeselective.The infant’sattention isdirectedat eventswhicharemoderately
novel:“oneobservesthatthesubjectlooksneitheratwhatistoofamiliar,becauseheisinawaysurfeited
withit,noratwhatistoonewbecausethisdoesnotcorrespondtoanythinginhis[schemes]”(OI,p.68).
Thismotivationalprinciplemayappeardeceptivelysimpleandtrite.Inreality,however,itrepresentsa
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pointofviewwhich isradicallydifferent fromprevious(andsomecurrent) theoriesand isonlynow
receivingtheattentionitdeserves.First,liketheprincipleofassimilation,themoderatenoveltyprinciple
isstronglyatoddswiththeorieswhichstressavoidanceofstimulationastheonlykindofmotivation.On
thecontrary,accordingtoPiaget’sview,thechildactivelyseeksoutnewstimulation—heisnotforcedto
lookatnovelobjects.Second,themoderatenoveltyprincipleisdifferentfromothermotivationaltheories
inthatitisarelativisticconcept.Thatwhichcatchesaninpidual'scuriosityisnotentirelythephysical
natureoftheevent.Itisnottheobjectpersethatattractsattention;instead,curiosityisafunctionofthe
relationbetweenthenewobjectandtheinpidual'spreviousexperience.Agiventoymayelicitinterestin
onechildandboredominanother.Presumablythefirstchildhashadexperiencewithtoysmoderately
different fromtheone inquestion; thesecondchildmayeitherhavehadexperiencewith toyshighly
similar to the newone or elsemay have had no experiencewith toys, inwhich case the new object
presumably“doesnotcorrespondtoanythinginhis[schemes].’’Insum,thenoveltyprincipleassertsthat
whatdeterminescuriosity isnot thephysicalnatureof theobject,but rather thedegree towhich the
objectisdiscrepantfromwhattheinpidualisfamiliarwith,which,ofcourse,dependsentirelyonthe
inpidual’sexperience.
Imitation
Animportantaspectoftheinfant’sbehavioris imitation.Piagetconsidersimitation, likeallother
behaviors, as yet another expression of the infant’s endeavors to comprehend reality and interact
effectivelywiththeworld.Consequently,thedevelopmentofimitationisseentoprogressconcurrently
withotheraspectsoftheinfant’sbehavior.
During stage2, aswehaveseen, the reflexesaremodified tobecomehabitsorprimarycircular
reactions.Thisextensionofthechild’shereditaryschemesleadstoarudimentaryandsporadicformof
imitation.Atthisstagethechildimitatesonlyactionswhichhehashimselfpreviouslyperformed.Since
the child’s repertory of actions is still restricted, imitation is confined to elementary vocal and visual
movements,andtograsping(prehension).Hereisanexampleoftheimitationofthisstage:
At0;1(21),Luciennespontaneouslyutteredthesoundrra,butdidnotreactatoncewhenIreproducedit.At0;1(24);however,whenImadeaprolongedaa,shetwiceutteredasimilarsound,althoughshehadpreviouslybeensilentforaquarterofanhour.
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At0;1(25)shewaswatchingmewhileIsaid“aha,ha,rra,”etc. Inoticedcertainmovementsofhermouth,movementsnotof suctionbutof vocalization. She succeededonceor twice inproducing some rathervaguesounds,andalthoughtherewasnoimitationinthestrictsense,therewasobviousvocalcontagion.
At0;3(5) Inotedadifferentation in the soundsofher laughter. I imitated them.She reactedby reproducingthemquiteclearly,butonlywhenshehadalreadyutteredthemimmediatelybefore.
At0;3(24)sheimitatedaa,andvaguelyarrinsimilarconditions,i.e.,whentherewasmutualimitation.(Play,Dreams,andImitationinChildhood,PDI,p.10)
The early forms of vocal imitation are characterized by two major features. First, there is the
phenomenon of “vocal contagion.” A person called a “model”makes a sound, and the infant tries to
reproduce it. Limited abilities, however, prevent the infant from perfect reproduction of the sounds.
Nevertheless,stimulatedbythemodel’ssounds,theinfantcontinuestoproducevocalizationsofmany
kinds having little relation to the model’s sounds. “Vocal contagion” refers, then, to the model’s
stimulationofdiffusevocalactivityintheinfant.
Second,thereis“mutualimitation.”Ifthemodelreproducesasoundwhichtheinfantiscurrently
engagedinproducing,thechildisstimulatedtorepeatthesamesound.Ifthemodelagainimitatesthe
child,thereissetinmotionapatternofalternatingimitationbyinfantandmodelwhichcontinuesuntil
oneortheothertiresorlosesinterest.Thispatternofbehaviordoesnotoccurifthemodelmakesasound
whichisnewfortheinfant.
Piagetexplainsboththecontagionandmutualimitationphenomenabyreferencetotheprinciple
of functionalassimilation.Youmayrecall thatthechildhasatendencytorepeatschemeswhichhave
alreadybeenestablished.Inthecaseofvocalcontagiontheprincipleoffunctionalassimilationisapplied
inthefollowingway.Whenthemodelmakesasoundtheinfantdoesnotdistinguishitfromhisown;itis
asiftheinfanthadmadethesound.Becauseoftheprocessoffunctionedassimilation,theinfanttendsto
repeattheactivity(notdistinguishedfromhisown)whichhasalreadybeensetinmotion;thatis,the
infantcarriesontheactivityofmakingsoundsingeneral.
In the case ofmutual imitation a similar explanation is advanced.When the infant produces a
sound, the model’s imitation merely stimulates the process of functional assimilation. The infant’s
imitation is in away illusory; the infant does not somuch reproduce themodel’s behavior asmerely
continuehisown.Notethatinbothcases—contagionandmutualimitation—theinfantrepeatsbehavior
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ofwhichheisalreadycapable.Theinfantcannotyetreproducenovelactivitiesofamodel.
Categories of Reality
Thusfar,wehavedescribedtheinceptionofseveralaspectsoftheinfant’sbehavior.Inparticular,
wehavenotedthecontributionofexperiencetowardtheelaborationoftheinfant’sactivity,andtheways
in which he extends his behavior beyond the feeding situation. As the infant begins to manipulate
surroundingobjects,hegraduallydevelopsapractical “understanding”ofexternalreality. Inplaying
withtoys,blankets,hisownbody,andadults,helearnssomethingaboutthepropertiesofthesethings
andabouttherelationsamongthem.Andasskillsincreaseinnumberandscope,theinfantacquiresan
increasinglycomplexpracticalknowledgeofcertainfeaturesoftheenvironment.
During the sensorimotor period, the infant elaborates severed basic dimensions of reality,
especially theprimitivenotionsof thepermanentobject, space, time, and causality. At first, thesebasic
dimensions of reality are closely related to the infant’s bodily actions, to themovements of his arms,
fingers,legs,andeyes.Theinfant’sinitial“understanding”oftheworldisbasedentirelyonwhatPiaget
callsthe“planeofaction.”Onlylater,afteragradualprocessofdevelopment,doestheinfantbecomeable
to elaborate the categories of reality on the “plane of thought.”One of Piaget’s central themes is that
concrete action precedes and makes possible the use of intellect. Thus, the acquisitions of the
sensorimotorperiodformthefoundationsof the inpidual’smentaldevelopment.Wewilldiscussonly
one of these categories, the concept of the permanent object. The other notions follow a similar
development.
Object Concept (Stages 1 and 2)
TounderstandthedevelopmentofwhatPiagetcallstheobjectconcept,it is important tokeep in
mindoneessentialpoint.An“object,”accordingtoPiaget,issomethingwhichtheinpidualconceivesof
ashavingarealityofitsown,andasextendingbeyondhisimmediateperception.Forexample,aman
whohashunghiscoatinaclosetknowsseveralhourslaterthat,inalllikelihood,thecoatisstillthere.
Althoughhecannotseeortouchthecoat,heknowsthat itremainsbehindtheclosetdoor.Theobject,
therefore, involvesmore than thedirectperceptionofexternal reality; theobject is conceived toexist
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independentlyofaperson’sperceptionofit.Strangeasitmaysound,theinfantisatfirstincapableofthis
apparently simple notion, and it is only after a long process of development that he elaborates the
cognitiveskillsnecessaryforamatureobjectconcept.
Duringstage1theinfant’sreactionsareevokedonlybyimmediatelypresentsensoryeventswhich
maybeinternalorexternal.Feelingthepangsofhunger,theinfantcries;experiencingatouchonthe
lips,hesucks.Thesameholdsinthecaseofvisualperception.Ifthemother’sfacesuddenlyappearsin
the visual field, the infant stares at it. But when the face is just as suddenly withdrawn, the infant
immediatelystopslookingandresumesotheractivities.Itisclearthattheinfanthasnoconceptionthat
thefacecontinuestoexistwhenhelosesvisualcontactwithit.Instead,theinfantmerelyperceivesan
unrelatedseriesofimagesorpictures,asPiagetcallsthem,whichappearandthendisappear.
Certainbehavioralpatternswhichappearinstage2areafirststeptowardtheacquisitionofthe
objectconcept.Theinfantcoordinatesvariousperceptualschemeswhich,untilthen,hadbeenusedin
unrelatedways.Considerthecoordinationofvisionandhearing.Instage1,ifasoundhadoccurrednear
anewborn,hewouldhaveshownevidence(forexample,astartle)ofhavingheardit,buthewouldhave
madenoefforttobringthesourceofthesoundintosight. Instage2,however, the infanttriestoturn
towardthesoundhehearstoseewhatproducedit.Atfirsttheseeffortsareclumsy,butwithpractice,
theygraduallyimproveandbecomemoresuccessful.Becauseofthiscoordinationofvisionandhearing,
external reality isusuallyexperienced through twoormoresenses simultaneously.The result is that
afteratimetheinfantestablishesrelationsbetweenwhatisheardandseen.Hefindsthatcertainsounds,
like the voice, usually emanate from certain sources, like themouth. The infant begins to discover a
coherenceintheworld.Insteadofmerelyperceivingisolatedandunrelatedaspectsofreality,theinfant
learnsthatsightsandsounds(andotherkindsofperceptstoo)oftengotogetherinregularways.This
coordinationofbasicschemes,sinceitintroducesameasureofcoherencetotheinfant’sworld,isavital
firststeptowardacquisitionoftheobjectconcept.
Another accomplishment of stage 2 concernspassive expectation. The clearest example involves
vision.At this stage the infant can followamovingobjectwithhis eyes.Or, asPiaget says, the infant
accommodateshislookingschemetothemovingthing.Theinterestingobservationhereisthatoncethe
objectleavesthevisualfield,theinfantcontinuestostareatthespotwherethethingdisappeared.One
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mightalmostbe temptedtostate thathealreadyhastheobjectconceptand ishoping for thethingto
return.Butthisinterpretation,Piagetfeels,isfallacious,sincetheinfantdoesnotactivelysearch forthe
vanished object as he will do in later stages. Instead, the stage 2 infant merely pursues an action
(looking)which has been interrupted. If after a shortwhile the thing does not reappear, the infant
discontinues passive watching and turns to other elements of his surroundings. But this passive
expectation,whichdoesnotgobeyondthesimplerepetitionofthealready-activatedlookingscheme,is
the firststeptowardthe lateractivesearchforthemissingobjectandhencetowardacquisitionof the
objectconcept.
In summary, the first two stages are characterized by a passive attitude toward objects which
disappearfromtheinfant’simmediateperception.Instage1,theinfantimmediatelyturnsattentionto
thosethingshecansee;instage2,hemerelyrepeatsearlieractions(looking)whichoccurredwhenthe
objectwaspresent.Whilethesecondreactionrepresentsanadvanceoverthefirst,bothindicatethelack
ofthematureobjectconcept.
STAGE 3: 4 TO 10 MONTHS
Secondary Circular Reactions
Instage2, theprimarycircularreaction isalwayscenteredonthe infant’sownbody.The infant
learned,forexample,tobringthethumbtohismouth.Instage3,theinfant’shorizonsexpand.Hebegins
tocrawlandmanipulatethingsextensively.Thecircularreactionsofthisstagearecalled“secondary,”
sincetheynowinvolveeventsorobjectsintheexternalenvironment.Thesecondarycircularreactions
describetheinfant’snew-foundabilitytodevelopschemestoreproduceinterestingeventswhichwere
initiallydiscoveredbychanceintheexternalenvironment.Thefollowingexcerptisalengthyrecordof
suchareactionandillustratesPiaget’sskillandcautionasanobserver:
Laurent, from themiddleof the thirdmonth, revealedglobal reactionsofpleasure,while lookingat the toyshanging fromthehoodofhisbassinet. . . .Hebabbles, archeshimself,beats theairwithhisarms,moveshislegs,etc. ...At0;2(17)Iobservethatwhenhismovements inducethoseof thetoys,hestopstocontemplatethem,farfromgraspingthatitishewhoproducesthem....Ontheotherhandat0;2(24)Imadethefollowingexperiment....AsLaurentwasstrikinghischestandshakinghishandswhichwerebandagedandheldbystringsattachedto thehandleof thebassinet (topreventhim fromsucking), Ihad the ideaofusing the thing,and Iattachedthestrings to thecelluloidballshanging fromthehood.Laurentnaturallyshooktheballsbychance
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andlookedatthematonce(therattlemadeanoiseinsidethem).Astheshakingwasrepeatedmoreandmorefrequently Laurent arched himself, waved his arms and legs—in short, he revealed increasing pleasure andthroughthismaintainedtheinterestingresult.Butnothingyetauthorizesustospeakofcircularreaction....
Thenextday,at0;2(25)Iconnecthisrighthandtothecelluloidballs....Thelefthandisfree.Atfirstthearmmovementsare inadequateandtherattledoesnotmove.Thenthemovementsbecomemoreextensive . . .andtherattlemoves. . . .Thereseemstobeconsciouscoordinationbutbotharmsmoveequallyanditisnotyetpossibletobesurethatthisisnotamerepleasurereaction.Thenextday,samereactions.
At0;2(27),ontheotherhand,consciouscoordinationseemsdefinite,forthefollowingfourreasons:(1)Laurentwassurprisedandfrightenedbythefirstshakeoftherattlewhichwasunexpected.Ontheotherhand,sincethesecond or third shake, he swung his right arm (connected to the rattle) with regularity, whereas the leftremainedalmostmotionless.. . .(2)Laurent’seyeblinksbeforehandassoonashishandmovesandbeforetherattlemoves, as though thechildknewhewasgoing to shake it. (3)WhenLaurent temporarilygivesup thegameandjoinshishandsforamoment,therighthand(connectedtotherattle)aloneresumesthemovementwhiletheleftstaysmotionless.(4)Theregularshakes...revealacertainskill;themovementisregular.
At0;3(10) I attached a string to the left armafter six days of experimentswith the right. The first shake isgivenbychance:fright,curiosity,etc.Then,atonce,thereiscoordinatedcircularreaction:thistimetherightarm is outstretched and barelymobilewhile the left swings. . . . This time it is therefore possible to speakdefinitelyofsecondarycircularreaction.(OI,pp.160-62)
One interpretationof the infant’sbehavior is that a secondary circular reaction is involved.The
infant,lyinginhiscrib,bychancemakesanarmmovementwhichcausesthestringattachedtohishand
tomove and rattle the toys. Laurentdoesnot, of course, have this goad inmind from the outset. The
movementandrattlingareinterestingtotheinfant,andhedesirestocontinuethem.Overaperiodof
time, he learns the arm movements necessary to reproduce the interesting result. At this point, his
behaviorisintentional.
But another interpretation is possible, and it is particularly fascinating to observe how Piaget
attempts to rule it out. The alternative explanation asserts that the infant’s armmovements are not
intendedtoproducetheinterestingresult.Instead,justthereverseistrue:theinterestingeventcauses
armmovements inthe infant. Inotherwords, the infant initiallymoveshisarmbyaccident.Theballs
moveandmaketheinfanthappy.Aspartofhisjoytheinfantshowsphysicalexcitementwhichagain,by
accident,producestheshakingoftheballs;thisinturnstartsthecycleoveragainandisthecauseofthe
infant’shandmovements.
TheobservationsshowthatPiagetwasquitecautiousinhisinterpretations.Hedidnotacceptthe
first explanation (secondary circular reaction) until the facts made it abundantly clear that the
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alternative explanation was not plausible. For example, Piaget observed that Laurent seemed to
anticipate the result before it occurred; consequently, the result could not be an accident. In fact, the
sequenceofobservationsshowswhyPiaget’sobservationalprocedureisnotnecessarilyinferiortothe
formalexperimentalmethod; theadvantagesofdetailedknowledgeof thechild’shistoryareobvious,
andmanyoftheobservationsperformthesamefunctionascontrolgroupsinordinaryexperiments.
The explanation of the infant’s learning of secondary circular reactions involves many of the
principlesthatwereinvokedearlier.First,theinfant’saccidentalmovementproducesanexternalresult
which is moderately novel and which therefore interests him. Second, the infant perceives that his
actionsarerelatedtotheexternalresult.Piagetassertsthatiftheinfantdoesnotperceivetheconnection,
nofurtherlearningispossible.Third,oncetheinterestandtheconnectionbetweenactandresultare
established,theinfantdesirestorepeattheinterestingevent.Inotherwords,aftertheinfantlooksatand
listenstothetoysrattling(or,inmoretechnicallanguage,assimilatestheinterestingeventintothevisual
andauditoryschemes),hewantstoreinstatetheinterestingeventsandassimilatethemonceagaininto
theschemesoflookingandlistening.This,ofcourse,isthefamiliarprincipleoffunctionalassimilation:
onceascheme(inthiscaseviewingandhearingthetoys)isabletofunction,ittendstorepeatitself.After
thispoint,theinfant’sgoalofrestoringtheinterestingeventsmotivatesanddirectsactions.
Thusfar,theinfanthasperceivedaninterestingresult,hasrecognizedthatitisconnectedtohis
actions,anddesires torepeat theresult.The fourthstep involvesaccommodation; the infantneeds to
learn the hand movements necessary for consistent reproduction of the result. Part of the process
involvesrediscoveringthemovementswhichwerepreviouslyeffective.WhilePiagetdoesnotmakethe
matterentirelyexplicit,itisclearfromhisobservationsthatadirectedtrial-and-errorprocessisinvolved.
Theinfant’sbehaviorisdirectedinthesensethatthedesiretoreproducetheinterestingresultguides
hisactionsandinthesensethatheattemptsonlybehaviorswhichareclearlyrelevant:theinfantdoes
notkickhis feet,but limitshiseffortstoarmmovements.Withintheseconstraintstheprocess involves
trialanderrorsincetheinfantdoesnotknowatfirstpreciselywhicharmmovementsareeffective.He
has to try them out to seewhichmeetwith success andwhichwith failure. It is also clear from the
observations,andagainnotexplicitinPiaget’sexplanation,thattheinfantdoesnotsimplyrediscoverold
movements.Thismaybetheoriginalobjectiveandaccomplishment,butwithpracticetheinfantdevelops
movementswhicharemoreprecise,skilled,andeffectivethanthosewhichoriginallyandaccidentally
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obtainedthegoal.
Theresultofthisactivityisasecondarycircularreactionwhichisafarmorecomplexstructurethan
anythingtheinfanthaddevelopedearlier.Nowtheinfantisinterestedintheexternalenvironmentand
isabletodevelopbehaviorswhichserveasaprimitivemeansforobtainingvariousends.However,the
secondarycircular reactionhas twodeficiencies.First, it isnot fully intentionalas the infantdoesnot
haveagoalinmindfromtheoutset;rather,thegoalhasbeendiscoveredbyaccident,anditisonlyafter
thischanceeventhasoccurredthatthegoalguidesbehaviorandgivesittherebyapurposivecharacter.A
seconddeficiency is that the behavior is essentially conservative. The infant’s aim is to reproduce, to
duplicatesomebehaviorwhichproducedinterestingresultsinthepast.Hedoesnotattempttoinvent
newbehaviors.ThesetwodeficienciesleadPiagettomaintainthatthesecondarycircularreactiondoes
notyetconstituteintelligentbehavior.
Primitive Classes
OneofthemostinterestingaspectsofPiaget’stheoryhastodowiththeinfant’sformationofclasses
ormeaning.Theirdevelopment,accordingtoPiaget,beginsveryearlyinlife.Thefollowingobservations
illustratethematter:
At0;6(12)Lucienneperceivesfromadistancetwocelluloidparrotsattachedtoachandelierandwhichshehadsometimes had in her bassinet. As soon as she sees them, she definitely but briefly shakes her legs withouttryingtoactuponthemfromadistance....Sotoo,at0;6(19)itsufficesthatshecatchessightofherdollsfromadistanceforhertooutlinethemovementsofswingingthemwithherhand.
From0;7(27) certain too familiar situationsno longer set inmotion secondary circular reactions, but simplyoutlinesofschemes.Thuswhenseeingadollwhichshehasactuallyswungmanytimes,Luciennelimitsherselftoopeningandclosingherhandsorshakingherlegs,butverybrieflyandwithoutrealeffort.(OI,pp.186-87)
Inessence,Piagethasobservedthatwhentheinfantcomesintocontactwithsomefamiliarobjecthe
does not apply to it the secondary circular reaction which normally would be employed. Instead,
Lucienneexhibitsanabbreviatedformofthebehavioranddoesnotseemtointendtoproducetheusual
result.Theabbreviatedactiondoesnotseemmechanical,likeaconditionedresponse.Further,theinfant
is‘‘perfectlyserious”andrepeatstheactiononanumberofdifferentoccasions.
Piaget’s interpretation is that theabbreviatedactsarespecialcasesofrecognitoryassimilation. If
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youwill recall, inearlier stages the infant’sovertbehaviorshowed theability todistinguishbetween
variousobjects;forexample,whenhungryhesuckedthenipplebutrejectedapacifier.Thus,theinfant’s
behaviorissaidtoinvolverecognitoryassimilationwhenheisselectiveinapplyingspecificschemesto
variousaspectsoftheenvironment.
Thecaseofabbreviatedmovements involvesasimilarselectivity.Lucienne, forexample,kicks in
responsetotoyswhichshehasswung,butnotinresponsetoothertoys.However,thepresentinstance
involvesmorethanselectivity.Theinfant’sbehaviorisabbreviated;shedoesnotchoosetodisplaythe
entireschemewhenitwouldbequitefeasibletodoso.Piagetinterpretstheabbreviationasabehavioral
precursorofclassificationormeaning. Lucienne,of course,doesnothaveanabstract conceptionof the
parrot.Shecannotverbalizeitspropertiesoridentifyitasaninstanceoftheclassofanimaltoys.Butthe
abbreviatedbehaviorshowsthatLuciennemakesabeginningattemptatclassificationoftheobject.The
brief kicking, for instance, is the first step toward thinking the thought, "That’s the parrot; that’s
somethingtobeswung."Her"understanding"isofcoursequiteprimitiveanddoesnotyetoperateona
mentallevel.Nevertheless,shehasmadeprogressoverstages1and2,sinceshedisplaysbehaviorwhich
indicatesthattheinitialstepstowardinternalizationofactionareoccurring.Theabbreviatedschemeis
thefirstapproximationtothought.
Piagetproposesatechnicalterminologyfordescribingtheseevents.Hedesignatesasasignifieran
objectoreventthatstandsforsomethingelse;thechild’sreactiontotheobjectoreventisthesignified.In
thepresentcasethesignifieristheparrot,andthesignifiedisthechild’sbriefkicking.Thesignifieristhe
“thing,”andthesignifiediswhatitmeanstotheinfant.Withdevelopment,thesignifiermaybenolonger
athingbutaword,andthesignifiedmaybenotabehaviorbutanactofintellectualunderstanding.
Primitive Relations
Asweshallseelater,inChapter4,classificationisconsideredavitalaspectofthechild’sthought
andisinvestigatedingreatdetail.Similarly,weshallseeinthesamechapterthatthenotionofrelation
occupies a prominent place in Piaget’s theories. And relations, too, have primitive behavioral origins
whichariseinthecourseofthefirstseveralstages.Hereisanexample:
Intheeveningof0;3(13)Laurentbychancestrikesthechainwhilesuckinghisfingers...hegraspsitandslowly
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displaces itwhile looking at the rattles.He then begins to swing it very gentlywhich first produces a slightmovement of thehanging rattles and an as yet faint sound inside them. Laurent thendefinitely increasesbydegrees his ownmovements: he shakes the chainmore andmore vigorously and laughs uproariously at theresultobtained.—Onseeingthechild’sexpressionitisimpossiblenottodeemthisgradationintentional.(OI, p.185)
Inotherwords,theinfantseemstoseethedifferencebetweenaslightmovementonhispartanda
strongone;similarly,hecandiscriminatebetweenaloudandasoftrattle.Theinfantcanputtwosounds
or two movements into relationship with each other. Furthermore, the infant seems to see that the
intensity of his movements is directly related to the intensity of sounds made by the rattle. These
perceptionsofdifferences in intensity are theoriginsof quantitative thought.We shall see laterhow
theserelationshipsaredevelopedinstage4.
Imitation
Instage3theinfant’sattemptsatimitationbecomeincreasinglysystematic.Throughthesecondary
circularreactionstheinfantacquiresincreasinglyextensiveexperienceoftheenvironment.Theinfant’s
schemesincreaseinnumberandrange,withtheresultthatheismorecapablethanformerlyofbehavior
whichmatchesthatofamodel.Sincehecannowassimilatemoremodels,thereisgreateropportunityfor
imitation. It is still the case, however, that the infant continues to imitate onlywhat is familiar—only
actionswhichhealreadycando—andcannotyetreproducenovelactions.Thisconservativefeatureof
imitationisanalogoustothatdisplayedbythesecondarycircularreactions.
Object Concept
Instage2wesawthattheinfantmadenoattempttosearchforavanishedobject.Stage3,onthe
other hand, is characterized by the acquisition of four new behavior patterns which represent
considerableprogressintheformationoftheobjectconcept.
First,thereisvisualanticipationofthefuturepositionsofobjects.If,forexample,anobjectdrops
veryquicklyandtheinfantcannotseeallthemovement,hecanneverthelessanticipatethefinalresting
placeof theobject.At first the infantdoesthisbest ifhehimselfhasdroppedtheobject.Later,hecan
anticipatethepositionofanobjectdroppedbysomeoneelse.Considerthefollowingillustration:
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At0;6(3) Laurent, lyingdown,holds inhis handabox five centimeters indiameter.When it escapeshimhelooksforit intherightdirection(besidehim).Ithengrasptheboxanddropitmyself,vertically,andtoofastfor him to be able to follow the trajectory.His eyes search for it at once on the sofa onwhichhe is lying. ImanagetoeliminateanysoundorshockandIperformtheexperimentathisrightandathisleft;theresultisalwayspositive.(TheConstructionofRealityintheChild,CR,pp.14-15)
Herewesee that the infantno longercontinuespassiveviewingof theplacewherehesawthe
objectvanish,ashedidinthepreviousstage,buthenowvisuallysearchesforitinanewlocation.This
behavior shows that the infant anticipates that the object’smovementwill continue even though he
himself isunable tosee it. In thissense the infantconferson theobjectapreliminarysortof intrinsic
permanencewhich,however,remainssubjectivesinceitiscloselyrelatedtohisownactions.Hesearches
fortheobjectchieflyifhehimselfhascauseditsdisappearance.
Asecondachievementof thisstage iswhatPiagetcalls interruptedprehension.This is the tactual
equivalent to the above-mentioned behavior of visual accommodation to rapid movements. In other
words,iftheinfanthasalreadysetinmotioncertainmovementsofthehandorfingersforthepurposeof
graspinganobjectandthenlosesitordoesnotsucceedingraspingit,hewillsearchfortheobjectby
continuingthemovements.
Asinthecaseofvisualaccommodation,theinfantattributesonlyasubjectivepermanencetothe
object.Theobjectexistsonly inrelationto theactionhewasperformingwhen itvanishedorslipped
fromhisgrasp.
Theinfantoriginatesnonewmovementstoretrievethelostobject,butmerelyrepeatspastgestures
ofholdingorattemptingtoholdtheobject.Also,ifnomovementstowardtheobjecthadbeeninitiatedin
thefirstplace,theinfantmakesnoactiveattempttosearchforadisappearingobject.
Third,wecanobserveduringthisstageabehaviorwhichiscalleddeferred,circularreaction.Inthis
caseacircularreactioninvolvinganobjectisinterruptedandresumedspontaneouslybytheinfantata
latertime.Theresumptionoftheactionsonanobjectimpliesthattheinfantexpectsittocontinuetobe
available.Forexample,
At0;8(30)Lucienne isbusy scratchingapowderboxplacednext toheronher left, but abandons that gamewhensheseesmeappearonherright.Shedropstheboxandplayswithmeforamoment,babbles,etc.Thenshesuddenlystopslookingatmeandturnsatonceinthecorrectpositiontograspthebox;obviouslyshedoesnotdoubtthatthiswillbeatherdisposalintheveryplacewheresheuseditbefore.(CR,p.25)
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This is an important step forward, since suchbehavior isnotmerely a continuationofprevious
movementswhenanobjectislostfromsightortouch.Heretheactionhasbeencompletelyinterrupted
andreplacedbyanotherquitedifferentpatternofbehavior.Yetatalaterpoint,nottoofarremovedin
time,theinfantofhisownaccordreturnstotheplacewherehehadbeenplayingandexpectswhathe
hadbeenplayingwithtobetherestill.Thisshowsthattheinfantattributesatleastsomepermanenceto
theobject.Despitethisaccomplishment,theinfant’sobjectconceptisnotyetfullydeveloped.Bycontrast
with advances to bemade in the future, the infant’s behavior in the present stage is still too closely
associatedwithapracticalsituationandpreviousactivities,anddoesnotyetinvolveanentirelymature
objectconcept.
Ina fourthreactiontypicalof thepresentstage, the infantcannowrecognizean invisibleobject
evenwhenabletoseeonlycertainpartsofit.Iftheinfantisshownatoywhich(whilehewatches)is
completelycoveredbyacloth,hemakesnoattempttosearchforthetoy.If,however,certainpartsareleft
visible the infant tries to lift the cloth todiscover the rest of the toy.But even this ability is curiously
limited; he is able to recognize thewhole onlywhen some portions are visible. For example, one of
Piaget’schildrenwasabletorecognizehisbottleonlyifeitherendwasvisibleandthemiddlehidden.If
onlythemiddleportionwereshown,hewasnotabletorecognizethebottleandmadenoattempttosuck
onit.
Therecognitionofpartlyhiddenobjectsoccursonlyafterthechildhasacquiredsufficientskillin
manipulating things. While handling a variety of toys and other objects, the infant explores them
visually.Byvaryingthedistancesandanglesofthesethings,bringingthemclosertotheeyes,turning
themaround,andmovingthemfromsidetoside,theinfantwillgraduallygainabetterknowledgeof
theirshapeandtheirotherproperties.Thissortofknowledge,ofcourse,isnecessaryforsuchactivityas
therecognitionofpartlyhiddenobjectsandthuscontributestowardthedevelopmentofagenuineobject
concept.
In brief, we see that the four behaviors of the present stage—(1) visual anticipation of rapid
movements, (2) interruptedprehension, (3)deferred circular reactions, and (4) reconstructionof an
invisiblewholefromavisiblefraction—allpresentsimilarlimitationsandshortcomingswithrespectto
the object concept. These behaviors all indicate that at this stage the object does not have a fully
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independent or inpidual existence but is closely related to the infant’s own action.When the object
disappears, the infant is content to repeat actions that were being performed at the time of its
disappearance.Theinfant’sattemptstorediscoverthelostobjectconsistonlyofarepetitionofthepast
actionsassociatedwiththeobject.Nonovelbehaviorisintroduced.
STAGE 4: 10 TO 12 MONTHS
Coordination of Secondary Schemes
Thefollowingobservationsshowhowafterinitialfailurethechilddevelopsthebehaviorpatterns
characteristicofstage4:
at 0;6(0) I present Laurent with a matchbox, extending my hand laterally to make an obstacle to hisprehension.Laurenttriestopassovermyhand,ortotheside,buthedoesnotattempttodisplaceit.AseachtimeIpreventhispassage,heendsbystormingattheboxwhilewavinghishand....Samereactionsat0;6(8),0;6(10),0;6(21),etc.
Finally,at0;7(13)Laurentreactsquitedifferentlyalmostfromthebeginningoftheexperiment.Ipresentaboxofmatches abovemyhand, but behind it, so that he cannot reach itwithout setting theobstacle aside.ButLaurent,aftertryingtotakenonoticeofit,suddenlytriestohitmyhandasthoughtoremoveorlowerit;Ilethimdo it tomeandhegrasps thebox. I recommence tobarhispassage,butusingasascreenasufficientlysupplecushiontokeeptheimpressofthechild’sgestures.Laurenttriestoreachthebox,andbotheredbytheobstacles,heatoncestrikesit,definitelyloweringituntilthewayisclear....
Moreover,onenotesthattheintermediateactservingasmeans(removingtheobstacle) isborrowedfromafamiliarscheme:theschemeofstriking.WerecallthatLaurentfrom0;4(7)andaboveallfrom0;4(19)hasthehabitofhittinghangingobjectsinordertoswingthemandfinallyfrom0;5(2)ofstrikingtheobjects. . . .Now,thisistheusualschemeofwhichLaurentmakesuseatthepresenttime,nolongerinthecapacityofanendinitself(of
afinalscheme)butasameans(atransitionalormobilescheme).(OI,pp.217-18)
The interpretationofLaurent’sbehaviorutilizesmanyof theprinciplesdiscussed inconnection
withstage3.Thereare,however,someimportantdifferences.OnedifferenceisthatLaurenthasthegoal
inmindfromtheoutset.Ifyouwillrecall,instage3theinfantaccidentallydiscoversagoalandonlythen
pursuesit. Instage4,ontheotherhand,Laurent initiallyperceivesthepresentedobjectasafamiliar
goal. The infant has already developed schemes for dealing with the goal and immediately tries to
assimilateitintothem.Orinsimplerlanguage,theinfantalreadyknowswhattodowiththeobjectand
wantstodoit.Thedirectionalforceaffectingtheinfant’sbehavior—hisdesiretoachievethegoal—is,of
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course, once again a matter of functional assimilation. Once the scheme of the goal—grabbing the
matchbox—isactivated,itneedstofunction.
Butanobstaclearises(thefather’shandorthecushion)whichpreventsthechildfromattaining
thegoal.Nowwecanseethesecondfeaturewhichdistinguishesbehaviorinstage4fromthatinstage3.
Theinfantisnowrequiredtodevelopnewmeansforremovingtheobstacletoachievehisends.Unlike
stage3,itisnotnowsimplyamatterofrediscoveringsomebehaviorwhichearlierled(accidentally)to
thegoal.Theinfantmustshowsomedegreeoforiginalitytoremovetheobstacle.Butthisoriginalityisof
avery limitedsort. Insteadof inventing newmeans fordealingwith theobstacle, Laurent attempts to
utilizeasmeansschemeswhichhavebeendeveloped inconnectionwithothersituations.That is,he
generalizespatternsofpreviouslylearnedbehaviortothenewproblem(generalizingassimilation).In
thecourseofthisgeneralization,theolderschemesmaybesomewhat,butnotfundamentally,modified.
Also,hemaytryoutseveralschemes,butintheendretainsonlytheonewhichworksbyremovingthe
obstacle.Accommodationisonceagaindependentonpracticalsuccess.Theresultisacoordinationoftwo
secondaryschemes,eachofwhichhadbeenlearnedearlier,andeachofwhichisonlyslightlymodified
for the present occasion. One scheme serves as the means and the other as the ends. The child’s
originalityrestsnotininventingtwoseparateschemesbutincombininginanovelwaytwopreviously
learnedpatternsofbehavior.
Several features of this coordination are emphasized by Piaget. First, it is still essentially
conservative.Theinfant’saimistotreatthegoalobjectinthesamewayaspreviously.Oncetheobstacleis
removed,theinfantappliesafamiliarscheme.Second,theinfant’sbehavioratthisstageisforthefirst
timetrulyintentionalandtherefore“intelligent.”Piaget’scriteriafortheexistenceofintentionarethree
innumber:(1)theinfanthasthegoalinmindfromthebeginninganddoesnotdiscoveritaccidentally
as was the case in stage 3, (2) an obstacle arises which prevents direct attainment of the goal and
necessitates some kind of indirect approach, and (3) to overcome the obstacle, the infant employs a
scheme(means)whichisdifferentfromthatemployedinthecaseofthegoal(ends).
AthirdfeatureofthiscoordinationemphasizedbyPiagetisthatthebehaviorunderdiscussionis
mobile.Thenovelcoordinationbetweentwoschemesnotpreviouslyassociatedismadepossiblebythe
infant’srelativelynewabilitytodetachhisschemesfromtheirusualcontents.Inotherwords,thescheme
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usedasmeansisgeneralizedortransferredfromthesituationinwhichitwasoriginallylearned.This
flexibilityintheapplicationofschemesiswhatconstitutesmobility.
Relations
Instage3wediscussedtheveryfirstmanifestationsofrelationsintheinfant.Withthecoordination
ofschemesinstage4,theinfantbecomescapableofestablishingmorecomplexrelationships.
Letus recall, forexample,Laurent’s coordinationof secondary schemes: removinganobstacle to
attainagoal.WhenLaurentdoesthis, it isas ifhe“understands” that theobstaclestands inacertain
relationshiptothegoal.Theobstacleisinfrontofthegoal,anditmustberemovedbeforethegoalcanbe
attained.Inotherwords,justasanabbreviatedperformanceofoneschemeisaprimitiveindicationofa
class,sothecoordinationoftwoschemesimpliesabehavioralanalogueoftheunderstandingofrelations.
Letustakeanotherexample:
at0;9(17),Laurentliftsacushioninordertolookforacigarcase.Whentheobjectisentirelyhiddenthechildlifts thescreenwithhesitation,butwhenoneendof thecaseappearsLaurent removes thecushionwithonehand and with the other tries to extricate the objective. The act of lifting the screen is therefore entirelyseparate from that of grasping the desired object and constitutes an autonomous “means,” no doubt derivedfromearlierandanalogousacts.(OI,p.222)
Thusthesequenceisaclearcaseofsecondarycircularreaction.Laurenthaslearnedhowtogetthe
goal.Buthashenotalsolearnedsomethingoftherelationbetweenobstacleandgoal?Laurent’sbehavior
maybeinterpretedasshowingaconcreteunderstandingofcertainrelations:thecushionisontopofthe
cigarboxwhichinturnisunderthepillow.Weemphasizeonceagainthatthechild’s“understanding”of
relationsisnotabstractliketheadult’s;instead,itisentirelycontainedinhismeans-endbehavior.
Perhapsthemostremarkablefeatureofrelationsisthateveninthefirstfewstages,theyinvolvean
elementofquantity.Forexample,
At 0;9(4) Laurent imitates the soundswhich he knows how tomake spontaneously. I say “papa” to him, herepliespapaorbaba.When I say “papa-papa” he repliesapapa orbababa.When I say “papapapapapapa” herepliespapapapa,etc.Thereexistsaglobalevaluationofthenumberofsyllables:thequantitycorrespondingto2isinanycasedistinguishedfrom3,4,or5....
At0;10(4)LaurentrepeatspawhenIsay“pa,”papafor“papa”andpapapaforanumberof4ormorethan4.
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(OI,p.241)
Thus the infant shows a primitive appreciation of number in the ability to discriminate among
differentnumbersofsyllables.
Anticipation
If youwill, recall that in connectionwith the abbreviated schemes of stage 3,we discussed the
developmentoftheoperationsofclassificationandtherelationbetweenthesignifierandthesignified.
Forexample,whenLuciennebrieflyshakesherlegsatthehangingparrots,thesightofthetoysisthe
signifierandtheabbreviatedmotionisthesignified—theprimitivemeaningoftheparrotsforthechild.
Inthepresentstage,thesystemofmeaningsisusedintheserviceofanticipation.(Thisoccursalsoin
stage3,butinrudimentaryform.)HereisanexampleconcerningJacqueline:
At0;9(16)...shelikesthegrapejuiceinaglass,butnotthesoupinabowl.Shewatcheshermother’sactivity.Whenthespooncomesoutoftheglasssheopenshermouthwide,whereaswhenitcomesfromthebowl,hermouthremainsclosed. ...At0;9(18) Jacquelineno longerneeds to lookat thespoon.Shenotesby thesoundwhether the spoonful comes from the glass or from the bowl and obstinately closes hermouth in the lattercase....
Luciennehas revealedmostof thesamereactions.Thusat0;8(23)shealsocloseshermouth to thespoonfulcomingfromthebowl(ofsoup)andopensittothosecomingfromtheglass(offruitjuice).(OI,p.249)
Howcanwe interpret these reactions?First, note that theyareanticipatory. The infantdoesnot
avoidthesoupwhenitisinhermouth,butbeforeitgetsthere.Apparentlythesightofthesouporeven
itsdistinctivesoundisasignifier,andthesignifiedistheunpleasanttasteofthesoup.Inotherwords,
theinfantseesorhearsthesoup,anditsmeaningforherisanunpleasantexperience.Shethencloses
hermouth,notinresponsetotheactualtasteofthesoup,buttothemeaningthatsouphasforherbefore
it entershermouth. Furthermore, the infant in this stagedoesnot formonly anticipationswhich are
connectedwithherownactions.Forexample, Jacquelineoncecriedwhenshesawsomeonewhowas
sittingnexttohergetup.ApparentlyforJacquelinethesightofthepersongettingupwasasignifierof
his expected imminent departure (the signified), and it was to this signified (the expectation of
departure)thatshereacted.
Howdotheseanticipationsdevelop?Formerly,Jacquelinehadobservedthatthesignifier—inthis
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case the person getting up—was followed by another event, his departure. She had consequently
perceivedaconnectionbetweenthe twoevents, so thatnowthesignifiergivesrise toananticipation
concerningtheeventtofollow.
Imitation
Considerable progress in imitation occurs during stage 4. The infant can now establish
relationshipsbetweenthemovementsofamodelandthecorrespondingmovementsofinvisiblepartsof
hisownbody.Also,hebeginstoimitatenewactionsofmodels.
Considerthisexampleofthefirstcase:
at0;8(4)Jacquelinebeganbymakingaslightnoisewithhersalivaasaresultofthefrictionofherlipsagainstherteeth,andIhadimitatedthissoundattheoutset.[Onthesameday]Jacquelinewasmovingherlipsasshebit her jaws. I did the same thing and she stopped andwatchedme attentively.When I stopped she beganagain.Iimitatedher.Sheagainstoppedandsoitwenton.(PDI,pp.30-31)
Herewe see that Jacqueline establishes a connection betweenwhat she sees in themodel (the
movement of his lips) and what she cannot see in herself, but can only feel, namely, her own lip
movements.Howdoesshemanagetodothis?Atfirstwithhersalivashemakesasoundwhichisimitated
byPiaget. Jacquelinerepeatsthissoundandat thesametimecarefullywatchesthemovementsof the
model’smouth.NowwhilesheisreproducingthesoundofthesalivaandwatchingPiaget’smouth,she
becomes aware of certain tactile-kinesthetic feelings. The sound becomes associated on the one hand
withthesefeelings,andontheotherwiththesightofthemodel’slipmovements.Thus,thesoundisa
commondenominatorlinkingthevisualandkinestheticcues.Laterthesoundisnolongernecessary,and
shebecomesabletoimitatemouthmovementswithouteitherthemodelorherselfhavingtoproducethe
soundfirst.
Thefollowingisanexampleoftheimitationofnewactionsofamodel:
At0;9(12)Ialternatelybentandstraightenedmyfinger,andshe[Jacqueline]openedandclosedherhand.At0;9(16) she reacted to the samemodel several times in succession bywaving her hand, but as soon as shestopped trying to imitate me she raised her finger correctly. When I resumed she again began to wavegoodbye.
At0;9(19)Itriedthesameexperiment.Sheimitatedme,butusedherwholehandwhichshestraightenedand
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bentwithouttakinghereyesoffmyfinger.
. . .Finallyat0;9(22)shesucceededinisolatingandimitatingcorrectlythemovementoftheforefinger.(PDI,pp.46-47)
HerePiagetinitiatesanewmovementinfrontofthechild.Jacqueline,contrarytoherreactionsof
theprecedingstage,nolongerignoresthenewmovement,buttriestoimitateit.Tworestrictionsonthe
initial imitationofnovelbehaviorareapparent inthe foregoingexample. Inthe firstplace, the infant
imitatesonlymovementswhicharesimilartothosesheisalreadyabletoperform.Forinstance,bending
andstraighteningthefingerisnottoodifferentfrombendingandstraighteningthehand.Theinfantis
consequently interested in imitatingsuchbehaviorsinceshecanassimilate it tosomeknownscheme.
Furthermore,imitationisonlyveryapproximateatthispoint.Theinfantrarelysucceedsinreproducing
thecorrectmovementon the first trial. Shegradually improvesher techniquewithpracticeand,bya
successionofadjustments,accommodatesherschemestothenovelmovement.
Object Concept
Thebehaviorofthestage4infanttowardobjectsshowsamarkedprogressincomparisonwiththat
ofthepreviousstageandisaresultoftheinfant’simprovedmanipulatoryskills.Sincetheinfantisnow
betterabletocoordinatehandandeyemovements,hecanexploreobjectsmoreadequatelythanbefore.
Byholdinganobjectwhilehebringsitclosertoorfurtherfromtheeyes,orbyturningitaroundinthe
hand,hebecomesawarethattheobjectremainsthesameeventhoughmanyvisualchangeshavetaken
place.Thisdiscovery leads to theattributionofqualitiesofpermanenceandsubstance toobjects.Asa
result,whenanobjectvanishestheinfanttriestofinditagainbyactivesearch.Henolongerattemptsto
rediscovertheobjectbymerelyprolongingorrepeatingtheactionsalreadyunderwaywhentheobject
disappeared.Instead,theinfantnowinitiatesnewmovementsandactionswhichindicatethattheobject
hasbecomedetachedfromitsprevioussubjectiverelationshipwiththeinfant’sownactivity.
Incertainconditions,however,theobjectconceptcontinuestoretainsomeofitssubjectivequalities.
Thisphenomenonmaybeseenclearlyfromthefollowingobservation:
At0;10(18)Jacquelineisseatedonamattresswithoutanythingtodisturbordistracther(nocoverlets,etc.).Itakeherparrotfromherhandsandhideittwiceinsuccessionunderthemattress,onherleft,inA.BothtimesJacquelinelooksfortheobjectimmediatelyandgrabsit.ThenItakeitfromherhandsandmoveitveryslowlybefore her eyes to the corresponding place on her right, under the mattress, in B. Jacqueline watches this
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movementbut at themomentwhen theparrotdisappears inB she turns toher left and lookswhere itwasbefore,inA.(CR,p.51)
Jacquelinepresentsthereactiontypicalofthisstage.Incertainsituationstheinfantisunabletotake
intoaccountthenumberorcomplexityofthemovementsofanobject,andattemptstolookfortheobject
intheplacewhereshehadpreviouslysucceededindiscoveringit.Inotherwords,ifthesituationistoo
complex, she tends to attribute to the object a sort of absolute or privileged position which is that
associatedwithpreviouslysuccessfuldiscoveries.If,ontheotherhand,theobjectsimplydisappearsin
onespot,theinfantsearchesforitintherightplace.
Instage4,then,theinfantsometimesattributestotheobjectqualitiesofsubstanceandpermanence.
Instraightforwardsituationstheobject isdetachedfromtheinfant’sactionsandisanobjectiveentity.
Should itsmovementsbecometoocomplicated for the infant to follow,however, theobjectonceagain
takesoncertainsubjectivepropertiesandbecomesrelatedtotheinfant’spastactions,especiallythose
whichhadpreviouslyprovensuccessfulindiscoveringtheobject.
STAGE 5: 12 TO 18 MONTHS
Tertiary Circular Reaction
In stage5behavior loses its conservativeemphasis, and the child,whohasnowbegun towalk,
beginstosearchfornovelty.HereisanobservationonLaurent:
at0;10(2)Laurentdiscoveredin“exploring”acaseofsoap,thepossibilityofthrowingthisobjectandlettingitfall.Now,whatinterestedhimatfirstwasnottheobjectivephenomenonofthefall—thatistosaytheobject’strajectory—but the very act of letting go. He therefore limited himself, at the beginning, merely toreproducingtheresultobservedfortuitously.
... at 0; 10(10) . . . Laurent manipulates a small piece of bread. . . . Now, in contradistinction to what hashappenedontheprecedingdays,hepaysnoattentiontotheactof lettinggowhereashewatcheswithgreatinterestthebodyinmotion...[thefallingbread].
At0;10(11)Laurentislyingonhisback....Hegraspsinsuccessionacelluloidswan,abox,etc.,stretchesouthis armand lets them fall.He distinctly varies thepositions of the fall. Sometimeshe stretches out his armvertically, sometimes he holds it obliquely, in front or behind his eyes, etc. When the object falls in a newposition (forexample,onhispillow),he lets it fall twoor threemore timeson the sameplace, as though tostudythespatialrelation; thenhemodifiesthesituation.Atacertainmomenttheswanfallsnearhismouth;nowhedoesnotsuckit(eventhoughthisobjecthabituallyservesthispurpose),butdropsitthreetimesmorewhilemerelymakingthegestureofopeninghismouth.(OI,pp.268-69)
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The striking thing about theseobservations is Laurent’s curiosity about theobjects inhisworld.
Laurentdoesnotfocusinterestonhimselforonthosepropertiesofanobjectwhichaidinattainingsome
goal;instead,heseemscuriousabouttheobjectasanobject,andheseemsdesirousoflearningallhecan
aboutitsnature.Thisinterestinnoveltyforitsownsakeiscalledatertiarycircularreaction.
Piaget’sexplanationbeginswithnotingthattheinfantoftendiscoverstheinitialresultbychance.
Forexample,intheprocessofplayingwithhissoapdishLaurentaccidentallydroppeditandobserved
thefall.Moreover,theinitialchanceeventintereststheinfant,andthisinterestcanbeexplainedinterms
of the moderate novelty principle described earlier. The infant, of course, desires to reproduce the
interesting event, and this behavior involves the principle of functional assimilation. Consequently,
Laurentrepeatstheoriginalactanddropsthecaseofsoapseveraltimesinsuccession.
Thusfartheinfant’sbehaviorisnodifferentfromthatofstage3:aninterestingresultaccidentally
occurs, and the infant attempts to find a means by which to conserve it. However, at this point two
distinctivefeaturesofthetertiaryreactionmanifestthemselves.First,insteadofcontinuingsimpleand
rigidrepetitionoftheinterestingevent,Laurentinitiatesbehavioralchangeswhichproducevariations
in theevent itself.Laurentdrops thebreadandthenthe toys fromdifferentheightsor fromdifferent
positions. Second, he acts as if he now has interest in the new actions of the objects themselves and
searchesfornovelties—fortheunexpected.Heseemstotreattheunanticipatedtrajectoriesofthetoysas
somethingtobeunderstood.
Theexplanationofthetertiarycircularreactioninvolvesseveralsteps:
1.Atfirsttheinfanttriestoassimilatethenewobjectsintohisusualschemeofdropping.Hefinds,however,thatthehabitualschemedoesnotworkverywellashemeetswithresistance.Thatis,theinfanttriestodropthepieceofbreadinthesamewayhedroppedthesoapcase;thenhetriestodroptheswaninthesamewayhedroppedthebread.Sincealltheseobjectsdonotfallinthesameway,hemeetswitharesistancewhichisimposedbytherealityoftheobjectsthemselves.Laurentfindsthathisavailableschemeofdroppingdoesnotapplyinthesamewaytoalloftheobjects.Eachobjecthaspropertiesofitsownwhichmustbetakenintoaccount.
2. The infant becomes interested in these resistances. Piaget points out that at this stage ofdevelopmenttheinfantismorecapablethanbeforeofappreciatingnovelty.Ifyouwill
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recall,the“interesting”wasdefinedasthatwhichismoderatelydifferentfromwhattheinfantrecognizesasfamiliar.Consequently,themorethingstheinfantisfamiliarwithand themoreschemeshehas, themoreobjectsandeventshe is able to recognizeasnovel and interesting. The newborn’s world is largely restricted to sucking; eventsoutsidetheoralsphere(asmosteventsare)cannotbeinterestingbecauseofthelackofschemesrelevanttothem.Buttheinfantatstage5hasdevelopedskillswhichpermitcontactwithincreasinglylargersegmentsoftheworld;consequently,thereismuchthathewillfindinteresting.Insummary,themorecomplexthesystemofschemes,themorethe infant will be attracted to novelty. He will then be interested in the resistancesencounteredbyapplyingoldschemestonewevents.
3.Theinfantisinterestedinthepropertiesofobjectsfromanotherpointofview,too.Atthisstagetheinfanthasbeguntoattributepermanencetoobjectsandrecognizesthattheyhaveanexistenceindependentofhisown.Infact,objectsareeven“centersofforces,”withpowers and properties of their own. This new objectification of the world alsocontributestotheinfant’sdesiretoexplore.
Oncetheinfantrecognizesandhas interest inthepotentialnoveltiesofasituation,hebeginsto
accommodate,by“groping”orusingakindoftrial-and-errorproceduretodiscoverthepropertiesofthe
objects. The infant’s groping does not involve completely random responses; rather each of his
explorationsguides thenext.The resultsof one “experiment” lead tonewexperiments. For instance,
Laurentmayreleasetheswanfrompointswhichareincreasinglyhighabovehisheadandobservethe
extenttowhichtheswanbounceswhenithitsthebed.Theinfant,ofcourse,doesnotknowbeforehand
whatwillhappen;hemodifieshisbehaviortofindout.Byexploringtheobjectandaccommodatinghis
ownbehaviortoit,theinfantmayeventuallybecomeabletomastertheobject—toassimilateitwithout
difficultyintohis(modified)schemes.Inthiswayhebeginstoexploreandunderstandnovelaspectsof
theworld.
Discovery of New Means
Theinfant’stendencytowardexperimentationpermitsthediscoveryofnewmeansforattaininga
goal.ConsiderthefollowingobservationonLucienneat1;0(5).Piagetpresentsherwiththisproblem.
Ona table is a largebox turnedupsidedown.Thebox is so arranged that itmovesonlybypivoting
arounditscenterpoint.Onthebox,awayfromtheinfant’sreach,isanattractivetoy,abottle.
Lucienneat first tries to grasp thebox, but she goes about it as though thehandkerchiefwere still involved.
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[PullingahandkerchiefwasaschemewhichPiagethadpreviouslyobservedinthechild.]Shetriestopinchitbetween two fingers, in the center, and tries this for amomentwithoutbeing able to grasp it. Then,with arapidandunhesitatingmovementshepushesitatapointonitsrightedge....Shethennotestheslidingoftheboxandmakesitpivotwithouttryingtoliftit;astheboxrevolves,shesucceedsingraspingthebottle.(OI, p.287)
Togettheobject,Lucienneatfirstattemptedtoapplyanalreadyavailablescheme;pinchingthe
boxlikeahandkerchief.Then,however,she“groped”andaccommodatedherbehavior inatrial-and-
errorsortofway.Theresultwasdiscoveryofanewmeans.Luciennestruckthebox,andthisactionwas
successfulinbringingthetoyclose.Butwhileherbehaviorwastosomeextentcharacterizedbygroping,
ortrialanderror,heractionswereneverthelessdirectedintwosenses.First,heraccommodationswere
directed by the goal: Lucienne wanted to get the bottle and was trying out various means for this
purpose.Themeanswerehardlyselectedinarandomfashion;shedidnot,forinstance,trytoobtainthe
toybytakingoffhersocks.Second,Lucienneinterpretedthegropingbymeansofheralreadyavailable
schemes.Thatis,afterLuciennebychancehittheboxandsawitmove,shewasable,throughherpast
experience,to“understand”themeaningofheraction.Sheinterpretedthehittingasanothermethodfor
displacingobjects.Thusthechild’sgroping isdirectedbothbythegoalandbyearlierschemeswhich
enablehertounderstandwhatishappening.Therefore,learningisnotexplainedsolelybycontactwith
the environment, that is, by experiencewith aworld that simply forces the infant’s behavior to take
certain forms. The infant herself also makes an important contribution as she interprets and gives
meaningtothedataofexperience.
Imitation
At stage5 the childbecomes capable of the systematic imitationof newmodels. In theprevious
stage, the infant had begun to imitate new models which were not too different from his own
spontaneousactions,buthewasrarelycorrectonthefirsttrial.Inthepresentstagetheinfantbecomes
moresystematicinhistechniquesofimitation.Hereisanexample:
At0;11(20)she[Jacqueline]watchedmewith interestwhenI touchedmy foreheadwithmy forefinger.Shethen put her right forefinger on her left eye, moved it over her eyebrow, then rubbed the left side of herforeheadwith the back of her hand, but as if shewere looking for something else. She reached her ear, butcamebacktowardhereye....
At 0; 11(28) J., confronted with the same model, continued merely to rub her eye and eyebrows. Butafterwards,whenIseizedalockofmyhairandmoveditaboutonmytemple,shesucceededforthefirsttime
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inimitatingme.Shesuddenlytookherhandfromhereyebrow,whichshewastouching,feltaboveit,foundherhairandtookholdofit,quitedeliberately.
At0;11(30)sheatoncepulledherhairwhenIpulledmine.ShealsotouchedherheadwhenIdidso,butwhenIrubbedmyforeheadshegaveup....Itisnoteworthythatwhenshepulledherhairshesometimesturnedherhead suddenly in an attempt to see it. This movement is a clear indication of an effort to discover theconnectionbetweentactualandvisualperception....
At1;0(16),J.discoveredherforehead.WhenItouchedthemiddleofmine,shefirstrubbedhereye,thenfeltaboveitandtouchedherhair,afterwhichshebroughtherhanddownalittleandfinallyputherfingeronherforehead.Onthefollowingdaysheatoncesucceededinimitatingthisgesture,andevenfoundapproximatelytherightspotsindicatedbythemodel.(PDI,pp.55-56)
Twopoints are of interest concerning these examples. First, they clearly show that the infant is
moreadeptthansheformerlywasattheimmediateimitationofnewactionsofmodels.Theinfanttriesto
controlhermovementsinasystematicway.Forexample,Jacquelinetriestolookatherhairwhenshe
pullsit.Second,theexamplesillustratesomegeneralprocessesofimitation.Thechiefaimofimitationis
toreproducetheactofamodel.Whenthemodel’sactionsarenew,asinthepresentcase,accommodation
is required. That is, the infant must modify her movements to make them like the model’s. Thus,
accommodationhaspriorityoverassimilation.Inthecaseofintelligentbehavior,ontheotherhand,the
processes of assimilation and accommodation are in balance. The infant attempts both tomodify her
behavior in response to the demands of the environment (accommodation) and to understand this
environmentintermsofherownschemes(assimilation).
Object Concept
Instage5theinfantisfinallyabletofollowcorrectlyavisiblesequenceofanobject’smovements.He
nowunderstandspositionalrelationshipsbetweentheobjectandotherelementsof theenvironment.
Therefore,eveniftheobjectdisappearssuccessivelyinanumberofplacestheinfantwillsearchforitin
theplacewhereitwaslastseen.Theinfantdoesnot,asinstage4,lookfortheobjectintheplacewhereit
hadpreviouslybeendiscovered.Thus,theobjectisnolongerconnectedwithapracticalsituation(the
infant’spastsuccesses),buthasacquiredapermanenceofitsown.Atthisstage,though,theinfantcan
understandonlyvisiblemovementsoftheobject.Ifheisunabletoseeallthedisplacementsandmust
therefore infer thatsomeare invisible, the infantreverts toanearlierreaction—looking for theobject
wherehehadbeensuccessfulinfindingitinthepast.Thereasonforthefailureisthatwheninvisible
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movementsoftheobjectareinvolved,theinfantmustinferrelationshipsofpositionbutisnotyetcapable
ofinference.Considerthefollowingillustration:
At1;1(18)Lucienne isseatedonabed,betweenshawlAandclothB. Ihideasafetypin inmyhandandmyhandundertheshawl.Iremovemyhandclosedandempty.Lucienneopensitatonceandlooksforthepin.Notfindingit,shesearchesundertheshawlandfindsit....
Butwithaberet,thingsbecomecomplicated.IputmywatchintheberetandtheberetunderpillowA(ontheright);Lucienneliftsthepillow,takestheberet,andremovesthewatchfromit.ThenIplacetheberet,againcontainingthewatch,undercushionBontheleft;LuciennelooksforitinBbut,asitishiddentoofardownforhertofinditatonce,shereturnstoA.
Then,twice,IraisecushionBsothatLucienneseestheberetobviouslycontainingtheobject;bothtimessheresumeslookinginBbut,notfindingthewatchrightaway,returnstoA!ShesearchesevenlongerinAthaninBafterhavingseentheobjectinB!(CR,pp.76-77)
Hereweseethattheobjectseemstobeendowedwithadualnature.Ontheonehand,iftheinfant
is able to follow the object’smovements perceptually, she believes in its permanence and continued
existence.If,however,shecannotfollowthemovementsvisuallybutmustimaginethem,theinfantno
longerendowstheobjectwiththepropertyofpermanence.Theobjectrevertstoitsearlierstatusofbeing
associatedwithapreviouslysuccessfulscheme.
STAGE 6: 18 MONTHS TO 2 YEARS
Beginning of Thought
Inthecourseofhisfivestagesofdevelopment,theinfanthasmostcertainlymadegreatprogress.
The newborn displays simple patterns of learning which are limited to the sphere of hereditary
mechanisms;theinfantinstage5hasagenuineinterestinthethingsoftheenvironment,exploresthem,
andevenhastheabilitytoinventnewwaysofdealingwiththeworld.Buttheinfant’sachievementto
thispointisasnothingcomparedwiththenextdevelopment.Beforestage6theinfantwasnotcapableof
thoughtorlanguageandsowaslargelylimitedtotheimmediatedataofexperience.Stage6,however,
formsthetransitiontothenextperiodofdevelopmentinwhichtheinfantisabletousementalsymbols
andwordstorefertoabsentobjects.Thisperiodofsymbolicthoughtbeginstofreetheinfantfromthe
concretehereandnowandintroduceshimtotheworldofpossibilities.InChapter3weshalldiscuss
symbolicthoughtindetail;atpresentwewilllimitourselvestoabriefdescriptionofitsbeginnings,as
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illustratedbytheseobservations:
Piaget isplayingwithLucienne, at1;4(0)andhidesanattractivewatch chain insideanempty
matchbox.
Iputthechainbackintotheboxandreducetheopeningto3mm.ItisunderstoodthatLucienneisnotawareof the functioningof theopeningandclosingof thematchboxandhasnot seenmeprepare theexperiment.Sheonlypossessestwoprecedingschemes:turningtheboxoverinordertoemptyitofitscontents,andslidingherfingers intotheslit tomakethechaincomeout. It isofcoursethis lastprocedurethatshetriesfirst:sheputsherfingerinsideandgropestoreachthechain,butfailscompletely.ApausefollowsduringwhichLuciennemanifestsaverycuriousreaction....
Shelooksattheslitwithgreatattention;then,severaltimesinsuccession,sheopensandshutshermouth,atfirstslightly,thenwiderandwider!
[Then]...Lucienneunhesitatinglyputsherfingerintheslit,andinsteadoftryingasbeforetoreachthechain,shepullssoastoenlargetheopening.Shesucceedsandgraspsthechain.(OI,pp.337-38)
Thisobservationrevealsanimportantadvanceinthechild’scapabilities.Luciennewasconfronted
withasituationforwhichanewsolutionwasrequired.Togetthechainoutoftheboxshetriedmethods
whichhadinthepastbeensuccessfulinsimilarsituations.Buttheseschemeswerenotadequateforthe
newproblem.Whatwould the stage 5 infant do in these circumstances?Hewould experimentwith
variousnewmeansuntiloneoftheinventionswassuccessful.Hisbehaviorwouldshowgroping.
ButLuciennedoesnotdothis.Instead,shepausesandlooksattheboxintensely.Herchiefovert
behavioratthistimeisonlyanopeningandclosingofthemouth.Afterthisdelay,sheimmediatelysolves
theproblem.Whatdoestheopeningandclosingofthemouthsignify?Piagetinterpretsitasshowingthat
shetriestothinkaboutwaysofsolvingtheproblem.Lucienneisnotyetproficientatthought;sheisnot
yetcapableofrepresentingthesituationtoherselffullyinmentalterms.Consequently,she“thinksout”
the problem partly by way of movements of the mouth. Even though her thought is not yet fully
internalized,itinvolvesaconsiderableshortcutoverthegropingofstage5.NowLucienneneednotact
outherattemptedsolution,forsheisatleastpartiallyabletoemployamoreeconomicalprocedure:to
think. Thus, Lucienne is on the threshold of a new period of intellectual development in which the
acquisitionofthesymbolicfunctionpermitsthegrowthoftruementalactivity.
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Imitation
The notable achievement of stage 6 is the appearance of the capacity to representmentally an
objectoractionwhichisnotperceptuallypresent.Thecapacityforsuchrepresentationhasrepercussions
fortheprogressofimitationandcontributestotheappearanceoftwonewreactionsduringstage6.In
thefirstplace,whenfacedwithnewmodels,theinfantnolongerneedstoperformovertlytrialattempts
at imitation; instead, he now tries out the variousmovementsmentally. Havingmade the necessary
mentaladjustments,theinfantcanthenperformthecorrectaction.Sincetheprocessislargelymental,
thestage6infantcanimitatemorequicklythantheonewhomustfirsttryoutallthemovements.The
internalizationof the trial-and-errorprocess consequently leads towhat appears to be an immediate
imitationofmodels.
Anotherfeatureofthepresentstageisthattheinfantbecomescapableofimitatingforthefirsttime
amodelwhichisnolongerpresent.Thisdeferredimitationisduetothefactthattheinfantcanimagine
themodeleventhough it isabsent.That is, the infant iscapableofevoking(representing) theabsent
modelinsomeinternalsymbolicform,forexample,bymeansofavisualimage.Considerthefollowing
exampleofdeferredimitation:
At1;4(3)Jacquelinehadavisitfromalittleboyof1;6whomsheusedtoseefromtimetotime,andwho,inthecourseoftheafternoon,gotintoaterribletemper.Hescreamedashetriedtogetoutofaplaypenandpusheditbackward,stampinghis feet. Jacquelinestoodwatchinghim inamazement,neverhavingwitnessedsuchascenebefore.Thenextday,sheherselfscreamedinherplaypenandtriedtomoveit,stampingherfootlightlyseveraltimesinsuccession.(PDI,p.63)
Theinternalizationoftheactionisquiteclear.Theinfantdoesnotreproducethesceneatthetime
of its occurrence, but at some later period. Therefore, representation was required for the child to
preservetheoriginalsceneforittobeevokedatalatertime.
Object Concept
Finally,atstage6theconceptofthepermanentobjectisfullyelaborated.Theinfantnotonlytakes
into account visible displacements of the object, but can also reconstruct correctly a series of invisible
displacements.Forexample,
At 1;7(23) Jacqueline is seated opposite three object-screens, A, B and C (a beret, a handkerchief, and her
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jacket)alignedequidistantfromeachother.Ihideasmallpencilinmyhandsaying,“Coucou,thepencil.”[Thechild had previously found it under A.] I hold outmy closed hand to her, put it underA, then under B, thenunder C (leaving the pencil under C); at each step I again extendmy closed hand, repeating, ‘‘Coucou, thepencil.”JacquelinethensearchesforthepencildirectlyinC,findsitandlaughs.(CR,pp.79-80)
JacquelinehasseenthepencildisappearonlyonceandintoPiaget’shand.Shedoesnot,however,
look into his hand to find the pencil, but under the last objectwhere he had placed his hand. This
reactionindicatesthatshebelievesthatthepencilcontinuedtoexistwithinthehandduringthewhole
sequenceofdisplacements,andthatshehasinferredthattheinvisibleobjectwasdisplacedfromAtoBto
C.Inotherwords,Jacquelinehasformedamentalimageofthepencilandcanfollowtheimagethrougha
seriesofcomplexdisplacements.
SUMMARY AND CONCLUSIONS
Theinfant’sdevelopmentinthesensorimotorperiodisatrulyremarkableachievement.Instage1,
the newborn depends heavily on reflexes for interaction with the environment. The environment,
however,doesnotsimplyturnonandoffthesetoolsprovidedbyheredity.Theinfant,eveninthefirst
monthoflife,profitsfromexperienceandactivelymodifiesthereflexschemes.Helearns,forexample,to
recognizethenippleandtosearchforit.
Instage2,theinfantshowsbehaviorpatternswhichareremovedfromthefeedingsituation.(1)He
developstheprimarycircularreactions,forexample,themotorcoordinationsnecessaryforbringingthe
handtothemouth.(2)Theinfantlearnsinaprimitivewaytoanticipatefutureevents.Whenplacedin
theappropriateposition, the infantanticipatesnursingby initiatingsuckingmovements. (2)The first
signs of curiosity appear. The infant shows an interest in moderately novel events. (4) The infant
sometimesrepeatsthebehaviorofmodels.Thisisaveryprimitivekindofimitation,sinceitoccursonly
whenthemodelperformsanactionhighlysimilartoaschemeavailabletotheinfant.Itisasiftheinfant
didnotdistinguishthemodel’sactsfromhisown;therefore,theapparentimitationismerelytheinfant’s
repetition of behavior no different from his own. (5) The infant lacks a mature object concept, but
developsseveralpatternsofbehaviorwhicharepreliminarystepsintherightdirection.Hecoordinates
the previously independent schemes of looking and hearing, among others, and shows passive
expectancybywatchingforabrieftimethespotwhereanobjecthasdisappeared.
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In stage 3, the infant’s behavior and interest extend beyond his own body and makes more
extensive,butstillimmature,contactwiththeexternalenvironment.(1)Theinfantdevelopssecondary
circularreactions.Bychance,hediscoversaninterestingenvironmentaleventandattemptstoreproduce
theactionswhichcausedit.(2)Theinfantshowspreliminaryindicationsofclassificationormeaning.
Presentedwith a familiar object, he sometimes reactsby showingmere abbreviationsof the actions it
usuallyelicits.Thisbehaviorappearstobeaprecursorofmentalrecognitionandunderstandingofthe
object.(3)Theinfant’simitationisnowmoresystematicandprecise.Heisfairlysuccessfulatimitationof
models, butonlywhen familiarpatternsofbehaviorare involved. (4)The infantmakes considerable
progresstowardattainmentoftheobjectconcept.Ifhehimselfhascausedanobject’sdisappearance,the
infantattemptsavisualortactualsearch.Thissearchonlyinvolvescontinuationofbehavior(likelooking
or grasping) which is already under way. To this extent the object concept remains subjective—
intimatelyboundtotheinfant’sownbehavior.
In stage4, the infant’s behavior is increasingly systematic andwell organized. (1)He is able to
coordinatesecondaryschemes.Hehasagoalinmindfromtheoutsetandusesoneschemeasameansfor
attaining the goal and a second scheme for dealing with the goal. This behavior is purposive and
therefore intelligent. (2) By interacting with the environment, the infant learns something about
relationsamongobjects.Inremovinganobstacletoagoal,forinstance,thechildachievesapreliminary
andconcreteunderstandingofthefactthattheobstacleisinfrontofthegoalandmustberemovedbefore
thegoalcanbeattained.(3)Theinfant’sincreasingunderstandingoftheenvironmentisapparentinthe
ability toanticipateeventswhichdonotdependonhisownactions.At thisperiodthe infantexpects
people toact in certainways;hebegins to recognize that theyare “centersof forces” independentof
himself.(4)Theinfantbeginstoimitatethenovelbehaviorofmodels,butisnotyetstrikinglysuccessful.
Alsohe imitatesactions—likestickingout the tongue—whichhecannot seehimselfperform. (5)The
infant’sobjectconceptisalmostfullydeveloped.Heemploysavarietyofbehaviortosearchforvanished
objects.Heclearlyattributestothingsadegreeofsubstanceandpermanenceandbeginstoconceiveof
objects as autonomous and as independent of his own subjective state. Nevertheless, he is not yet
successfulatfollowingacomplexseriesofdisplacementsofanobject.
Stage 5 is the climax of the sensorimotor period. (1) The infant shows an active interest in
producing new behavior and novel events. Before this stage, the infant’s behavior was essentially
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conservative.Hetriedtorediscoveroldactionswhichhappenedtoleadtointerestingresults.(2)When
confrontedwithanobstacletheinfantattemptstodevelopnewmeansfordealingwithitanddoesnot
relysolelyonschemeswhichweresuccessfulpreviously. (3)The infant isnow increasinglyadeptat
imitating new actions of models. The infant attempts, for instance, to produce sounds he has never
utteredbefore.(4)Theinfanthasreachedafurtherstageinthesensorimotordevelopmentoftheobject
conceptandcannowcomprehenda complex seriesofdisplacementsandsearch for theobject in the
properplace.
Stage6formsthetransitiontosymbolicthought.(1)Inourpreliminaryoverviewwesawthatthe
infantattemptedtothinkaboutaproblem,todevelopsolutionsonamentalratherthanaphysicallevel.
(2)Similarly,theinfantcannowimitateamodeleventhoughthelattermaynotbepresent.Itisapparent
thatafterobservingamodel,theinfantformsamentalrepresentationofit,sothatthelaterimitationis
basednotonaphysicallypresentmodel,butonitsmentalsurrogate.(3)Theinfantnowcanreconstruct
aseriesofinvisibledisplacementsofanobjectbecauseofthesenewabilitiesinrepresentation.
Inthemostgeneralsense,developmentrevealsaprocessofdecentration.Theinfantbeginslifein
anundifferentiatedstate,notseparatingselffromenvironmentorwishfromreality.Heiscenteredabout
theself.Forexample,wehaveseenhowtheinfantinthefirstfewstagesdoesnothaveamatureobject
concept.Athingceasestoexistwhenitpassesoutsidehis immediateperception.Furthermore, forthe
infant theworld ismerely a series of unstable andunconnected “pictures.”Neither self nor external
environmentexistasautonomousentities. Inthecourseofdevelopmentthe infantadvancesfromthis
“adualistic”orundifferentiatedstatetooneofgreaterseparationofselfandenvironment.Hedecenters
fromtheself.Inthecaseoftheobjectconcept,forexample,theinfantnowconceivesofthingsexisting
independently.Objectsnowarecentersofforcesandhavepropertieswhichdonotdependonhiswill.
Thisgreaterunderstandingoftheexternalworldisatthesametimeanincreasedcomprehensionofthe
self.Therealizationoftheseparatenessofthingsnecessarilyinvolvesthesimultaneousapprehensionof
theexistenceofself.Inotherwords,thepersonwhobelievesthathiswishesinfluencethemovementsof
thingsdoesnotunderstandeitherselforthings;thepersonwhobelievesthatthetwoareseparatehasa
greaterunderstandingofboth.
Piagetstressesseveredpointsconcerningdevelopment inthesensorimotorperiod.First, theage
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normsareonlyapproximate.Aswenotedearlieritisimpossibletogivepreciseagenormsbecauseonly
threeinfantsprovidethedataforstudy.Moreimportant,Piagetfullyrecognizesthatthetimingofthe
stagesdependsonahostof factorswhichvaryamongchildren.Development isa functionofcomplex
interactionamongmanyfactors,amongwhichmaybethenatureofthesocialenvironment,theinfant’s
rateofphysicalmaturation,andsoon.Giventhesecomplexities,itisclearthatinfants’progressthrough
thestageswillshowmanyinpidualdifferences.Forinstance,PiagetcitestheexampleofJacquelinewho
wasborninthewinter.Becauseshewasbundledupinthecarriagetoprotectheragainstthecold,she
did not have as much opportunity as did the other children, born in warmer weather, to develop
coordinationbetweenhandandeye.Fromfindings likethese,Piagetconcludedthatthesensorimotor
stagesdonotappearatpreciselydefinedagesintheinfant’slife.
Second, Piaget insists, however, that the ordering of the stages is invariant. A child must pass
throughstage3beforestage4,andthereversecannotoccur.Also,achildcannotskipastageentirely.
ThereasonsforPiaget’sassertionarebothempiricalandtheoretical.First,Piaget’sobservationsshowed
thathisthreechildrenfollowedthesequenceofdevelopmentintheorderdescribed.Second,eachstage
isbothaculminationoftheoneprecedingandapreparationfortheonetofollow.Sinceeachstagelays
thegroundworkforthefollowingstage,itishardtosee,onrationalgroundsalone,howtheorderofany
twostagescanbereversed.
Third,Piagetemphasizesthatdevelopmentisagradualandcontinuousprocess.Onedoesnotfind
suddentransformationsinaninfant’sbehaviorsothatonedayheischaracterizedbystage3andthe
nextbystage4activities.Developmenttakestime,andbecauseofthisoneseldomsees“pure”examples
ofthebehaviorswhichPiagetusestodescribeastage.Piaget’sstagesare,infact,idealtypeswhichare
abstractedfromthecontinuumoftheinfant’sdevelopment.Whiletheseabstractionsareveryusefuland
convenient,Piagetiscarefultoremindusthatinthenormalcourseofeventstheinfant’sbehaviortakes
many forms intermediary between those described by the stages. Also, development is not always
consistentacrossallspheresofbehavior.The“stage4infant”isagainonlyanabstraction.Infact,onesees
infants whose object concept may be characterized by stage 4, while at the same time their level of
imitationisstage3,andsoon.
Fourth,Piagetstressesthatthebehaviorscharacteristicofagivenstagedonotdisappearwhenthe
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infantattainsthenextstage.Instead,evenasnewabilitiesareaddedtheinfantretainsmanyoftheold
ones.Forexample,thestage5infant,confrontedwithanobstacleandtryingtoremoveit,mayfirstapply
schemeswhichhavebeensuccessfulinothersituations(stage4behavior),andonlythenmayheattempt
toinventnewmeans(stage5behavior).
Inconclusion,wewouldliketomakeafewgeneralcommentsaboutPiaget’stheoryofinfancyand
clarifysomeaspectsthatareoftenmisunderstood.First,Piaget’spositionontheroleoftheenvironmentis
subtle, and consequently oftenmisinterpreted.He feels that it is obvious that the environment exerts
effects on the infant, but acceptance of this proposition hardly solves any problems. The task then
becomes to discoverhowthe environment operates. Piaget feels that the environment does notmold
behaviorbysimplyimposingitselfonapassivesubject,evokingtheinfant’sresponseandrewardingit.
Instead, Piaget’s central theme is that the infant is active; that is, the infant seeks contact with the
environment. His curiosity does not permit waiting for environmental events to happen; rather he
searchesthemoutandseeksincreasedlevelsofstimulationandexcitation.Whensomeenvironmental
eventoccurs,theinfantdoesnotregisteritpassively,butinsteadinterpretsit.Itisthisinterpretation,not
theeventitself,whichaffectsbehavior.Supposewehavetwoinfants,onewhoiscapableofanticipations
concerningadultsandonewhoisnot.Bothwitnessanadultwhorisesandputsonacoat.Oneinfant
cries and the other remains calm. “Experience”—seeing the adult get up and put on the coat—has
affectedtheinfantsdifferently.Theexplanationisthatoneinfantexpectedhimtoleaveandtheother
didnot.Theinfantsinterpretedtheeventsindifferentways.Wemightevensaythatthereexistedtwo
different“realities,”eachoneconstructedbyaninfant.Theinfantsassimilatedtheperceivedeventinto
theirdifferingexpectationsconcerningadultbehavior.Thisassimilationorinterpretationgavetheevent
meaningandproducedthesubsequentbehaviors.Sotheinfantsdidnotpassivelyregisteramere“copy”
ofreality;instead,theyinterpreted,constructed,andassimilated,or,inshort,gavemeaningtotheevents.
Experience,then,doesnotexerteffectsonaninfant,butinstead,exertseffectswithaninfant.The
childmodifiesrawexperienceasmuchasitchangeshim.
Second,Piaget is sometimesmisunderstood concerninghis viewsof the rolesofmaturationand
learning.ItshouldbeabundantlyclearthatPiagetisnotasimplematurationist.Hedoesnotbelievethat
theinfant’sdevelopmentunfoldssolelyasaresultofsomekindofphysicalmaturation.Piaget’sposition
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isthatmaturationplaysaroleindevelopment,butitcertainlyisnottheonlyfactor.Aswehaveseen,he
believesthattheeffectsoftheenvironmentarequiteimportant,andtothisextentPiagetisinagreement
withtheenvironmentalists.But,ashasbeennoted,Piaget’saccountoflearningisquitesubtleandisin
manywaysatvariancewithothertheoriesof learning.Forexample,he introducesnovelmotivational
principles, such as assimilation and the moderate novelty principle, and emphasizes the infant’s
interpretationoftherawdataofsensoryexperience. Inshort,Piaget isneitheramaturationistnoran
environmentalist,atleastnotinthedominantbehavioristtradition.Hispositionincorporateselementsof
bothtraditions,and,inaddition,elaboratesontheminhighlyoriginalways.Hethinksofhimselfasan
“interactionist,”forhistheorystressesthatintellectualdevelopmentresultsfromaninterplaybetween
internalandexternalfactors.
AsweshallseeinChapter6,Piagethaselaboratedandsupplementedhisaccountofexperience
andmaturationsincehiswritingofthebooksoninfancy.Thelatertheoryof“equilibration”expandson
theroleofexperienceand,inaddition,introducestheconceptofinternedcognitiveconflict.
Third, thenatureofPiaget’sstages isoccasionallymisunderstood.Piaget issometimescompared
withGesell,whoofferedanaccountof infancy in termsofstagesofdevelopment.Gesell’sstageswere
merelylistingsofspecificbehaviorswhichoccurredatdifferentages.Forexample,theinfantisfoundto
crawlatsuchandsuchanage,towalkatanother,torunatanother,andsoon.Whilesuchinformation
may be valuable, it is clear that Gesell’s stages merely list the empirical phenomena and have no
theoreticalcontentwhatsoever.Bycontrast,Piaget’sstagesareatheoreticaltaxonomy.Take,forexample,
stage4,whichisconcernedwiththecoordinationofsecondaryschemes.Piaget’stheoryproposesthatin
this stage the infant can coordinate two previously disparate patterns of behavior to attain a
preconceived goal. This statement—the theory of this stage—is an abstraction which transcends the
detailsofanyspecificbehaviorsthatmerelyillustratethestage.Thestatementisintendedtoallowusto
understandwhat the infant does regardless of the particular behaviors involved. Piaget’s stages are
thereforetheoreticalorexplanatory,andassuchareradicallydifferentfromGesell’s.
Notes
1Forexample,seeInaC.Uzgiris,“OrganizationofSensorimotorIntelligence,”inM.Lewis,ed.,OriginsofIntelligence (NewYork:PlenumPress,1976).
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2Indeed,thereadershouldrecognizethatunorthodoxprocedureshaveledtomanyofthegreatdiscoveriesinpsychology,includingFreud’sfreeassociationtechnique,Wertheimer’sdemonstrationexperiments,Chomsky’sintrospectiveanalysesoflanguage,Brown’snaturalistic observations of the language of three children, Skinner’s studies of inpidual pigeons, and the Gardner’sexaminationofWashoe’ssignlanguage.
3Forexample,seeT.Appleton,R.Clifton,andS.Goldberg,“TheDevelopmentofBehavioralCompetenceinInfancy,”inF.D.Horowitz,ed.,ReviewofChildDevelopmentResearch,Vol.IV(Chicago:UniversityofChicagoPress,1975).
4Inthisandsubsequentchapters,whenabookisfrequentlycited,wegivefirstanabbreviatedtitle(e.g.,OriginsofIntelligence)followedbybriefinitials(e.g.,OI).Inlaterreferencesonlytheinitialsareused.
5Piaget’s“recognitoryassimilation”combinesseveralprocessesusuallytreatedunderdifferentrubricsbythetheoryofperceptuallearning.Theinfantdiscriminates(aswhenheseesthatoneareaofthebreastlooksdifferentfromanother);herecognizes(aswhenheknowsthathehasmadecontactwiththebreastbefore);andheidentifies(aswhenhelearnsthatthenipplegivesmilk).Forafullerdiscussionofperceptuallearning,seeE.J.Gibson,PrinciplesofPerceptualLearningandDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1969).
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The Years 2 through 11:The Semiotic Function and Piaget’s Early Work
The present chapter covers two broad topics. The first to be considered is the development of
cognitiveprocessesinthechildofapproximately2to4years.Atthistimesomeveryimportantadvances
occurinthechild’sthought.Onesuchadvanceistheonsetofthesemioticfunction.Wewillconcentrate
on the young child’s useofmental symbols andwords, andon symbolic play.The second topic tobe
consideredisthedevelopmentofcertaincharacteristicsofthoughtinthechildfrom4to11years.We
shallreviewPiaget’searlyworkonthistopicandcoversuchmattersasegocentrism,communication,and
moraljudgment.
THE SEMIOTIC FUNCTION
Thesensorimotorperiodinvolvesarapidandremarkabledevelopmentofbehavioralschemes.The
newbornenteredtheworldwithonlya limitedrepertoryofautomaticbehaviorpatternsprovidedby
heredity. Yet after a period of only about two years, the infant can interact quite effectivelywith the
immediateworldofthingsandofpeople.Hepossessesschemesenablinghimtomanipulateobjectsand
usethemasmeansfortheattainmentofhisgoals.Theinfantalsoexperimentswiththingstoachievea
practicalunderstandingoftheirproperties.Butalloftheseabilities,ad-thoughuseful,arenevertheless
concrete,thatis,limitedtoimmediatelypresentobjects.Forexample,whiletheinfantmaybeabletouse
asticktobringanobjectwithinreach,hecannotconceiveofrelationshipsbetweenobjectsthatarenot
withinhisimmediatescopeofvision.Theinfantisabletoactonlyonthingswhichareperceiveddirectly.
Towardtheendofthesecondyear,thechildbeginstodevelopnovelcognitive,ormental,processes.
One important aspect of cognitive development is the appearance of the semiotic Junction. This
refers to the fact that from2 to 4 years the child begins to develop the ability tomake something—a
mental symbol, aword, or anobject—stand foror represent somethingelsewhich isnotpresent. For
example,thechildcanuseamental“picture”ofabicycle,ortheword“bicycle,”orasmallschematictoyto
standfortherealbicyclewhenitisnotinimmediateview.Theabilitytorepresentinthiswaymakesit
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possibleforthechildtooperateonnewlevels.Atthisstagethechildisnotrestrictedtoactingonthings
in the immediate environment because the semiotic function allows the evocation of the past. For
example,hismentalsymbolofthebicyclepermitstherecollectionofpreviousexperiencewiththistoy.
Thesemioticfunctionmanifestsitselfinseveralways.Duringtheperiodfrom2to4yearsthechild
begins toemploymentalsymbols, toengage insymbolicplay,andtousewords.Letusrevieweachof
theseactivitiesinturn.
Mental Symbols
Oneexampleoftheuseofmentalsymbolsinvolvesdeferredimitation.Letusrecalltheexampleof
thetempertantrum:
At1;4(3)[Jacqueline]hadavisitfromalittleboyof1;6,whomsheusedtoseefromtimetotime,andwho,inthecourseof theafternoon, got intoa terrible temper.He screamedashe tried togetoutof aplaypenandpushed it backward, stamping his feet. J. stoodwatching him in amazement, never havingwitnessed such ascenebefore.Thenextday,sheherselfscreamedinherplaypenandtriedtomoveit,stampingherfootlightlyseveraltimesinsuccession.(Play,Dreams,andImitation,PDI,p.63)
The important featureof theobservation is that Jacqueline’s imitationwasdeferred: it occurred
sometimeaftershehadoriginallyseentheboythrowingthetantrum.Herbehaviorthereforedidnot
simply copy an immediately observable model. If she could not see the tantrum, on what was her
behaviorbased?Howcanweexplaindelayedimitation?OneinterpretationisthatwhenPiagetobserved
her,Jacquelinehappenedtothrowatantrumforthefirsttime,quiteindependentlyofanythingtheboy
haddone.Buttheexplanationisquiteimplausible,becauseherbehaviorwassomuchlikethatofthe
boy. Consequently, we are forced to postulate a more complicated explanation that involves mental
symbolism.Thereasoningisasfollows.WeknowthatinthrowingthetantrumJacquelinedidnotsimply
copy an immediately present model. Nevertheless, her behavior was clearly similar to the boy’s.
Consequently,weassumethat Jacquelinemusthave formedamentalsymbolof thetantrumandthen
basedherbehavioronthissymbol.Inotherwords,Jacquelinemusthavehadavailableamentalevent
whichstoodfororrepresentedtheboy’srealaction.Theabilitytosymbolizeinthiswayallowedherto
copytheboy’sbehavioratalatertime.
What is the nature of mental symbols? It is difficult to answer this question since we have no
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methodwhichpermitsadirect“look”atthechild’sthought.Onepossibility,however,isthatthechild’s
mental symbols are, at least in part, comprised of visual images. Perhaps Jacqueline “pictured” the
tantrum toherself.While visual imagerydoes indeedoccur (andmayormaynothavebeenusedby
Jacqueline),Piagetremindsusthatmentalsymbolsmaytakeotherformsaswell.Althoughsometimesa
personmayusevisualimagery,hemayatothertimesrepresentobjectsbytheirsounds,orevenbyan
abbreviatedformoftheirmovements.Piagetalsoproposesthattheinpidualmaynotevenbeconsciousof
thesementalsymbols.Achildmaydisplay imitativebehaviorwithoutrealizing that it isbasedon the
actions of anotherperson. Surely, after Freud’swork, it should come as no surprise thatmanyof our
thoughtprocessesareunconscious.
We have seen, then, that themental symbolmay ormay not be conscious andmay ormay not
involve visual imagery.Does themental symbol involve language?Was Jacqueline able to imitate the
tantrumbecauseshecarriedinherheadthewords,“Heis liftinghisarms,heisshouting,”andsoon?
Althoughthissortofinterpretation—averbalmediationapproach—hasitsadherents,Piagetrejectsit.
Hecitestwomajorreasons.First,certainexperimentswithanimalsshowthatchimpanzees,forinstance,
havementalsymbolswhichofcoursecouldnotbebasedonlanguage.Ifnonverbalsymbolismispossible
inanimals, thenwhynot inthehumantoo?Second,observationof thechildshowsthatbehavior like
deferredimitationoccurswhilelanguageskillsarestillveryprimitive.ItisquiteunlikelythatJacqueline
was at that time capable of a reasonably full verbal description of the boy’s temper tantrum. Yet, her
imitationwasquiteaccurate.Sinceamentalsymbolbasedonthechild’scrudelanguagecouldnothave
provided a basis for such accurate imitation, the linguistic explanation must be ruled out. Thus, to
explain Jacqueline’s deferred imitation,wemust postulate her use ofmental symbols. These symbols
probablydonotinvolvelanguagetoasignificantdegree,butwecannotconfidentlyspecifytheirexact
nature.
Asecondexampleofmentalsymbolismcanbeseeninthechild’sreactiontohiddenobjects.Ifyou
will recall, in stage 6 of the sensorimotor period, the child could reconstruct a series of invisible
displacementsofanobject. Inanobservationdescribed inChapter2,Piagethida smallpencil inhis
handandthenplacedthehandconsecutivelyunderaberet,underahandkerchief,andfinallyundera
jacketwhereheleftthepencil.Jacquelinedidnotlookforthepencilinherfather’shand,whichwasthe
last place shehad seen it, andwhich iswhere the younger child searches; instead, she immediately
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reachedunderthejacketandfoundthepencil.
Howcanweexplain Jacqueline’sbehavior? Itwasnotrandom,sincesheacted inessentially the
samewayonmanyoccasions.PiagetassumesthatJacquelineformedamentalsymbolofthepencil.When
Piagetcoveredthepencilinhishand,Jacquelinebelievedinitscontinuedexistence.Whenthehandwas
placedunderasuccessionofobjects, theuseof thementalsymbolenabledher to followmentally the
invisibledisplacements.Theavailabilityofamentalsymbolisthusnecessaryforamatureobjectconcept.
Thus far, we have seen two kinds of behavior—deferred imitation and search—whichmay be
interpretedasdemonstratingtheexistenceofmentalsymbolisminthechild.Wemaynowexplorethe
developmentofmentalsymbols.
The Formation of Mental Symbols
Howdoes thechild formmentalsymbols?Thereseemtobeat least twopossibleanswers to this
difficult question. One explanation is that the ability to symbolize is an entirely new functionwhich
suddenly makes its appearance when the child is about 2 years of age. Another possibility is that
symbolism has precursors in the sensorimotor period. Emphasizing continuity in intellectual
development,Piagetadoptsthesecondalternative.Hepostulatesthatthesemiotic function isderived
fromimitation.Considerthefollowingobservationfromthesensorimotorperiod:
At1;3(8)J.[Jacqueline]wasplayingwithaclownwithlongfeetandhappenedtocatchthefeetinthelowneckofherdress.Shehaddifficultyingettingthemout,butassoonasshehaddoneso,shetriedtoputthembackinthesameposition....Asshedidnotsucceed,sheputherhandinfrontofher,bentherforefingeratarightangleto reproduce the shape of the clown’s feet, described exactly the same trajectory as the clown and thussucceeded inputtingher finger into theneckofherdress.She lookedat themotionless finger foramoment,thenpulledatherdress,withoutofcoursebeingabletoseewhatshewasdoing.Then,satisfied,sheremovedherfingerandwentontosomethingelse.(PDI,p.65)
Herewehaveacaseofimitationputtotheserviceofunderstandinganunusualphenomenon.In
thecourseofplayingwithafamiliartoy,Jacquelinediscoveredthattheclowndidsomethingunexpected
andinitiallyunexplainable.Itsfeetcaughtherdressinawaythathadnotoccurredbefore.Jacqueline
immediatelytriedtounderstandthecauseoftheunexpectedevent.Hermethodofdoingsowasthrough
imitativeaction:sheformedherfingerintotheshapeoftheclown’sfoot,placedthefingerinherdress,
and thenpulled to seewhatwouldhappen. Shediscovered that the fingergot caught and therefore
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preventedfreemovementofherarm.Inthiswayshecametounderstandthattheshapeoftheclown’s
footsimilarlyrestricteditsremoval.Anotherwayoflookingattheobservationistosaythatitinvolvesa
specialkindofimitation:Jacquelineusedherownbodytorepresentorstandfortheclown’smovements.
Heractionssymbolizedthoseoftheclown.Thisisnotanisolatedobservation;Piagetfindsthatthechild
oftenimitatesthings.Forexample,henotedthatLucienne,uponobservingthatherfather’sbicyclecould
bemadetomovebackandforth,performedthesamemotionsherself.Sheswayedtoandfroataboutthe
speedofthebicycle.
Piagetarguesthatsuchimitationofthingsisthesensorimotorforerunnerofmentalsymbolism.The
infant’s swayingbackand forth is thebehavioral equivalentof theolder child’smental symbolof the
bicycle.Inotherwords,fortheinfanttheactionofswayingsignifiesabicycle,whereasfortheolderchild
amental symbol performs the same function. Toward the end of the sensorimotor period, the child’s
imitation “goes underground,” figuratively speaking. Instead of imitating things on the level of overt
behavior,theolderchilddoessointernally.Forinstance,inplaceofactuallyswayingbackandforth,the
olderchildmightimitatethebicyclebymakingveryslightandalmostimperceptiblemovementsofhis
muscles.Or,insteadofformingthefingerintheshapeoftheclown’sfoot,theolderchildmighttensehis
fingermusclessoslightlythatanobserverwouldnotnotice.Moreover,thisinternalimitationisnomere
oddity.Thechild’sinternalandalmostundetectablemovementsconstitutethementalsymbol.Thechild’s
musclesperformanabbreviatedimitationofswaying,andthesebodilysensationssymbolizeforhimthe
bicycle.Whenthechild’sfingertenseseversoslightly,thisinternalimitation,whichisnotnecessarilya
visualimage,signifiestheclown.
Wehaveseen,then, thatthesensorimotorchildrepresentsthingsbyacting likethem.Theolder
child, on the other hand, performs such imitation internally, and these abbreviated bodymovements
constitutethementalsymbol.Eventuallythechildbecomessoproficientat internedimitationthatthe
movementsareextremelyabbreviatedand,therefore,almostimpossibletodetect.
Several interesting points can be made concerning the formation of the mental symbol. First,
Piaget’stheorygivesusadditionalinsightintothenatureofthechild’smentalsymbols.Wesaidearlier
thattheymightinvolveavisualcomponentandthattheyprobablydonotconsistoflinguisticfeatures.
Nowweknowthatmentalsymbolsinitiallyinvolvethechild’sactionsinanimportantway.Themental
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symbol of the bicycle consists not only of a visual image, but it also may involve bodily sensations
correspondingtothebicycle’smovements.
Second,inreferringtothesymbolasconsistingofinternalimitation,Piagetusesthetermimitation
inaverybroadsensetoaccountforvisualimagery.Considerthishypotheticalexample.Whenaperson
seesatable,hisperceptionaccommodatestoit.Hiseyesmustfollowthetable’soutline,detectitscolor,
focus to localize the table in space, and so on. In these ways, the person establishes a number of
relationshipsconcerningthetable(space,color,etc.)whichtogetherformhisperceptionofit. Inother
words, the environment does not simply impose on him the perception of the table. Instead, the
perceptionisderivedfromhisownactivity—fromaseriesofintricatemovementsofhiseyesandfrom
complex activity in the brain and nervous system. Visual perception is an activity, just as the child’s
swaying is an activity. Nextwe see the role of imitation. At a later timewhen the table is no longer
present,thepersonmayrepeatinanabbreviatedformthemovementsinvolvedinhisinitialperception
ofthetable.Thatis,hiseyesmayagainmoveastheydidwhentheytracedthetable’scontour,adjustedto
itsdistance,andsoon.Thisinternalandabbreviatedimitationoftheperceptualactivityconstitutesthe
visual image of the table. Since an image of an object is seldom as rich or as detailed as the original
perception,theimagemerelyrepresentsorsymbolizestheactualobject.Inbrief,thementalsymbolmay
involve visual imagery, and the latter may be considered the internal imitation of the originally
perceivedobject.
Third, Piaget introduces a technical vocabulary for dealing with representations. As Figure 1
shows, the semiotic or representational function involves signifiers—mental events, words, or things
whichstandforsomethingelse—andthesignified,tobedescribedshortly.Signifierssignifyorrepresent
somethingtotheinpidual.Onetypeofsignifieristhesymbol,whichmaybepersonalandidiosyncratic,
andresemblesthethingitstandsfor.Foronechild,atoymaysymbolizethebicycle;foranotherchild,the
visualimage(resemblingthebicycle’sappearance)maysuffice.Consequently,oneperson’ssymbolmay
not transmit to another person any information at all about the action or object that is represented.
Abbreviated movements, as in swaying like a bicycle, seem to be the developmental forerunners of
symbolism.Symbolsmaybemental or concrete. Concrete symbols,whichwe shall review shortly,may
involveusingoneobject(e.g.,ahandkerchief)tostandforanother(e.g.,ablanket).Mentalsymbolstake
several forms.Wehave already seen thatone typeof symbol is thevisualimage; other types include
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auditoryimages.Thesymbolinvolvesapredominanceofaccommodation.Thisissobecausethesymbol
consistsofinternalimitation,andimitationinvolvesmodifyingone’sbehaviortofitthatofamodel,orin
broader terms, tomeet the demands imposed by the social or physical environment. Another type of
signifieristhesign,whichtypicallyreferstoawordusedinconventionallanguage.(Thesigncouldalso
refer to other conventions like mathematical notation, football diagrams, etc.) A word is social, not
personal,andisarbitrarilyrelatedtothethingitstandsfor.“Bicycle,”forexample,isnotanidiosyncratic
term:mostofusagreethat“bicycle’’standsforthesameobject,andthereforeuseofthetermtransmits
considerableinformation.Also,theword“bicycle”bearsnoresemblancetotherealthing;ifourlinguistic
communitysodecreed,wecouldlegitimatelysubstitute“elephant”for“bicycle.”Insummary,signifiers
involvevarioustypesofsymbolsandsigns.
FIGURE1Schematicoutlineofthesemioticfunction.
ThecomplexityofPiaget’sterminologyshouldnotobscurethefactthattheabilitytoformmental
representations is an achievement of great magnitude. In the sensorimotor period this capacity was
lacking.Ifyouwillrecall,theonlysignifierswereconcreteattributesofthings.Forexample,themother’s
voiceorfootstepssignifiedtotheinfantthatshewouldsoonarrive.However,thisprimitivesignifier,or
“index,” was linked to the infant’s actually hearing the voice or footsteps. He had no mental
representationfortheseevents;therefore,thesignifierhadmeaningfortheinfantonlywhentheevents
actuallyoccurred.Bycontrast,theolderchildcanusementalrepresentationstostandforabsentevents
orthings.Thingsnolongerneedtobepresentforthechildtoactonthem.Inthissense,theabilityto
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representeventuallyliberatesthechildfromtheimmediatepresent.Hecanimaginethingsthatareboth
spatially and temporally separate from himself. It may therefore be said that the use of mental
representationspermitsthechildtotranscendtheconstraintsofspaceandtime.
Meaning
HavingreviewedPiaget’stheoryoftheformationofmentalsymbols,weshallnowdealwiththe
processbywhichtheyacquiremeaning.Letusconsideranapparentlysimplequestion:Towhatdoesthe
child’smentalsymbol,likeswayingbackandforth,refer?Wemayposethesamequestionwithregardto
theword:Whatdoes“bicycle”designate?Ourfirstresponsetothisquestionistosaythatboththemental
symbol and the word obviously refer to the real bicycle. But according to Piaget, thematter is more
complicatedthanthat.The“signified”(whatthesymbolorwordstandsfor,oritsmeaning)isnotthereal
object, but rather the child’s understanding or intellectual construction of the real object. To put it
differently, symbols orwords do not refer to things, but instead stand for one’s knowledge of things.
Supposeonechildusestheword“bicycle.”Forhim,abicyclehastwowheels,aseat,andhandlebars.A
bicycle is something that goes delightfully fast, and, also, it is one kind of vehicle. For another child,
however,thesignifiedmaybesomewhatdifferent.Thischildagreesthatabicyclehastwowheels,aseat,
andhandlebars,buthavingoftenfallenfrombicycles,hethereforefeelsthattheyarefrighteningand
dangerous.Further,hehasnoconceptionofthebicycleasavehicle.Notethatforboththesechildrenthe
word “bicycle” evokes some commonmeaning: twowheels, handlebars, and soon.Both children can
thereforeeasily identifywhatabicycle isandwhat it isnot. Inthis“denotative”sense,theworddoes
refer to the real object. But the children also disagree as to theword’smeaning; for one, a bicycle is
delightfulandfortheotheritisfrightening.Also,foronechilditisamemberoftheclassofbicycleswhich
inturnisincludedinthelargerclassofvehicles.Theotherchild,ontheotherhand,employsnosuch
classhierarchy. InPiaget’s terms, each childhas assimilated theword “bicycle” into adifferent set of
schemes(thesignifiedorthemeaning).Therefore,theword“bicycle,”orthechildren’spersonalmental
symbolsforit,doesnotrefertotherealthingbuttotheirunderstandingofit.
Tosummarize,internalimitation(accommodation)providesthechildwithsymbols.Thechildthen
endows these symbols and words too with meaning, assimilating them into his mental schemes.
Therefore, what the symbol or word refers to (the signified) is always personal, if not idiosyncratic,
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although in thecaseofwords there isa sufficientamountof commonsignification for communication
amonginpidualstooccur.
Symbolic Play
Afurtherexampleofanactivityimplyinguseofthesymbolicfunctionissymbolicplay.Hereisan
observation.
[At1;3(12)Jacqueline]...sawaclothwhosefringededgesvaguelyrecalledthoseofherpillow;sheseizedit,heldafoldofitinherrighthand,suckedthethumbofthesamehandandlaydownonherside,laughinghard.Shekepthereyesopen,butblinkedfromtimetotimeasifshewerealludingtoclosedeyes.(PDI,p.96)
Theobservation involves several interesting features. First, Jacqueline acted toward the cloth in
roughlythesamewayasshebehavedtowardapillow.Sheputherheadonit,suckedherthumb,andso
on.Second, Jacqueline’sbehaviorrevealedacertainplayfulness; that is,she laughedatwhatshewas
doing.Apparently,shethoughtheractionswerequitefunny.
One simple interpretation of this behavior is that the childmerely confused the clothwith the
pillow.Butthisexplanationisnotveryplausiblebecauseitfailstoexplainwhythechildlaughed.After
all,Jacquelinedidnotordinarilygiggleupongoingtobed.
Piagetinterpretsthebehaviorasacaseoftheplayfuluseofconcrete(notmental)symbols.Itisclear
fromJacqueline’slaughterandfromherattitudeofpretensethatsheknewperfectlywellthatthecloth
wasnotreallyapillow.Herplayfulness indicates thatsherealized that theclothwasasubstitute for
anotherthing.Inotherwords,theclothwasasymbolorsignifier,andwhatitsignifiedwasthepillow.
Thecloth,ofcourse,wasaconcreteobjectandnotamentalsymbol.
How did this assignment of meaning to the cloth come about? Piaget’s interpretation is that
meaningisachievedintermsofassimilation.WhileinthepastJacquelinehadperformedtheactionsof
lying down, closing the eyes, and so on only in connection with the pillow, she now extends these
schemestoanobjectwhichsheknowsisnotapillow.WecanthereforesaythatJacquelineassimilated
theclothintoschemespreviouslyappliedonlytothepillow.Itistheprocessofassimilationtoschemes
(thesignified),then,whichprovidesthemeaningforthesymbol.Moreover,Jacquelineisawareofthe
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make-believecharacterofheracts.Herplayfulnessshouldnotmakeusunderestimatetheseriousness
and importanceofheraccomplishment: shehasachievedaprimitivecomprehensionof thenatureof
symbols.Indeed,weoftenfindthatthechild’s“play”involvessignificantintellectualactivity.
ItisinterestingtonotethatPiagetfeelsthatsymbolicgamesplayanimportantroleinthechild’s
emotional lifeaswell.Thechildfrom2to4yearsis inaveryvulnerablestageofdevelopmentinthe
sensethatheisbeginningtoacquireanewsetofwaysofdealingwiththeworldaroundhim.Thechild
alsofindsthathemustconformtoasetofsocialrules,nottheleastofwhichislanguage.Thechildmust
accept the fact that words stand for things without any apparent justification. His capacity for self-
expressionvialanguageisextremelylimitedandrudimentaryandthewordsavailablefrequentlyare
inadequate to expressneeds and feelings. The childmust obey commandswhosepurposehe cannot
understand.Thechild’snaturalspontaneityisbeingcompressedintothesocialmoldofhisculture,and
heisgenerallypowerlesstoresist.
These feelingsof inadequacy lead to frustration for the child and, subsequently, to conflictwith
surroundingpersons.Symbolicplay,whichformsa largepartof thechild’sactivity inthisstage, isan
appropriatemeans of providing an adjustment to reality.With this form of interaction the child can
assimilate the external world almost directly into his own desires and needs with scarcely any
accommodation.Hecanthereforeshaperealitytohisownrequirements.Furthermore,insymbolicplay,
the child can act out the conflictual situations of real life in such a way as to ensure a successful
conclusioninwhichhecomesoutthewinner,andnot,asissometimesthecaseinreallife,theloser.In
brief,symbolicplayservesanecessarycatharticpurposeandisessentialforthechild’semotionalstability
andadjustmenttoreality.Indeed,symbolicplayoftenservesasthebasisforpsychotherapywithyoung
children.
Language
Wehavenowseentwodifferentmanifestationsofthesemioticfunction:theuseofmentalsymbols
andsymbolicplay.Wewillturnnowtoathirdaspectofthesemioticfunctionandseehowthechilduses
languageandgivesitmeaning.
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Inthesixthstageofsensorimotordevelopment,thechild’sfirstuseofwordsisnotrepresentational
inthesenseofreferringtoabsentobjects.Insteaditisintimatelyrelatedtohisongoingactions.Consider
thisexampleconcerningLaurent:
at 1;5(19) “nomore” meant going away, then throwing something on the ground, and was then used forsomethingthatwasoverturned(withoutdisappearing).Hethussaid“nomore” tohisblocks.Later “nomore”merelymeantthatsomethingwasatadistancefromhim(outsidehisfieldofprehension),andthenitreferredto the game of holding out an object for someone to throwback to him. At 1;6(23) he even said “nomore”whenhewantedsomething someonewasholding.Finally, at1;7 “nomore” became synonymouswith “beginagain.”(PDI,p.218)
Note thatLaurentdidnotuse “nomore” in a representationalway.Hedidnotmake thewords
standforanabsentthingoreventasinthesentence,“Thereisnomorewaterinthegarden.”Instead,
Laurent’suseof“nomore”wasconcreteintwosenses.First,heemployedthewordsinconnectionwith
objects that were immediately present like the overturned blocks. Second, the words were used to
expresshisimmediatedesires,aswhenhewantedsomethingapersonwasholding.Inadditiontobeing
tied toconcrete thingsoractions, thechild’s firstwordsareveryunstable.Thephrase “nomore”was
usedtorefertogoingaway,tosomethingoverturned,tosomethingatadistance,andsoon.Themeaning
of words is not constant for a young child. In fact, for him, words have little socially agreed upon
meaning; instead, they are quite personal, and in this respect they resemble idiosyncratic mental
symbols.
Thenextstepinthedevelopmentoflanguageinvolvestheuseofwordsinarepresentationalway.
Atabout2yearsofage,thechildgraduallybeginstousewordstostandforabsentthingsorevents.For
example,at1;11(11)afterreturningfromatrip,Jacquelinetoldherfatheraboutit.Shesaid,“Robertcry,
duck swim in lake, gone away” (PDI, p. 222). These events had occurred some time previously, and
Jacqueline was able to remember them. Moreover, she was capable of using words to stand for past
events. Thus, through a gradual evolution, words are no longer used by the child to refer solely to
ongoingactions,desires,orimmediatelypresentevents.
Nowthatwordshavegenerallyassumedarepresentationalcharacterandrefertoabsentthings,
we may ask whether the child uses them in the same way as the adult. For example, we saw that
Jacquelineusedthewords“duckswimin lake” torefer toevents in thepast.Despite the fact that the
wordsarerepresentational,doesthechildgivethemthesamemeaningthatanadultdoes?Anotherway
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ofputtingthequestionistoaskwhetherthechild’sconceptofduck,orthemeaningassignedtotheword
“duck,”isthesameastheadult’s.Themerefactthatthechildusestheworddoesnotnecessarilyimply
thathegivesitwhatweconsideritsordinarymeaning.Herearesomeobservationswhichmayclarifythe
issue:
at 2;7(12), seeing L. [Lucienne] in a new bathing suit, with a cap, J. [Jacqueline] asked: “What’s the baby’sname?”Hermotherexplainedthatitwasabathingcostume,butJ.pointedtoL.herselfandsaid:“Butwhat’sthenameofthat?”(indicatingL’sface)andrepeatedthequestionseveraltimes.ButassoonasL.hadherdressonagain,J.exclaimedveryseriously:“It’sLucienneagain,”asifhersisterhadchangedheridentityinchangingherclothes.(PDI,p.224)
TheobservationshowsthatJacqueline’sconceptofhersister,andtheuseoftheword“Lucienne,”
arequitedifferentfromtheadult’s.Jacqueline’sthinkingattributeslittleinpidualitytohersister.Thereis
not one Lucienne who is the same person regardless of superficial changes; instead, as a result of
wearingdifferentclothing,therealLucienneisseenastwodifferentlittlegirls.Thechildatthisagefails
torecognizethatapersonOrthingremainsthesame,orconservesitsidentity,whenitundergoesminor
variationsinappearance.
Inadditiontoperceivinginsufficientinpiduality,thechildalsoshowsotherunusualusesofwords.
OnceJacquelinewasinthegardenandwalkedonthelandlord’sflowers.Sheremarked“MespoilUncle
Alfred’sgarden”(PDI,p.224).Shehadhadearliercontactwithheruncle’sgarden,andinthepresent
caseused thephrase “UncleAlfred’s garden” to refer to the landlord’s. Inotherwords, sheusedone
phrasetorefertotwodifferentthings.Allgardensare“UncleAlfred’sgarden.”Inthecaseofhersister,
Jacquelinesawthesameinpidualunderdifferentguisesasdifferentinpiduals;inthepresentinstance
shesawdifferent“inpiduals”(gardens)asthesame“inpidual.”Clearly,inneithercasedidJacqueline’s
useofwordscorrespondtoanadult’s.Theconceptsormeaningsevokedby“Lucienne”or“UncleAlfred’s
garden”werequiteprimitive.Inasense,thechild’searlywordsresemblesymbols—theyarepersonal
andidiosyncratic.
Reasoning
Duringtheyears2to4,thechildshowsthreedifferentkindsofreasoning.Inonetype,thechildis
facedwithasimplesituationwhichhasbeenexperiencedbefore.Thechild then“reasons”about the
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situationveryconcretelyintermsofwhathadoccurredinthepast.Forexample,at2;4(16)Jacqueline
calledherfatherwhodidnotanswer.Sheconcludedfromthis:‘‘Daddydidn’thear.”Ataboutthesame
timeJacquelinesawherfathergettinghotwaterandreasoned:“Daddy’sgettinghotwater,sohe’sgoingto
shave”{PDI,p.231). Inbothcases, Jacquelinehadhadpreviousexperiencewithherfather insimilar
situations.Her“reasoning”aboutthemwas limitedmerelytosimplememoryofwhathadoccurredin
thesesituationsinthepast.Piagetfeelsthatthistypeofreasoningissimplyanapplicationofprevious
experiencetoacurrentsituationandisnottobeconfusedwiththegenuinelydeductivereasoningofthe
matureperson.
In a second kind of reasoning, the child’s desires distort thinking. For example, at 2; 10(8)
Jacquelinewantedtoeatoranges.Herparentsexplainedthatthiswasimpossiblebecausetheoranges
were still green and not yet ripe. Jacqueline “seemed to accept this, but amoment later, as shewas
drinking her chamomile tea, she said: ‘Chamomile isn’t green, it’s yellow already . . . Give me some
oranges!”’(PDI,p.231).ApparentlyJacqueline,havingastrongdesirefororanges,reasonedthatifthe
teawereyellowthentheorangesmustbeyellowtoo,andthereforeshecouldhavethemtoeat.Atthis
stage,thechildattemptstoreasontoachievesomegoal,butthoughtdistortsrealityinaccordancewith
desire.ThisissimilartoFreud’snotionofwishfulfillment.(Aswillbeevidentshortly,theteaobservation
isalsoanexampleoftransduction.)
A third type of reasoning iswhat Piaget calls “transductive.” In logic a distinction is sometimes
madebetweendeductionand induction.Deduction isusuallycharacterizedasaprocessofreasoning
fromthegeneraltotheparticular.Forinstance,ifweassumethatallmenhaveheartsofgold,andifwe
arethenshownaparticularman,wededucethathehasaheartofgold.Inductionisusuallyconsidered
a method for reasoning from the particular to the general to establish general principles from
examinationofparticularcases.Forinstance, ifwehavemeta largenumberofmenallofwhomhave
heartsofgold,wemightconcludethatallmenhaveheartsofgold.AccordingtoPiaget,theyoungchild’s
reasoning lies in between induction and deduction. The child does not go from the general to the
particular(deduction),orfromtheparticulartothegeneral(induction),butratherfromtheparticularto
theparticularwithouttouchingonthegeneral.Transductivereasoningseesarelationshipbetweentwo
ormoreconcrete(particular)itemswhenthereisnone.Forexample,onanafternoonwhenLucienne
did not take a nap, she said: “I haven’t had my nap so it isn’t afternoon” (PDI, p. 232). In this case,
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Lucienne’sthoughtproceededfromthenap(oneparticular)totheafternoon(thesecondparticular)and
concludedthattheafternoondependedonthenap,whenofcoursetherelationshipwasofadifferent
type.
Summary and Conclusions
Intheperiodfrom2to4yearsthechildachievesthecapacitytoformmentalrepresentationswhich
stand for absent things or events. To deal with things, the child no longer requires that they be
immediatelypresent;instead,thechildisabletocreateamentalsubstitutefortherealthing.Thisability
freesthechildfromtheimmediatehereandnow.Insteadofhavingtomanipulatethings,heworkswith
theirsubstitutes.Thechildformsmentalsymbolsthroughimitation.Thechildlooksatthings,handles
them,andactslikethem,andinthesewaysincorporatesagreatdealofinformationaboutthem.These
actions of the child lay the foundation formental symbolism. In fact, imitationmay be considered to
bridgethegapbetweensensorimotorandlaterintelligence.Duringthesensorimotorperiodtheinfant
developsabilitiesinimitativebehavior.Whenthechildisproficientatimitationatalaterage,hebegins
toimitateinternally,andtherebyformsthementalsymbol.InPiaget’sterminologymentalsymbolsare
signifiers.Thesymbol ispersonalandresembleswhat itrefersto.Forexample,Lucienneswayedback
andforthtorepresentabicycle.Oncementalsymbolsareformed,thechildgivesthemmeaningthrough
theprocessofassimilation.Heassimilatesthemintotheschemeswhicharealreadyavailable.Therefore,
what the symbol refers to (the signified) is always personal and intimately related to the child’s
experience.Agoodexampleoftherelationbetweenthesymbolanditsmeaningisthechild’splayfuluse
ofsymbols.Inamake-believefashion,thechildmakessomethings(symbols)standforothers.Thechild
playfullyassimilatessomeobjects intoschemesappropriate forothers.Another typeofsignifier is the
signorwordwhichisalsousedtorefertosomethingelse.Theword,however,usuallydoesnotresemble
itsreferent,buthasaconventionallyagreed-uponmeaningtofacilitatecommunication.
Duringthisperiodthechilduseswordsinseveralways.Afterapreliminarystageinwhichwords
arecloselyrelatedtoongoingactionsanddesires,thechilduseslanguagetorefertoabsentthingsand
events. The child, however, does not use words in the same way that an adult does; the meaning
assignedtowords,ortheconceptassociatedwiththem,isstillquiteprimitive.Thechild’sconceptsarein
factonlypre-concepts:theyaresometimestoogeneralandsometimestoospecific.Thechildalsoshows
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signsofan initialreasoning.Sometimes it issuccessful,butonlywhen itdoesnotgo farbeyondmere
memoryforpastevents.Atothertimesthereasoningmaybefaulty.Thisiseitherduetothetendencyfor
wishes to distort thought or to the transductive nature of the child’s thought: he reasons from the
particulartotheparticular.
These, then, are the beginnings of symbolic activity in the young child. His initial efforts are
imperfect,andfromtheadultpointofviewinvolvemany“errors.”Alongevolutionisnecessarybefore
thechildcanachievematurityinthought;logicalthinkingdoesnotemergefullyformedinthechildof2
years.
Piagetarguesthatlanguageplaysalimitedbutnotnegligibleroleintheformationofthechild’s
thought.Clearly, languagedoesnotfullyshapethechild’smentalactivities.Despitehisnewabilityat
language,thechildoftenthinksnonverbally.Heformsmentalsymbolswhicharebasedonimitationof
things andnoton theirnames. Languagedoes, however,makea contribution. For example,whenan
adult uses awordwhich refers to a class of things, the child is given a glimpse at one facet of adult
reasoning. An adult’s language forces the child, to some degree, to consider the world from a new
perspective.Nevertheless,itisprobablyfairtosaythatthechild’sthoughtdependslessonhislanguage
thanthechild’slanguagedoesonhisthought.Aswesawearlier,thechildinterpretswordsintermsof
hisownpersonalsystemofmeanings,andthechild’smeaningisnotnecessarilythesameastheadult’s.
Although the culture provides the childwith language, the latter does not immediately socialize the
child’s thought. In other words, language does not completely impose on the child the culturally
desirablewaysofthinking.Instead,thechilddistortsthelanguagetofithisownmentalstructure.The
childachievesmaturethoughtonlyafteralongprocessofdevelopmentinwhichtheroleoflanguageis
butonecontributingfactor.
THE CHILD FROM 4 TO 11 YEARS (PIAGET’S EARLY WORK)
Wehavenowreviewedtheinfant’saccomplishmentsinthesensorimotorperiod(0-2years)and
the child’s acquisition of the semiotic function (2-4 years). It is hard to emphasize sufficiently the
magnitudeof theseachievements. In thespaceofonlya fewyears, thechildhas transformedhimself
from an organism almost totally dependent on reflex and other hereditary equipment to a person
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capableof symbolic thought.During theyears to follow (after theageof4), neither sensorimotornor
symbolicactivitiesdisappear.Thechildolderthan4yearscontinuestodevelopsensorimotorschemes
applicabletoawiderangeofobjects,toimproveskillsinlanguage,andtoacquirementalrepresentations
forincreasinglylargeportionsofthesurroundingworld.Butatthesametimethechild’sdevelopment
extendsintoanumberofnewareas.
Thepresentsectionoffersanaccountofintellectualgrowthinthechildfromabout4to11years.
Recall that Piaget’s first five books cover this age span and present preliminary and tentative
conceptualizations.Laterworksoffermoreelaborateandmaturetheorizingonthesameagerange.We
willdescribeherePiaget’searlyviewsonthechildfrom4to11years;Chapter4reviewsthelaterwork.
Asweshallsee,Piaget’searlywork,althoughpreliminary,isstillquitefascinatingand,accordingtosome
criteria,ratesamonghisfinestaccomplishments.
The Use of Language
Piaget’searlyworkbeginswithaconsiderationofchildren’suseoflanguage.Attheoutsetheposes
afundamentalquestion:Whatisthefunctionofthechild’slanguage?Ourfirstresponseisprobablythat
thepurposeoflanguageiscommunication.Thechild,liketheadult,mostlikelyuseslanguagetoexpress
thoughtstoothers,andtotransmitinformation.Butalittlereflectionshouldsufficetoconvinceusthat
evenintheadult,languageisnotentirelycommunicative.Whenalone,adultsoftentalktothemselveson
amentallevel.Occasionally,theyevenspeakaloudwhennooneelseispresent.Therefore,ourinitial
hypothesisaboutthecommunicativenatureoflanguageisnotalwaystrue.
If this is so, then several questions immediately arise. How much of language—particularly
children’s language—iscommunicativeandhowmuch isnot?What is thenon-communicativevariety
like?Andwhenitisnotcommunicative,whatpurposedoeschildren’slanguageserve?Toanswerthese
andotherquestions,Piagetcarriedoutaseriesofinvestigations.Hebeganbyobservingtwo6-year-old
boys for about a month in their class at school. The children, who were from the poorer sections of
Geneva, attended a progressive class. The students could drawormakewhat they liked, couldwork
inpiduallyat“games”ofmathematicsandreading,hadthefreedomtotalkorplaytogether,andcouldgo
without permission from one room to another. As the two boys pursued their activities, Piaget and
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another observer took down in full detail the children’s speech as well as the context in which it
occurred.Piagetattemptedtoavoidinterferingwiththechildren’sactivitiesandtriednottoinfluence
their behavior in any way. The intention, of course, was to obtain a full record of the child’s use of
languageinhisnaturalschoolenvironment.Ifyouwillrecall,Piagetusedsuchnaturalisticobservation
inhisstudiesofinfancyandtheperiodfrom2to4years.Severaloftheadvantagesanddisadvantagesof
thismethodhavealreadybeendiscussedinChapter2.Onequestionthatwasnotconsiderediswhether
ornotPiaget is correct in assuming that the children’s behavior is not affectedby thepresenceof an
observer.Dochildrenactandspeakdifferentlywhenwatchedbyanadult?Unfortunately,thereislittle
empirical evidence on this issue. At themomentwe can only use our informal experience in similar
situationstohazardaguessthatafterashortperiodof timeyoungchildrengenerally learnto ignore
adultobserversandseemtobehavequitenaturally.
Afterrecordingthetwochildren’sspeech,Piagetattemptedtocategorizeeachsentencespokenby
each child. He discovered several varieties of both communicative and non-communicative language.
Non-communicativeor“egocentric”speechmaybepidedintothreetypes.Onetypeisrepetition,which
involvesthechild’smimickingsomethingshehasjustheard;forexample,“JacsaystoEz:‘Look,Ez,your
pantsare showing. ’ Pie,who is in another part of the room [andwas one of the two childrenPiaget
observed],immediatelyrepeats:‘Look,mypantsareshowing,andmyshirttoo.(LanguageandThought,LT,
p. 35). The statement clearly involved copying another’s speech since Piewas in fact quite properly
dressed.ThusPie’sutterancewasaclearcaseofrepetitionanddidnotserveacommunicativefunction.
Very often too the child is not aware that he ismerely repeatingwhat another person has said, but
believesthathisstatementisanoriginalone.AccordingtoPiaget’srecords,repetitionmadeupabout1or
2percentofthetotalnumberofstatements.
Asecondkindofegocentricspeechisthe inpidualmonologue.Thistypeoccurswhenthechild is
aloneandyettalksaloud,oftenatgreatlength.Forexample,“Levsitsdownathistablealone:7wantto
dothatdrawingthere...Iwanttodrawsomething,Ido.Ishallneedabigpieceofpapertodothat’”(LT,p.37).
Sincenooneelsewaspresentapartfromtheobserver,whobythistimepresumablynolongerdisturbed
the child, Lev’s statement clearly did not involve communication. In the case of Pie, monologue
constituted5percentofhisspeech,andforLevthefigurewas15percent.
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Perhaps themost interesting kind of egocentric speech is the collectivemonologue. This occurs
whentwoormorechildrenaretogetherandoneofthemspeaksasoliloquytowhichtheothersdonot
listen. The speakermay intend to interest the others in his remarks andmay in fact believe that the
othersarelistening.Buttheegocentricnatureofthemonologuepreventstheothersfromunderstanding
him even if they wanted to. Despite the fact that the speaker is in a group, his statements are not
communicative; he is merely talking to himself aloud. For example, when sitting with some other
childrenandapparentlyplayingwithtoysordrawing,Levsaid,“Isay,I’vegotaguntokillhimwith.Isay,
Iamthecaptainonhorseback.Isay,I’vegotahorseandagunaswell”(LT’p.41).NotethatLev’scontinual
useofthephrase“Isay”seemstoindicatethathewantedtheotherstolistentohimandthatheintended
to transmit information. But at the same time, Lev’s statement is unclear: we do not knowwhom he
intended tokillwith thegun,whowas thecaptainonhorseback,andsoon.Moreover,Lev’s remarks
wereunrelatedtoanyoneelse’sanddidnotsucceedinmakingtheotherchildrenlisten.Infact,each
child,althoughapparentlyworkingwithandspeakingtotheothers,offeredsoliloquieslikeLev’s.There
wasno“giveandtake”amongmembersofthegrouporanycontinuityinthediscussion;eachchildspoke
aboutwhat interested him at themoment, and this involvedmostly his own activities. The collective
monologue is therefore neither truly social nor communicative as it is merely the simultaneous
occurrence of at least two monologues. According to Piaget’s calculations, the collective monologue
involved23percentofLev’sspeechand30percentofPie’s.Egocentricspeechasawhole—repetition,
monologue, and collective monologue—represents 39 percent of Lev’s and 37 percent of Pie’s total
numberofsentences.
Theremainderofthechildren’sspeechiscommunicativeor“socialized.”Inthiscasethechildtakes
into consideration the point of view of the listener and attempts to transmit information to him. For
example,hetellsanotherchildcertainsimplefacts, forexample,howtooperateatoy.Orhecriticizes
anotherchild,oraskshimquestions,orinotherwaysinteractswithhim.Whileservingacommunicative
function,suchspeechneverthelessshowscertaindeficiencies.Youngchildrendonotattempttoexplain
eventstooneanother,andtheydonotspeakintermsofthecausesofevents.Also,youngchildrendonot
try to give proof or logical justification forwhat they have proposed. One reason is that they do not
considerthepossibilitythatthelistenermayhaveacontraryopinion.
AfterestablishingthesefactsinthecaseofLevandPie,Piagetthenwentontostudyalargergroup
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oftwentychildrenvaryinginagefrom4to7years.Again,themethodwasnaturalisticandinvolvedthe
recordingofthechildren’sspontaneousremarks.Ingeneral,thefindingsreplicatedthedataonLevand
Pie.Asignificantproportionofspeechwasegocentric,andthisproportionwasespecially large in the
speechoftheyoungestchildren,ataboutage4.
These, then, are the results of Piaget’s naturalistic observations. There seems to be a decline in
egocentrismandanincreaseincommunicationasthechildgetsolder.Thechild’slanguage,especiallyin
the early portion of the years from 4 to 5 or 6 years, does not entirely serve the function of
communication.Often,thechilddoesnotassumethepointofviewofthelistener;hetalksofhimself,to
himself,andbyhimself.
Howcanweexplainthenon-communicativenatureofthechild’sspeech?Whatpurposesdoesit
serve? Piaget offers a number of interesting hypotheses which he regarded as tentative, and not
conclusive.First,considerverbalrepetition,wherethechildsimplymimicswhatotherssayorrepeats
phrasesofhisown.Piaget’s interpretationisthatrepetitionis"simplythe joyofrepeatingfor itsown
sake...thepleasureofusingwords...forthesakeofplayingwiththem"(LT’p.35).Youwillnodoubt
observethatthisexplanationisanotherversionoftheprincipleoffunctionalassimilation—thetendency
torepeatschemesandtoexercisethem. Inthepresentcasethechildmimicsbothhisownwordsand
thoseofothers,justasearlierinthesensorimotorperiodherepeatedpatternsofbehavior.Consequently,
repetitionisnotmotivatedbythedesiretocommunicate,butbytheneedtoexerciseverbalschemes.
Butrepetitioncomprisesonlyasmallportionofthechild’sspeech.Letusnowturntotheinpidual
monologuewhich involves a substantial proportionof the total numberof statements. To explain the
monologue,Piagetofferstwohypotheseswhicharenotmutuallyexclusive.Onehypothesisisthatthe
inpidualmonologueservesthepurposeofwishfulfillment.Whenthechild’sactionsarenotsuccessfulin
producinganintendedresult,heuseswordstoachievehisgoal.If,forexample,hewouldliketomovea
boxbutcannotbecause it is tooheavy, thechildmighttellthebox tomove, thususingwords tobring
aboutwhathisactivitiescannotaccomplish.Thechild’slanguage,therefore,isinpartakindoffantasy,a
wordmagic.Asecondexplanationofinpidualmonologueisthatwordsandactions,forthechild,arenot
yet fully differentiated.When beginning to learn language, the 2- or 3-year-old child often calls an
immediatelypresentobjectbyitsnameorusesawordtodescribeongoingactions.Consequently,inhis
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initialexperiencewithlanguage,thething(oraction)andthewordforitaresimultaneouslypresent,
andthetwoareseenasawhole.Thewordisinasensepartofthething,andviceversa.Ittakesalong
timeforthechildtodisassociate fullythewordfromitsreferent;hemust learnthatthewordbearsa
totallyarbitraryrelationtothattowhichitrefersandthatthewordisnotapartofit.Evenintheperiod
underdiscussion(4to7years), thechildhasnotfullygraspedtherelationbetweenwordandthing.
Consequently,whenheacts—playswithtoys,draws,andsoon—hetendstosaythewordsassociated
withhisbehavior.Thus,themonologueisinasenseapartofthechild’sactionandisnotdesignedfor
thepurposeofcommunication.
Inthecaseofthecollectivemonologue,similarexplanationscanbeemployed.Sometimesthechild
inagroupmerelyrepeatswhatanothersaysbecauseoffunctionalassimilation;sometimeshisremarks
are magically intended to produce results which he otherwise cannot achieve; and, finally, his
utterancesoftenmerelyaccompanyactivitiesinwhichheisengaged.
All three types of speech—repetition, inpidual monologue, and collective monologue—may be
characterizedasegocentric.Piagetdoesnotusetheterminthesenseofselfishorself-serving.Theyoung
childischaracterizedasegocentricnotbecauseofconceitorbecauseofanattempttosatisfydesiresatthe
expenseofotherpeople,butbecauseheiscenteredabouthimself(orhisownegointhegeneralsense)
and fails to take intoaccount theother’spointofview.Whendeliveringamonologue inagroup, the
desires of the egocentric child do not necessarily clash with those of other children; rather he is
insensitivetowhattheothersneedtohear.Tocommunicate,onemustconsiderwhat informationthe
listenerdoesanddoesnothaveandwhatheisandisnotinterestedin,andthistheyoungchilddoesnot
do.
Onemay criticize the naturalistic study of the child’s language in severalways. Perhaps Piaget
foundtheuseofnon-communicativelanguagetobeextensiveonlybecauseoftheliberalatmosphereof
theschoolwheretheemphasiswasoninpidualratherthangroupactivity.Ifyouwillrecall,thechildren
wereallowed todowhat they liked,and thesituationwassodevised that thechildren learned from
inpidual play.Under these circumstances, itmight be the case that the children felt no real need for
communication,andconsequentlytheydidnotdisplaytheseabilities.
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We may, however, cite as evidence against this argument an experiment by Piaget on verbal
communication.Briefly,thetaskinvolvedanexperimenter’sgivingsomeinformationtoonechild(the
speaker)whowasthensupposedtotransmitittoanotherchild(thelistener).Piagetmadecleartothe
speakerthatthetaskwastocommunicate.Theseinstructionspresumablyorientedthechildtowardthe
goalof communicationrather than thatofplay.Therefore, theexperimentmightgive insight into the
child’sabilitytotransmitinformationwhenhefelttheneedtodoso.Theexperimentwasalsousedto
obtain information about the listener’s ability to understand the speaker. Even if the speaker were
communicative,didthelistenercomprehendwhatwassaid?However,sincethemethodsusedtoassess
thelistener’sunderstandingwereratherpoor,wewillnotconcentrateonthisaspectofthestudy.
Letusnowdescribetheexperimentingreaterdetail.Inoneportion,pairsofchildrenwereusedas
subjects. There were thirty children at ages 7 to 8 years and twenty at ages 6 to 7 years. The
experimentersentoneofthepairoutoftheroomandtoldtheotherastory.Thischild,tobereferredtoas
the speaker,was instructed to listencarefully sincehewouldhave to tell the samestory to theother
child,whomwewillcallthelistener.Thentheexperimenterreadastory,repeatedthedifficultparts,
and tried to make the speaker attend carefully. Several different stories, varying from six to nine
sentencesinlength,wereused,althoughatanyonetimethespeakerwasrequiredtotellonlyonestory
tothelistener.Next,thelistenerwasbroughtintotheroom,andthespeakertoldhimthestory.
The experimenter took down everything that was said and, in addition, questioned both the
speakerandthelistenertodeterminethedegreetowhichtheyunderstood.Aftertheexperimentwith
stories, the same pairs of children were used to investigate communication concerning mechanical
objects.Thistime,theexaminerexplainedtothespeakerhowafaucetorasyringeworks.Diagramswere
usedtomakethematterclear,andthespeakerwaspermittedtomakeuseofthediagraminexplaining
themechanicalprocess to the listener.Again, the experimenter recordedeverything that the speaker
said.
Whiletheexperimentyieldedmanyresults,weshallfocusontheverbalizationsofthespeaker.Did
children in the experiment succeed in producing communicative speech, and if not, what was their
language like? In general, the experiment on communication replicated the results of Piaget’s earlier
naturalisticobservations;thatis,inbothcasesasubstantialproportionofspeechwasnon-communicative
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or egocentric. For example, the experiment on communication showed that young children often use
pronounsanddemonstrativeadjectives—suchashe,she,it,that,this—withoutindicatingclearlytowhat
theyarereferring.Inthemidstofanexplanationofthefaucet,thespeakermightsay“Ifyoumoveitwith
thatotherthing,thenitwillgo.”Thischildfailstoconsiderthatthelistenermightnotknowwhat“it”and
“thatother thing”designate.This tendency is carried so far thatoften the speaker completely fails to
nametheobjectsinvolvedinamechanicalexplanation.Thechildisalsopooratexpressingtheorderof
events.Onechildexplaininghowafaucetworksbeganbytellinghowthewaterfallsintothebasin,and
onlylaterdidhebothertosayhowthewatergoesthroughthepipe.Or,intellingastory,thechildmight
beginwiththeendandendwiththebeginning.
Ayoungchildmayalsoexpresscausalrelationspoorly,andseldomconnectthecausewithitseffect.
Forexample,intellingastoryinwhichafairyturnedcertainchildrenintoswans,onechildsaid,“There
wasafairy,awickedfairy.Theyturnedthemselvesintoswans”(LT,pp.126-27).Notehowthechilddid
notexpressthecentralcausalrelation;itwasthefairywhocausedthechildrentobecomeswans.The
childmerelymentionedthetwoeventswithout indicatingtheirconnection.Thesecondsentencealso
illustratesthetendencytousepronounswithoutdescribingtheirreferents.Towhomdoes“they”refer?
Oftenthechildmayalsoomitlargepartsoftheexplanationorstory.Eventhoughheunderstands
andremembers theseportions (asshownbyPiaget’s laterquestioning), thechildmay fail tomention
them.Ineffectheassumesthatthelisteneralreadyknowspartsofthestoryorexplanation.Omissionsof
thiskindclearlyrevealalackofsensitivitytotheneedsofthelistener.
Another aspect of egocentric speech is manifested in the observation that the child’s story or
explanationdoesnot forma coherent and integratedwhole.The account is fragmentary; it ismerely
composedofalargenumberofspecificandunrelateditemswhicharejuxtaposedoneupontheother.
Forexample,hereisonechild’saccountofhowafaucetworks:
Thehandleisturnedonandthenthewaterruns,thelittlepipeisopenandthewaterruns.There,thereisnowaterrunning,therethehandleisturnedoff,andthenthereisnowaterrunning,andherethewaterisrunning.There,thereisnowaterrunning,andherethereiswaterrunning.(LT;p.130)
Clearlythisexplanationinvolvesamerecollectionofinpidualstatementswhicharenotintegrated
intoareasonablewhole.Oneaspectofsuchjuxtapositionisatendencyalreadydescribed:theinabilityto
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statecausedrelations.
Insummary,theprecedingfivepropertiesoftheyoungchild’sspeech—thefaultyuseofpronouns
and demonstrative adjectives, the incorrect ordering of events, the poor expression of causality, the
tendency toomit important features, and finally, juxtaposition—all are concretemanifestationsof the
child’s egocentrism—the inability to take into consideration the other person’s point of view. With
development theseegocentricmanifestationsdecreaseandspeechbecomesmore communicative.The
speakerbecomesawareoftheviewsofothersandadaptshisspeechaccordingly.
Piaget’s experiment on verbal communication also studies the understanding of the listener.
Althoughthemethodologywasquestionable,severedofPiaget’simpressionsareofinterest.Theresults
showedthat, ingeneral, the listenerdoesnotunderstandthespeakerverywell.Partof the listener’s
inabilitytounderstandisclearlyduetothespeaker’sfaultypresentation.Fewpeoplecouldcomprehend
theexplanationofthefaucetjustdescribed.ButPiagetfeelsthatpartofthelistener’sdifficultyisdueto
his own patterns of thought and not to the speaker’s egocentric speech. Even when the speaker is
relativelyclear,thelistenerdistortshisutterancesinseveralways.One,thelisteneralmostalwaysthinks
thatheunderstandswhatthespeakersays,evenwhenitisveryobscure.Thelistenerveryseldomasks
questionstoclarifyapointortoobtainadditionalinformation.Thelistenerfeelsconfidentthathehas
understoodwhen in fact he has not. Two, the speaker’s remarks evoke in the listener a kind of free
association.InPiaget’sterms,thelistenerassimilatestheremarksintohisownschemeswhichoftenbear
littlerelationtowhatthespeakerisattemptingtocommunicate.Forexample,afterlisteningtothestory
inwhichthebadfairyturnedseveralchildrenintoswans,one6-year-oldchilddistortedtheaccountin
importantways. Insteadof saying that thechildrenwere turned intoswans,hemaintained that they
weredressedinwhiteclothes.Thenheelaboratedonthispropositionuntiltheendofthestorywasno
longerrecognizable.Hetransformedonepartofthestoryand,givingfreereintohisimagination,went
onfromtheretoconstructanewtaleofhisown.Inbrief,whilethespeakerfailstotakeaccountofthe
needsofthelistener,thelisteneralsodistortswhathehears,elaboratesonit,andissatisfiedthathehas
understood,whereas,inactualfacthehasnot.
ItiseasytoseethatPiaget’sexperimentoncommunicationisdeficientinseveralways.Piagetdoes
notmakeclearthemethodsusedtoassesseitherthespeaker’sorthelistener’sunderstandingofthestory
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orexplanation.Themeasurementofcomprehensionisadifficultanddelicatematterthatrequiresmore
attentionthanPiagethasgiventoit.Piagetalsomaynothavefullyeliminatedthepossibilitythatfaulty
memory, and not egocentrism, may sometimes underlie the speaker’s lack of ability to communicate.
Perhapstheyoungchildisnotabletotellalengthystorysimplybecauseofthefailuretorememberlarge
partsofit.DespitePiaget’sattemptstocontrolforthememoryfactorbyquestioning,itisnotaltogether
cleartowhatextenthewassuccessful.
AnotherfactortobeconsideredisthatPiaget’ssubjectswerepoorchildren.Isitnotpossiblethat
lower-classchildrenhavedifferentverbalabilitiesfrommiddle-classchildren?Ifso,Piagetistooquickto
generalizehisfindingstochildreningeneral.Whiletheseandothercriticismsmayberaisedandseem
tohavevalidity,onemustrememberthatPiaget’sfirststudieswereintendedasexploratory.Theiraim
wastouncoverinterestingissuesforinvestigation,toproposepreliminaryhypotheses,andnottoreach
firmconclusions.Piaget’sstudiesoncommunicationseemtohavefulfilledhisoriginalgoals.Hisresearch
raisesinterestingquestions.Forexample,isittruethattheyoungchildcannotexpresscause-and-effect
relations, or that the listener so extensively distorts what the speaker says? Despite its deficiencies,
Piaget’sresearchisofgreathistoricalsignificance:itwasoneofthefirstattemptsinchildpsychologyto
deedwiththecrucialissueofthefunctionsofhumanlanguage.
Thusfarwehaveseenthattheyoungchildfromabout4to7yearsdisplaysasignificantamountof
egocentric speech and that the older child after about 7 years is increasingly proficient at verbal
communication. Why does egocentric speech decrease as the child gets older? Piaget proposes an
interestinghypothesis toexplain thewaningofegocentrism.Whenthechild isyoung,particularly in
infancy,adultstakegreatpainstounderstandhisthoughtsanddesires.Themothermustknowwhich
toytheinfantwantsorwhatbothershimandisnotabletorelyexclusivelyonwordstounderstandhim.
Consequently,theyoungchilddoesnotneedtocommunicateclearly;evenifhisspeechisunclear,adults
willmakeeveryefforttounderstand.Asthechildgrowsolder,however,heisthrownmoreandmore
intothecompanyofolderchildrenwhoarenotassolicitousasadults.Otherchildrendonottrysohard
topenetratetheobscuritiesofhislanguage.Moreover,theyarguewithhim;theychallengewhathesays
andforcethechildtodefendhimself.Itisundersocialpressuresofthesekindsthatthechildisgradually
forced to adopt better modes of communication. In the attempt to express himself and to justify his
arguments,thechildeventuallylearnstotakeintoaccounttheother’spointofview.Nottodosoistobe
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misunderstoodandtolosetheargument.Inthisway,then,doesegocentrismdiminish.
Clinical Method
Piaget’searlyworkwasinpartconcernedwiththecontentsofthechild’sthought.Heattemptedto
discover thespontaneous ideasof thechildatdifferentstagesofhisdevelopment.What is thechild’s
conceptionofthenatureofdreams,orwhatishisexplanationofthefactthatboatsfloatonwater?The
studyofcontentisparticularlydifficult,becauseaswehaveseenintheprevioussection,youngchildren
havegreatdifficultyincommunicatingtheirthoughts.Itisthereforecrucialfortheinvestigatorofcontent
toemploysensitiveandaccuratemethods.Piagethasdevotedcareful consideration to thechoiceofa
propermethod.Hehasrejectedthetestingapproach,assignedalimitedroletonaturalisticinvestigation,
andadoptedtheclinicalprocedure.Letusconsidereachofthesedecisionsinturn.
Theessentialfeatureofthetestingmethodisaseriesofquestionswhichareposedinthesameway
to all who take the test. If we are investigating the origin of the sun, for instance, wemight ask all
children,“Wheredidthesuncomefrom?”Itisimportantthatthequestionbeputinpreciselythesame
waytoallchildren.Infact,thereadingofthequestion(theintonation,stress,andsoon)shouldbeas
consistentaspossible.Ifachilddoesnotseemtounderstand,theexaminermayrepeatthequestion.But
this is usually themaximumof flexibility permitted: the examinermay not rephrase the question or
otherwise alter it. The purpose of a standardized administration is to guarantee that all subjects are
facedwith thesameproblems.Then if4-year-oldsgenerallygiveone typeofanswerand8-year-olds
another,theexaminermayreasonablyconcludethatthereisarealdifferencebetweentheagegroups.If,
ontheotherhand,theformofthequestioningvariedacrossagegroups,theexaminerwouldnotknow
whether the difference in answers is genuinely related to age or is due simply to the difference in
questions.Whilethetestingmethodhasimportantpsychologicaluses,Piagetfeelsthatitisnotsuitable
for his task—the discovery of content (or the discovery of structure, a problem to which Piaget also
appliestheclinicalmethod).
Thetestingmethodhasthedisadvantageofinflexibility.Ifachildgivesaninterestingresponse,the
examinercannotpursueit.Ifachildmisunderstandsthequestion,theexaminercannotclarifyit.Ifthe
child’s answer suggests an additional topic for investigation, the examiner must leave the matter
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unexplored.Inaddition,thetestproceduremaybesuggestive.Ifthechildisasked,“Wheredidthesun
comefrom?”thequestionimpliesthatthesundidhaveanorigin,andthisideamaynothaveoccurredto
thechildbefore.Consequently,hisanswermaynotrevealthecontentsofhisspontaneousthought,but
maybemerelyahastilyconsideredresponsetoaquestionencounteredforthefirsttime.And,finally,the
testmethoddoesnotusuallyallowtheexaminertoestablishthestabilityofthechild’sresponse.Ifachild
isaskedwhatthesumof2and2is,andsays“4,”hisanswermaybetentativeorfirm.Ifheisunsure,
furtherquestioningmayinducethechildtochangehismind.Ifhisbeliefisfirm,nothingwillswayhim.
Inthetestingprocedurethechildgivesananswerandthatistheendofit:atentative“4”isasgoodasa
sureone.Forthesereasons,then,Piagetrejectsthetestingapproach.
Anothermethodfortheinvestigationofspontaneouscontentisthenaturalisticprocedureasused
inPiaget’sstudyofinfancyorlanguage.Inasense,thisisanidealmethod.Supposeweobservethata
childspontaneouslyasksthequestion:“Whomadethesun?”Thestatementgivesaclearinsightintothe
contentofhisthought.Itisimmediatelyobviousthathebelievesthatsomeagent,perhapsapersonor
perhapsGod,intervenedtocreatethesun,andthatitdidnotevolvenaturally.Surelythisspontaneous
questionisfarmorevaluablethanaresponsetoastandardizedquestion.
Thenaturalisticmethod,however,issubjecttoanumberofdrawbacks.Onemayobserveachildfor
a very long time before he will say anything of interest. Suppose we are interested in the child’s
conceptionoftheoriginofthesun;itisextremelyunlikelythathewillasktherelevantquestionwhile
being observed. Consequently, the naturalisticmethod, despite its clear utility, cannot be used as the
chiefinstrumentofresearch.Atbest,naturalisticobservationcanserveonlyasubsidiaryroleintwoways.
It can suggest questions for intensive clinical examination. If, for example,wehear a child ask, “Who
madethesun?”thenwecaninterviewalargenumberofchildrentotestthegeneralityoftheassumption
underlyinghisquestion.Second,thenaturalisticobservationcanserveasacheckontheresultsofclinical
questioning.Ifinterviewingsuggeststhatchildrenbelievethatcloudsarealive,thenpatient,naturalistic
observationmayfurnishdatatosupportorrefutethishypothesis.
Piaget feels that the clinical method avoids the deficiencies of the testing and naturalistic
procedures,andinadditionoffersanumberofattractivefeatures.Theclinicalmethodishardtodescribe
since it is so flexibleandprovidesageneral framework forquestioning thechild rather thanasetor
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standardizedform.Thisaccountisthereforeintendedonlyasanoutlineoftheclinicalmethod.Thebasic
aimofthemethodistofollowthechild’sthoughtwithoutdeformingitbysuggestionsorbyimposingthe
adult’sviewsonthechild.Oneimportantfeatureisthattheexperimentertriestoadoptthelanguageof
thechildandkeepthelevelofquestionsaccessibletothechild.Termswhicharebeyondhisreachare
avoided and replaced asmuch as possible by thosewhich the child has spontaneously emitted. The
examinerusuallybeginsbyaskinganondirectivequestion.Insteadofsaying,“Whomadethesun?”or
“Howdidthesunevolve?”theexaminermightask,“Howdidthesuncomeabout?”Ifthechilddoesnot
understand,theexaminerisfreetorephrasethequestionbyasking,forexample,“Howdidthesunget
there?” After the child answers, the experimenter forms an hypothesis concerning the nature of the
child’sbeliefs.Forexample,ifthechildfirstanswered,“Itwasputthere,”theexaminermightguessthat
thechildbelievesthatapersoncreatedthesun.Subsequentquestionsareusedtotestthishypothesis.
Theexaminermightthenask:“Canyoutellmehowitwasputthere?”Ifthechildsays,“Godputitthere,”
then the examiner might follow up aspects of this response. Does the child really believe in pine
intervention,oristhisjustasuperficialmimicryofwhathehasbeentaughtinSundayschool?Toanswer
this question, the examinermay challenge the child’s belief to see how firmly he holds to it. Or the
examinermaywonderwhetherthechildmeanstosaythatthesunalreadyexistedbeforeGod“putit
there”orthatGodcreatedittoo.Furtherquestionsmustbeaskedtodecidebetweenthetwoalternatives.
Ofcourse,iftheexaminer’shypothesisisnotconfirmed,hemustallowthechild’sanswerstoleadhimto
thecorrectinterpretation.Itiseasytoseethatnotwoclinicalexaminers,eveniftheyaretestingthesame
child,willpursuethesamelineofquestioning.It isalsoclearthatclinicalquestioningisverydelicate
andsubjecttoseveralkindsoferrors.Theexaminermaytalktoomuchandtherebysuggestanswersto
thechild.Ortheexaminermaynottalkenoughandfailtoposethequestionsnecessaryfordetermining
thechild’smeaning.Piagetfeelsthatatleastayearofdailypracticeisnecessarybeforetheexaminercan
achieveproficiencyatclinicalquestioning.
Wemayraiseanumberofcriticismsoftheclinicalmethod.HowdoweknowthatPiagetisagood
clinical examiner? His books give only portions of selected clinical interviews. It is possible that the
publishedinterviewsareexceptional—fromthepointofviewofmethodandsupportforPiaget’stheory
—andthattheunpublishedprotocolsarepoorlydone.Perhapsinthelattercasetheexaminersuggested
answers to the child, asked thewrong questions, and so on. Also, wemaywonderwhether Piaget’s
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diagnoses—thejudgmentsderivedfromtheinterview—arereliable.Thatis,wouldotherpersonsagree
withtheinterpretations,orarePiaget’sdiagnosesquiteidiosyncratic?Itisalsotruethatsincetheclinical
interviewsareunstandardized,itisverydifficultforindependentinvestigatorstotestPiaget’swork.If
anotherpsychologistattemptedtorepeatPiaget’sresearchandobtaineddifferentresults,thePiagetian
criticism could always be that he failed to use the clinicalmethod properly. Another criticism that is
raised is that Piaget usually commits a large number ofmethodological sins unrelated to the clinical
method.Forexample,hedoesnotusuallyreportthenumberofsubjectsseeninaninvestigation,ortheir
exactages,ortheirsocialbackgrounds.Indescribingtheresultshepresentsonlyfragmentsofinterviews
andfailstogiveastatisticalsummaryofthechildren’sreactions.Tosummarize, theclinicalmethodis
deficient.Perhapsthechiefobjectionisthatitrequiresustotakealotonfaith:thatPiagetconductsthe
interview without suggestion, that he interprets the results properly, and so on. As we well know,
scientistsprefertotakeaslittleonfaithaspossible.
ThedeficienciesinPiaget’sresearcharereal.Yetwemustbecarefulnottoexaggeratethem;we
mustevaluatetheclinicalmethodintheoverallcontextofPiaget’swork.Piagetfeltthattheearlyportion
ofhisresearchwasessentiallyexploratory.Hisgoalwastoopenupnewareasforinvestigationandto
proposepreliminaryhypothesesforfurtherexamination.Theearlyworkwasnotintendedtoprovea
theoryortopresentdefinitiveviewsonintelligence,andPiagetfeltthatmethodsshouldbeasflexibleas
possible at the preliminary stages of research. It seemed premature to him to introduce rigorous
procedureswhenalmostnothingwasknownabout thesubjectmatter,andwhen itwasbynomeans
clearwhat the propermethods should be. If Piaget had attempted to establish every pointwith the
maximumofcertainty,thenheprobablywouldnothaveadvancedbeyondthestudyofchildren’sverbal
communication(oneofhisfirstresearchtopics).Oncethepioneeringresearchhasbeendone,thenitis
alwayspossibletochecktheresultsbymorestandardizedmethodsandrevisethetentativehypotheses.
The Content of Thought
Piaget’searlyinvestigationsofcontentareextensive.HistwobooksonthesubjectareThe Child’s
ConceptionoftheWorld(CCW)andTheChild’sConceptionofPhysicalCausality(CCPC).Theycoveralarge
numberoftopicswhichincludethechild’sbeliefsconcerningdreams,meteorology,theoriginoftrees,
thenatureofshadows,theexplanationofthesteamengine,andsoon.Toillustratethisworkweshall
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describeonlyonetopic:theoriginsofthesunandmoon.
AccordingtoPiaget’sfindingstherearethreestagesinthechild’sconceptofthesunandmoon.The
stagesoccurinsequencesomewherebetweenabout3and12years.Piagetdoesnotattempttospecify
precise age norms because there are large variations in responses. Here is an example of a stage 1
protocol,a6-year-old’sbeliefs:
Howdidthesunbegin?—Itwaswhenlifebegan.—Hastherealwaysbeenasun?—No.—Howdid itbegin?—Because it knew that life had begun.—What is itmade of?—Of fire.—But how?—Because therewas fire upthere.—Wheredidthefirecomefrom?—Fromthesky.—Howwasthe firemade in thesky?—Itwas lightedwithamatch.—Wheredid it come from, thismatch?—God threw it away. . . .Howdid themoonbegin?—Becausewebegantobealive.—Whatdidthatdo?—Itmadethemoongetbigger.—Isthemoonalive?—No...Yes.—Why?—Becausewearealive.(CCWp.258-59)
Theprotocolillustratesthreekindsofbeliefscommontochildreninthefirststageofdevelopment.
The firstbelief isanimism.Thechildbelieves that thesunandmoonarealive in thesamesense that
people are alive; that is, the sun is credited with knowing that life had begun. The second belief is
artificialism.The childasserts that the sun resulted from theactionsof anoutsideagent. Itwasnota
natural process that formed the sun, but an act of intervention on the part of God. The third belief
illustrated by the protocol contains the idea of participation. The child perceives some continuing
connection,or someparticipation,betweenhumanactivitiesand thoseof things.Hisbelief is that the
moonbeganbecausepeoplebegantobealive.Note that thisexplanation isnotartificialism,since the
childdoesnotassertthatpeoplecreatedthemoon.Hisconceptionisvague,andhemerelyassumesadim
relationbetweenpeopleandtheplanets;hebelievesthatthereissomesortofinfluenceorparticipation
betweenthem.
Thesecondstageofthechild’sconceptofthesunandmoonistransitionary.Thechildcontinuesto
believeinartificialismandanimism,butlessblatantlythanbefore.Thefollowingexcerptinvolvesan8-
year-oldchild:
Howdidthesunbegin?—Itwasabigcloudthatmadeit.—Wheredidthecloudcomefrom?—Fromthesmoke.—Andwheredidthesmokecomefrom?—Fromhouses. . . .—Howdidthecloudsmakethesunshine?—It’s alightwhichmakesitshine.—Whatlight?—Abig light, it issomeoneinHeavenwhohasset fireto it.(CCW, p.274)
Notethatatthebeginningoftheprotocolthechildinvokedonlynaturalphenomenatoexplainthe
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sun’sorigin.Thesunwasformedbycloudswhichinturnderivedfromsmoke.However,whenasked
wherethesmokecamefrom,thechildproposedanartificialistexplanation.Thesmokecamefromhouses
and,byimplication,fromfireswhichpeoplecreated.Artificialismisevenmoreapparentinthesecond
partoftheprotocolwherethechildmaintainsthatsomeoneinHeavenhascreatedalightthatmakesthe
sunshine.
Inthethirdstage,thechildgivesupnotionsofartificialism,animism,andparticipation.Whilehis
explanations are often crude and incorrect, he attributes the sun’s formation to natural processes in
whichhumanorpineagentshavenorole.Sometimes,ofcourse,thechild’saccountsarebasedonwhat
hehasbeentoldinschool.Yetsometimestheyarenot,andeventhenthechildproposesexplanations
invokingphysicalprocessesoftheplanet’sorigins.
Moral Judgment and Behavior
Piaget’s earlywork covered awide range of topics including verbal communication, concepts of
physical causality, andmoral judgment and behavior. This last topicwill be considered now. Piaget
beginshisstudyofmoralbehaviorandjudgmentwithadetailedconsiderationofchildren’sgamesof
marbles.Hedescribeshowchildrenconceiveofthegameandfollowitsrules.Atfirstglanceitmayseem
quite unusual to study morality by means of the apparently trivial game of marbles. Our intuitive
definitionofmoralityprobablyrelatestosuchmattersaslyingandstealing,andnottomeregames.But
accordingtoPiagettheessentialaspectofmoralityisthetendencytoacceptandfollowasystemofrules
which usually regulate interpersonal behavior. Our society has gradually developed norms which
control how an inpidual treats others, behaves toward property, and so on, and these regulations,
supplementedby the inpidual’sownconceptions, constitute themoral system.Oncloser inspection it
wouldseemasiftherulesgoverningthegameofmarblesfulfillallthedefiningconditionsofamoral
system. The rules control how inpiduals behave toward one another in terms of the actions which
comprisethegame,theydetermineinpidualandpropertyrights,andtheyareaculturalproductwhich
hasbeenpasseddownfromgenerationtogeneration.Thegameofmarblesalsohasauniqueadvantage
fromthepointofviewofchildpsychology.Theruleshavebeendevelopedlargelybychildren,andthe
game is played almost exclusively by children. Therefore, the child’s conception of the game and his
playingof it reflect theworkingsofhisownmindand issubject to littleadult influence.Unlikerules
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dealingwithlyingorstealing,thegameofmarblesisthechild’screation,nottheadult’s.Ifwequestion
thechildaboutthegame,hisanswersdonotsimplyparrottheteachingsofadults,butgiveagenuine
indicationofhisownthought.Butisnotthegamejustplay,somethingthatisnotatalltakenseriously,
andthatthereforebearsnorelationtomorality,whichisagravematter?Wemayanswerthiscriticismby
pointing out that the child does take the game seriously.While a game has its “fun” aspects, if one
observeschildrenplaying,onerealizesthattheyaredeeplyengrossedintheiractivities,considerthe
otherplayers’actionsofsomeimportance,andarenotentirelydisinterestedintheoutcomes.Istheadult
who“plays”thestockmarketverydifferent?
Tostudychildren’sbehaviorinthegameofmarbles,Piagetfirstacquiredathoroughknowledgeof
therulesofthegame.Thenheaskedabouttwentyboys,rangingfrom4to12or13yearsofage,toshow
himhowtoplay.(InSwitzerlandthegameofmarblesisplayedexclusivelybyboys.)Inthecourseofhis
gamewiththechild,Piagettriedtoappearasignorantaspossibleabouttherulessothatthechildwould
feel that he had to explain them. In this way Piaget was able to determine both whether the child
understoodtherules,and,ifso,whetherhefollowedthem.SometimesPiagetobservedpairsofchildren,
particularlyyoungerones,playthegamewithouthim.Piagetalsoquestionedthechildaboutthenature
of the rules. He was interested, for example, in whether the child believed that the rules might be
changedandinthechild’sconceptionoftheoriginofrules.
Letusconsiderthepracticeofrules,ormoralbehavior.Fromaboutages4to7years,anegocentric
stageoccurswherechildrendonotknoworfollowtherules,buttheyinsistthattheydo.Asanexampleof
thisstage,letusexaminethefollowing:
Piagetseparatelyexaminedtwoboyswhowereinthesameclassatschool,wholivedinthesame
houseandoftenplayedmarbleswithoneanother.Thefirstboydescribedandplayedbyasetofrules
whichwashighlyunusualandidiosyncratic.Thesecondboydidnotunderstandthefirstboy’srulesand
moreoverproposedanunusualsystemofhisown.Thus,eachoftheboys,whooftenplayed“together,”in
factfollowedhisownsystemofruleswhichborelittlerelationtotheotherchild’s.Therewaslittlenotion
of“winning,”intheadultsense,andlittlegenuinecompetitionbetweenthetwoplayers.Fortheyoung
child,“winning”means“havingagoodtime,”anditwas,therefore,quitepossibleforallplayerstowinin
thisparticulargame.Eachchildwasmerelyplayinganinpidualgameanddidnotreallyneedtheother.
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Atthesametime,thechildrenbelievedthattheywereplayinglikeotherchildrenandthattheyknew
andfollowedtherulesquitewell.
Thebehavioratmarblesissimilartothespeechofchildrenofthesameageandis,therefore,called
egocentric.Inbothcasesthechildiscenteredabouthimselfandfailstotakeintoaccountanotherperson’s
pointofview.Inthegameofmarblestheyoungchildplaysforhimselfandnotwithsomeoneelse.Hehas
hisownsetofrulesandisrelativelyuninfluencedbywhattheotherdoes.Inthecaseofspeech,thechild
talks by himself and not with someone else. He speaks for his own purposes, and hismonologue is
relatively unaffected by the other’s comments. Egocentrism is therefore a tendency common to both
speechandmoralbehavior.
Thenextstage,thatofincipientcooperation,lastsfromabout7to10or11years.Thegamebeginsto
acquire a genuinely social character, and the child has a much firmer grasp of the rules. While his
knowledgeofthegameisnotperfect,hehasmasteredthebasicrulesandattemptstolearntherest.The
childofthisstagebothcooperatesandcompeteswithhispartner.Thereiscooperationinthesensethat
thechildagreeswithhispartneronacommonsetofruleswhicharethenfollowed.(Cooperationdoes
not mean here that the two or more children assist each other to attain a common goal.) There is
competitioninthesensethateachchildtriestowinforhimself,whileatthesametimeheadherestothe
mutuallyagreed-uponframework.Nevertheless,playisnotyetfullymature.Sincethechildhasnotyet
masteredalloftherules, thegamedoesnotproceedsmoothly,andtherearedifficultiesandconflicts.
Again,thereisaparallelbetweenplayandspeech.Inbothinstances,thechildofabout7yearsofage
beginstotakeintoaccountanexternalpointofview.Inmarblesheallowsasetofrulestogovernhis
behavior,andheinteractswiththepartner.Inspeechhetriestoanticipatewhatthelistenerneedsto
know,andheacceptslinguisticconventionswhichfacilitaterealinteraction.
Thefinalstageofmoralbehavioristhatofgenuinecooperationwhichbeginsatabout11or12years
ofage.Nowthechildacquiresathoroughmasteryoftherules.Asbefore,heagreeswiththeothersonthe
waytoplaythegame,anditiswithinthiscommonframeworkthathetriestowin.Inaddition,however,
the older child shows a kind of legalistic fascinationwith the rules.He enjoys settling differences of
opinionconcerningtherules,inventingnewrules,andelaboratingonthem.Heeventriestoanticipate
allthepossiblecontingenciesthatmayarise.
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Piagettellsadelightfulanecdoteaboutthelegalistictendenciesofthisstage.Heobservedagroup
ofboysaged10and11whowerepreparing tohaveasnowball fight.Beforegettingonwith it, they
devoted a considerable amount of time topiding themselves into teams, electingofficers, devising an
elaboratesetofrulestoregulatethethrowingofsnowballs,anddecidingonasystemofpunishmentsfor
transgressors.Beforetheyhadactuallysettledonalltheselegalisticaspectsofthegame,itwastimeto
returnhome, andno snowball gamehadbeenplayed.Yet, all theplayers seemedcontentwith their
afternoon.
Wemay summarize by stating, then, that there are three major stages of the practice of rules:
egocentrism,whereeachchilddoesnotknowtherulesorhowtoapplythembutthinkshedoes;incipient
cooperation,wheremasteryoftheruleshasimprovedandchildrenbegintosharethemtocompete;and
finally,thestageofgenuinecooperation,wherechildrenknowtheruleswellandenjoyelaboratingupon
them.
Afterestablishingthechild’sknowledgeandpracticeofrules,Piagetwentontoquestionthechild
abouttheirinviolability.Heaskedthechildwhethertherulesmightbechanged,whethertheyalways
existedintheirpresentform,andhowtheyoriginated.Indeterminingthechild’sconceptionoftherules,
Piagetofcourseusedtheclinicalmethod(ashedidinestablishingknowledgeoftherules).Hefound
thattherearetwomajorstagesinnotionsconcerningtheinviolabilityofrules.Thefirststage,whichisin
turnpidedintotwoparts,lastsfromabout4or5yearstoabout9or10years.Thusitoverlapsthefirst
twostagesof thepracticeofrules(egocentrismandincipientcooperation). Inthe firstpartof the first
stage,whichweshallcalltheabsolutisticstage,thechildbelievesthatsomeauthorityoriginatedtherules
ofmarblesandthatnooneeverplayedthegamebeforethatauthorityplayedit.Moreover,theauthority
conveysontherulesasacred,unchangeablecharacter:theyareabsoluteandcannotbealtered.Hereis
partofaprotocolofa5-year-oldillustratingsomeofthesebeliefs:
Howdidyouget toknow the rules?—When Iwas quite littlemy brother showedme.MyDaddy showedmybrother.—Andhowdidyourdaddyknow?—MyDaddyjustknew.Noonetoldhim....—Tellmewhowasbornfirst, yourdaddyor your granddad?—MyDaddywas born beforemy granddad.—Who invented the game ofmarbles?—MyDaddydid.(MoralJudgment,MJ,p.55)
We see that the child believes that the rules emerged, fully formed, from his father, who is so
prestigiousthathewasbornbeforehisownfather.
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Whilebelievinginthesanctityofrules,theyoungchildfromabout4to6yearsinthefirstpartof
stage1isalsowillingtoacceptchangesintherules.Heagreestoplacethemarblesinacircle,whereasa
square is theusualconvention.Thisseemsparadoxical: thechild thinks that therulesaresacredbut
easilyconsentstotheirmodification.Piagetfeelsthatthechild’sacceptanceofchangesisonlyapparent.
Hehassuchapoorgraspofwhattherulesarethathebelievesthechangestobemerelyalternativeand
quitelegitimateversionsoftherules.Inotherwords,thechildconsentstoalterationsonlybecausehe
doesnotknowthattheyreallyarealterations.
In the latterpartof the firststage(fromabout6 to10years), thechild’sknowledgeof therules
increases,andheisconsequentlyabletorecognizearealchangeintheruleswhenitisproposed.Now
herefusestoacceptthesealterationsandassertsthattherulesareimmutable.Forexample,Piagetasked
oneboyof6yearstoinventanewgame,andherefused,saying“I’veneverinventedgames.”Then,after
Piagetsuggestedanewgameofmarblestohim,theboyplayeditforatime.Butwhenasked,“Couldthis
gameeverbecomeafairgame?”theboyresponded“No,becauseit’snotthesame[astheusualgameof
marbles]”(MJ,P-60).
If you will recall, many of the children who are in stage 1 of the conception of rules are
simultaneouslyinstage1ofthepracticeofrules(egocentrism).Thismeansthatatthesametimethatthe
childbelievestherulestobesacredandimmutable,healsodoesnotknowthemtoowellanddoesnot
followthem.Againweseemtobefacedwithaparadox:howcanheplacesomuchfaithinthesamerules
that he consistently breaks? To understand this apparent contradiction,wemust consider the child’s
acquisitionofrules.Usuallyhelearnsthemfromanolderchildwhomheconsiderssimilartoadults,and
whomhethereforeimbueswiththesamerespectandauthoritythathegivestoadults.InPiaget’sterms,
there is a relationship of constraint or unilateral respect between older and younger children; the
former’sauthority isunconditionallyacceptedso that theyoungerchildassigns to therules thesame
authoritythatheconsiderstheolderchildtohave.Sincetheadultandtheolderchildareconsidered
infallible,soaretheruleswhichtheypropagate.Inaddition,theyoungchildisegocentric.Aswesawin
the case of language, he cannot take thepoint of viewof others. Since he iswrappedup in his own
concerns,hecannotunderstandthevalueofruleswhichprotecttheinterestsofothers.Itisnotsomuch
thatheisselfish;ratherhedoesnotperceivethelegitimateneedsthatotherpersonshave.Sincethisis
so,hedoesnotunderstandthepurposeofrules.Forhimtheyaremerelyexternalthingswhichcannotbe
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changed.
Wecansay,then,thattheyoungchildimbuesruleswithabsoluterespectsincetheyderivefroma
prestigiouspersonandthatheseestherulesasexternalobjectswhichcannotbechangedbecausehis
egocentrismpreventshimfromunderstandingthepurposeofrules.
Piagetthennotesthatallofthefactorsmentioned—therelationofunilateralrespect,egocentrism,
theconceptionoftherulesasauthoritativeandexternal—preventtheyoungchildfromparticipationin
theformationofrules.Sincetheyoungchildcannotassumetheolderchild’spointofview,howcanhe
cooperate indeveloping fairrules?Because theyoungchilddoesnotparticipate inmaking therules,
theyremainquiteexternaltohim.Therulesarenotreallyhis;theyareakindofforeignbodyimposed
onhim.Itshouldcomeasnosurprisethattheydonoteffectivelytransformhisbehavior.Inotherwords,
becausethechildhasnotcooperatedindevisingtherules,hedoesnotunderstandthemand,therefore,
isnotabletofollowthem.
Inthesecondstageoftheconceptionofrules,beginningatabout10or11years,thechildbelieves
that the rules can be changed, that they originated through human invention, and that they are
maintainedonlybymutualconsentamongequals.Consequently,thechildwillagreetoamodificationof
thegamesolongasalloftheotherplayersagree,andsolongasthechangeisafairone.Sincehehimself
participatesasanequalintheinventionofnewrules,hefeelsobligatedtofollowthemanddoesso.
Toexplaintheshiftfromtheabsolutisticmoralityoftheyoungerchildtotheflexibilityoftheolder
child,Piagetproposesasociallearningtheory.HebeginsbynotingthatasthechildinWesternsociety
growsolder,hebecomesprogressivelyfreeofparentalandotheradultsupervision.Duringthefirstfive
yearsorsooflife,thechildisverycloselytiedtohisparents.Afterthatpointhegoestoschool,spendsan
increasingamountoftimewithpeers,andgenerallyassumesgreaterresponsibilityforhisownlife.As
theseeventstakeplace,thechildgraduallylearnstomakedecisionsforhimselfanddoesnotnecessarily
acceptasauthoritativetheviewsofotherpersonswhoarenowconsideredhisequals.Inotherwords,the
child escapes from the attitude of unilateral respect toward elders and begins to adopt a position of
mutualrespect.Asaresultofthisdevelopmenthedoesnotunquestioninglyacceptrulesasbindingand
immutable.Becausehenowseeshimselfastheequalofothers,hedesirestoassistintheformationand
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modificationofthemoralcode.
Anotherandrelatedfactorinfluencingthedeclineoftheabsolutisticconceptofrulesisthechild’s
increasingcontactwithpergentpointsofview.As thechildwidenshissphereofcontactsbeyondthe
immediatefamily,hediscoversthatthereareperseandconflictingopinionsandcustoms.Hefindsthat
not everyone accepts the views promulgated by his parents. This conflict betweenwhat he has been
taughtandwhatotherpeoplebelieve forces thechild toreassesshisownpositionand toresolve the
differencesinopinion.Inattemptingtodoso,thechildreasonsaboutrulesandcomestotheconclusion
thattheymust,tosomeextent,bearbitraryand,therefore,changeable.
Tosummarize,ashegrowsolderthechildevolvesfromapositionofsubmissiontoadultstooneof
equality. He also is confronted with beliefs contradictory to those he has been taught. Both these
experiencesinfluencethechildtoseerulesashavingahuman,andhencefallible,origin,andtoagreeto
participateintheirformationandalteration.Sincethechildnowhasahandintheformationofrules,
theynolongerexistasaforeignentityimposedonhisconscience;theynolongerexistasacodewhich
maybeunquestionablyrespected,occasionallyobeyed,andseldomunderstood.Thechildnowchooses
tofollowruleswhicharehisownoratleastfreelyagreedupon.
Piagetgoesontoexaminethedevelopmentofjudgmentsconcerningexplicitlymoralsituations.To
study this he told children stories which posed a moral dilemma and asked them to resolve it. For
example,ifachildstolesomeapples,whatwouldhispunishmentbe?InthiswayPiagetattemptedto
discover the child’s conception of justice, punishment, lying, and similar matters. To illustrate these
investigations,wewillfocusontheconceptionofgoodnessandnaughtiness.
Piagetpresentedhissubjectswithaseriesofstoriesoftwotypes.Inonestory,thecentralcharacter
performed an actwhich unintentionally resulted in considerable damage; in the other, he caused a
negligibleamountofdamageasaresultofadeliberatelyimproperact.Thesubject’staskwastodecide
whowasgoodandwhowasnaughty.
Hereisanexampleofthefirsttype:
AlittleboywhowascalledAugustusoncenoticedthathisfather’s inkpotwasempty.Onedaythathisfatherwasawayhethoughtoffillingtheinkpotsoastohelphisfather,andsothatheshouldfinditfullwhenhecame
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home.Butwhilehewasopeningtheinkbottlehemadeabigblotonthetablecloth.(MJ,p.122)
Thecorrespondingstoryinvolvingnegligibledamageisasfollows:
TherewasalittleboycalledJulian.HisfatherhadgoneoutandJulianthoughtitwouldbefuntoplaywithhisfather’sinkpot.Firstheplayedwiththepen,andthenhemadealittleblotonthetablecloth.(MJ,p.122)
After telling eachpair of stories, Piaget askedwhether the two childrenwere equally guilty, or
whichofthetwowasthenaughtierandwhy.Heusedtheclinicalmethodtoprobethechild’sresponses.
The results were that until the age of 10, children give two kinds of answers. One of the answers
maintainsthatthecharacter’sguiltisdeterminedbythenatureofhismotives.Theboywhowantedto
helphisfatherbutcausedagreatdealofdamageislessguiltythantheboywhoengagedinanimproper
actwhichresultedinnegligibledamage.Piagetcallsthisa“subjective”conceptionofresponsibilitysince
thechildtakesintoaccountthemotives(thesubjectivestate)ofthecharacter inthestory.Thesecond
typeofjudgmentfoundinthisstage(andfound,moreover,inmanyofthesamechildrenwhosometimes
giveasubjectiveanswer)islessmature.Thisanswermaintainsthatthecharacter’sguiltisdetermined
notbyhismotives,butbythesheeramountofdamagehehascaused.Theboywhowantedtohelphis
fatherisneverthelessguiltybecausehemadealargestain,whereastheboyplayingwiththepenisnot
guiltysincehisstainwassosmall.Considerthisprotocol,fromagirlof7years:
Whichisthemostnaughty?—Theonewhomadethebigblot.—Why?—Becauseitwasbig.—Whydidhemakeabigblot?—Tobehelpful.—Andwhydidtheotheronemakealittleblot?—Becausehewasalwaystouchingthings.Hemadealittleblot.—Thenwhichofthemisthenaughtiest?—Theonewhomadeabigblot. (MJ,p.126)
Itisevidentfromtheprotocolthatthechildwasperfectlyawareofeachcharacter’sintentions,and
yet ignored them.Whatdeterminesguilt isnot intentionbutquantityofdamage.Piagetcharacterizes
sucharesponseasacaseofmoralrealism.Thejudgmentis“realistic”inthesensethatthecriterionof
guiltisnotsubjective(theintention)butmaterialor“real”(theamountofdamage).Thechildconsiders
onlythefactsofdamage,notthesubjectivestateofmotive.Also,thechild’sjudgmentobservestheletter
andnotthespiritofthelaw.Therule(inthiscase,“Thoushaltnotspillink”)isanabsolute,sothatany
actionwhichconformstoitisgood,andanywhichdoesnotisbad.
Piagetfindsthattheyoungchild’smoralrealismispervasive.Considerthedefinitionofalie.One
6-year-oldgaveatypicalresponseinsaying:“It’swhenyousaynaughtywords”(MJ,p.141).Hewenton
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toagreethat“fool”isaliebecauseitisawordyoushouldnotsay.Weseethenthatthechild’sdefinition
is“realistic”:alieisabadthinganddoesnotatallrefertotheintentiontodeceive.Asecondexample
concernsyoungchildren’scomparisonofthemagnitudeoflies.TostudythissortofjudgmentPiagetread
thechildrentwostories.Inonestoryaboywasfrightenedbyadogandtoldhismotherthatthedogwas
“asbigasacow.”Inasecondstoryaboydeliberatelydeceivedhismotherabouthisschoolgrades.Young
childrenoftenmaintainedthatthestoryaboutthedogwasagreaterliethanthestoryaboutthegrades.
Thereasonwasthatseeingadogthesizeofacowwasalessprobableeventthangettinggoodgrades.In
thecaseofthedogthereisamuchgreaterdiscrepancybetweenactualfacts(therealsizeofthedog)and
thelie(thedogbeingaslargeasacow)thaninthecaseofgrades,wherethelie(agoodgrade)seems
almostaslikelyasthefact(abadgrade).Inotherwords,seeingadogaslargeasacowisfarlesslikelyto
occur than having good grades and, therefore, appears to be a bigger lie. Intention to deceive is
irrelevant,andtheimportantcriterionhastodowiththeprobabilityofoccurrenceoftheevents.Thusthe
youngchild’s judgmentof liesisas“realistic”ashisdecisionconcerninggoodnessandnaughtiness.It
focusesontheexternalormaterialaspectofthequestionandfailstotakeintoaccounttheintentionalor
subjectiveaspect.
Whydoesasignificantproportionoftheyoungchild’sresponsesinvolvemoralrealism?Partofthe
reasonisprobablythatparentsaresometimes“realistic”themselves.Someadultspunishthechildmore
forbreakingfifteencupsunintentionallythanforpurposelydestroyingonecup.Butthisisnotthewhole
story.Parentspunishastatement intendedtodeceive(areal lie)morethanamereexaggeration(for
example,thedogasbigasacow).Thechild,however,thinksthattheexaggerationisnaughtierthanthe
intentiontodeceive,soitseemsthatthechild’sjudgmentdoesnotsimplyreflectthepunishmentswhich
hehasactuallyreceivedfromadults.Itisapparent,then,thattwoadditionalfactorsareinvolved.One
factor is therelationofunilateral respect.Since theparent is respected, soarehisrules. If theparent
forbidsthebreakingofcups,thentheactofdoingsoisbadregardlessofintention.Anotherfactoristhe
child’segocentricpatternsofthought.Sincehecannotassumepointsofviewdifferentfromhisown,he
cannotseetheother’sneedfortruth,andconsequently,heisnotawareofthefactthathis“lies,”inwhich
hehimselfoftenappearstobelieve,aredeceivingthelistener.Unilateralrespectandegocentrism,then,
contributetomoralrealismjustastheydototheconceptofrulesasinviolableandsacred.
Thechildgraduallyabandonsmoralrealisminfavorofamore“subjective”approach.Injudgments
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ofgoodnessandnaughtinesshefocusesonmotivation,notextentofdamage.Injudgmentsoflyinghe
considerstheintentiontodeceive,notjustthelikelihoodthattheeventcouldhaveoccurred.Aswasthe
case in the conceptionof rules, the child’sprogress isdue largely tohisnew independence from the
family,tohisincreasedinteractionwithothers,tohiscontactwithpergentviews,andtosimilarfactors.
We may make severed comments concerning moral behavior and judgment. First, Piaget
emphasizes that thevariousstagesoverlap, that thesamechildmaybe inbothstagessimultaneously
dependinguponthecontentofaparticularsituation,andthatprimitive formsofmoral judgmentare
oftencharacteristicofadultsaswellaschildren.Neitherthestagesnorthecourseoftheirdevelopment
areclear-cut,andPiagetdoesnotwishtogiveanimpressionoforderlinesswherelittleistobefound.
Second,Piaget’s social learning theory—thatprimitivemoral judgmentderives in fact fromunilateral
respectandmatureconceptionsfromcooperationandsimilarfactors—isspeculativebecausethereisno
direct evidence linking adult constraint with moral realism. Nevertheless, the theory points in
interesting directions. The effect of the social environment on intellectual processes has hardly been
considered.Undoubtedlythetheorywillrequireclarificationandelaboration,particularlywithregardto
thereciprocaleffectwhichseemstoexistbetweencooperationandthediminutionofegocentrism.Does
the child take the other’s point of viewmainly because the two persons interact, or do they interact
mainlybecausetheycaneachtaketheother’spointofview?Or,asseemsmoreplausible,coulditbethat
thereisacomplexrelationshipbetweencooperationandthepassingofegocentrism?
AthirdcommentisthatPiaget’stheory,likeFreud’s,issomewhatpessimistic.AccordingtoFreudit
is inevitable for both social and biological reasons that the childwill experience anOedipal conflict,
whichwillresultintheadoptionofaharshandauthoritariansuperegoorconscience.ForPiaget,too,it
seemsinevitablethattheyoungchildwilldisplayegocentricthoughtandthathewillstandinarelation
ofunilateralrespecttotheadult.Egocentrismdefinescertainpropertiesofthoughtobservedinyoung
childrenwhichappeartobeunavoidableandwhichmustbeovercomebeforethechildcanreachamore
mature level of cognitive functioning. Unilateral respect is inevitable too; even if the parent tries, he
cannotcreateatotalatmosphereofmutualrespect.Theparentmustarbitrarilyimposeuponthechild
someregulationsbecausethechildcannotunderstandtheircomplexrationale.Sinceegocentrismand
unilateralrespectareinevitable,soistheirproduct,moralrealism.
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AfourthcommentisthatPiagethasnotyetfullydemonstratedthatthemoraljudgmentselicitedby
his questioning on stories correspond to moral judgments in "real life." Piaget’s arguments may be
convincing—forexample,thatchildrentakethegameofmarblesseriously—butnoamountofargument
canresolvetheissue.Whatisrequiredisnaturalisticstudy.Weneedtoseewhethermoralrealism,for
example,isindeedfoundinchildren’smoraljudgmentsinthenaturalsituation.
A fifth comment concerning moral behavior and judgment is that Piaget’s work has certainly
fulfilleditsoriginalpurpose:tostimulatefurtherexperimentationandtheorizing.Moraljudgmenthas
been a popular topic for research, and in the main, independent investigators’ findings have been
consonantwiththoseofPiaget.1
Reasoning
Piaget’searlyworktoucheduponthechild’sreasoning,too.Theresearchagainwaspreliminary,
andasweshallseeinChapter4,helaterintensivelyelaborateduponthesametopics.Atthispointwe
willconsiderseveraltypesofreasoning:syncretism,juxtaposition,andordinalandpart-wholerelations.
InoneofhisstudiesPiagetpresentedthirty-five9-year-oldboysandgirlswithaseriesofproverbs
andacollectionofexplanatorysentences.Thechild’staskwastoconnecteachproverbwiththeproper
explanatorysentence.Forexample,oneproverbis,“Drunkenoncewillgetdrunkagain.”Thesentence
which expressed the same idea is, “It is difficult to break old habits,” and not, “Some people are
continuallydrunk.”Piagetalsoquestionedeachchildconcerningthereasonsforhischoice.
One8-year-oldchildsaidthatthesentencecorrespondingto“Whenthecat’sawaythemicecan
play”is“Somepeoplegetveryexcitedbutneverdoanything.”WhenPiagetaskedhisjustification,he
responded:
Becausethewordsareaboutthesame. . . . Itmeansthatsomepeoplegetveryexcited,butafterwardstheydonothing, theyare too tired.Thereare somepeoplewhoget excited. It’s likewhen cats runafterhensorchicks.Theycomeandrestintheshadeandgotosleep.Therearelotsofpeoplewhorunaboutagreatdeal,whogettooexcited.Thenafterwardstheyarewornoutandgotobed.(LT,p.149)
Thechild’sprocessofreasoningiscertainlyveryconfused.Onewaywemaycharacterizeit is in
termsof syncretism, a tendency to connect a series of separate ideas into one confusedwhole. In the
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present case the child tries to tie together an absent cat with excited people. The child assigns to
disparatethingsasimilaritywhichisalmostunfathomabletotheadult.Howdoesthetendencytoward
syncretismwork?AccordingtoPiaget,whenthechildreadstheproverbheconstructsaninterpretation
ofit.Thisinterpretationmaybeonlylooselyrelatedtotherealmeaningoftheproverbbecausethechild,
ineffect,freeassociateswhenhehearsthewords.
Inthecaseofthesubjectwhoseprotocolwasjustdescribed,subsequentquestioningrevealedthat
heinterpretedtheproverbasmeaning“Thecatrunsafterthemice.”Thechildthensearchedamongthe
alternativesentencestofindtheonecorrespondingtotheproverb.Hisinterpretationorunderstanding
guidedthisprocess,sothatheviewedthesentencesintermsofhisinterpretationoftheoriginalproverb.
InPiaget’sterminology,thechildassimilatesthesentencesintotheschemewhichoriginallycontributed
towardhisunderstanding.Thesubjectcitedthusperceivedasimilaritybetweenhisunderstandingof,
“Thecatrunsafterthemice,”andthesentence,“Peoplegetexcited.”Then,afterthechildhasinterpreted
aproverbandseenarelationbetweentheinterpretationandasentence,hesaysthatthesentenceand
theproverbhavethesamemeaning.Bymeansofanintermediary—theschemewhichenabledhimto
understand in the first place—he has conglomerated two apparently disparate items. In a sense,
syncretismisacaseofassimilationgonewild.Thechilddoesnotaccommodatetotherealmeaningofthe
proverb;rather,heassimilatesitintohisownscheme,andthenhegoesoninthesamewaytoassimilate
thesentenceintothisschemetoo.
Nowwewill consider thephenomenonof juxtaposition. If youwill recall, in his study of verbal
communicationPiaget found thatyoung children seldomexpress causal relations. Indescribing some
mechanicaldevice,thechildmerelysaysthataandboccurred;hedoesnotsaythatacausedb.Insteadof
beingrelatedonetotheother,thetwoeventsaremerelyjuxtaposed,thatis,placedoneaftertheother.
Toinvestigatethismattermoredirectly,Piagetperformedanexperimentonfortychildrenfromabout6
to10 years of age.He gave each child an incomplete sentence endingwith theword “because,” and
askedhimtocompleteit.Forexample,hemightask,“Watergetshotbecause...”.Ifthechildanswered,
“thefirewasturnedon,”thenPiagetmightcontinuebyasking,“Andthefirewasturnedonbecause..
.’’.In thisway, he attempted todetermine if children coulduse thenotionof causalitywhen they are
almost directly asked to do so. The responses to the sentences and to clinical questioning revealed a
frequentinabilitytoexpresscausalrelations.Herearesomeexamples:2
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themanfellfromhisbicycle,becausehebrokehisarm....Ihadabath,becauseafterwardsIwasclean....I’velostmypenbecauseI’mnotwriting....Hefelloffhisbike,becausehefellandthenhehurthimself. (JudgmentandReasoning,JR,pp.17-18)
At leasttwoexplanationsofthechild’sresponsesarepossible.Accordingtooneexplanation, the
child’sanswersexpresssophisticatedrelationships.Thesentence“Ihadabath,becauseafterwardsIwas
clean”means“WecantellthatIhadabathbecauseafterwardsIwasclean”or“Mycleanlinessimplies
that I had taken a bath.” A second interpretation of the same sentence is that the child has a poor
understandingofcausality:hereversescauseandeffectandmerelyjuxtaposesoneeventaftertheother.
Which explanation is correct? A number of factors seem to support the second interpretation,
juxtaposition.Inhisnaturalspeechthechildseldomusestheword“because”orothersimilarwordsto
expressrelations,causalorotherwise,betweenevents.Also,someoftheanswerstoPiaget’stestdonot
revealsophisticatedrelationshipsofthetypeproposedbythefirsthypothesis.Anexampleis,"Hefelloff
hisbike,becausehefellandthenhehurthimself."Thisstatementdoesnotdirectlyconnectfallingwith
injury;thetwoeventsaremerelyjuxtaposed.Themoreaccurateinterpretationofthechild’sresponses
seemstobethattheyrevealafailuretoperceivecausality(letalonemoresophisticatedrelations)and
indicateatendencymerelytoplaceeventsoneaftertheotherwithoutspecifyingtherelationsamong
them.
Juxtaposition can also be seen in another anddifferent context, namely, the child’s drawing. In
depictingabicycle,forinstance,thechilddrawsmanyofthepartsbutdoesnotsynthesizethemintoa
properwhole.Hemaydrawthechainbutnotconnectittothewheel;hemaydrawtheseatbutnotattach
ittotheframe.Weseethatthechildconsidersonlyisolatedeventsandignorestherelationsbetween
them.
Sincesyncretismandjuxtapositionseemtobeopposites,theirsimultaneousexistenceintheyoung
childposesaparadox.Howcanthesamechildbothignorethepartsinfavorofthewhole(syncretism)
and ignore thewhole in favorof theparts (juxtaposition)?Piaget attempts to resolve theparadoxby
arguing that both juxtaposition and syncretism are expressions of a common mode of thought—the
inabilitytothinkaboutseveredaspectsofasituationsimultaneously.Juxtapositioninvolvesfailingtosee
anyrelationamongthepartsofawhole,andtheresultisthattheyareseenasdiscreteandunrelatedto
eachother.Thechildisthusunabletothinksimultaneouslyaboutthepartsasseparatethingsandabout
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therelationswhichunite them.Similarly, in theuseofsyncretism, thechildperceivesawholeor the
commonrelationships,butfailstorecognizethedifferenceswithinthewhole.Healsohasfocusedonone
aspect of the situation at the expense of the other. In other words, since the child cannot focus
simultaneouslybothonthedifferencesamongthingsandontheircommonrelationships,heisapttosee
either a succession of unrelated events (juxtaposition) or a conglomerated whole (syncretism). Both
typesofdistortionsresultfromthesamedeficiencyinthought.
InyetanotherinvestigationPiagetstudiedrelationalthinking.Hepresentedanumberofchildren
withthisproblem:“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichis
thedarkest,Edith,Suzanne,orLili?”(JR.,p.87).TheproblemineffectinvolveswhatPiagetwaslaterto
callordinalrelationships. Supposewe know thatb is a smellier number than c and thatb is a larger
numberthana.Whichisthelargestnumber?Theanswer,ofcourse,isc.IfwesubstituteLilifora,Edith
forb,andSuzanneforc,and“haslighterhairthan’’ for“isasmallernumberthan,”thenwehavethe
sameprobleminthetwocases:bothdealwiththeunderstandingofrelationsofordering,whetherthese
beintermsoflightnessofcolor,sizeofnumber,andsoon.Bothproblemspresentthechildwithpartial
informationconcerningtheordering(e.g.,thatb<candb>a)andaskhimtodeducetheentireordering
(thata<b<c).Piagetfoundthatchildrenevenasoldas13yearsfoundtheproblemtobeverydifficult.
Forexample,a9-year-oldsaid:“Youcan’ttell,becauseitsaysthatEdithisthefairestandthedarkest”(JR,
p. 88). Piaget again explains their difficulty in terms of an inability to consider severed aspects of a
situationsimultaneously.Itisbecausethechildcannotatthesametimefocusonb<candb>athathe
failstodeducea<b<corthatSuzanneisthedarkestofthelot.
Another investigation yielded remarkably similar results. The study dealt explicitly with the
relationsoftheparttothewhole.Theaimwastodiscoverwhetherthechildbelievedthatthepartwas
includedin thewhole.Thequestionswerephrasedintermsoftherelationsbetweencities(theparts)
andcountries(thewhole).Hereisanexample:
Stu(7;8)saysthat“GenevaisinSwitzerland”andthat“Switzerlandisbigger[thanGeneva],"ButGenevansarenot Swiss. “Then where must you come from to be Swiss?”—“From Switzerland.” We draw a circlerepresenting Switzerland, and ask Stu to put the cantons in their places. . . . Stu inscribeswithin the circlethreeorfoursmallerones—Geneva,Vaud,etc.,buthestillmaintainsthatGenevansarenotSwisspeople.TheSwissaretheinhabitantsofthebigcircle.(JR,p.123)
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Notethatattheoutsetthechildseemstomaintainthatthecityispartofalargerwhole(“Genevais
inSwitzerland”).Butwhenheisquestionedaboutthematter,hedeniesthatGenevansareSwissorthat
the part is in fact included in the whole. The child again sees part andwhole separately: they are
unrelatedentities.
We see in summarizing that Piaget’s studies of reasoning find that the child has a tendency to
grouptogethervariousdifferenteventsintoalooseandconfusedwhole(syncretism),thathesometimes
fails to see the relations among separate events (juxtaposition), that he fails to understand ordinal
relations, and that he cannot dealwith the relations between a part and thewhole ofwhich it is a
member.Allthesetypesofreasoningrevealacommondeficiency:aninabilitytothinksimultaneously
aboutseveralaspectsofasituation.
Piagetmakesanextremelyinterestinggeneralcommentabouthisinvestigations.Hepostulatesthat
hisfindings,sincetheyaretheresultsofquestioningchildren,holdtrueonthe“planeofverbalthought”
butnotonthe“planeofaction.”That is,whilechildrenmayfailaproblemwhenitssolutionrequires
verbalexpression,theymaybequiteabletodealwiththesamedilemmaonapractical,behaviorallevel.
Whilethechildfirstsolvesproblemsontheplaneofaction,hethenmustrelearnhissolutionsonthe
planeofverbalthought.Inasense,actionismoreadvancedthanverbalthought(forthechildfrom7to
11years);thelatterlagsbehindtheformer.Piagettermsthelagaverticaldécalage.Theverticalityrefers
toanascendingagescale:whatthechildlearnsatage7ontheplaneofaction,hemustrestructureatage
11ontheplaneofverbalthought.“Décalage”referstothegaporlag.
GENERAL SUMMARY AND CONCLUSIONS
Piaget’s early work is greatly varied. The first studies deal with the child’s use of language.
Naturalisticobservationrevealsthatchildrenyoungerthantheageof7yearsoftenfailtousespeechasa
vehiclefortransmittinginformationtooneanother,andinsteadfrequentlyrepeatanother’sremarksor
engage in inpidual or collective monologues. An experiment confirms these findings: when young
childrenaregiventheexplicittaskofconveyinginformationtoanotherchild,theyfailtocommunicate.
Theydonot consider the informationalneedsof the listener.Moreover, the listenerdistortswhat the
speakersaysbygivingitidiosyncraticinterpretations.
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InotherinvestigationsPiagetusestheclinicalmethod.Herejectsthetestingapproachbecauseofits
rigidityandrejectsthenaturalisticapproachbecauseofitsfailuretoyieldasufficientamountofrelevant
information.Theclinicalapproach,hefeels,ismoreflexibleand,therefore,isespeciallywellsuitedto
theexploratoryaimsof initialstagesofresearch.Heusestheclinicalmethodto investigatethechild’s
conceptionoftheworld,andfindsthatthechildexhibitsseveralprimitivethoughtpatterns.Animism is
thetendencytoconsidernaturaleventstobealiveinthesamesenseashumanbeingsare.Artificialism is
the tendency tobelieve thatsomeagent—humanorpine—creatednaturalevents.Participation is the
vagueideathathumanactionsandnaturalprocessesinteractandarerelated.
Afurtherstudy,againusingtheclinicalmethodinpart,dealswithmoraljudgmentandbehavior.
Childrenbelowtheageof7yearsfailtofollowtherulesofagamewhileatthesametimebelievethatthe
rulesaresacredandinviolable.Olderchildrendisplaybothagreatertendencytofollowtherulesandto
believe that theycanbechanged. Inexplicitlymoral situations,youngchildrenbelieve thatguiltand
moral responsibility are determined not by intention but by the amount of damage produced. These
“realistic”moraltendenciesareseeninthecaseoflyingaswell,anddeclinewithage.
Instudiesofreasoning,Piagetfindsthattheyoungchild’sthoughtischaracterizedbysyncretism,
thetendencytogrouptogetherintoaconfusedwholeseveralapparentlyunrelatedthingsorevents,and
byjuxtaposition,thefailuretoseetherealconnectionsamongseveralthingsorevents,andthefailureto
understand either part-whole or ordinal relations. All these tendencies reflect a common pattern of
thought:theinabilitytoconsiderseveralaspectsofasituationsimultaneously.
Piagetemploysasociallearningtheorytoexplainthechild’sdevelopmentparticularlyintheareas
oflanguageandmoraljudgment.Hepostulates,forexample,thatthechild’sprimitivemoraljudgmentis
theresultofegocentricthoughttendenciesandtherelationofunilateralrespecttowardtheadult.The
child’smoraljudgmentbecomesmorematurewhenheadoptsapositionofmutualrespecttowardadults
andcomesintocontactwithnewsocialinstitutionsandpointsofview.
ThereareseveralcommentswemaymakeconcerningPiaget’searlyresearch.First,whatarethe
relations among the various findings? The young child is egocentric in communication, has an
absolutisticconceptofrules,isrealisticinhismoraljudgment,andinhisreasoningdisplayssyncretism
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andjuxtaposition.Thesevariedtermsatfirstmayseemtorefertodifferentandunrelatedphenomena.
Onemightthinkthatmoralrealismandsyncretism,forinstance,refertodifferentpatternsofthought,
andthatthereisnocommonalitybetweenthem.ButPiagetfeelsthatsuchaviewismistaken:thereis
indeed a strong similarity amongmany of the young child’s reactions to the problems posed by the
variousinvestigations.
The common pattern underlying these apparently perse reactions is the inability to deal with
severalaspectsofasituationsimultaneously.Thisisduetotheegocentricnatureofthechild’sthoughtor
theincapacitytoshiftattentionfromonetoanotheraspectofasituation.Inthecaseofspeech,theyoung
childcannotconsiderboththeother’spointofviewandhisownatonce,andthereforecenterssolelyon
hisownpointofview.Inthecaseofrules,theyoungchildfailstoconsiderbothhisowninterestsandthe
needs of others. Consequently, he often breaks the rules. He sees the origin of rules from a limited
perspective, too. Emanating from a person whom he regards as prestigious, they must likewise be
prestigious.Thechildfailstoconsiderboththeparent’sprestigeandhisreasonsfordevisingtherules.In
thecaseofmoraljudgment,thechildcannotconsiderbothdegreeofdamageandintention,andhebases
hisjudgmententirelyontheformer.Asfarasreasoningisconcerned,wehavealreadyseenhowboth
syncretismandjuxtapositionareexpressionsofasingletendency,namely,thatoffocusingonalimited
aspectoftheproblem.Thesamemaybesaidoftheunderstandingofordinalandpart-wholerelations.In
theformer,thechildconsidersonlycertainpartsofrelationsbutnotothers;inthelatter,hefocuseson
thepartbutnotthewhole,orviceversa.
As thechildgrowsolderandcomes into contactwithopposingpointsofviewandvariedsocial
institutions,his thoughtgoes throughaprocessofdecentration. Inspeech,heconsidersbothwhathe
wantstoexpressandthelistener’sneeds.Ingames,heconsiderstheother’sinterestsaswellashisown
and is, therefore, willing to follow and modify the rules. In moral judgment, he considers both the
outcomesofaperson’sbehavioranditsintent.Andinreasoning,hetriestoconsiderthecomplexitiesof
problems—boththedifferencesandsimilaritiesamongthesamesetofevents.Thus,thechilddecenters
histhoughtjustasinthesensorimotorperiodtheinfantdecenteredhisbehavior.Thenewbornactsasif
theworld is centered about himself andmust learn to behave inmore adaptiveways. Similarly, the
young child thinks from a limited perspective andmust widen it. Both infant and young childmust
decenter—theformer,hisactionandthelatter,histhought.
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Inadditiontocharacterizingtheyoungchild’sthoughtintermsofcentration,Piagetoccasionally
described it inFreudian terms.Freuddescribedseveralprimitivementaloperationsusually found in
certainkindsofmentalillnessandinthedeepestlayersofthenormalperson’sunconscious.Freudfelt
thatthistypeofthinking,called“autisticthought,”displayscertainregularities.Forinstance,itshowsa
tendencytofusedisparatethingsintooneimage.Thus,inadreamwemayperceiveacharacterwhoisa
“condensation”oftwodistinctpersons.InhisearlyworkPiagetproposedthatthethoughtofthechildis
intermediatebetweenautisticandadultthinking.Forexample,thechild’ssyncretismissimilarto,but
more mature than, the tendency toward condensation. While at the beginning of his career Piaget
borrowedafewideasfrompsychoanalysis,hewasneveradiscipleofFreudbutalwaysanindependent
investigator.Astimewenton,hislimiteddependenceonFreuddiminishedfurtherwiththeresultthat
Piaget’slaterworkistotallydevoidofFreudianconcepts.
Piaget not only abandoned Freudian ideas, but became dissatisfiedwith the clinicalmethod as
administered at that time.He came to feel that it relied tooheavily on language. The child thinks in
nonverbalwaystoo,andtheexclusivelyverbalclinicalmethodwasnotalwayseffectiveintappingthese
thoughtprocesses.Consequently,heturnedtosomewhatdifferentmethodswhichwewilldescribein
thenextchapter.
Despitetheirmethodologicaldeficiencies,Piaget’searlyinvestigationsmaybeconsideredamong
themost interesting of his achievements. Themajor part of the early studies dealt with socially and
practicallyrelevantphenomena: thechild’sability to communicate information, to followrules, and to
makemoraljudgments.Allthesemattersareobviouslyimportantforthechild’spracticalsuccessinthe
worldandforhisinteractionswithothers.
Bycontrast,Piaget’s laterworkdeals,asweshallsee,withmoreabstractphenomena:thechild’s
understanding of number or classification. These have less obvious relevance to the child’s ordinary
activities.Probably,hisabilitytounderstandthecardinalityofnumbermakeslessofadifferencetohis
daily life than his ability to communicate to other children. Also, in his early books, Piaget showed a
strong interest in the role of social factors indevelopment. Later research, aswe shall see, convinced
Piagetthatotherfactorsofequalimportancewereinvolved.Withtimehisinterestshavetendedtofocus
onthesefactorsratherthanonthesocialenvironment.
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Finally,wemaynote that the explanatory conceptswhich evolved fromPiaget’s earlywork are
vague. They are stated in ordinary language and are often not entirely clear. Much confusion, for
example, has arisen over the concept of egocentrism. But as we have stated repeatedly, Piaget fully
recognized that his early conceptswere only preliminary and tentative, not final and conclusive.He
hoped that his earlyworkwould stimulate research by others, and that he himself could clarify his
conceptsatalatertime.Thefirstofhisexpectationshasbeenfulfilled:therehasbeenmuchresearchon
moral judgment, for example. We will see in the next chapter how Piaget elaborated and even
formalizedsomeofhisearlyandtentativenotions,includingordinalandpart-wholerelations.
Notes
1Forareviewofthisliterature,seeT.Lickona,ed.,MoralDevelopmentandBehavior(NewYork:Holt,RinehartandWinston,1976).
2Thesentencetobecompletedisinromantype,andthechild’sanswerisinitalic.
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4 The Years 2 through 11:
Piaget’s Later Work
ThischapterdealswithaspectsofPiaget’slaterwork(fromapproximately1940onward)onthe
childfromabout2to11years.AswasshowninChapter1,thisportionofPiaget’sresearchandtheoryis
voluminous and covers suchmatters as the child’s conception of chance, space, geometry,movement,
number,andother topics.Sincewecannotreviewall the laterworkhere,weshall focusonwhatwe
consider tobebasic issues and conceptswhich reappear in andapply to almost all ofPiaget’s recent
writings.We will consider (1) the revised clinical method, (2) the child’s classification of objects or
events, (3) the ability to place them in ordinal relations, (4) the concept of number (particularly its
conservationovertransformations),(5)thenatureofmental imagery,(6)thedevelopmentofmemory
andconsciousness,and(7)somegeneralcharacteristicsofthought.
THE REVISED CLINICAL METHOD
WesawinChapter3thatPiaget’soriginalclinicalmethodwashighlydependentonverbalizations.
Theexaminerposedthequestionsinwords,andthechildwasrequiredtogivetheanswersinthesame
way.Theexaminer’squestionsusuallydidnotrefertothingsoreventsthatwereimmediatelypresent,
andtheproblemsdidnotalwaysinvolveconcreteobjects
whichthechildcouldmanipulateorevensee.Forexample,theexaminermightdepictachildwho
had unwittingly broken some cups andmight then ask the subject being questioned for a judgment
concerningthechild’snaughtinessandthepunishmenttobemetedout.Insuchasituationasthis,the
subjectisrequiredtodoseveralthings.Hemustinterprettheexaminer’sdescriptionsoastopicturethe
scenetohimself;hemustmakeaspecialefforttocomprehendcertaincrucialaspectsofthequestion,like
theword“naughty”;andhemustexpresshisjudgmentinwords.
Aftersomeexperiencewiththismethod,Piagetcametofeelthatitwasinadequatebecauseitrelied
too heavily on language. The childmight not understand everything said to him, particularly if the
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wordsdidnotalwaysrefertoconcreteobjects.Evenifthechilddidunderstand,perhapshecouldnot
adequately express in words the full extent of his knowledge. Consequently, Piaget modified his
procedures, and the result iswhatwe shall call “the revised clinicalmethod” (sometimes called the
“method of critical exploration”). The new method involves several features. First, the examiner’s
questionsrefer toconcreteobjectsoreventswhichthechildhasbeforehim.No longermust thechild
imaginethesethingsmerelyonthebasisofaverbaldescription.Second,aneffortismadetoletthechild
expresshisanswerbymanipulatingtheobjects,andnotsolelyexpresshimselfthroughlanguage.
For example, let us suppose that the examinerwishes to knowwhether the child can form two
distinctclasses.Toinvestigatethematterhemightpresentthechildwithanarrayofcirclesandsquares
allmixedtogetherinnoorder,andaskhimtoputtogethertheonesthatbelongtogether,orsortouttwo
distinctpiles.Whatthechilddoeswiththeobjects—whatsortofpileshemakes—andnotwhathesays
aboutthem,constitutestheprimarydataofthestudy.Ifafterencouragementachildstillcannotforma
pileofcirclesseparatefromapileofsquares,thentheexaminermightconcludethathedoesnothavethe
classificationskillsunderinvestigation.Whilecompletelynonverbaltestsaredesirable,itisoftenhardto
inventthem.ThisisespeciallytrueforPiaget,sinceheusuallyinvestigatesthechild’sunderstandingof
abstractconceptsthatarenoteasilymanifestedinthebehavioralmanipulationofconcretematerials.The
revisedclinicalmethod, therefore,mustoftendepend for itsdataon thechild’sverbal responses.But
evenwhenthisisnecessary,thechild’sanswersrefertoaproblemstatedintermsofconcretematerials
whicharepresent.
Third, Piaget introduced the use of counterarguments or countersuggestions. These involve
presentingthechildwithapointofviewthatcontradictshisown,andaskinghimwhathethinksofthe
opposingview.Thepurposeofthesecounterargumentsistodeterminethestabilityandauthenticityof
thechild’sthinking.Childrenwhohavemasteredaconceptwillresistthecountersuggestion;thosewho
havenottendtobeswayedbythecontradictoryargument.
Afourthfeatureoftherevisedclinicalmethodisnotnew:theexaminer’squestioningisflexible.
Ratherthanemployastandardizedlistofquestions,hemodifiesthemoraddsnewonesasthesituation
demands.Asbefore,Piagetstillfeelsthatthereisnopointeitherinaskingachildaquestionthathedoes
notunderstandorinfailingtoclarifyananswer.
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To summarize, the revised clinical method involves posing questions concerning concrete
materials; allowing the child to “answer” by manipulating the materials, if this is at all possible;
introducing counterarguments; and, as in the earlier clinicalmethod, statingquestions andpursuing
answersinaflexibleandunstandardizedway.Whetherornottherevisedclinicalproceduregivesan
accurateassessmentofthechild’sabilitiesisamatterfordebate.Ingeneral,mostpsychologists(outsideof
Geneva) do not use this method in research, mainly on the grounds that it is not sufficiently
standardized.Wethink that thisattitude ismistaken,especiallysince thereareverygoodreasons for
avoiding standardization.1 In any event, the revised clinical method is less exclusively verbal than
Piaget’searlierprocedureandattemptstogiveanaccurateassessmentofthechild’sthoughtprocesses
whichinlargemeasuremaybenonverbal.
CLASSIFICATION
Piaget has used the revised clinical method to study classification in the child. The preceding
chaptershavealreadytouchedonthisandrelatedmatters,anditmaybeusefultoreviewsomeofthe
materialhere.Wesawthatthereisaprimitivesortofmotorclassificationinthesensorimotorperiod(0to
about2years)whentheinfantappliestoobjectsintheenvironmentabbreviationsoffamiliarschemes.
Forexample,Luciennesawatoyparrothangingabovehercribandkickedherfeetveryslightly.Thiswas
anabbreviationofaschemewhichshecouldquiteeasilyhaveappliedtothepresentsituation.Itseemed
asifheractionclassifiedtheparrotasa“thingtobeswung.”Moreover,theabbreviationshowsthatthe
behaviorwasbecominginternalized.Eventuallyitcouldbereplacedbythethought:“That’stheparrot;
that’s something I can swing.” But the abbreviated schemes are not yet instances of legitimate
classification.Onereasonisthattheschemesapplytoindividualobjectsoveraperiodoftimeandnottoa
collectionofobjects.Forexample,Luciennekickedfromtimetotimewhenevershesawparrotsandthus
indicatedrecognition.Butthis
recognitiondoesnotimplythatsheconsideredtheparrotstobelongtoaclass.Matureclassification,
on the other hand, involves the conception of a collection of things, whether they are immediately
presentorimagined.AsecondreasonwhyitisnotpossibletocreditLuciennewithclassificationhasto
do with inclusion relations, which will be expanded on shortly. Briefly, this refers to the ability to
constructahierarchicalclassification,suchthattoyparrotsareasubclassofalarger,moreinclusiveclass
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liketoysingeneral.
From about 2 to 4 years the child begins to classify collections of objects in away that is quite
primitive. He uses the preconcept. Sometimes he fails to see that one individual member of a class
remains the same individual despite slight perceptual changes, and sometimes he thinks that two
different members of the same class are the same individual. Between 5 and 10 years, the child’s
classificationisstillfaultyinseveralways.Thereisthephenomenonofjuxtaposition,theinabilitytosee
thatseveralobjectsareindeedmembersofthesameclass.Thereisalsosyncretism,thetendencytogroup
togetheranumberofdisparateeventsintoanill-definedandillogicalwhole.
As was pointed out, Piaget’s investigations of the preconcept, syncretism, and juxtaposition,
conductedinthe1920sand1930swerepreliminaryandtentative.First,thereexistedmethodological
defects:thedatawerealmostexclusivelyverbalsothatPiaget’sinterpretationwasbasedlargelyonwhat
the child said. Second, Piaget’s concepts—syncretism, juxtaposition, the preconcept—were somewhat
vagueandneededelaboration. Inthe1950sPiagetreturnedtothestudyofclassificationinthechild
fromabout2to12years.Theseinvestigationsmakeuseoftherevisedclinicalmethod;theyalsomodify
thenotionsofpreconcept,syncretism,and juxtapositionandsuggestnewwaysofconceptualizingthe
child’sclassificatoryactivities.
Some Properties of a Class
BeforeexaminingPiaget’sresearchintoclassification,wemustclearlyunderstandwhathemeans
byaclass.Supposewehavebeforeusanumberofobjectsallmixedtogether.Thearraycontainsalarge
red triangle, a small blue circle, a large pink circle, and a small black triangle. All the objects are
discriminablydifferentonefromtheother.Thatis,thereisnodifficultyinperceivingthatanyoneobject
isdifferentfromanyoftheothers.Forexample,thelargeredtriangleisveryobviouslylargerandredder
thanthesmallblacktriangle.Suppose,too,thatwewishtoplacetheseobjectsintotwodifferentclasses.
Onewayofdoingthisistoputinoneseparatepilethelargeredtriangleandthesmallblacktriangle.In
thesecondpilewouldgothesmallbluecircleandthelargepinkcircle.Iftheoriginalarraycontained
additionaltriangularobjects,regardlessoftheir
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sizeorcolor,theywouldofcoursegointhefirstpile.Similarlyallothercircularobjectswouldgoin
thesecondpile.Thetwopileseachrepresentaclass.Ofcourse,wemightclassifytheobjectsinanother
way.Wecouldputinonepilethetwosmallobjects(regardlessoftheircolororshape)andinthesecond
pilethetwolargeobjects.Thereareusuallymanydifferentclassesthatonemayformfromagivenarray
ofobjects.
Piagetmakesanumberofpointsabouttheclassesformedfromtheoriginalarray(forpurposesof
illustrationconsiderjustourfirstexample,theclassoftrianglesandtheclassofcircles):
1.Noobjectisamemberofbothclassessimultaneously.Forexample,thelargeredtriangleisintheclassoftrianglesandnotalsointheclassofcircles.Thus,theclassesaremutuallyexclusiveordisjoint.Thisholdseven if therearemore than twoclasses formed. (Forexample, wemight divide some animal pictures into the classes of lions, tigers, andelephants,allofwhicharedisjoint.)
2.Allmembersofaclasssharesomesimilarity.Forexample,thesmallbluecircleandthelargepinkcirclebothsharethepropertyofcircularity.Circularityisthedefiningproperty,thecrucialattribute,oftheclass;thatis,weincludeintheclassofcirclesanyobjectwhichiscircular.Anotherwayofputtingitistosaythatcircularityistheintensionoftheclass.Thedefiningpropertyorintensionoftheotherclassistriangularity.
3.Eachclassmaybedescribedintermsofalistofitsmembers.Insteadofdescribingaclassintermsofitsdefiningpropertyorintension(forexample,theclassoftriangularobjects),wemay simply list theobjects in the class (forexample, large red triangleandsmallblack triangle). Sucha list is theextensionof the class.Note that the listmay involveconcreteobjects(likelarge,bluecircles)orabstractideas,events,actions,andsoon(likethelistofthepartsofspeech).
4. The defining property of a class determineswhat objects are placed in it. Anotherway ofstatingthisisthatintensiondefinesextension,orthe“fieldofapplication”ofaconcept.Forexample,ifweknowthatoneclassistobeformedonthebasisoftriangularityandanotheronthebasisofcircularity,wecanpredictthecontentofthelistofobjectsineachclass.
Thesearesomefundamentalpropertiesofclasses,asPiagetdefinesthem.(Thereareothercrucial
attributestoo,likeinclusionrelations,whichwewilldiscusslater.)Piagetthenaskswhetherthechild
classifiesobjectsinaccordancewiththeseproperties.Whenaskedtogroupobjects,doesthechildform
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mutuallyexclusiveclasses?Dohisclasseshavedefiningpropertieswhichdeterminethelistofobjectsin
eachclass?
Piaget discovers three stages of development. The first two—both of which we may call
preoperational—occur roughlyduring theyears2 to7.The third stage—thatofconcrete operations—
occursroughlyfromtheyears7to11.
Stage 1
To investigate classification,Piagetperformedanumberof experimentswhichused the revised
clinicalmethod.Inonestudy,hetestedanumberofchildrenfromabout2to5yearsofage.Theywere
presentedwith flat geometric shapes ofwood and of plastic. The shapes included squares, triangles,
rings,andhalf-rings,allofwhichwereinseveralcolors.Theshapesweremixedtogetherandthechild
wastold:“Puttogetherthingsthatarealike.”Sometimesadditionalinstructionsweregiven:“Putthemso
thatthey’reallthesame”or“Putthemhereifthey’rethesame,andthenoverthereifthey’redifferent
fromthisonebutthesameaseachother”(EarlyGrowthofLogic,EGL,p.21).
Thechildrendisplayedseveralmethodsofgroupingtheobjects.Onemethod iscalledthesmall
partialalignment.Withthismethodthechildusesonlysomeoftheobjectsintheoriginalarrayandputs
them together in severalways apparentlywithout any overall guiding plan. For example, one child
beganbyputtingsixhalf-rings(semicircles)ofvariouscolors inastraight line; thensheputayellow
triangle on top of a blue square; later she put a red square in between two blue triangles; then put
squaresandtrianglesinnoparticularorder,inastraightline.Thereareseveralpointstonoteaboutthis
performance. Sometimes similarities among objects determine the collection. For example, the subject
whoseperformancewas just describedbeganwith a line of half-rings. At other times the same child
groupedthingsonthebasisofnodetectablesimilarity;thatis,sheputayellowtriangleonabluesquare,
oraredsquarebetweentwobluetriangles.Inbothofthesecases,thereisnosimilarityofeithercoloror
form.
Itisclearthatsmallpartiedalignmentsarenottrueclassesforseveralreasons.Oneofthemisthat
intension does not define extension; that is, no consistent defining property determined which
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geometric formswereput invariouscollections.Thechilddoesnotoperateunderanoverallguiding
plan like a system of rules (defining properties) which organize theway in which he arranges the
objects.
Otherchildrenofthisageusethegeometricfigurestoconstructaninterestingformorpicture.One
childarrangedanumberofcirclesandsquarestorepresentalongverticalobjectandthenproclaimedit
tobetheEiffelTower;anotherchildplacedanumberofhalf-ringsinbetweenseveredsquares,allina
horizontalline,anddescribedtheresultasabridge.Piagetcallstheseproductionscomplexobjects.Itis
obviousthatlikethesmallpartialalignments,andlikesomeothertypesofcollectionsnotdescribedhere,
thecomplexobject isnotatrueclass.Figuresarenotplaced inthecomplexobjectbecausetheyshare
somedefiningproperty;rather,extensionisdeterminedsolelybytherequirementsofthepictureunder
construction.
Inanotherinvestigation,Piagetpresentedchildrenofthesameagewithnongeometricfiguresfor
classification—little toyswhich included people, houses, animals, and so on. Once again, the results
showedaninabilitytoformclasses.Onechildputtwodollsinacradle,thentwowheelbarrowstogether,
thenahorse.Whentheexamineraskedthechild forall theobjects likeahorse,shegavehimall the
animalsandthenababyandtwotrees.Thisexampleillustratesthefactthatalthoughtheyoungchild
may perceive similarities among the objects, these do not fully determine what objects go into the
collection. That is, the child saw that all animalswere in some respect similar and gave them to the
examinerwhenaskedforobjectslikethehorse.Ifthechildhadstoppedthere,shemighthaveformeda
classwhichwasbasedonthedefiningpropertyof“animalness.”However,shewentontothrowinthe
babyand two trees.The similarity (intension) that she firstperceiveddidnot fullydeterminewhich
objectswere to be grouped together (extension). It is as if the child forgot about the initial defining
property(animalness)andthenswitchedtosomeother.
Wemaymakeseveral commentson these investigations.First, theymakeclear thenatureof the
revisedclinicalmethod.Theexaminergivesthechildconcreteobjectstoworkwith.Thetaskinstructions
andquestionsarestillverbal,ofcourse,buttheyrefertorealthingsthatthechildcanmanipulate.The
childisrequiredtosayverylittle.Mostofhisresponsesarenotverbalbutbehavioral.Hedoesnothaveto
saythatalloftheanimalsdoordonotgotogether;rather,hecanputthemtogetherorfailtodoso.
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Second,althoughtherevisedclinicalmethod isan improvementoverwhatwasusedbefore,we
wonderwhetherthetaskwasentirelycleartothechild.Theinstructions(e.g.,“Puttogetherthingsthat
arealike”)seemrathervagueandsusceptibletomanyinterpretations.Wesuspectthatdifferentmethods
of presenting the task to the child might produce entirely different results. Piaget considered this
objectionandtriedanessentiallynonverbalmethod.Hebegantoclassifytheobjectshimselfandasked
thechildtodothesamething.Theresultagainwasnottrueclassification,but“complexobjects,”andso
on.Whilethismethodwasnotsuccessful,itdoesnotexhaustthepossibilities.Otherinvestigatorshave
exploreddifferentprocedures,withsomesuccess.2
Stage 2
Childrenfromabout5to7yearsproducecollectionsthatseemtoberealclasses.Whenpresented
withthesituationdescribedearlier,onechildproducedtwolargecollections,onewhichcontainedall
thepolygonsand theother the curvilinear forms.Moreover, eachof these collectionswas subdivided
further. Thepolygons, for instance, contained separatepiles of squares, triangles, and so on, and the
curvilinearformsinvolvedseparatecollectionsofcircles,half-rings,andsoon.Thus,thechildnotonly
seemstoformclasses,butarrangesthemhierarchically,asinFigure2.Therearetwogeneralcollections
(polygons and curvilinear forms) at the top of the hierarchy, and these both branch out into several
subcollections below (squares, triangles, etc.). The child’s activities may be characterized in several
additionalways.(1)Heplacesintheappropriatecollectionalloftheobjectswhichwereintheinitial
array.Theyoungerchilddidnotdo this;he leftsomeobjectsunclassified. (2) Intension fullydefines
extension.Thatis,ifthechilddefinesacollectiononthebasisofthedefiningpropertyofcircularity,all
circlesgointothatpile,andnoneisplacedinanyotherpile.(3)Atagivenlevelofthehierarchy,similar
definingpropertiesareusedtodeterminecollections.Forexample,atthelowerlevelofthehierarchyin
Figure2,allthecollectionsaredefinedintermsofgeometricform—squares,triangles,andsoon.Itisnot
thecasethatsomecollectionsaredefinedbyformandsomebycolor.Tosummarize,itwouldseemthat
thechildfromabout5to7yearsproducesratherelaboratehierarchicalcollectionswhichdeservetobe
calledtrueclasses.
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FIGURE2Classificationofgeometricobjects.
Piaget feels, however, that the child of this stage fails to comprehend one crucial aspect of the
hierarchyhehasconstructed.Thechilddoesnotunderstandkeyrelationsamongthedifferentlevelsof
thehierarchy.Thisistheproblemofclassinclusionwhichwewillnowillustrate.Supposewearegivena
randomly organized array of blue and red squares and black and white circles. We construct an
arrangement(seeFigure3)suchthattherearetwomajorcollections(squaresversuscircles)andwithin
eachofthesetherearetwofurthersubdivisions(blueversusredsquaresandblackversuswhitecircles).
Thus,thereisahierarchywhosehigherlevelisdefinedbyshapeandwhoselowerlevelisdefinedby
color.Consider for themomentonlyone-halfof thehierarchy,namely, thesquareswhicharedivided
intoblueandred.Ifweunderstandinclusionrelations,thenwecanmakestatementsofthissort:(1)All
ofthesquaresareeitherblueorred.(2)Therearemoresquaresthantherearebluesquares.(3)There
aremoresquaresthanthereareredsquares.(4)Iftheredsquaresaretakenawayfromthesquares,then
theblueonesareleft.(5)Ifthebluesquaresaretakenawayfromthesquares,thentheredonesareleft.
(6)Allthebluesaresquares,butonlysomeofthesquaresareblue.These,then,aresomeofthepossible
statementsaboutinclusionrelations—therelationsofthepartstothewhole,ofthewholetotheparts,
andthepartstotheparts.Theymayseemveryobvious,butsodomanyotherprincipleswhichchildren
failtounderstand.
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FIGURE3Classificationofsquaresandcircles.
Piaget investigated the understanding of inclusion relations in children of various ages. Let us
considernowthechildfromabout5to7years.Piagetpresentedeachofhissubjectswithanumberof
picturesof flowersandotherthings.Thechildwasfirstrequiredtogroupthepicturesinanywayhe
wished, and then he was asked a number of questions concerning inclusion relations. The results
concerning spontaneous classification replicatedwhatwas found earlier: the child from5 to 7 years
constructscollectionswhichseemtoinvolveahierarchy.Onechildformedtwolargecollections:flowers
versusotherthings;thenhefurthersubdividedtheflowersintoprimulasversusotherkindsofflowers.
IntermsofFigure4,thechildseemedtohaveconstructedthetoptwolevelsofthehierarchy.(Hedidnot
makeafurthersubdivisionintermsofyellowversusotherprimulas.)Itwouldseemthattheconstruction
ofsuchahierarchyimpliestheunderstandingofinclusionrelations.Ifthesubjectdividedtheflowers
intoprimulasversusotherkinds,musthenotunderstand that therearemore flowers than thereare
primulas? The results of Piaget’s questioning, however, point to different conclusions. Consider this
protocolofachildaged6years2months:
A little girl takes all the yellow primulas andmakes a bunch of them, or else shemakes a bunch of all theprimulas.Whichwaydoesshehavethebiggerbunch?—Theonewith theyellowprimulaswillbebigger. [Hethencountedtheyellowprimulasandtheotherprimulasandfoundthattherewerefourofeachkind]Oh no,it’sthesamething....—Andwhichwillbebigger:abunchmadeupoftheprimulasoroneofalltheflowers?—They’reboththesame.(EGL,p.102)
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FIGURE4Classificationofflowersandotherthings.
Although this child had earlier constructed a hierarchical arrangement of the materials, he
maintainedthattheyellowprimulasdidnotformasmallercollectionthantheprimulasasawholeand
thattheprimulasdidnotformasmallercollectionthantheflowersasawhole.Bothoftheseanswers,of
course,arequitewrong.Inbothcases,thepartissmallerthanthewholefromwhichitderives.
What is the explanation for the child’s inability to comprehend inclusion relations? Piaget
postulates that once the child has divided a whole into two subgroupings, he cannot then think
simultaneouslyintermsofthelargercollectionandthesubdivisionswhichhehasconstructedfromit.
For example, suppose a child divides a collection of flowers (thewhole) into primulas versus other
flowers(subdivisionsofthewhole).Whenheisasked“Aretheremoreprimulasormoreflowers?”he
mustconsiderboththeoriginalcollection(flowers)andoneofhissubdivisions(primulas)atthesame
time.Hemustcomparethe“size”ofoneagainstthatoftheother.Undertheseconditions,hefocusesor
centersonthecollectionhecansee(theprimulas)andignorestheoriginalcollection(alloftheflowers),
whichisnolongerpresent in its initialstate(acollectionoftheprimulasandotherflowersallmixed
together).Andsincehecentersonthepart,ignoringthewhole,hisanswerstoinclusionquestionsare
oftenwrong.
Stage 3
Childrenfromabout7to11yearsofagearebothcapableofconstructinghierarchicalclassifications
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andofcomprehendinginclusion.Forexample,afterconstructingahierarchy,onechildof9yearsand2
monthswasasked:
Whichwouldmakeabiggerbunch:oneofalltheprimulasoroneofalltheyellowprimulas?—Alltheprimulas,ofcourse,You’dbetakingtheyellowonesaswell.—Andalltheprimulasoralltheflowers?—Ifyoutakealltheflowers,youtaketheprimulastoo.(EGL,p.109)
Thisprotocolmakesquiteclearthechild’sabilitytothinksimultaneouslyintermsofthewholeand
itsparts(e.g.,“Ifyoutakealltheflowers,youtaketheprimulastoo”).Whilehephysicallyseparatesthe
flowersintoprimulasandotherkinds,thechildisabletoreasonbothabouttheoriginalwholeandits
part at the same time.His thought hasdecentered from exclusive preoccupationwith the part or the
whole.
Piagetalsofoundthatwhenthechildofthisagewasaskedthesamequestionsabouthypothetical
objects,thesubjectoftenfailedtogivecorrectanswers.Apparently,thechild’sclassificationisconcrete:
he understands the inclusion relations of a group of real objects, but fails to comprehend the same
relationswhenimaginaryclassesareinvolved.Thegapbetweenhypotheticalandconcretereasoningis
anotherexampleofverticaldécalage.
Wemaysummarizebystatingthatthechildfrom7to11hasreachedthemostadvancedstageas
farastheclassificationofconcreteobjectsisconcerned:hecanconstructahierarchicalarrangementand
understand the relations among the levels of the hierarchy. Piaget then proposes that this
accomplishmentcanbedescribedintermsofalogicomathematicalmodel.Letusexplorethisidea.
Rationale for the Use of a Logicomathematical Model
WehaveseenthatPiagetattemptstodescribethebasicprocessesunderlyingtheclassificationof
objectsor events.Heproposes that the stage1 child (2 to4or5years) fails to constructhierarchical
arrangementspartlybecauseafterashortwhileheforgetsthedefiningproperty(intension)whichhe
hasusedtoformacollection.Thestage2child(5to7years)canconstructahierarchybecauseofthe
ability to use a defining property to determinewhich objects go in a collection, but at the same time
cannot understand inclusion relations because of the inability to simultaneously consider several
immediatelypresentcollectionsandthelargeronefromwhichtheywerederived.Thestage3child(7to
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11years)cancorrectlyanswerquestionsconcerninginclusionbecauseofhisabilitytothinkoforiginal
classesandtheirderivativesatthesametime.
Thusfar,wehavedescribedthesebasicprocesses(theabilitytothinksimultaneouslyofsubclasses
andlargerclasses)intermsoftheordinarylanguage.Manypsychologistsbelievethatthisistheproper
procedure;butothers,includingPiaget,feelthatdescriptionsofstructureshouldbephrased,asmuchas
possible,inaformallanguagelikemathematics.
Letusconsiderfirst,however,someaspectsoftheuseofthecommonlanguage.Mostpsychological
theorieshavebeenstatedinthisway.Freud,forexample,wroteexclusivelyinGermanandnotinlogic
nor mathematics, and no doubt there is not a single formula in the entire corpus of psychoanalytic
doctrine.AnotherexamplefromanotherpointonthepsychologicalspectrumisTolman,anexperimental
psychologist,whoproducedhistheoriesoflearninginordinaryEnglishandmadeuseofonlyafew(and
nonessential) symbols.TolmanandFreudarehardly isolatedexamples.Today, too, themajorpartof
psychological theorizing is done in English, or Russian, and so forth. Several advantages are usually
claimedforthisprocedure.Theordinarylanguagemaybericherandsubtlerthanformallanguages,and
alsoitisgenerallyeasiertoreadthanmathematicsorlogic.
However,anotherapproachtothisproblemispossible.Piagetfeelsthatforscientificpurposesthe
ordinary language is fundamentally ambiguous and must be supplemented by formal approaches.
Anyoneevenslightly familiarwith thehistoryofpsychologyknows thatmost, ifnotall,psychological
theories stated in the common languagehavebeenvagueandeasily susceptible tomisinterpretation.
Even today there aremany fruitless arguments over themeaningofwords like “concept” or “ego” or
“learning.”Asanexample,letusconsidertheword“thought,”whichwehaveusedwithoutdefinition
quitefrequently.Nodoubt“thought”meansquitedifferentthingstodifferentreaders.Tosomeitmay
mean “ideas,” and to some “consciousness”; to others it may mean “mental effort,” “meditation,”
“concentration,”“opinion,”andsoforth.Isitanywonderthatagivenpsychologicaltheorywhichuses
words like this will elicit a variety of interpretations and, hence, considerable argument and
misunderstanding?PerhapsaprimeexampleofthedifficultyisPiaget’sownuseofverbaltheoriesinhis
earlywork.Considerableconfusionstillsurroundstheterms“egocentrism,”“moralrealism,”andsoforth.
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Piaget feels, then, that the ordinary language produces obscure and ambiguous psychological
theorizing, andmust therefore be supplemented, if not replaced, by othermodes of description. The
physical sciences have convincingly shown that mathematics is an extremely powerful tool for
communicating certain precise ideas. Piaget—along with increasingly large numbers of other
psychologists—feelsthatitwouldbefruitfulforpsychologytoadoptasimilarapproach,andhehimself
has attempted to do so in the case of classification and othermatters. Let us now explore his formal
descriptionofthestructureofclassification.
FIGURE5Classificationhierarchy.
Grouping I
The formal description called a Grouping3 begins with this situation: we have a classification
hierarchyofthesortconstructedbythe7-to11-year-oldchildreninPiaget’sexperiments(seeFigure5).
Thisiswhatwestartwith(thatis,itisagiven)andtheGroupingdescribeswhatthechildcandowith
thehierarchy.Atthetopofthehierarchythatthechildhasconstructedarethetwoclasses,flowerswhich
weshallsymbolizeas(C)andotherthings(C').Onthemiddlelevelofthehierarchywefindprimulas
(B)andotherflowers(B').Onthelowestlevelthereareyellowprimulas(A)andprimulasofothercolors
(A').Eachoftheclasses(A,A',B,B',C,C')isanelementofthesystem.Thereisonebinaryoperatorthatmay
beappliedtotheelements,namely,combining.Wewillsymbolizecombiningby+,althoughthereader
shouldbeawarethatcombiningclassesisnotpreciselyequivalenttoaddingnumbers.Theoperator+is
binarysinceitcanbeappliedtoonlytwoelementsatatime.Justaswecanaddonlytwonumbersatany
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onetime,sowecanonlycombinetwoclassesatatime.
Given theelements and thebinaryoperator, the fiveproperties describe theways inwhich the
operatormaybeappliedtotheelements.
Thefirstpropertyiscomposition(usuallyreferredtoinmathematicsasclosure)whichstatesthat
whenwecombineanytwoelementsofthesystemtheresultwillbeanotherelementofthesystem.For
example,ifwecombinetheyellowprimulaswiththeprimulasofothercolors,wegetthegeneralclassof
primulas.ThismaybewrittenasA+A'=B.Orifwecombinetheyellowprimulaswithalltheprimulas,
wegetall theprimulas.WemaywritethisasA+B=B.Thispropertydescribesaspectsofthechild’s
abilitytounderstandahierarchy.Forexample,hecanmentallyconstructalargerclassbycombiningits
subclasses.
Thesecondpropertyisassociativity,whichmaybestbeillustratedinaconcretemanner.Suppose
we want to combine three classes such as yellow primulas, primulas, and flowers (A, B, and C,
respectively). Remember thatwe cannot just add all three of them together simultaneously since the
operator (combining) is binary; that is, it can be applied to only two elements at a time. Given this
limitation,thereareatleasttwowaysofaddingA,B,andC.Wemightfirstcombinetheyellowprimulas
andtheprimulasandgetprimulas.Thatis,wedoA+B=B.Thenwemightcombinethisresult(B)with
flowers-in-general(C)andgetflowers-in-general.Thus,wedoB+C=C.Tosummarize,wefirstperform
A+B=BandthenB+C=CsothatourfinalresultisC.Anotherwayofstatingthisis(A+B)+C=C.
There is yet a second way of combining the classes. We could start by combining the yellow
primulas(A)withthecombinationofprimulasandflowersingeneral(B+C)andfinishwiththesame
result:flowers-in-general,(C).ThuswecanwriteA+(B+C)=C.Notethatthefinedresultofperforming
theoperationbyeithermethodisC,sothatthetwomethodsmaybeconsideredequivalent.Wemaywrite
thisequivalenceas(A+B)+C=A+(B+C).Thisequationexpressesthefactthatthechildcancombine
classesindifferentordersandcanrealizethattheresultsareequivalent.
The third property is identity, which states that there is a special element in the system (the
“nothing” element), that produces no changewhen combinedwith any of the other elements. If we
combine the nothing elementwith the yellowprimulas the resultwill be the yellowprimulas. Ifwe
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symbolize nothing by 0, thenwe have A + 0 = A.More concretely, if we do not combine the yellow
primulaswithanyoftheotherclasses,then,ofcourse,westillhavetheyellowprimulas.
Thefourthpropertyisnegationorinverse,whichstatesthatforanyelement(class)inthesystem,
thereisanotherelement(theinverse)thatproducesthenothingelementwhencombinedwiththefirst
element.Thatis,ifweaddtotheclassofyellowprimulasitsinverse,thenweareleftwithnothing.The
inverseisequivalenttotheoperationoftakingawaythesameclass.Ifwestartwithyellowprimulasand
combinewiththisclassitsinverse,weareineffecttakingawaytheyellowprimulaswiththeresultthat
weareleftwithnothing.WecanwritethisasA+(-A)=0orA-A=0.Theinverserulemightapplytoa
trainofthoughtlikethis:“SupposeIcombinetheyellowprimulaswithalloftheotherprimulas.ThenI
havealloftheprimulas.ButifItakeaway[inverseornegation]alloftheotherprimulas,thenIamleft
again just with the yellow primulas. ’ ’ Note how this train of thought is reversible. First, the other
primulasareadded,butlatertheyaretakenaway,sothatthethinkerisonceagainatthepointwherehe
started.Negation,then,isonekindofreversibility.
Theinversealsomaybeusedtoexpressaspectsofclassinclusion.Supposewestartwiththeclassof
primulas (B) and take away (or add the inverse of) the primulas which are not yellow (A'). This
operationleavesuswiththeyellowprimulas(A).WemaywritethisasA=B+(-A')orA=B-A'.Thistype
ofreasoningunderliesthechild’sabilitytosaythattherearemoreprimulasthanyellowones,thatthe
yellowprimulasareincluded intheclassofprimulas,orthattheyellowprimulasareonlysomeofthe
primulas.
Thefifthpropertyactuallyencompassesseveralaspects.Oneofthemisrelatedtospecialidentity
elements.Supposewecombinetheclassofyellowprimulaswithitself.Theresultisyellowprimulas.We
maywritethisasA+A=A.Inthisequation,Afunctionsasanidentityelementlike0.AddingAtoAislike
adding0toA:theresult,A,isunchanged.Piagetcallsthistautology.Anotheraspectisresorption.Ifwe
combinetheclassofyellowprimulaswiththeclassofprimulas,theresultisprimulas.Wemaywritethis
asA+B=B.Here,too,Afunctionsasanidentityelement.AddingAtoBislikeadding0toB;theresult,B,
isunchanged.Inasense,thisisanotherwayoflookingatinclusionrelations.Theyellowprimulasmust
be includedintheclassofprimulas(ormustbesomeoftheprimulas)sinceaddingtheformertothe
latterdoesnotchangethelatter.
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These,then,aresomeoftheaspectsofGroupingIandareintendedasaformaldescriptionofthe
processes underlying the child’s classification. The model involves elements (classes), the binary
operatorofcombining,andfivepropertiesgoverningtheapplicationoftheoperatortotheelements.
Discussion of Grouping I
AfewgeneralremarksshouldbemadeconcerningGroupingI.First,Piaget’suseofmathematicsis
notatallmeanttoimplythatthechildunderstandsthelogicomathematicalmodelinanyexplicitsense.It
is obvious thatmost children have never heard of the special identity element, let aloneGrouping I.
Clearly,thechildisnotamathematicianatthislevel.Infact,heoftencannotdescribeinanyclearway,
mathematicalorotherwise,hisprocedureforsolvingaparticularproblem.Hisreportisoftenincoherent.
Piagetusesthelogicomathematicalmodel,therefore,nottocharacterizethechild’sconsciousness,butto
describetheprocessesunderlyinghisclassification.
Second,GroupingIisnotmetricallyquantitativeinthesensethatitdoesnotinvolvenumbers.The
operations involve classes whichmay be of any size. It does notmatter whether there are 5 yellow
primulasand6whiteones,or5,000yellowprimulasand300whiteones.Inbothcasestherearemore
primulasthantherearewhiteprimulas,andsoforth.
Third,wemayexpandonourearlierpointthattheGroupingisintendedtodescribethestructure
ofthechild’sclassification.Piagetisnotinterestedintheminordetailsofthechild’sperformance;thatis,
whetherheisclassifyingflowersorfishorwhetherhefirstputtheflowersinanarrangementandthen
theanimals.Piaget insteadattempts tocapture theessenceof thechild’sactivitiesand to identify the
processesunderlyingthem.TheGroupingisPiaget’swayofdescribingtheseprocessesinaclearway.
Therefore,theGroupingisnotsimplyaprotocol listingeverythingthatthechilddoes. It is insteadan
abstractionwhichdescribesbasicprocessesliketheabilitytocombinementallytwosmallerclassesintoa
largerone,ortotakeawayoneclassfromanother.
The grouping also is a comprehensive and integrated structure. It is comprehensive since it
describes the processes underlying basic classification activities. The Grouping describes the
potentialities of the child, and not necessarilywhat he does in any one task at any one time. Let us
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suppose that a child constructs a hierarchy of classes. In doing so hemay notmake use of inclusion
relations.Inthiscase,theGroupingdoesnotsomuchdescribewhatthechildactuallydoes,butwhathe
iscapableofdoingundertheproperconditions.
Also,theGroupingisanintegratedsysteminthesensethateachofthepropertiesdoesnotstand
alonebut isrelated toallof theothers.Onthemathematical level, this iseasy tosee.Thepropertyof
associativitydescribestheorderinwhichelementsmaybecombined,butthepropertyofcompositionor
closure is needed to interpret the result of the associative combination. In other words, associativity
showsthattwodifferentordersofcombiningelementsareequivalent,andcompositionrevealsthatboth
oftheseordersofcombinationresultinanotherelementwhichmustbeinthesystem.Thus,theproperty
ofassociativitywouldbemeaninglesswithoutthepropertyofcomposition.Wecannothaveoneproperty
withouttheother.ThisfeatureoftheGroupingis,ofcourse,intendedtoreflectanimportantaspectofthe
child’s activities: the child’s successful classification (including the understanding of inclusion)
presupposes an interrelatedwhole, a structure of mental operations. For example, suppose the child
recognizesthattherearemoreprimulasthanyellowprimulas.Thisachievement impliesanumberof
interrelatedmentalacts.
Thechildmustbeawarethattheprimulas(whicharenolongerpresentinasinglecollection)are
thecombinationofyellowprimulasandprimulasofother colors (A+A'=B).Thechildmustalsobe
aware thatwhenyellowprimulasare takenaway from theprimulas, there remainprimulasofother
colors(B-A=A').These, then,aresomeoftheoperationsunderlyingthechild’sanswertoaquestion
concerninginclusion.Whenthechildcorrectlyanswersthequestion,hemaynotfirstactuallyperformall
theseoperations.However,theyareimplicitinhisanswer;hecouldnotanswercorrectlyifitwerenot
possibleforhimtoperformalltheoperationsinvolvedintheclassificationsystem.Tosummarize,any
particularresponsethatthechildmakestoaclassificationproblemcannotbeconsideredinisolation.His
responsepresupposesacomplexstructure,and it is thiswhichPiagetdescribesas theGrouping.The
Grouping,inotherwords,describesthementaloperationswhichmakeitpossibleforthechildto“really”
understandclassification.
Fourth, the Grouping explains and predicts behavior. Insofar as the Grouping describes the
processes underlying the child’s classification, it may be said to explain performance. The Grouping
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statesthatthechildcancombinetwoclassestogetalargerone.Thisoperation,amongothers,underlies
thechild’sabilitytounderstandinclusionrelationsandinthissenseexplainsit.InsofarastheGrouping
isgeneral itmaybesaidtopredictbehavior.TheGrouping isnot limitedtotheobjectsPiagetusedto
studyclassification.BecausetheGroupingprovidesadescriptionofstructure,itgoesbeyondthedetails
ofanyparticularproblemandallowsustopredictwhatthechild’sperformanceislikeonothersimilar
tasks.
Fifth,PiagethasdescribedseveralotherGroupingsallofwhichareintendedtorefertothechild’s
ability(from7to11)todealwithconcreteobjectsorthoughtaboutthem.Therefore,stage3istermed
concreteoperational.
Sixth,towardtheendofhislife,PiagetbegantofeelthattheGroupingmodelisnotfullyadequate
as an account of the concrete operations. While the facts concerning children’s performance on the
classificationtasks(andothersaswell)remainaswellestablishedasever,theGroupingmodelsuffers
fromseveraldeficiencies.“[TheGrouping]model...hasgeneratedlittleenthusiasmfromlogiciansand
mathematiciansbecauseof itsunavoidable limitations . . . and consequent ‘lackof elegance’ ” (Piaget,
1977b).(Indeed,onemightevengofurtherandclaimthatthelogicofthemodelisnotonlyinelegant,
butnotentirelycoherent.)“[TheGroupingmodel]...wastoocloselylinkedtothetraditionalmodelof
extensional logic and truth tables” (Piaget, 1980, p. 5, quoted in Beilin, 1985). In view of these
limitations, Piaget felt it is necessary to develop new formal models to characterize the essence of
concrete operational thought. “Abetterway, I nowbelieve, of capturing thenatural growthof logical
thinkinginthechildistopursueakindoflogicofmeanings”(Piaget,quotedinBeilin,1985b).While
Piagetdidnothave the time todevelopsuchmodels indetail,hebegan theeffortby introducing the
notion of “correspondences,” which we describe in our discussion of pre-operational strengths. It is
importanttorealize,asBeilinpointsout,“thatPiagetwasnotirrevocablycommittedtoaparticularlogic
or abstract model; consequently, following Piaget’s example, others are free to [select] the logical or
mathematicalmodelsthatbestexplainthedataofcognitivedevelopment”(Beilin,1985,p.112).
Inbrief,Piagetbelievedthatwhilethinkingisbestdescribedintermsof logicalmodels,hisown
effortsinthisareawerenotentirelysuccessful.Henceitisnecessarytoexpandthetheorybydeveloping
newmodels.AsPiagetclaimed,hehimselfwasthechief“revisionist”ofPiagetiantheory.
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Summary and Conclusions
Piaget’searlywork(inthe1920sand1930s)dealtwithclassificationinapreliminaryway.Inthe
1950shereturned to theproblem,using therevisedclinicalmethod.Hepresented2- to11-year-old
childrenwithanarrayofobjectstobeclassified.Thefindingswerethatinstage1(2to5years)thechild
fails to use consistently a clear rule or defining property to sort the objects into different classes. He
insteadconstructsgraphiccollectionswhicharesmallpartialalignmentsorinterestingforms.Instage2
(5 to 7 years), the child sorts the objects by a reasonable defining property and even constructs a
hierarchical classification, but fails to comprehend inclusion relations. Stages 1 and 2 are termed
preoperational.Instage3,whichisconcreteoperational(7to11years),thechildhasamaturenotionof
class, particularly when real objects are involved. The child sorts them by defining properties,
understands the relations between class and subclass, and so forth. To describe clearly the processes
underlyingthechild’sactivities,PiagetproposesalogicomathematicalmodelwhichhecallsGroupingI.
ThisGroupinginvolvessomeelements,abinaryoperator,andfivepropertiesrelatingtheoperatortothe
elements.Also,theGroupingisnotmetricallyquantitativeinthesensethatitdoesnotmatterhowbigor
small(innumericalterms)arethevariousclassesinvolved.Thechild,ofcourseisnotconsciousofthe
Grouping; rather theGrouping is intended todescribe thebasic structuresofhis activities. Inhis last
years,Piagetrecognizedtheshortcomingsof theGroupingmodelandproposedthedevelopmentofa
new“logicofmeanings.”
Piagetstressesthattheagenormsdescribingclassificationareonlyapproximate.Aparticularchild
maypassfromstage1tostage2at6yearsandnotnecessarilyat4or5years.Onechildmayspendthree
years in stage 1while another childmay spend four years in the same stage. Piaget doesmaintain,
however,thatthesequenceofdevelopmentisinvariant.Thechildmustfirstbecharacterizedbystage1
before he can advance to stage 2 and then to stage 3. Piaget also points out that a child may not
necessarilybe inthesamestageofdevelopmentwithrespecttodifferentareasofcognition.That is,a
childmaybeinstage1withrespecttoclassification,andinstage2ofnumberdevelopment.Thus,achild
maybeslightlymoreadvancedinsomecategoriesofthoughtthaninothers.
Oneimportantissueregardingclassification,andindeedalltheconceptsstudiedbyPiaget,isthe
generalityofthefindingsforchildrenindifferentcultures.Recently,muchcross-culturalworkhasbeen
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carriedouttodeterminewhetherchildrenindifferentculturesemploythetypesofreasoningdescribed
byPiaget, andwhether the sequenceof stages is invariant across cultures, asPiagetproposes.Opper
(1971;andinDasen,1977)hasexaminedanumberofPiagetianconcepts,includingclassification,in
rural and urban children in two Southeast Asian countries, Thailand andMalaysia. Likemany other
investigators(forareview,seeDasen,1977),Opperfindsthatalthoughtheagesmayvary,thesequence
ofdevelopmentisthesameindifferentcultures:first,Thaichildrenarecharacterizedbystage1,then
stage2,andsoon.
Moreover, Opper finds that Thai andMalaysian children present responses similar to those of
Swisschildren.Forexample,whenaMalaysiangirlinstage2ofclassificationwasaskedwhetherthere
aremorerosesorflowersinabunchofsevenrosesandtwoorchids,sheresponded,“Therearemore
roses than flowers.” The examiner said, “Show me the flowers.” The child then pointed to the two
orchids.
AThaiboy,inthesamestage,waspresentedwithsevenrosesandtwolotus.He,too,maintained
thattherearemorerosesthanflowers.Moreroses.—Morethanwhat?—Morethanflowers.—Whatarethe
flowers?—Roses.—Are there any others?—There are.—What?—Lotus.—So in this bunch, which is
more,rosesorflowers?—Moreroses.—Thanwhat?—Thanlotus.
Turningtothestage3child,wealsofindthesameresponsesastheSwisschildren.Forexample,a
Malaysiangirlsaid:Therearemoreflowersbecauseifit’sroses,it’sonlythese[pointingtoroses],butthe
flowersareplus thesealso [pointing to orchids].We see then that inmany casesThai andMalaysian
children’sargumentsarevirtuallyidenticaltothoseofSwisschildren.
How can we evaluate Piaget’s work on classification? On the one hand, Piaget has been very
successfulatwhathehasattemptedtodo.Anumberofindependentinvestigatorshaveconfirmedthat
stage1classificationtakesunusualforms(e.g.,Vigotsky,1962),thatyoungchildrenexperiencegenuine
difficulty with class inclusion (Klahr andWallace, 1972), and that the course of development with
respecttoclassificationisgenerallyasPiagethasdescribed(Kofsky,1966).Ontheotherhand,itshould
bepointedoutthatPiaget’sapproachtoclassificationisofaveryspecificsort.Hefocusesmainlyonthe
hierarchicalstructureofclasses,forexample,classinclusion.Heisnotparticularlyconcernedwithother
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aspectsof conceptswhichnowseemtobequite important.ThusNeisser (1967)haspointedout that
everyday concepts are often vague and difficult to define, and Rosch (1973) has developed a new
approachfocusingonnonlogicalaspectsofchildren’sconcepts.Thedefiningpropertyorintensionofa
classisoftenquitevague,aparticularobjectmayfitintoseveralclassessimultaneously,theboundaries
betweenclassesmaybe fuzzy,and itmaynotbepossible to formasimplehierarchy. Inbrief,Piaget’s
approachfocusesononlyoneofmanyimportantaspectsofclasses.
RELATIONS
In Chapters 2 and 3 we have already reviewed several aspects of relations, a problem (like
classification)withwhichPiagethasbeenconcernedsincehisearliestworkinpsychology.Wesawthat
in the sensorimotor period the infant displays precursors of relations. He can broadly discriminate
withinthedimensionsofnumerosity,intensityofmusculareffort,andloudnessofsounds(amongother
dimensions).Inthecaseofnumerosity,youwillrecallthatLaurentsaid“papa”whenPiagetsaid“papa,”
thatLaurentsaid“bababa”whenPiagetsaid“papa-papa,”andthatLaurentsaid“papapapa”inresponse
to “papapapapapapa.” Laurent’s imitation, although not exact, nevertheless implies an ability to
discriminateorhearthedifferenceamongseveralsoundswhichdifferedinnumberofrepetitionsofone
syllable.Similarly,inthecaseofmusculareffort,Laurentappearedabletodetectthedifferenceamong
thevariationsinvigorwithwhichheswungachain,andalsohewasabletodiscriminateamongsounds
ofdifferentdegreesofloudness.Thus,theinfantcandifferentiategradationswithindifferentkindsof
stimuli:somethingsarelouderthanothers,ormorenumerous,orbigger,andsoforth.Hecanperceive
differencesinvariousaspectsofhisworld.Theabilitytomakesuchdiscriminationsisaprerequisitefor
reasoningaboutdifferences.
Piaget’s early research on the child from about 5 to 10 years investigated reasoning about
differences, but not the perception of differences. He presented children with this verbal problem
(amongothers):“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichisthe
darkest,Edith,Suzanne,orLili?”{JudgmentandReasoning,p.87).Theresultsshowedthatchildrenfrom
5to10yearsareunabletodealwithproblemsofthissort,calledtransitivity,ataverballevel.
Asinthecaseofclassification,Piagetreturnedtotheproblemofrelationsinhislaterwork.Using
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therevisedclinicalmethod,heperformedseveralinterestingstudiesonordinalrelations,whichwewill
nowcharacterizebriefly.
Some Properties of Ordinal Relations
Piaget’sdefinitionofordinalrelationsinvolvesseveralfeatures.Supposewehaveseveralnumbers,
suchas17,65,25,3,and1,0OI.Itispossibletoarrangetheminorderofincreasingsize.Wemayusethe
symbol<tostandfor“isasmallernumberthan”andwrite3<17<25<65<1,0OI.Thesequenceisan
orderingofthenumberswiththesmallestbeingfirst,thenextsmallestsecond,andsoforth.Notethatthe
absolutesizeofthenumbersmakesnodifference.Thesecondnumberdoesnothavetobeexactlyone
morethanthefirstorexactlytwiceasbigasthefirst.Thelastnumber,solongasitislargerthan65,may
beofanysizewhatsoever.Also,wedonotneedtohavezeroas thebeginningof theseries.Theonly
requirements forordering thenumbersare that theyaredifferent fromoneanother, thatat leastone
numberissmallerthantherest,thatanotherislargerthanalltherest,andthatanynumberinbetween
thesmallestandthelargestisbothlargerthantheoneimmediatelyprecedingitintheseriesandsmaller
than the one immediately following it. Of course, orderings are not limited to numbers.Wemay also
ordersoundsonthedimensionofloudness.Supposesoundaisverysoft,bismuchlouderthana,andc
isslightlymoreloudthanb.Thenwehavea<b<c,where<means“issofterthan.”Againtheprecise
degreeofloudnessdoesnotaffecttheordering.
Piaget’s work deals with such matters as the child’s ability to construct orderings or ordinal
relationsandtomanipulatetheminvariousways.Thesestudies,involvingchildrenfromabout4to8
yearsofage,usuallydetectthreedistinctstagesofdevelopment:stage1lastingfromabout4to5,stage2
fromabout5to6,andstage3fromabout7andabove.Thefirsttwostagesarepreoperational,andthelast
isconcreteoperational.Whiletheagenormsareapproximate,thesequenceiscrucial.
Stage 1
Onestudywasconcernedwiththeabilitytoconstructanorderingofacollectionoftenstickswhich
differedonly insize.Wewillcall theshortestof thesticks(about9centimeters in length)A, thenext
largerB,andsoonthroughJ,thelargest(about16centimetersinlength).AdifferedfromBbyabout.8
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centimeters,andthisalsowastrueofBandC,andsoon.Piagetpresentedthechildwiththesticksina
randomlyorganizedarrayandaskedhimtoselectthesmallestofthelot.Afterthiswasdone,Piagetgave
aninstructionlikethis:“Nowtrytoputfirstthesmallest,thenonealittlebitbigger,thenanotheralittle
bitbigger,andsoon”(Child’sConceptionofNumber,CCN,pp.124-25). Inanotherstudythechildwas
askedtomakeastaircasefromthesticks.
Whenconfrontedwiththisproblem,childreninstage1showedseveredreactions,noneofwhich
wassuccessful. Somechildrenproducedrandomarrangementsof the sticks, likeH,E,B, J, and so on.
Otherchildrenmanagedtoorderafewofthesticks,butnotallofthem.AnexampleofthisreactionisA,B,
C,D,H,F,E,andsoon.
Anotherstrategywastoplacethelargersticksinonecollectionandthesmallersticksinasecond
collection.Withineachofthesecollections,however,thestickswereinarandomorder.Amoreadvanced
reactionalsoappearedwhichmaybeconsideredatransitiontothenextstage.Thechildstartedwith
somestick,likeB,apparentlyselectedatrandom;thenhetookanotherstick,likeH,andmadethetopofit
extendslightlyabovethetopofB;athirdstick,forexample,A,wasmadetoextendslightlybeyondthe
topofB;andsoforth.Theresultwasthatthetopsofthesticksformanordering;Hisslightlyhigherthan
B,andAslightlyhigherthanH,andsoforth,asinFigure6.Butthebottomsofthesticksalsodifferedina
randomway,andfailedtolieonastraightlineastheyshould.Thus,thechildconstructsanordering,but
onlybyignoringthelengthofeachstick.Thisprocedurefreeshimfromthenecessityofcomparingeach
stickwiththeoneimmediatelyprecedingitandwiththeonetofollow.Onewayofcharacterizingthese
activitiesistosaythatthechildfocuses(centers)ononeaspectoftheproblem(puttingthetopsinorder)
butignoresanother,equallyimportantaspect(arrangingthebottomsinastraightline).Tosummarize,
thechildatthisstagefrequentlycannotformasystematicorderingofanynumberofobjectsalthoughhe
issometimesabletoorderafewofthem.
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FIGURE6Orderingofsticks.
Stage 2
Presentedwiththesameproblem,childreninthesecondstagegenerallysucceedinconstructing
theordinalarrangementofsticks,sothatA<B<C<D<E<F<G<H<I<J.Butthechilddoesnotbuildthe
orderingswithout difficulty. Sometimes he begins by ignoring the bottomsof the sticks, as in stage 1.
Sometimeshemakesmanyerrors,likeA<D<B,andsoon,andtakesalongtimetorecognizeandcorrect
them.Thechildcontinuallyrearrangeshisordering,andshiftsthesticksfromonepositiontoanother.
Essentiallythechild’sprocedureisoneoftrialanderror,lackinganoverallplanorguidingprinciple.
Forexample,ifhehaschosenAasthesmallest,hemightthenchooseanothersmallone,like
D,andlineitupnexttoA.Thenhemightchooseanothersmallone,likeC,andplaceitnexttoDand
seethatitissmallerthanD.Sincethisisso,hemightrearrangethesticksplacingCafterAbutbeforeD.
AfterbeginningwithA,thechildfailstolookforastickthatislongerthanAbutsmallerthanalltheones
remaining. If this rule is followed, then each step of the ordering can be constructed without any
difficulty.However, thechildat this stagedoesnotemploysucha logicalprocedure.He fails tomake
systematic comparisons between a given stick and the one immediately preceding it and all those
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following.
This tendencywas furtherrevealedby theadditionofonemoreproblem.Afterconstructing the
orderingAthroughJ,thechildrenweregivenanewcollectionoftensticks,a,b,c,d,e,f,g,h,i,j.Eachof
thesenewstickscouldfitinbetweenapairofsticksofthefirstseries.Thatis,ifthenewsetofstickswere
orderedcorrectlyalongwiththefirstset,thearrangementwouldbeA<a<B<b<C<c<D<d<E<e<F<
f<G<g<H<h<I<i<J<j.Thechild’staskwastodopreciselythis;tofitthenewsticksintotheordering
alreadyconstructed(AthroughJ),soastomakeanewordinalarrangementinvolvingalltwentysticks.
Childrenofthisstagehadgreatdifficultywiththeproblem.Infact,manyfailedtosolveit.Partof
one child’s orderingwasC e d D, and another producedH g G I h j c, and so forth. Other children
succeededinproducingthecorrectordering,butonlyafterconsiderabletrialanderror.
Thesedifficultiesseemduetoseveralfactors.Onefactorappearstobethatthechildperceivesthe
originalseriesasawholeandfindsithardtobreakuptheseriesintosmallerunits.Also,childrenofthis
stagedonotapproachtheproblemwithaguidingprinciple.Theyfailtousearulelike,“Startwiththe
smallestofa-j)insertitinbetweenthepairofthesmalleststicksinA-J)thentakethesmallestofb-jand
insertitbetweenthesmallestpairofsticksinB-J)andsoforth.”Notonlydidthechildrenfailtousearule
likethis,buttheyalsohaddifficultyindecidingthatagivenelementofa-jwasatthesametimebigger
thanonestickinA-JandsmallerthanthenextlargerstickinA-J.Toplacedproperly,thechildmustsee
thatd<EandthatD<d.Hemustcoordinate thesetworelationsbutfailstodosoconsistently.That is,
somechildrenwouldtakeeand,seeingthatitwaslargerthanB,wouldplaceitrightafterB.Theyfailed
toconsiderwhetherewasatthesametimesmallerthanC,andthereforemadeanerror.
Afterinvestigatingthechild’sabilitytoconstructanorderingandplacenewelementsinit,Piaget
wenton to study the child’s ability to construct equivalencesbetween two separateorderings (which
involveequalnumbersofelements).Toillustratethis,letustakeaclasswithfifteenboysandfifteengirls
andordereachofthesegroupsintermsofheight.Wefindtheshortestboy,thenext-to-shortestboy,and
soon,andwedothesameforgirls.Wecanseethatthetwoorderingsareequivalentinsomewaysand
differentinothers.Somedifferencesarethattheheightoftheshortestboymaybe48inches,whereasthe
height of the shortest girl is 44 inches. Also, the second shortest boymay be 4 inches taller than the
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shortestone,whereasthesecondshortestgirlisonly1inchtallerthantheshortestgirl.Despitethese
realdifferences,thereareimportantsimilaritiesbetweenthetwoorderings.Theboywhois48inches
tallandthegirlwhois44inchestall,despitetheirdifferenceinheight,areequivalentintermsoftheir
positionintheordering.Theyareboththeshortest.Thesameholdstrue,ofcourse,forthetallestboyand
girl,thenexttotallest,andsoforth.
Piagetthenraisesthe issueofwhethertheyoungchildcanrecognizetheequivalencesbetween
twodistinctorderings.Doesheunderstandthattwoobjects,whiledifferinginheight,forexample,canat
thesametimebeequivalentintermsoftheirrelativepositioninanordering?Tostudythematterhefirst
presentedchildrenwithtendolls,A-J,whichwerepresentedinarandomdisplayandwhichcouldbe
arrangedinorderofheight;andwithtensticks,A'-J',alsorandomlyarranged,whichcouldbeorderedin
size.Thesticksweresmallerthanthedolls,andthedifferencesbetweenadjacentpairsofstickswere
smallerthanbetweenpairsofdolls.Thechildwastoldthatthedollsaregoingforawalkandthateachof
themmust have the proper stick. The intention of the instructions, of course,was to get the child to
produceanorderingofthedollsandofthesticksandtomakeeachmemberofoneorderingcorrespond
totheappropriatememberoftheotherordering.Thus,dollAshouldhavestickA',dollBshouldhave
stickB',andsoon.Piagetcallsthisprocesstheplacingoforderingsintoone-to-onecorrespondence.
Theresultsshowedthatchildrenofthisstagecanproduceaone-to-onecorrespondenceofdolls
andsticks,butonlyinatrial-and-errorfashion.Themostcommonprocedureistoorderthedolls(bytrial
anderror)andthentoorderthesticks(bytrialanderror).Onlyaftertwoseparateorderingshavebeen
constructedaretheelementsofeachputintoone-to-onecorrespondence.Thatis,thechildfirstidentifies
thelargestdoll,thenexttolargestdoll,andcompletestheorderingofdolls;thenhegoesontoorderthe
sticks.Itisonlyafterthisisdonethatthechildplacesthelargeststickwiththelargestdoll,thenextto
largest stick with the next to largest doll, and so forth. While this procedure works, it is somewhat
cumbersome.Aneasiermethodistobeginbyidentifyingthelargest(orsmallest)dollandthelargest(or
smallest)stickandimmediatelyplacingthetwotogether.Thesecondstepistochoosethe largestdoll
andstickofallthoseremainingandtoplacethemtogether,andsoforth.Inanyevent,thechildinthis
stage does succeed in setting the two orders into one-to-one correspondence. He seems to have
establishedthattheorderingsareequivalent.
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FIGURE7Theequivalenceofrelativeposition(dollsandsticks).
The next problem concerns the stability of the equivalence established by one-to-one
correspondence.Letussupposethatthesticksareplacedveryclosetogetherwiththeirorderpreserved
(asinFigure7).Theshorteststickisclosesttothethirdtallestdoll,thesecondstickisclosesttothefourth
tallestdoll,andso forth.Doesthechildrecognizethat thesecondtalleststick isstill equivalent to the
secondtallestdoll,eventhoughtheformerisnowclosesttothefourthtallestdoll?Thatis,doesthechild
conservetheequivalenceofrelativepositionwhentheovertone-to-onecorrespondenceisdestroyed?
Piaget presented this and similar problems to a number of children. He placed the sticks close
togetherandaskedwhichstick“goeswith”whichdoll.Piagetdiscoveredseveredmethodsofattacking
theproblem.Themostprimitivereactionistoassertthatadollisequivalenttothestickclosesttoit.Thus,
thesecondlargeststickandfourthlargestdollareconsideredtobelongtogethersimplybecauseoneis
belowtheother.Thechild’sjudgmentisdominatedbyspatialrelations.Otherchildrentrytosolvethe
problembycounting,buttheyfailtodosoproperly.Forexample,onechildsaidthatthefourthlargest
stickwasequivalenttothethirdlargestdoll.Thereasonforhismistakewasthathenoticedthatthere
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werethreesticksprecedingthefourthlargeststick;hethencountedoutthreedolls,stoppedthere,and
identifiedthethirddollwiththefourthstick.Thismethodisquitefrequentamongchildrenofthisstage;
thatis,theyfindadollcorrespondingtothenthstick,countingtheprecedingn-1sticks,thencountthe
dolls,stoppingatthen-1thelement.Thechildconfusesthepositiontobefound(say,stick4)withthe
numberofprecedingelements(3).
Stage 3
Afterabouttheageof6-7years,thechildissuccessfulinallofthetaskswehavedescribed.When
askedtoconstructasingleorderingofsticksdifferinginsize,thechilddoessoquiteeasily.Theordering
isguidedbyanoverallplan.Thechildusuallybeginswiththesmallest(orsometimes,withthelargest),
then thenext smallest, and so forth, in sequenceuntil theordering is complete.This strategymaybe
characterizedasstartingwiththesmallestandcontinuingtotakethesmallestofeverythingthatisleft,
untilthestickshavebeenexhausted.Whenaskedtoplaceadditionalsticks(a-j)intheirproperpositions
within the ordering (A-J) already constructed, the child does so with almost no errors. The process
underlyingthisachievementisthecomparisonofoneofthenewsticks(say,d)withtwointheoriginal
orderingsimultaneously.That is, toascertaind'sproperposition, thechilddeterminesthat it isat the
sametimebiggerthanDbutsmallerthanE.Tophrasethematterdifferently,hecoordinatestwoinverse
relations—biggerandsmallerthan.
Inasimilarwaytheconcreteoperationalchildeasilyplacestwoseparateorderingsintoone-to-one
correspondence.Onechildimmediatelyputthebiggestdollwiththebiggestball(ballsweresometimes
usedinplaceofsticks),thenexttobiggestdollwiththenexttobiggestball,andsoforth.Hisstrategywas
to identify thebiggestdollandballofall thoseremainingand toplace the twotogetheratonce.This
procedureismoreeconomicalthanthatoftheyoungerchildwhofirstordersthedolls,thentheballs,
and finallybegins toput them together.When thisone-to-onecorrespondence isdestroyed, thechild
conservestheequivalenceofrelativeposition.Herealizesthatthesmallestdollisstillequivalenttothe
smallestballandnottotheballtowhichithappenstobeclosestinspace.
Insummarizingthematerialontheconcreteoperationalchild,then,wecanstatethatheisadeptat
understanding and manipulating ordinal relations. However, as in the case of classification, one
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limitation applies: he can deal with relations on a concrete level only; that is, when real objects or
thoughtsaboutthemareinvolved.Nevertheless,histhoughtisfarmoreadvancedthanthatofthechild
in stages 1 and 2. The child can construct orderings, put two such orderings into one-to-one
correspondence,andconservetheresultingequivalences.Asinthecaseofclassification,theprocesses
underlying the child’s ability tomanipulate relations form integrated and comprehensive structures.
Each of his mental operations cannot be understood without reference to the others of which he is
capable. These processesmust be interpreted in terms of complex systemsof operations. To describe
thesesystems,Piagethasdevelopedseverallogicomathematicalmodels,similartoGroupingI(although
they,of course,deadwithrelations,notclasses).Also,Piagethas investigatedseveralotheraspectsof
ordinalrelations,suchastransitivity(ifa>bandb>c,thena>c),whichwewillnotcoverhere.
NUMBER
Theabilitytounderstandclassesandrelations,accordingtoPiaget,isbasictomatureconceptsin
many areas. The several groupings which describe the processes underlying the older child’s
performance in problems of classes and relationsmay also be used to characterize concepts of space,
chance,geometry,andsoforth.Sincewecannotreviewall theseconcepts,wewillconcentrateonone
thatisparticularlyinterestingandthathasreceivedconsiderableattentionintheAmericanandBritish
researchliterature,namely,theconceptof(whole)number.
First,wemustunderstandwhatPiagetdoesanddoesnotmeanbytheconceptofnumber.Hedoes
notmean and isnot interested in computational abilities as taught in the first few grades of school.
Whetherthechildcanadd2and2,orsubtract3from5,isnottheissue.ThereasonforPiaget’slackof
interest in thesematters is that simple addition and subtraction of whole numbers, aswell as other
manipulationsof them,canbecarriedoutentirelybyroteandwithoutunderstanding.Thechildcan
simply memorize the addition and subtraction tables and fail to comprehend the basic concepts
underlyingthem.Piagetdoesnotdenythatitisusefultomemorizethefactsofadditionandsubtraction;
for purposes of computation, we all find it helpful to do so. He asserts, however, that for mature
understanding of number, such rotememorization is not sufficient andmust be accompanied by the
masteryofcertainbasicideas.
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Amongthese ideasareone-to-onecorrespondenceandconservation.Letus firstconsiderone-to-
onecorrespondence.SupposewearepresentedwithacollectionorsetofdiscreteobjectsasinFigure8.
Thesizeoftheobjects,theircolor,andsofortharecompletelyirrelevant.Allthatisrequiredisthattheset
contain a finite number of discrete objects. We are then given a box of objects and are required to
construct from it another setwhich has the same number property as the first set. It does notmatter
whethertheobjectsinthesecondset(whichwewillcallsetB)arethesamecolor,size,andsoonasthose
inthefirstset(setA).WhethersetAcontainselephantsandsetBcontainsgeraniumsisirrelevant.The
onlyrequirementisthattheyhavethesamenumber.OnewayofconstructingasetBsothatitwillhave
thesamenumberpropertyasAisbycountingtheobjectsinA(say,therearefive)andthentakeoutofthe
boxthesamenumberofobjects.Thisprocedure,whichofcourseisquiteadequate,probablyoccursfirstto
adults.Butsupposewecannotcount.SupposewedonotknowthenumberofobjectsinsetA.Evenwith
theselimitationsthereisasimplewayofconstructinganewset,B,whichwillhavethesamenumber
propertyasA.ThismethodmerelyinvolvesputtingnexttoeachmemberofsetAone,andonlyone,new
object.Thesenewobjects,aftertheone-to-onecorrespondencehasbeenestablished,formaset,B,with
thesamenumberasA.Ofcoursewedonotreallyhavetophysicallyplaceeachnewobjectnexttoonein
A;wecannotetheone-to-onecorrespondencementally.That is,wecan“saytoourselves,”“Thisnew
object corresponds to the first in the lineof setA,” and soon.The important idea is not thephysical
placingtogetherofthesets,butthepairingofonememberinsetAwithoneinsetB,howeverthisisdone.
FIGURE8Collectionofobjects.
Althoughverysimple, the ideaofone-to-onecorrespondence isbasicandpowerful,andmaybe
usedinavarietyofsituations.Ifwewanttodeterminewhethertherearethesamenumberofseatsas
peopleinanauditorium,allwehavetodoisaskeveryonetositdown(withnooneallowedtositon
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anyoneelse’s lap!). Ifall thepeopleare inseats(inone-to-onecorrespondencewith theseats)and if
noneoftheseatsisempty,thenthenumbers(whatevertheymaybe)ofpeopleandseatsareequal.If
therearepeoplestanding,thenthisdefinestherelationofmorepeoplethanseats.Ifthereareempty
seats, then this defines the relation of more seats than people. In brief, one-to-one correspondence
establishesthatanytwosets—regardlessofthenatureoftheobjectscomprisingthem—areequivalentin
number.Countingorotherproceduresarenotneeded.Lackofone-to-onecorrespondenceestablishes
thatonesetislargerthantheother(andonesmallerthantheother).
FIGURE9Conservationofnumber.
ThesecondbasicideawhichPiagetinvestigatesisconservation.Supposethatwehaveestablished
thatsetsAandBareequalinnumber,asinFigure9A.Thatis,wehaveputsetAinaline,andbeloweach
memberofsetAwehaveputanewobject.The lineofthenewobjects issetB.Supposethatwethen
compress themembers of set B, as in Figure 9B, so that the perceptual one-to-one correspondence is
destroyed.NoweachmemberofsetBisnotdirectlybelowadifferentmemberofsetA.Theproblemis
whetherthetwosetswhichnowdifferinphysicalarrangementstillareequalinnumber.Inotherwords,
istheequivalenceestablishedinFigure9AconservedwhentherearrangementshowninFigure9Bis
performed?Toadults,thismayseemlikeafoolishquestion.Ofcourse,theequalityofnumbershasnot
changed!Buttheproblemiswhetherchildrenacceptthissimpleandbasicidea,too.Iftheydonot,then
theirworldofnumbermustbeverychaoticindeed.Ifquantityisseentochangewhenevermerephysical
arrangement isaltered, thenthechild fails toappreciatecertainbasicconstanciesor invariants in the
environment.
Piagethasconductedanumberof investigationsonthechild’sunderstandingofthesetwobasic
ideas: one-to-one correspondence and conservation of the equivalence of twonumbers.He finds that
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youngchildrenfailtounderstandthesetwonotionsandthataperiodofdevelopmentisrequiredbefore
thechildachievesthementaloperationsnecessaryforthoroughcomprehensionofnumber.Letusnow
reviewtheexperiments.
Stage 1
Tostudytheabilitytoconstructsetsofequivalentnumber,Piagetpresentedchildrenwithavariety
ofproblems.The simplestof these involvedplacingbefore the childa rowof sixor sevenpenniesor
buttonsorsweets,andsoon.Theexaminerthenaskedthechildtopickoutthe“samenumber”or“as
many” from a large collection of similar objects. Thus the childwas given set A andwas required to
constructasecondset,B,whichwasequivalentinnumber.Thechildrenwere,ofcourse,nottoldhowto
constructsetB.Hereisaprotocoldescribinghowastage1child,4yearsand7monthsofage,dealtwith
theproblem.Piagethadplacedsixsweetsinarowandtoldthechildthattheybelongedtohisfriend
Roger:
“Putasmanysweetshereastherearethere.Those...areforRoger.Youaretotakeasmanyashehas.”(Hemade a compact row of about ten,whichwas shorter than themodel.)—“Are they the same?”—“Not yet”(addingsome).—“Andnow?”—"Yes.”—“Why?”—“Becausethey’relikethat”(indicatingthelength).(CCN,p.75)
FIGURE10Failuretoconstructequalsets.
The example makes clear the predominant tendency of this stage. The child does not use the
methodofone-to-onecorrespondence.Instead,hethinksthatthetwosetsareequivalentinnumberif
theyhavethesamelengths.InPiaget’sterms,thechildcentersononedimension—thelength—ofsetA
(Roger’ssweetsorthemodel)andbaseshisconstructionofsetBsolelyintermsofthatonedimension.
TheresultispicturedinFigure10.Thelengthsofthetworowsareequal,buttheirnumbersarenot.The
newrowisdenser;thatis,therearesmallerspacesbetweenthesweets,thanRoger’srow,butthechild
ignoresthisfactandconcentratesonlyonthelengths.Sincehefailstocoordinatethetwodimensionsof
lengthanddensityatthesametime,hecannotconstructsetsequivalent innumberexceptwhenvery
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smallnumbersareinvolved,orexceptbyaccident.
In another investigation, Piaget tried tomake the child understand the principle of one-to-one
correspondence,andthenperformedtheconservationexperiment.Inthisstudy,setAwasarowoften
vasesandsetBconsistedofflowers.Onechild,4yearsand4monthsofage,
put13flowersclosetogetherinarowopposite10vasesrathermorespacedout,althoughhehadcountedthevases from 1 to 10. Since the rowswere the same length, he thought that the flowers and vaseswere “thesame.”—“Thenyoucanputtheflowersintothevases?”—“Yes.”—Hedidso,andfoundhehad3flowers[left]over.(CCN,p.50)
Thechild,then,initiallyconstructedsetBsoastomakeitthesamelengthassetAandthoughtthat
thetwosetswerethereforeequalinnumber.Theexaminerthenmadethechildconstructaone-to-one
correspondencebetweentheflowersandvases;thatis,thechildputeachflowerinavase.Theresult
was ten flowers in ten vases (or two sets equivalent in number), and the three extra flowers were
discarded. The question now iswhether the child realizes that the two sets are really equivalent in
number.Doesthechildconservetheequivalencedespiteamerephysicalrearrangementoftheobjects?
Tofindout,Piagetcontinuedtheexperimentwiththesamechild.
The flowerswere taken out andbunched together in front of the vases. [That is, they formed a shorter rowthan did the vases.] “Is there the same number of vases and flowers?”—“No.”—“Where are there more?”—“There are more vases.”—“If we put the flowers back into the vases, will there be one flower in eachvase?”—“Yes.”—“Why?”—“Becausethereareenough.”(Thevaseswereclosedupandtheflowersspacedout.)—“Andnow?”—“Therearemoreflowers.”(CCN,p.50)
Notethatafterthechildhadhimselfestablishedaone-to-onecorrespondencebetweentheflowers
andvases,hefailedtoconservethenumericalequivalenceofthetwosets.Whentheflowerswereput
intoashorterrowthanthevases,thechildbelievedthatthenumberswerenolongerequalandthatnow
thereweremorevases.Hemaintainedthiseventhoughherealizedthattheone-to-onecorrespondence
couldbereestablished;that is, that theflowerscouldbereturnedtothevases.Thenwhentherowof
vaseswasmadeshorterthanthatoftheflowers,hechangedhismindonceagain.Heassertedthatnow
thereweremore flowers. Clearly, this child centered on the lengths of the rows and used only this
informationtomakejudgmentsofequivalenceorlackofequivalenceofnumber.Whentherowswerethe
samelength(aswhentheflowerswereinthevases),hesaidthattheywereequalinnumber.Whenthe
rowsdifferedinlength,hebelievedthatthelongerlinehadthegreaternumber.
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Piagetalsoinvestigatedtheroleofcounting,questioningthewayinwhichcountingthetwosets
affectsthechild’sjudgment.Onechild,5yearsand3monthsofage,failedtheconservationproblem.He
saidthatsetA(sixglasses)wasgreaterthansetB(sixbottles)becauseonewaslongerthantheother.
Thentheexaminersaid:
“Can you count?”—“Yes.”—“Howmany glasses are there?”— “Six.”—“And how many bottles?”—“Six.”—“Sothere’sthesamenumberofglassesandbottles?”—“Therearemorewhereit’sbigger[thatis,longer].”(CCN, p.45)
This examination shows thatwhile the child can count, the act ismeaningless in deedingwith
conservation.Althoughhecanreciteastringofnumbers,hedoesnotcomprehendwhattheysignify.The
fact that he counted six bottles and also six glasses does not imply to him that the sets are equal in
number. For him, equality of number is determined solely by equality of lengths, and counting is an
extraneousandirrelevantact,whichdoesnotassureeithertheequivalenceofsetsoritsconservation.4
Stage 2
The child of this stage easily constructs two sets equivalent innumber, but fails to conserve the
equivalencewhenthesetsarerearranged.Per,achildof5years,7months,
hadnodifficultyinmakingarowof6sweetscorrespondingtothemodel.[Piagetuses“model”torefertosetA, the row to be copied, and “copy” to refer to set B.] The model was then closed up: “I’ve got more.”—“Why?”—“Becauseit’salongerline.”(Theprocesswasreversed.)—Nowtherearemorethere,becauseit’sa big line.” But a moment later, Per said the opposite: “Are there more here [referring to the longerrow]?”—“No.”—“Why not?”—“Because it’s long.”—“And there [the shorter row]?”—“There are more there,becausethere’salittlebundle”[Thechildmeantthattheshorterrowwasdenser].—“Thenaretheremoreinalittlebundlethaninabigline?”—“Yes.”AfterthisPerwentbacktousinglengthasthecriterion,madethetworowsthesamelengthagainandsaid:“Nowthey’reboththesame.”(CCN,p.79)
Theprotocolshowsthatthechildofthisstageeasilyconstructsasetequalinnumbertoanother.He
also establishes the equivalence by the method of one-to-one correspondence. That is, in order to
constructsetB,heplacesanewsweetjustbeloweachinsetA.Buttheone-to-onecorrespondenceisnot
fullyunderstood;itisjust“perceptual.”WhensetBismadeshorterthansetA,thechildfailstoconserve
the equivalencewhich he so easily constructed. The protocol also shows that the child is ambivalent
about thecriteriaused toestablishequalityor inequalityofnumber.Sometimeshemaintains that the
longerrowhasmorebecauseitislonger;atothertimeshebelievesthattheshorterrowhasmorebecause
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it is denser. In Piaget’s terms the child sometimes centers on the lengths (ignoring densities) and
sometimes centers on the densities (ignoring lengths). This tendency is an improvement over what
occursinthepreviousstage,sincetheyoungerchild(instage1)consistentlycentersononlyoneofthe
twodimensions,usuallylength,anddoesnotconsidertheother,usuallydensity,atall.Bycontrast,the
childinstage2haswidenedthesphereofhiscentrations.Henotices,albeitatdifferenttimes,thatboth
dimensionsmayberelevantandusestheinformationfromeitherofthesedimensionsseparatelytomake
ajudgment.Thisuseofpartialinformationiscalledregulations.Wewillseenexthowthechildinthe
periodofconcreteoperationscoordinatesthetwodimensions.
Stage 3
The results of this stage are easy to describe. The child can now construct a set numerically
equivalenttoanothersetandcanconservetheirequivalencedespitechangesinphysicalarrangement.
Hereisaprotocolillustratingthisstage:
“Takethesamenumberofpenniesastherearethere[therewere6 insetA],Hemadearowof6underthemodel,butputhismuchclosertogethersothattherewasnospatialcorrespondencebetweentherows.Bothendsof themodel extendedbeyond thoseof the copy. “Haveyougot the samenumber?”—"Yes.”—“Are youandthatboy[referringtothehypotheticalownerofsetA]justasrichasoneanother?”—“Yes.”—(The penniesof the model were then closed up and his own were spaced out.)—“And now?”— “Thesame.”—“Exactly?”—“Yes.”—“Whyaretheythesame?”—“Becauseyou’veputthemclosertogether.”(CCN,p.82)
Thisprotocolcontainsseveralinterestingfeatures.OnefeatureisthatinmakingsetBequaltosetA,
theconcreteoperationalchilddoesnotbothertoplaceeachelementinBdirectlyundereachelementin
A.Hedoesnotneedtorelyontheperceptionofspatialproximitybetweentheelementsofeachset.How
thendoesheconstructnumericallyequivalentsets?Onemethod,ofcourse,issimplytocountthenumber
ofobjectsinsetA,andthenmerelycountoutthesamenumberforsetB.Probablysomechildrenusedthis
method,butPiagetconcludedfromhisclinicalexaminationsthatotherchildrendidnotusecounting.
Theyseemedtousethemethodofone-to-onecorrespondence,butinamoresophisticatedwaythanthe
youngerchild.Theconcreteoperationalchild’stechniquemaybedescribedasfollows:toconstructsetB
equaltosetA,heputsoutonepennyforthefirstpennyinsetA,andsoforth.Itdoesnotmatterwherehe
putsthemembersofsetB.TheonlycrucialrequirementisthathematcheachmemberinsetAwithone
andonlyonememberinsetB(anonspatialone-to-onecorrespondence).Thechildmustnotforgettoput
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outapennyforeachmemberofsetA(thatis,hecannotskipanymemberofsetA)andmustnotputout
morethanonepennyforeachmemberofsetA(thatis,hemustnotcountanymemberofsetAtwice).
Theprocessofestablishingsetsequalinnumbermaybedescribedintermsofclassesandrelations.
Asfarasrelationsareconcerned,thechildusesthemethodofvicariantordering.SupposethatsetA(the
model)isalineofpennies,andthechildmustconstructasetB(thecopy)fromalargesupplyofcandies.
Hebeginsbypointingatthepennyontheextremeleftandputsoutasweet.Thenhepointstothesecond
pennyfromtheleft,putsoutasweetforit,andcontinuesuntilthelineofpennieshasbeenexhausted.
Thisprocessofpointingtoonepennyatatime,beingcarefultocounteachpennyonceandonlyonce,is
anordering. It isequivalent tosaying: “Thispennycomes first, thisonesecond, thisone thirdandso
forth.Inaway,theorderingofpenniesislikearrangingaseriesofsticksordollsinorderofheight.There
is a first stick, a second stick, and so forth, just as there is a firstpennyanda secondone.Therefore,
something like the ability to construct ordinal relations underlies the child’s construction of sets
equivalentinnumber.
Despite theevident similarity, the twoprocesses—constructingordinal relations (as inordering
thesticks)andvicariantordering(thepennies)—arenotidentical.Inthecaseofthesticks,thereisone
andonlyoneshorteststickwhichmustcomefirst intheseries,oneandonlyonesecondshorteststick
whichmustcomesecondintheseries,andsoforth.Inthecaseofthepennies,itdoesnotmatterwhich
pennyisconsideredfirstintheseries,whichcomessecond,andsoon.Onecouldstartcountingatthe
extremeleft,attheextremeright,inthemiddleorwhereveronepleased,justsolongasoneiscarefulnot
toomitpointingtoeachofthepenniesandnottopointtoanyofthemmorethanonce.Theorderingof
penniesiscalled“vicariant”forthisveryreason:theorderinwhichthepenniesarecounteddoesnot
matter.
Other aspects of relations are involved too.When putting out one and only one sweet for each
penny,thechildiscoordinatingtwoorderings.Thisissimilartotheproblemofdollsandsticks.Justasthe
childcangivetotheshortestdolltheshorteststick,tothesecondshortestdollthesecondshorteststick,
andsoforth,socanheplacethefirstsweetwiththefirstpenny,thesecondsweetwiththesecondpenny,
andsoforth.Ofcourse,theone-to-onecorrespondenceofpenniesandsweetsisvicariant,whereasthe
one-to-onecorrespondenceofdollsandsticksisnot.Inthelatterinstance,thereisoneandonlyonestick
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(theshortest)whichgoeswiththeshortestdoll,andsoforth.Inthecaseofpenniesandsweets,itdoes
notmatterwhichsweetisplacedintocorrespondencewithanypenny,solongasoneandonlyonesweet
isusedforeachpenny.
Theconstructionofequivalentsetsalsoinvolvesclassification.Tothechild,thepenniesinsetA,for
instance,areinsomewaysallthesameandinsomewaysdifferentfromoneanother.Theyaredifferent
inthatacertainpennyiscountedfirst,anotheronesecond,andsoforth.Theyarethesameinthatitdoes
notmatterwhichiscountedfirst,whichsecond,andsoforth.Inotherwords,itisonlythechild’sactof
pointingtoeachinturnthatdifferentiatesthepennies;otherwise,theyareallequivalent.Insofaraseach
ofthepenniesisanelementequivalenttoalltherest,theyareallmembersofthesameclass.Thesameis
true,ofcourse,ofthesweetsinsetB.
Thus far we have seen how the child’s ability to construct sets equivalent in number may be
analyzedintoanumberofcomponentskills.Underlyingthechild’sovertperformance(e.g.,placingona
table seven sweets corresponding to seven pennies) are a number of concrete operations: vicariant
ordering, one-to-one correspondence of two vicariant orderings, and classification. Some of the
operations involveclassesandothers relations.Thus,number isaunionof classesandrelations.The
operationsareconcretesincethechildcanapplythemonlytoimmediatelypresentobjectsorthoughts
about them.Theyareoperations since theyare actionswhich the childperformsmentally andwhich
have the added property of being reversible. This means that for each particular mental action, for
instanceaddition, thechildcanperformitsoppositeaction, in thiscasesubtraction,which leaveshim
wherehestarted.Asoperations,theymayalsobedescribedintermsofoverallstructuresorsystems,that
is,intermsoftheGroupings,anexampleofwhichwehavegiveninthecaseofclassification.5
Inthestageofconcreteoperations,thechildcanalsoconservenumber.Afterconstructingtwosets
equivalent in number, the child recognizes that the sets remain equivalent despite mere physical
rearrangementofthesets.Ifthesevensweetsarecompressedtomakeashortlinewhilethelineofseven
penniesremainsthesame,thetwosetsareneverthelessstillequalinnumber.Theequivalencehasbeen
conserved.
Whatenablestheconcreteoperationalchildtoconservewhilethepreoperational(stages1and2)
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childfailstodoso?Recallthemechanismunderlyingthepreoperationalchild’sfailure:centration.The
youngerchildcentersononlyalimitedamountoftheinformationavailable.Whentherowofsweetsis
compressed,henoticesonlythatthelineofpenniesisnowlongerthanthelineofsweets.Heignoresthe
fact that the line of sweets is denser (has smaller spaces between adjacent elements), and bases his
judgmentonlyonthelengths.Thepreoperationalchildknowsthatempiricalreversibilityispossible:he
realizesthatifthesweetswerereturnedtotheiroriginalpositions,therewouldbeonesweetforeach
penny.Thisknowledgedoesnothelp,however;despite it, he feels that thenumberof a set changes
whenitsappearanceisaltered.Perceptualfactorshavetoostrongaholdonthechildatthisstage.They
arenotyetsufficientlycontrolledbymentalactionswhichcancompensateformisleadinginformation.
Bycontrast,theconcreteoperationalchilddecentershisattention.Heattendstoboththerelevant
dimensionsandusesthisinformationinseveralways.
1.Henoticesthatthelineofpennieshasbecomelongerthanthelineofsweetsandthatthelineofsweetshasbecomedenserthanthelineofpennies.Moreover,hecoordinatesthetwodimensions. He mentally manipulates the visual data available to him. This mentalactivity leads him to realize that while the length of the line of pennies increases(relativetothesweets)byacertainamount,thedensityofthelineofsweetsincreasesbyanequivalentamount.Inotherwords,thechildconceivesthatthepennies’increaseinlengthisbalancedby,orcompensatedfor,bythesweets’increaseindensity:thereisarelation of reciprocity or compensation between length and density. In effect, oneincreasecancelsouttheotherwiththeresultthatthesetsremainequivalentinnumber.Thisreciprocityisoneformofreversibility.Sincetheincreaseinlengthcounteractstheincreaseindensity,theresultisareturn,orareversal,totheoriginalsituation,whichisequalnumber.
2.Theconcreteoperationalchildalsocomestousetheoperationofnegation.Wehavealreadyseenthatwhentherowofsweetsiscompressed,theconcreteoperationalchildrealizesthatthesweets’ increaseindensityisreciprocatedbythepennies’ increaseinlength,and that, as a result of these reciprocal transformations, the number of the two setsremains equivalent. The concrete operational child is also able to imagine that thesechangescanbeannulledornegated.Hereasonsthattheactionofcontractingthesweetscanbenegatedbytheinverseactionofspreadingthemout.Theoneactionisannulledby theother. Suchannulmentornegation isanother formof reversibility; that is, thechild mentally reverses the action of contracting the row of sweets. As a result heattributesequalnumberstothetwosets.Notethatthestage3childbothreversestheactofcontractingandrecognizesthatthefinalresultistheoriginalarrangementofsweets
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andpennies.Thestage2child,whoiscapableofempiricalreversibility,recognizesthatthesweetscanbereturnedtotheiroriginalpositionbutdoesnotfocusonorappreciatetheactofrearrangement.Heattendstostates,nottransformations.
3. The concrete operational child sometimes uses an identity argument, reasoning that thenumbersmustbethesamesincethesameobjectsareinvolved:nothinghasbeenaddedortakenaway.
Thestage3child’s thought isconcrete inaspecialsensewhichSinclair(1971),oneof themost
importantGenevaninvestigators,expressesquiteclearly:“Concreteoperations...doesnotmeanthatthe
childcanthinklogicallyonlyifhecanatthesametimemanipulateobjects....Concrete,inthePiagetian
sense,meansthatthechildcanthinkinalogicallycoherentmanneraboutobjectsthatdoexistandhave
realproperties,andaboutactionsthatarepossible;hecanperformthementaloperationsinvolvedboth
whenaskedpurelyverbalquestionsandwhenmanipulatingobjects....Theactualpresenceofobjectsis
nointrinsiccondition”(pp.5-6).
Tosummarize, thestage3child,havingenteredtheperiodofconcreteoperations,canconstruct
two sets equivalent in number, and can conserve this equivalence despite changes in appearance.
Underlyingtheseachievementsareanumberof thoughtprocesses.Theability toconstructequivalent
setsrequiresvicariantorderingandclassification.Theabilitytoconserve,whichisacquiredasaresultof
thedecentrationofthechild’sattention,issupportedbythreetypesofoperationswhicharesometimes
explicitlyexpressedinthechild’sjustificationofhisresponse:reciprocity,negation,andidentity.These
areaspectsofconcreteoperations,whichmaybedescribedbythegroupings.Thechilddoesnotalways
performallofthethoughtprocesseswhenpresentedwithaproblemofconstructingequalsets,nordoes
herefertoallthreeargumentswhenaskedforajustificationofconservation.Hemightonlyrefertoone
or perhaps two of them. The child is, however, capable of performing all the concrete operations,
althoughhemaynot alwaysdo so. In fact, after a periodof time the concrete operational child takes
conservation for granted.He immediately recognizes that number is conserved anddoes not need to
proveconservationtohimselfbymeansofnegationorreciprocity.Whenaskedwhynumberisconserved,
hethinksthatthequestionissillyandthatthefactofconservationisself-evident.Forhim,conservation
has become amatter of logical necessity. This is evidence that the child has acquired an underlying
structureofmentaloperations inwhicheach isdependentupon theotherandnone isperformed in
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isolation.Thestage3child’sthoughtisconcreteinthespecialsensethathecanthinkcoherentlyabout
anddealwithrealobjectsbutnothypotheticalentities.
In conclusion, Piaget’s work on number has been extraordinarily productive. It has stimulated
volumes of research on children’s number, and many of Piaget’s findings have been successfully
replicated,eveninnon-Westernsocieties(seeDasen,1977).AsweshallfindinChapter6,theworkhas
alsohadimplicationsforeducationalcurricula.Likemanymajorcontributionstopsychology,thework
has aroused a good deal of controversy, and several alternative views have been proposed (see, for
example,GelmanandGallistel,1978;andGinsburg,1982).
CONSERVATION
Thus far, we have described only the conservation of number—that is, the child’s ability to
recognize that thenumericalequivalencebetween twosets remainsunchangeddespitealterationsof
physical arrangement. Piaget has also investigated severed other conservations which include
continuous quantity, substance, weight, and volume. The conservation of continuous quantity may be
definedbythissituation.Thechildispresentedwithtwoidenticalbeakers(AandB),eachfilledwith
equalamountsofliquid(seeFigure11),andisaskedwhetherthetwoglassescontainthesameamount
ornotthesameamounttodrink.Afterheagreestotheequivalenceofquantities,theliquidispouredby
either the experimenter or the child from one of the two identical beakers (say, B) into a third,
dissimilarlyshapedbeaker(C).Thecolumnoftheliquidinthethirdclass(andtheglassitself)isboth
shorterandwiderthanthatintheremainingoriginalglass(A).Thechildisnowaskedwhetherthetwo
beakers(nowAandC)containequalamounts.Ifheassertsthattheydo,heisaskedtoexplainwhy.The
liquid inC is then returned to theoriginalbeakerB, and the child is againasked ifA andB contain
identicalamounts.Themanipulationisrepeated,thistimewithaglass(D)whichistallerandthinner
thantheoriginalbeakers.Finally,theliquidofeitherAorBispouredintoaset(E)ofaboutthreeorfour
smallerglassesandthesamequestionsareaskedofthechild.Ifthechildcontinuouslyassertsineach
casethattheamountthathasbeenpouredfromBintothedifferentbeakersisalwaysthesameasthe
amountremaining in theoriginalbeaker(A), thenhehasconservedcontinuousquantity.That is, the
childrecognizesthatmerelypouringtheliquidfromBtoCorDorE,doesnotincreaseordecreasethe
quantity;the“amount”ofliquidremainsthesame(orisconserved)whetheritisinBorinC.Sincethe
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quantitiesAandBwereequal,andsincepouringtheliquidofBintoCdoesnotchangeitsquantity,then
thequantitiesinAandCmustalsobeequal.Ifthechilddoesnotconsistentlyassertthisequality,thenhe
hasfailedtoconserve.
FIGURE11Conservationofcontinuousquantities.
Inthecaseofconservationofsubstance,thechildispresentedwithtwoidenticalballsofPlasticine
(orclay,etc.).HeisfirstaskedwhetherthereisthesameamountofPlasticineinbothballs.Ifhedoesnot
think so, he is asked to take away or add some clay tomake them identical. Then, the experimenter
changesoneoftheballstoasausageshape,whilethechildwatches.Thechildmustnowdecidewhether
ornottheballandthesausagehaveequalamountsofsubstance.As inthe liquidsituation, theball is
changed into a varietyofdifferent shapes. If the child consistently asserts that thebelli and thenew
shapesdohaveequalamountsofsubstance,thenhehasconservedsubstanceandhasrecognizedthat
merelychangingtheshapedoesnotaltertheamountofmatterinvolved.
To test theconservation ofweight, the experimenter again presents the childwith two identical
ballsofPlasticineandplacesthemonabalance.Thechildseesthatthetwoballsweighthesame.Then
theyareremovedfromthebalanceandoneballistransformedintotheshapeofasausage.Thechildis
askedtoanticipatetheresultsofplacingtheballandthesausageonthetwosidesofthebalance.Will
theystillremainbalancedorwillonesidebeheavierthantheother?Thequestioniswhetherthechild
recognizesthatweightisconserveddespitechangesinshape.Hereagainaseriesofchangesaremadeto
oneoftheballsandthequestionastotheidentityofweightisrepeated.
Inthecaseofconservationofvolume,twoballsofPlasticineareplacedintwoidenticalbeakers,each
filledwithequalquantitiesofliquid.Thechildseesthattheballsdisplaceanequalvolumeofliquidin
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bothbeakers.Or,inthechild’sterms,theliquidgoesupanequaldistanceinbothcases.Thentheballs
areremovedfromthebeakers,andoneballischangedintotheshapeofasausage.Thequestionnowis
whetherthechildrecognizesthatbothballandsausagecontinuetodisplaceequalvolumes,orwhether
thewatergoesupanequalamountinbothcases.
All theseconservationsaresimilar.Theyinvolvea firstphase inwhichthechildmustrecognize
thattwoamounts—liquidquantity,substance,weight,orvolume—areequal.Mostchildrenabovetheage
of 4 years are quite successful in this task. All the conservations also involve a visible transformation
whichmaybedonebyeitherthechildortheexperimenter.Whilethechildwatches,orasaresultofhis
ownactions,theliquidispouredfromonebeakertoanother,ortheballischangedintoasausage.Itis
quiteapparentthatnoliquidorPlasticineisaddedortakenaway.It isalsoapparentthatthingsnow
lookdifferent.Thecolumnofliquidisshorterandwider,andtheballisnowasausage.And,finally,all
theconservationsinvolveasecondphaseinwhichthechildmustonceagainjudgewhethertheamounts
inquestion are still the same.Of course, they are equivalent, and the issue iswhether the childwill
recognizethisorbemisledbytheobservedchangesinappearance.
Piaget’sgeneral findingsare that there isasequenceofdevelopmentwithregard toeachof the
conservations.Childrenbeginbyfailingtoconserveandrequireaperiodofdevelopmentbeforetheyare
able to succeedat the task.Forexample, in the caseof continuousquantities, childrenarenotable to
conserveuntilabouttheageof6or7years.Inthefirstphaseoftheproblem(twoidenticalbeakers,each
filledwithequalamountsofliquid),theyoungestchildren,around4or5yearsofage,correctlyconclude
that theamountsof liquidareequal.Since thechildhaseitherpouredout the liquid into thesecond
beaker,orhastoldtheexperimenterwhentostoppouring,thisisnotsurprising.Ifaskedtojustifythe
identity,thechildwillsaythatthewatercomesuptothesamelevelineachglasssothattheamountsare
equal.Whentheliquidinonebeakerispouredintoathirdglasswhichisdifferentinshapefromthefirst
two,thechildnowmaintainsthattheamountsarenolongerequal.Oneglasshasmoretodrinkthanthe
other.Askedtoexplainhisanswer,hesaysthattheglasswiththetallercolumnofliquidhasthegreater
amount.Thisjudgmentofamountsistiedexclusivelytotheheightsofthecolumnsofliquid:whenthe
heightsare the same (as inphase1), the child thinks that theamountsare the same;when theyare
different(asinphase2),thentheamountsmustbedifferenttoo.
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Instage2,thechildof5or6yearsvacillatesinhisresponsestotheconservationproblem.Whilehe
usuallyfailstoconserve,hisapproachtotheproblemvariesfromtimetotime.Inthesecondphaseofthe
experiment(whenonebeaker isshorterandwiderthantheother), thechildsometimessaysthatthe
tallerbeakerhasmore todrink,andsometimesmaintains that thewideronehas thegreateramount.
Unlikethestage1child,hedoesnotconcentrateexclusivelyontheheightsofthecolumnsofliquid,but
sometimesbaseshisjudgmentsonthewidthsaswell.
Instage3,thechildiscapableofconservation.Whenaskedwhytheamountsdonotchangeafter
thepouring,hegivesatleastoneofseveralreasons.OneisthatiftheliquidinCwerereturnedtoits
originalcontainer,B, thenthetwoinitialbeakers,AandB,wouldcontain identicalcolumnsof liquid.
Thisisthenegationargument.Asecondreasonistheidentityargument:it’sthesamewater.Youhaven’t
addedanyortakenanyaway.Athirdargument,involvingcompensationorreciprocity, isthatthethird
glass,C,isshorterthantheoriginalbeaker,A,butwhatClostinheightwascompensatedbyC’sgainin
width;therefore,theamountinCmustbeequaltotheamountinA.
Towardtheendofhislife,Piagetreturnedtotheproblemofconservationandstressedtheroleof
commutability. Inoneexperiment,Piaget (1979)presentedchildrenwithaconservationofsubstance
problemofthefollowingtype.Aballofclayispresentedandthenapieceisremoved.Thechildisasked
iftheballhasthesameamount,andsaysno,sincesomethinghasbeentakenaway.Thepiecethathad
beenremovedfromonesideoftheballwasplacedontheothersideandthechildwasagainaskedifthe
ballhasthesameamountnow(withthepieceaddedtotheotherside)asdidtheoriginalball.Piaget
findsthatundertheseconditions,childrenassertconservationataveryyoungage.Theysayessentially
that“It’sthesamething,youtookitawayandthenputitbackandit’salwaysthesame”(p.21).Inother
words,thechildrenhaveunderstood“thatthereisdisplacement,andthatwhenonedisplaces,whatis
addedatoneplacehasbeentakenawayfromanotherplace”(p.21).ThisPiagetcalls“commutability”
andclaimsthatitisoneimportantfactorinconservation.Commutabilitybearsasimilaritytothenotionof
compensation.
In the case of conservation of substance, weight, and volume, a similar progression to that of
quantityappears.Inthefirststage,thechildfailstoconserveapparentlybecauseofaconcentrationon
onlyoneofthestimulusdimensionsinvolved.Thatis,inthecaseofweighthemaysaythatthesausageis
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heavier than the ball because the former is longer. In the second stage, he again fails to conserve,
although now he vacillates between the two dimensions involved. For instance, he may sometimes
believethattheballisheavierbecauseitiswiderandatothertimesassertthatthesausageisheavier
because it is longer. In the third stage, the child conserves, for reasons similar to those cited for
continuousquantities.
Whilealltheconservationsfollowasimilarcourseofdevelopment,thereisastrikingirregularityas
well—thephenomenonofhorizontaldécalage.Thisreferstothefact,whichhasbeenwellsubstantiated,
thatthechildmasterstheconservationofdiscontinuousquantityandsubstanceataboutage6or7;does
notachievestage3oftheconservationofweightuntilage9or10;doesnotunderstandtheconservation
ofvolumeuntilapproximately11or12.Ineachcasetheargumentsusedarethesame,sometimeseven
involvingthesamewords.Buthavingmasteredconservationinonesubstantivearea,likesubstance,the
child is not able to generalize immediately to another area like that of weight. First, he acquires
conservationofdiscontinuousquantityandsubstance,andthenweight,andthenvolume.Thedécalage,
orlackofimmediatetransfer,illustrateshowconcreteisthethoughtofthechildduringtheagesofabout
7to11years.Hisreasoningistiedtoparticularsituationsandobjects;hismentaloperationsinonearea
maynotbeappliedtoanother,nomatterhowusefulthismightbe.
GENERAL CHARACTERISTICS OF THOUGHT
Wehavereviewedthedevelopmentofvariousaspectsofthought:classes,relations,number,and
conservation.Itwouldseemusefulatthistimetotakeabroaderlookatsomegeneralcharacteristicsof
cognitivedevelopment.
Underlying Patterns of Thought
There are striking regularities in the child’s cognitive development. In each of the two major
periodsofdevelopmentdiscussedinthischapter(preoperationalandconcreteoperational),thechild
usesdistinctivepatternsofthoughttoapproachdifferentsubstantiveproblems.Thereappeartobesome
generalpatternswhichcharacterize the thoughtof thepreoperational childandsomeotherpatterns
manifestedintheconcreteoperationalchild’scognition.
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Consider,first,thechildfromabout4to7yearsinthepreoperationalperiod.(Rememberthatthis
age designation is only approximate, since a child as old as 9 or 10 years typically shows a
preoperationalapproachtotheconservationofvolume.)Onegeneralcharacteristicofcognitiveactivity
duringthisperiodiscentration.Thechildtendstofocusonalimitedamountoftheinformationavailable.
In the conservationofnumber, he judges two sets equalwhen they are the same length and ignores
anotherrelevantvariable,thedensity.Intheconservationofcontinuousquantity,thechildjudgestwo
amountsequalwhen theheightsof thecolumnsof liquidare thesameand ignores thewidth. In the
constructionofordinalrelations(theproblemoforderingtensticksintermsofheight),hesucceedsonly
byconsideringthetopsof thesticksand ignoringthebottoms,orviceversa. Inall theseproblems, the
preoperational child deploys his attention in overly limitedways. He focuses on one dimension of a
situation,failstomakeuseofanother,equallyrelevantdimension,andthereforecannotappreciatethe
relationsbetweenthetwo.(Thenotionofcentration issomewhatsimilar toPiaget’searlierconceptof
juxtapositionwhichisthetendencytothinkintermsofthepartsofasituationandnotintegratethem
intoawhole.)
Bycontrast, theconcreteoperational child is characterizedbydecentration. He tends to focus on
severeddimensionsofaproblemsimultaneouslyandtorelatethesedimensions.Intheconservationof
number,hecoordinateslengthanddensity:twosetshavethesamenumberwhenthefirstislongerthen
the second but the second is denser than the first. In the conservation of continuous quantity, he
recognizes thatamountsareequalwhenonecolumnof liquid isat thesametimetallerbutnarrower
than a second. In the construction of ordinal relations, he determines whether a given object is
simultaneously bigger than some objects and smaller than others. In all these problems, the concrete
operational child attends to severed aspects of the situation at once. Centration anddecentration are
generalpatternsofthought,underlyingstructures.
Thetwomajorperiodsofdevelopmentcanbecharacterizedinotherwaysaswell.Thethoughtof
thepreoperationalchildisstaticinthesensethatitcentersonstates.Intheconservationofsubstancehe
focuses on the shape of Plasticine (sometimes a ball and sometimes a sausage) and ignores the
transformation,thatis,thechangefromonestatetotheother.Intheconservationofcontinuousquantity
he focuses on the heights of the columns of liquid and not on the act of pouring. He lacks adequate
representationsofanobject’sshiftfromonepositiontoanother.Ingeneral,heconcentratesonthestatic
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statesofasituationandnotonitsdynamictransformations.
Theconcreteoperationalchild,ontheotherhand,isattunedtochanges.Intheconservationshe
concentratesonthetransformation:theactofpouringtheliquid,orspreadingapartasetofobjects,or
deformingaballintoasausage.Heformsmoreorlessaccurateimagesofthechangeswhichhavetaken
place,and,therefore,canreason,forexample,thatasasetexpandsinlengthitsimultaneouslydecreases
indensity.
The preoperational child’s thought lacks reversibility. He may be able to predict an empirical
reversibility as, for instance, in the case of the liquidswhere hewould agree that if thewaterwere
pouredbackintoB,therewouldbethesamequantityasbefore.Butthisempiricalreversibilitydoesnot
changethefactthatnowhebelievesthereismore(orless)waterinthenewglassC.Itisasifpouring
fromBtoC,andfromCtoBweretotallyunrelatedactions.Theolderchild,ontheotherhand,realizes
thatpouringfromCtoBreversesornegatestheactionofpouringfromBtoCandisawarethatitisthe
sameactionperformedinanotherdirection.Bycarryingouttheactionmentally,thatis,byreversingthe
pouringinhismind,heisabletoascertainthatthequantityofwaterinC(thelowerwiderglass)isthe
sameasinB.Hecanperformamentaloperationwhichleadshimtoacertainconclusion,andthendothe
reverseofthisoperationwhichenableshimtoreturntohisoriginalstartingpoint.
Theconcreteoperationalchildcanalsoperformanothertypeofreversibilitywhenoperatingon
relations.Thisisreciprocity.Forinstance,intheexampleofliquidquantity,whenthechildsaysthatone
glassislongerandthinner,whereastheotherisshorterandwider,heiscancelingoutthedifferences
betweenthetwoglassesbyanactionofreciprocity.Onedifferencebalancesouttheother,withtheresult
thattheyhaveareciprocalrelationship.
Tosummarize,thepreoperationalchild’sthoughtisirreversibleandattentivetolimitedamountsof
information, particularly the static states of reality. The concrete operational child focuses on several
aspects of a situation simultaneously, is sensitive to transformations, and can reverse the direction of
thought. Piaget conceives of these three aspects of thought— centration-decentration, static-dynamic,
irreversibility-reversibility—asinterdependent.Ifthechildcentersonthestaticaspectsofasituation,he
isunlikelytoappreciatetransformations.Ifhedoesnotrepresenttransformations,thechildisunlikelyto
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reversehis thought.Bydecentering,he comes tobeawareof the transformations,which thus lead to
reversibilityinhisthought.Inconclusion,wecanseethatoneaspectofthoughtisnotisolatedfromthe
rest.Eventhoughthenatureofthesystemmayvarywiththedevelopmentofthechild,thoughtprocesses
formanintegratedsystem.
Invariant Sequence
Another striking regularity in cognitive development involves invariant order: the sequence of
activities (for example in classification, partial alignments, collections, class inclusion) assumes an
invariantorderdespitewidevariationsinculture.Cross-culturalresearchprovidesrelevantevidenceon
thisissue.WithinWesterncultureschildrenprogressthroughthevariousstagesintheorderdescribed
byPiaget.Inthecaseofconservationofcontinuousquantities, forexample,researchshowsthatSwiss,
British,American,andCanadianchildrenfirstfailtoconserve,thenvacillateintheirresponse,andlater
conservewithstability.Whilechildrenintheseculturesdonotnecessarilyachievethevariousstagesat
thesameaverageages, thesequenceofdevelopment—theorderof thestages—seems identical inall
cases.Eveninotherandverydifferentcultures,liketheThaiorMalaysian,thesamesequenceofstages
andtypeofresponsesappear.ChildreninThailand,forexample,exhibitclassificationactivitieswhich
arevirtuallyidenticaltothoseusedbyWesternchildren,andproceedthroughthesequenceofstagesin
theorderdescribedbyPiaget(Opper,inDasen,1977).Thereisgreatcross-culturalgeneralityinPiaget’s
findings.Atthesametime,wemustmakeonequalification:apparently,membersofsomeculturesdonot
advanceasfarinthesequenceofstagesasdoWesterners.Thus,forwhateverreasons,insomecultures,
individualsmaynot complete the stageof formaloperations.Not everyoneachieves thehighest level
possible in terms of Piaget’s stages. Yet, until their progress terminates, these individuals proceed
throughthesequenceofstagesinthestandardorder.Whiletheultimatelevelofdevelopmentmaydiffer
amongcultures, thesequenceseemstobe invariant,asPiagetproposes.Thephenomenadescribedby
Piagetarethusnearlyuniversal,occurringacrossextremevariationsincultureandenvironment.Piaget
hassurelycapturedsomethingverybasicinhumancognition.6
Irregularities
Piaget has gone to great lengths to dispel some misinterpretations concerning his theory. In
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particular,heshowsthattherearecertainirregularitiesindevelopment.Hepointsout,first,thattheages
atwhichthestagesoccurvaryconsiderablybothwithinandamongcultures.NotallGenevanchildren
attainstage3ofnumberdevelopmentat6or7years,andchildreninMartiniquelagbehindGenevans
byapproximatelyfouryears.InThailand,urbanchildrenattainstage3atthesametimeaschildrenin
Geneva,but ruralThai children lagbehindbyapproximately threeyears. InMalaysia, rural children
attainthenumberconceptoneyearaheadofurbanchildren,whointurnlagbehindSwisschildrenby
twoyears.Thus therateofdevelopmentseems tovary fromgroup togroup.Second, thecourseofan
individual’sdevelopmentiscontinuous.
Thechildisnotcharacterizedbystage1onedayandbystage2thenextday.Rather,thetransition
is gradual, occurring over a long period of time, and the child exhibits many forms of behavior
intermediary between the two stages. Indeed, an individual child’s behavior takes many forms in
addition to those Piaget describes as being typical of the various stages. Piaget’s stages are idealized
abstractions;theydescribeselectedandsalientpointsonanirregularcontinuumofdevelopment.Third,
thechildisnotalwaysinthesamestageofdevelopmentwithregardtodifferentareasofthought.The
childmaybe characterizedby stage2 in the case of classes, and stage1 in the case of relations. It is
unlikely,however,thathewillbeinstage1forclassesandstage3forrelations.Onlyinfrequentlydoes
onefindextremediscrepanciesbetweenstagelevelsindifferentareas.Fourth,aswehavealreadyseen,
there exists the phenomenon of horizontal décalage, in which the child displays different levels of
achievementinregardtoproblemsinvolvingsimilarmentaloperations;forexample,hemaybeableto
conservesubstancebutnotnumber.
Preoperational Strengths
Piaget (On the Development of Memory and Identity, 1968) tries to correct a widespread
misconception concerning preoperational thought. Typically, we characterize the young child as
intellectuallyincompetentsincehecannotconserve,cannotusereversibility,andcannotdecenter.Piaget
feelsthatthisviewisexaggerated;asaresultofrecentresearch,Piagetproposesthatthepreoperational
childpossessesanumberofimportantintellectualstrengthswhichmustnotbeoverlooked.Inparticular,
theyoungchildiscapableofidentity,functions,andcorrespondences.
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While unable to conserve, the young child nevertheless appreciates certain basic identities. For
example, in the standard conservation problem, the young child recognizes that the same liquid is
transferredfromonebeakertoanothereventhoughonelooksquitedifferentfromtheother.Heseesthat
thebasicsubstancedoesnotchange,eventhoughitsappearanceisalteredandeventhoughhefalsely
believesthattheamountofliquidhaschanged.Heappreciatesidentitybutfailstoconservequantity.
Piagetproposesthatthenotionofidentitymayderivefromthechild’sperceptionofhisownbody’s
growth.WithGilbertVoyat,Piagetaskedchildrentodrawthemselveswhentheywerebabies,whenthey
were a little bigger, and so on; then the experimenters questioned the children concerning the
maintenanceof their identitydespiteobviousphysicalchanges.Theexperimentersalsoposedsimilar
questions concerning the identityofotherobjects, includingplants.The results showed that children
easily appreciated their own identity despite changes in size, and were less likely to accept the
continuing identity of a plant over its various changes in appearance. Perhaps, then, the notion of
identity derives from the child’s perception of his ownbody’s growth and later is generalized to the
worldofobjects.
Thepreoperationalchildcanalsoperceivefunctionalrelationsintheenvironment.Oneexample
ofsuchfunctions(givenbySinclair,1971)involvestheopeningofacurtain:“thechildunderstandsthat
whenonepulls thecordofacurtain, thecurtainopens; the fartheronepulls, the farther thecurtain
opens”(p.4).Inotherwords,thereisafunctionalrelation,aco-variationbetweenpullingandopening,
and the child perceives that the two factors are positively related. (Theremay evenbe precursors of
functionsin infancy:thisexampleisreminiscentoftheinfantLaurentwhoseemedtorealizethatthe
morevigorouslyheshookachain,thelouderwouldbethesoundproducedbytheattachedrattles.)Itis
veryimportant,ofcourse,forthechildtorecognizesuchfunctionalrelationsintheenvironment:they
pervadeit.Thetallertheperson,thestrongerheislikelytobe;theharderonehitsanotherchild,the
more likely is the child to protest and even cry; the bigger the glass, themoremilk it holds. Despite
limitations in other areas of thought (for example, centration), the preoperational child has some
appreciation for basic functional relations, and this is of great value to him in coping with the
environment.
At the same time, Piaget points out that these functions are incomplete: they constitute only a
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semilogic.Foronething,thechild’sappreciationoffunctionsisimprecise.Toreturntotheexampleofthe
curtain, thechilddoesnotrealizeexactlyhowthepullingof thecord isrelatedto theopeningof the
curtain and cannot quantify the results with any degree of precision. Another Piagetian experiment
makes this clear. Children were presented with three toy fish, 5, 10, and 15 centimeters long,
respectively,andweretoldtofeedeachfishitsproperdietofmeatballs.Themiddle-sizedfishshouldget
twiceasmanymeatballsasthesmallest,andthelargestfishthreetimesasmany.Preoperationalchildren
understoodthefunctionalrelationbetweensizeof fishandnumberofmeatballsonly inanimprecise
way.Theyrealizedthatthelargerthefish,themoreitneedstoeat.Buttheywerenotabletoworkoutthe
functioninaprecisemanner(forexample,bygiving2,4,and6or3,6,and9meatballstotherespective
fish).
Toward the end of his life, Piaget (1979) stressed the role of “correspondences.” He used this
notiontorefertothechild’stendencytocompareobjectsorevents,todeterminethewaysinwhichthey
“correspond,” or are similar and different. This tendency appears at all levels of development, from
infancyonward,althoughittakesdifferentformsatdifferentlevels.
Forexample,aninfantfirsthitsatoyparrottomakeitswingandthenappliesthehittingschemeto
otherhangingobjectsaswell.Inasensehehascomparedthenewobjectwiththefamiliarparrotand
notedthesimilaritybetweenthem(thecorrespondenceofoneobjecttoanother).
Note:Ablackmarbleandawhitemarblearegluedtoaplate,withthewhiteoneabovetheblack
one(asinFigure12A).Thentheplateisrotatedsothatblackoneisabovethewhiteone(asinFigure
12B).
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FIGURE12CorrespondenceofMarbles.
The preoperational child displays different forms of correspondence. For example, in one
experiment,Piaget(1979)showedchildrentwoobjectsonarotatingdisk.Imaginethattheobjectsarea
whitemarbleandablackmarble,gluedtoadish,as inFigure12A.Whenthemarblesareon the left
(Figure12A),thewhiteisabovetheblack.Whenthedishisrotatedsothatthemarblesareontheright
(Figure12B),thentheblackisabovethewhite.Thepreoperationalchildobservesthesituations—the
marblesontheleftandontheright—andgraduallynotesthecorrespondencesbetweenthem.Thechild
seesthatwhenthemarblesareontheleftside,thewhiteishigher,butwhentheyareontheright,the
whitebecomesthelower.Atfirst,thechild’sapproachissimply“empirical”:torecordthefactswithout
interpreting them. But “the child discovers suddenly that there is a general order” (p. 24). He
determines,inotherwords,thatthereisareversalofposition.It’snotjustthatthewhiteishigherinone
situationandlowerintheother,butthatthewhitehasswitchedpositions.This insight thengradually
leadsthechildtoanother:thepositionswereswitchedbecauseatransformationtookplace.Therotation
ofthedishcausedtheswitchinposition.
We see then that the child begins by comparing two states, noting some basic similarities and
differences(theswitchinposition).Thesecorrespondencesareimportantbecausetheypavethewayfor
thechild’sappreciationoftransformations.Andaswehaveseen,anappreciationoftransformationsisat
theheartofconcreteoperationalthinking.
In brief, preoperational thought is not characterized solely by incompetence. Young children
appreciatecertainbasicaspectsofidentity,perhapsasaresultofexperiencewiththeirownbodies.They
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alsounderstand,albeitinanimprecisemanner,varioussimplefunctionalrelationsintheenvironment.
Theydetectcorrespondences,andthisleadsthemtoanappreciationoftransformations.Indealingwith
youngchildrenonemustbeawareof these strengthsaswell asof the commonly cited limitations, as
GelmanandGallistel(1978)andothercontemporarywritersconcurinmaintaining.
The Concept of Stage
Piaget’s theory describes a sequence of stages. For example, in the case of the conservation of
numberwehavereviewedthetransitionfromcentrationtodecentration.Nowitisimportanttoconsider
thenatureofsuchstages.WhatdoesPiagetmeanbystageandhowusefulaconceptisit?
AccordingtoPiaget(BiologyandKnowledge, 1971a,p. 17) thenotionof stage isusedwhen the
followingthreeconditionsarefulfilled.First,theremustbeaninvariantsequenceofactivities.Thus,in
thecaseofconservation,thereis,first,afailuretorecognizeequivalence;thenthereisvacillation;and,
finally,thereissuccess.Theorderofappearanceoftheactivitiesisthesameforallchildren.Second,each
stageinthesequenceischaracterizedbyanunderlyingstructure,acoresystemdeterminingthechild’s
overt behavior. Thus, underlying the child’s failure to conserve is the strategy of centration—the
tendencytofocusonlimitedamountsofinformation.Third,eachofthestructurespreparesthewayfora
succeedingone.Thus,inthecaseofconservation,theinitialcentrationpreparesthewayforavacillation
amongtheavailabledimensions,andthisinturnleadstothesubsequentdecentration.Inbrief,Piaget
proposes that stages are characterized by invariant sequence, underlying structures, and successive
integrations.
Piagetalsoemphasizedthatdespitetheexistenceofstages,developmentiscontinuous.Thechild
doesnotenteranewstageovernight;instead,thechangesaregradual,andindeedbarelyperceptible
fromclose-up.Piagetexplainedthisintermsofthescaleofmeasurement.Ifwelookcloselyatachild’s
development,observingeverydayandthususinga finescaleofmeasurement, it ishardforustosee
dramaticchanges;fromonedaytothenextwewillnotnoticedifferencesinstages.Butifwestandback,
observing the child infrequentlyand thususinga crude scaleofmeasurement,wewillbe impressed
withchanges;fromoneyeartothenextwewillseeprogressfromonestagetothenext.
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Wehavealreadyreviewedresearchconcerningthenotionsofinvariantsequenceandunderlying
structure. Cross-cultural study demonstrates that the sequence described by Piaget is extremely
widespread,ifnotuniversal.Also,thereseemtobedistinctunderlyingpatternsorstructuresineachof
the major periods under consideration—preoperational and concrete operational. Consider next
Piaget’sthirdconditionfortheexistenceofastage—therequirementthateachstagepreparethewayfor
thenext.Whileitishardtoadduceevidencesupportingthisnotion,itseemstohaveacertainamountof
facevalidity;forexample,afocusontwodimensionsseemsnaturallytofollowfromafocusonone.In
brief, the evidence concerning invariant sequence, underlying structures, and successive integrations
seemstosupportPiaget’spropositionconcerningtheexistenceofmajorstagesofdevelopment.
Atthesametime,thestagenotionsuffersfromanumberofdifficulties.One,alreadyalludedto,is
theexistenceof irregularities indevelopment.Wehaveseen that thechild isnotalways in thesame
stagewithregardtodifferentareasofthought.Thus,hemaybeinstage1withrespecttoclassesand
stage2inthecaseofrelations.Also,thephenomenonofhorizontaldécalageisverystriking:thechildmay
displaydifferentlevelsofachievementinregardtoverysimilarareasofthought.Thus,hemayconserve
substance but not number. The existence of these irregularities seems dissonant with the notion of
distinctunderlyingpatternsorstructuresofthoughtcharacterizingthemajorstagesofdevelopment.If
thepatternsaresostrongandpervasive,whyarethedécalagessostriking?
Anotherdifficultywiththestagenotionisthatthestructurespresumablyunderlyingastagemay
alsobeimplicatedinstagesoccurringearlierinthesequence.ThuswehaverecentevidencebyTrabasso
(1975), for example, to the effect thatunder certain conditions, preoperational children canperform
concreteoperationaltasks.Ifthesamestructuresunderliebehavioratdifferentstages,dowenotthen
have toalterournotionof stages?The issueof stages isextremely complexand isnow the subjectof
considerablerethinking(foranexcellentdiscussionseeFlavell,1985).
Indeed,towardtheendofhislife,Piagetseemstohaverethoughtthestagenotionhimself.Thelast
tenyearsofPiaget’sresearchrevolvedlargelyaroundissuesofcognitivechangeanddevelopmentand
did not employ stage notions to any significant degree. In this sense, Piaget became less of a
“structuralist”(onewhodealswiththeanalysisofmentalstructuresunderlyingthestages)andmoreof
a“functionalist”(onewhodealswiththefactorsdeterminingdevelopment).AsweshallseeinChapter
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6,Piaget’stheoryofequilibrationplacedtheemphasisongradualchangesorineffectonmanyfleeting
substages.WhatwasimportantforthelaterPiagetwasnotaconceptofbroad,stablestages,butatheory
ofthecontinuouschangeanddevelopmentofthechild’sintellectualstructures.
MENTAL IMAGERY
Afterhisbriefexaminationduringthe1920softhecontentofthought,Piaget’smainconcernhas
beenwiththeoperativeaspectofcognition.Thisreferstoactionsusedtodealwithorevenchangethe
world. These actions may be either overt or internal. Examples of overt actions abound in the
sensorimotorperiod.Theinfantkickstoshakearattle,orusesasticktodrawanobjectclose.Thepresent
chapterhascoveredtwomajorsubdivisionsofinternalizedactions:theisolatedandunrelatedactionsof
preoperationalthoughtandthestructuredandcoordinatedonesofconcreteoperationalthought.
Piaget has also shown an interest, albeit a lesser one, in the figurative aspect of cognition. This
referstothreewaysinwhichthechildproducesanaccountofreality.Oneisperception,asystemwhich
functionsbymeansofthesensesandoperatesonanimmediatelypresentobjectorevent.Itisthrough
perceptionthatthechildachievesarecordofthethingsinthesurroundingworld.Thisrecordisoften
inexact, as in the case of the visual illusions. A second subdivision is imitation, by which the child
reproducestheactionsofpersonsorthings. It is truethat imitation involvesactionsonthepartof the
child,buttheseactionsneverthelessfallunderthefigurativeaspectsincetheyproduceacopyofreality
butdonotmodifyit.Athirdportionofthefigurativeaspectismentalimagery.AswesawinChapter3,
mentalimageryreferstopersonalandidiosyncraticinternaleventswhichstandfororrepresentabsent
objectsorevents.Whenwe“picture”toourselvesourfirstbicycle,orthestrollwetooklastweek,thenwe
areusingmentalimagery.Asweseefromthislastexample,thetopicofmemoryiscloselyboundupwith
thefigurativeaspectofthought.Memory(recall)typicallyinvolvesretainingknowledgegainedthrough
thefigurativemode.
In recent years, Piaget has conducted important investigations into two important aspects of
figurative cognition, specifically imagery and memory. His theory stands in stark contrast to the
traditionalempiricistviewofthesematters.Thelatterassumesthatperceptionstampsontheindividual
a literal copy of reality. Given sufficiently frequent repetition of the initial event, a mental image
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mirroring the reality is formed and is stored in memory. If there is no further experience with the
originalevent,thememoryimagegraduallyfades,losingitsfidelitytothereality;itisforgotten.Piaget
criticizesthistraditionalviewonseveralgrounds.Mostimportant,hebelievethatrealitydoesnotsimply
imposeitselfonapassiveorganism.Rathertheindividualassistsintheconstructionofhisownreality.
Hisintellectualactivities—theoperativemodeofthought—servetoshapetheresultsofencounterswith
theenvironment.The resulting figurativeknowledge isnot simplya copyof reality.This theme—the
influence of operative structures on figurative knowledge—dominates Piaget’s discussion of mental
imageryandmemory.Wewillnowconsiderthesetwotopicsinsuccession.
History
Mentalimagerywasoneofthefirsttopicsstudiedbyexperimentalpsychologists.Attheendofthe
nineteenthcentury,theschoolofWundtusedtheintrospectivemethodtoanalyzethenatureofmental
imagery.TheWundtiansbelievedthatimageswerecomposedofabundleofsensationstiedtogetherby
meansofassociation.Atthebeginningofthetwentiethcentury,thestudyofimageryfellintodisrepute
fortworeasons.First,theWurzburgpsychologistsfoundthatmuchofthoughtdidnotseemtoinvolve
imageryatall,andsecond,thebehavioristrevolutionwhichoccurredintheUnitedStatesmaintained
thattheintrospectivemethodwasapoorone.Thebehavioristsfeltthatthedataofintrospection—one’s
impressions of one’s own consciousness—were not public enough. How could another psychologist
determine if an introspectionwere reliable and accurate?As a result of the behaviorist attack on the
methodofintrospection,thestudyofimagerywasconsidered“unscientific”andwaslargelyabandoned.
Recently,however,psychologistshaveshownarenewedinterestintheancientproblemofimagery,and
thetopicisonceagainbecomingcentraltoexperimentalpsychology(Neisser,1976).
Incontrasttomoderninvestigators,Piagethasbeenstudyingimagerysinceatleastthe1930s.In
Chapter3wediscussedPiaget’sworkonimageryintheyoungchilduptotheageof4years.Ifyouwill
recall,thistheoryproposedthatmentalimagesdonotoccuruntilaboutthemiddleofthesecondyear.
Before this timethechilddidnotpossessmentalrepresentationsof theenvironmentand,asaresult,
reactedmainly to events occurring in the present. After imagerymakes its appearance the child can
represent tohimselfbothevents thatoccurred in thepastandobjects thatareno longerperceptually
present. Also, according to Piaget’s theory, imagery results from imitation. At first, the child overtly
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imitatestheactionsofthingsorpeople; later,hisimitationbecomesinternalizedandabbreviated.It is
through this internalactivity that imagesarise.Clearly,Piaget’sviewscontrast stronglywithWundt’s.
Imagesarenotmerelybundlesofsensations,imposedbytheenvironmentandconnectedbyassociation;
rather,theconstructionofimagesinvolvestheactivityofinternalizedimitation.
Later,with Inhelder, Piaget returned to the studyof imagery (1971).His laterworkdealswith
childrenabovetheageof4,andposesanumberofinterestingquestions.Forexample,aretheredifferent
typesof imagesatdifferentstagesof intellectualdevelopment? If so,what is therelationbetweenthe
imagesandthementaloperationsofagivenstage?
Method
Whilethesequestionsareinteresting,thestudyofmentalimagesisverydifficult,especiallyinthe
caseofchildren.Imagesarepersonal,idiosyncraticeventswhichcannotbevieweddirectly.Onecannot
“see”anotherperson’simagery;theinvestigatormust,therefore, infertheirexistenceandnaturefrom
otherphenomena,suchasaverbalreport.Piagethasusedavarietyofmethodstostudyimagery.Oneof
thesemethodsistoaskapersontodescribehisownimages.Butlanguageisnotfullyadequateforthis
task,orevenfordescribingsomethingasconcreteastheimmediateperceptionofanobject.Wearenever
able to convey bywords the precise nature of whatwe see. In our attempt to describe percepts, we
inevitably emphasize certain features and neglect others.We have difficulty in describing shades of
colors,orgradationsof textures.Wecannotgivean impressionof theentireperceptatonce,butmust
describeitsdetails insequence,andtherebyoftenlosetheessenceofthewhole.If languagesopoorly
conveysperceptualeventswhichcontinuetoremainbeforeoureyesforfurtherinspection,howmuch
moredifficultisittodescribementalimageswhichoftenarefleetingandunstable?
Anothermethodof studyingmental images isbydrawing.Here theperson is asked todrawan
objectpreviouslypresented.Sincetheobjectisnolongerpresent,hemustproduceanimageofittoyield
the drawing. The drawing, therefore, gives some insight into the nature of the image, which is the
internal “picture” of the object. The method of drawing, however, presents several shortcomings.
Drawingisnotasimpleanddirectreflectionofimages; italsoinvolvesotherprocesses.Somepersons
havepoormemory.Iftheyhaveforgottentheirimageofanobject,theycannotverywelldrawit.Other
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personssimplycannotdrawwell.Itisnottheirimagethatisatfault,buttheirartisticskill.
A thirdmethodattempts tobypass theshortcomingsoforiginaldrawings.Thesubject isgivena
collection of drawings made by the experimenter, and must select from them the one most closely
correspondingtohisimageofwhathehadpreviouslyobserved.Thismethod,ofcourse,isnotaffectedby
variationsinsubjects’artisticabilitiesandreducesthedifficultiescreatedbyapoorevocativememory.
Buteventhemethodofselectionfromacollectionofdrawingsisnotaltogethersatisfactory.Oneproblem
is that the drawings presented are not likely to be exact copies of the person’s mental image. The
drawingsmayomitdetailsoftheoriginalimageoraddnewfeatures.Ineitherevent,thesubject’schoice
doesnotgiveafullyaccurateindicationofhisimage.
To study imagery, Piaget has used all thesemethods—verbal report, drawing, and selection of
drawings—either alone or in combination. As is customary with the explorations carried out by the
Genevaschool,themethodsweresupplementedbyverbalquestioningcarriedoutintheclinicalmanner.
Major Findings
One experiment was concerned with kinetic images, or the imagery of an object’s movement.
Childrenfromabout4to8yearsofagewerepresentedwithtwoidenticalblocks,oneontopoftheother
(seeFigure13A).Eachsubjectwasaskedtodrawthesituation,andgenerallydidthisquitewell.Then
thetopblockwasmovedsothatitslightlyoverlappedthebottomone,asinFigure13B.Afterthechild
hadhadachancetolookatthisforawhile,thetopblockwasreturnedtoitsoriginalposition(Figure
13A).Thechildwasthenaskedtodrawtheblockinitsdisplacedposition(Figure13B),whichwas,of
course, no longer visible. After this, a collection of drawingswas presented. This contained a correct
rendering of Figure 13B as well as an assortment of incorrect drawings which represented errors
typicallymadebychildrenofthisage.(Thistechniqueissimilartotheuseofcountersuggestionsinthe
interview.)Thechildwasaskedtoselectthedrawingwhichhefeltcorrespondedmostcloselytowhathe
hadseen.Inthefinalstepanothercontrolwasadded.Thetopblockwasonceagaindisplaced,andthe
childwasaskedtodrawthesituationwhileitwaspresent.Ifthechildcouldaccuratelydrawtheblocks
whenpresent,thenanyofhispreviouserrorsofdrawing(whentheblockswereabsent)mustbedueto
faultyimageryormemoryandnottofaultydrawingability.
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FIGURE13Movementofblocks.
Tosummarize,thechildFirstdrewthedisplacedblocksaftertheywerenolongervisible;thenhe
selectedfromagroupofdrawingsoneresemblingthedisplacedblocks;andfinally,whenthedisplaced
blockswereonceagainbeforehim,hedrewthem.
The findings show that before the age of 7 years, children candraw the displacedblocks quite
correctlywhentheyarepresent,butnotwhentheyareabsent;norcanthechildrenchooseadrawing
whichcorrespondstothesituation.Ingeneral,childrenofabout4and5yearsproducedandselected
drawingsofthetypesAthroughE(seeFigure14),whereaschildrenof6yearsmadeerrorslikethoseof
typesFandG.Itwasonlyat7yearsthatover75percentofthesubjectsbothdrewandchosethecorrect
drawings.
FIGURE14Drawingofblocks.
Across-culturalstudyofthisprobleminThailand(Opper,1971)showsthatThaichildrenmake
thesametypesoferrorsasdoSwisschildren,althoughitisnotuntil10yearsofagethat75percentof
theThaisubjectsmakecorrectdrawingsofthetwoblocks.
The responses of the younger child would seem to indicate that he forms only a very general
pictureofthesituation,thatis,thatoneblockhasbeenmoved.Whenaskedtodrawtheexactdetails,heis
unabletodoso.Thechildthereforereproducesthisgeneralimpressionofmovementbydetachingthe
topblockfromthebottom(cf.C),byasymmetricalmovementofshrinkingorenlargementofoneofthe
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twoblocks(cf.DandE),or,finally,bytheretentionofonecommonboundaryoridenticallineforthetwo
blocks, inadditiontomakingchangesontheothersideof theblocks(cf.FandG).His imagedoesnot
appeartocorrespondtotheactualsituation.Thechildseemstocenterononedimension,thatis,onone
particularaspectofthesituation—forexample,theoverlappingofthetopblockindrawingsEandF,or
theoverlappingof thebottomblock indrawingsDandG.However, thechilddoesnotcoordinate the
movementofoneblockwiththefinalstateofthetwoblocks.Apparentlythechilddoesnotanalyzethe
situationinsufficientdetailbutmerelyformsaglobalimpressionofwhathashappened.Heisawarethat
theblockhasmoved,but the intimatedetailsof themovementandtheensuingdisplacementseemto
haveescapedhisattention.Asaresult,hismentalimageisinadequate.
A second typeof imagery is static imagery. In this instance the image reproduces a collectionof
objects,ascene,orapicture—inbrief,anysituationinwhichtheelementsremainunchangedineither
shape or position. Piaget finds that the child is able to produce adequate static imagery earlier than
kinetic.
We have reviewed only a small sampling of Piaget’s experiments on imagery. Their results,
together with those of a great many more studies, have led Piaget to draw the following general
conclusionsconcerningimageryanditsrelationtointelligenceasawhole.First,imagerydevelopsina
gradualmanner.Theevolutionofimageryisnotasdramaticasthatofthecognitiveoperationswhich
display a clear-cut sequence of stages. There appears to be only one major turning point in the
developmentof images.Thisseemstooccurataroundtheageof7or8yearsandcorresponds to the
onsetoftheperiodofconcreteoperations.Beforethebreak,thatis,fromtheageof11/2toabout7years,
thechildseemscapableofproducingwithanydegreeofaccuracyonlystaticimages,andeventheseare
farfromperfect.Thechildcannotrepresentcorrectlythemovementsofanobjectorevensimplephysical
transformations;theimagesproducedforsuchsituationsaregrosslydeformed.
Piagetbelieves that thereason for thisdeficiency isoneaspectofoperativecognition,namely,a
tendencytoconcentrateontheinitialandfinalstatesofagivensituationandtoneglecttheintervening
events which are responsible for the changes. We have already seen this tendency, which is called
centration, operating in the case of conservation. If youwill, recall the situationwhere the childwas
presentedwitha lineofvases,eachofwhichcontainedaflower.Theflowerswereremovedfromthe
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vasesandspreadapart.Whenthisoccurs,theyoungchildusuallybelievesthattherearemoreflowers
thanvases,sincethelineofflowersisnowlongerthanthelineofvases.Hehascenteredonthelengths
andignoredanumberofotherfactors.Hehasfailedtodecenterandtoconsiderthedensityofthelines,
aswellastheirlength,andhehasignoredtheintermediarytransformation(theremovalandspacingof
theflowers).Thus,thechildfocusesmainlyontheinitialandfinalstates(theflowersinthevasesand
the flowersspacedout)and fails to integrate these impressionswithallelse thathasoccurred.Thus,
beforetheageof7or8imageryisextremelystatic.Asaresult,thechildproducesadistortedpictureof
realitycharacterizedbyanemphasisonsuperficialfeatureswhichareeachisolatedfromothersandnot
coordinatedintoacoherentwhole.
Fromabout theageof7yearsonward,however, thechildbecomescapableofproducing images
whichcanreproducekineticsituations.Thisimprovementisduetothefactthathecannowimaginenot
onlytheinitialandfinalstates,butalsotheintermediarytransformations.Hisimageryhasbecomeless
static.Ofcourse,itisneverpossibletoreproducealltheinterveningevents,sinceinsomecases(likethe
pouringofliquid),theyoccurrapidly.Butthechildrecognizesthatasequenceisinvolvedandthatthere
hasbeenaseriesofinterveningstepsbetweentheinitialandfinalstates.
Afinalquestionconcernstherelationbetweendynamicimagesandtheconcreteoperations.Kinetic
imagesoccuratapproximatelythesametimethatthechildbecomescapableoftheconcreteoperations;
whatthenistherelationbetweentheoperativeandfigurativeaspectsofthoughtatthisstage?Onthe
onehand,wehavealreadyseenthatoperativecognitioninfluencesthenatureofthechild’s imagery.
Thus,theconcreteoperationalchild’sdecentrationcontributestothedynamicnatureofhisimagery.In
Piaget’s theory, figurative cognition (here, imagery) is dominated by operative cognition (here, the
concrete operations).On the other hand, images canplay an auxiliary role in thinking. For example,
considerthenumberconservationtaskinvolvingflowersandvases.Theconcreteoperationalchildcan
formaccuratetransformational imagesofthedisplacementoftheflowers.Afterthetransformationhas
beendone,hecorrectlypicturesthewayinwhichtheflowershavebeenremovedfromthevases.The
ability to form imagesof this sortdoesnotguarantee that the child can conservenumber; aswehave
alreadyseen,theprocessesunderlyingconservationarenotsolelyperceptualorimaginal.Nevertheless,
thechildwhohasacorrectimageofthetransformationiscertainlyaheadofthechildwhodoesnot.In
otherwords, images are a useful andnecessary auxiliary to thought during the concrete operational
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stage. By providing relatively accurate representations of the world, images assist the process of
reasoningalthoughtheydonotcauseit.
Summary and Conclusions
Images represent absent objects or events. They are “symbols,” in the sense of bearing some
resemblance to the object represented, and are personal and idiosyncratic. Images do not give as
completeanddetailedareproductionoftheobjectasisprovidedbydirectperception.Imagesfirstmake
theirappearancearoundthemiddleofthesecondyearoflife,andtheyarisefromaprocessofimitation
whichgraduallybecomesinternalized.Untiltheageofapproximately7years,thechildisonlyableto
produceapproximatelycorrectmentalimagesofstaticsituations.Heconcentratesonstatesratherthan
ontransformations.Thelimitedimageryofthechildispartlytheresultofimmatureoperativestructures.
Asthesestructuresdevelop,sodoeshisimagery.Aftertheageofabout7years,thechildbecomescapable
ofcorrectkineticimagery.Thisnewabilitypermitsafurtherunderstandingofreality:thechildnowhas
availableamoreaccurateanddetailedrenderingoftheeventsonwhichtofocushisreasoning.
MEMORY
Memory,too,isinfluencedbyoperativecognition.Beforeexploringthis,itisnecessarytobeginby
clarifyingsometerminology.
Definitions
Inordinarylanguage,weusethewords“memory”or“remember”inseveraldifferentsenses.Here
isananecdotetoillustratethepoint.Anadulthasnotriddenabicyclesincechildhood,someyearsago.
Nowhis own child gets a bicycle and askswhether the adult “remembers” how to ride. “Of course, I
rememberhow to rideabicycle,” says theadult.Asked (skeptically) toprove it, theadult geton, and
pedals around a bit. Despite the lack of practice over a long period of time, he is able to ride very
smoothly,muchtothesurpriseofthechildwhoownsthebicycleandwhonowwonderswhetherhewill
gettorideit.Astheadultispedalingdownthestreet,he“remembers”ridingthebicyclewhichheowned
asachild.Hehasafairlyclearmentalpictureofitsoverallshapeandform,aswellastheplacesinwhich
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herode.
This example illustrates two very different kinds of “memory.” In the first kind, the adult
remembers how to do something. Although there has beennopractice formany years, he hasnot lost
general bicycle-riding skills. He “remembers” how to ride not just a specific bicycle, but any bicycle.
Through experience, he has acquired a physical skill of a general nature, and remembers it. In this
instance,weusethetermmemorytoindicatethatthepaststillexertsaninfluenceonthepresent.The
adult’s ability to ride a bicycle, acquired through a set of earlier learning experiences,was somehow
preserved within him. Note that after childhood this ability existed as a potential, since until this
incident hedidnot actually engage in thebehavior.Note, too, that the element of earlier learning is
crucialtothedefinition.Itwouldnotmakesensetosay,“Irememberhowtosneeze,”sincesneezingwas
neverlearned.Yetitwouldmakesensetosay, ‘‘Irememberhowtokeepfromsneezing”sincethatwas
learned.Inbrief,thisisonevaliduseofmemory:apersoncanretain,overaperiodoftime,abehavioral
potentialwhichistheresultofpreviouslearning.
Theothersenseofmemory isquitedifferent.When theadult ‘‘remembers”ridinghischildhood
bicycle,heisreferringtoaspecificeventandthinginthepast.Hehasaholdonaparticularsliceofhis
own history. He ‘‘remembers” a bicycle with wide tires, and a heavy frame—a Schwinn, in fact. He
remembers riding it up Commonwealth Avenue to a park with a certain kind of path. This kind of
memoryismorespecificandconcretethanthefirst.Inthiskindofremembering,theadultretainsspecific
eventsorthingsfromthepast;intheotherkindofremembering,hepreservesthegeneralskillsacquired
in the past. Often the two types of memory occur together. A person remembers how to type (thus
preservingthegeneralability)andalsoremembersthespecifictypewriterusedinhisearlylessons(thus
retaininginformationconcerningaspecificthingfromthepast).Butthetwotypesofmemorydonothave
tocoexist.Apersonmayrememberhowtotypeandyetmayhavetotallyforgottenthespecifictypewriter
orhisearlylessons.Similarly,apersonmayrememberthetypewriterandlessons,butnotrememberhow
totype.Thus,wehaveusedsomeexamplesofphysicalskillstoillustrateadistinctionbetweentwotypes
ofmemory.
In the intellectual domain, Piaget’s theory (Piaget and Inhelder,Memory and Intelligence,MEM,
1973)proposesasimilardistinctionbetween“memoryinthewidersense”and“memoryinthespecific
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sense.”Theformerrefersto“theconservationoftheentirepast,oratleastofeverythinginthesubject’s
pastthatservestoinformhispresentactionorunderstanding”(MEM,p.1).Moreprecisely,memoryin
thewidersensereferstothe“conservationofschemes,”totheretentionofacquiredpatternsofbehavior
orthought,liketheconcreteoperations.Bycontrast,memoryinthespecificsense“refersexplicitlytothe
past,” to specific eventsor thingsorpersons in an individual’shistory.Anotherwayof lookingat the
distinctionistosaythatmemoryinthewidersenseinvolvestheoperativeaspectofthought:itistheway
inwhichgeneraloperationsorwaysofdoing thingsarepreservedover time.Memory in the specific
senseisgenerallyfigurative: itpreserves information concerning specific things—a face, anobject, an
activity. (These “things” include actions, but only specific actions that are thought to have actually
occurred,notthepotentialforactionsofageneraltype.)
Piagetgoesontoproposesomefurtherdistinctionsconcerningmemoryinthespecificsense.This
typeofmemory—andweshallnowsimplyusethewordmemorytorefertoit—maytakeoneofseveral
forms.Perhapsthemostprimitiveisrecognition.Thisoccurswhenapersonencountersthings(anevent,
person, thing, etc.)previously experiencedand “has the impressionofhavingperceived thembefore
(rightlyorwrongly,fortherearefalserecognitions)”{MEM,p.5).Thus,weseesomeoneknownbefore,
and“saytoourselves”thatthepersonisfamiliar,eventhoughhisnamemayeludeusandwecannot
recallwhereweknewhim.Similarly,thebabyinthesensorimotorperiodrecognizesfacesandplaces
whentheyareencountered.Orthebabyshowsthroughhisabbreviatedschemesthatherecognizesatoy
he has played with. Recognition, then, is one form of (specific) memory, involving an impression of
familiarityuponanencounterwithapreviouslyexperiencedobject.
Recall isamuchmoresophisticatedanddifficultformofmemory.Itinvolvesproducingamental
account of a previously experienced thing in the total absence of that thing. One examplewould be
remembering your childhood bicycle or your first grade teacher.Recall sometimes involves a mental
picture,sometimeswords,sometimesanodor.Thecrucialaspectofrecallisthattheindividualproduces
some kind ofmental representation of the previously experienced event.7 It is evident that recall is
closely linkedwith the semiotic function, alreadydiscussed, since the latter involves the formationof
mentalrepresentationsforabsentthingsorevents.
The General Hypothesis
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Piaget’smaininterestisinthefunctioningofmemoryinthespecificsense—recognitionandrecall.
Howdoesspecificmemoryoperate?
According to some empiricist views, memory works in the following manner. An individual
perceivesanobjectandstoreswithinhimitsreplicaortrace.Themorefrequentlyorrecentlytheobjectis
perceived,thestrongerthetrace,andhencethestrongerandmoreaccuratethememory.Inthisclassic
view,memoryissimplyacopyofsomethingreal,andtheaccuracyofthecopydependsonsuchfactorsas
frequency,recency,andthe like.Notethat intheclassicview,theindividual ismainlypassive:things
imposethemselvesonhim;theymakeanimpressiononhim;theyformatraceinhimasapieceofchalk
leavesarecordonaslate(hencetheexpressiontabularasa,orblankslate).8
Piaget’sview isdifferent.Heproposes that the childdoesnot simply record reality inapassive
manner,storingacopyinthewarehouseofmemory.Instead,asPiagetseesit,thechildassimilatesand
interpretsreality,sothatmemoryisinpartafunctionofthechild’sintellectualoperations.Memorystems
notonlyfromexperiencebutfromintelligence.This,then,isthegeneralhypothesiswithwhichPiaget
beginshisempirical investigations.Giventhis theoretical framework,Piagetgoesonto investigate the
specificwaysinwhichmentaloperationsaffectmemory,especiallyrecall.
Experiments on Memory of a Series
Tostudytheinfluenceofknowingonremembering,Piagetconductedseveralexperiments,oneof
whichinvolvedmemoryforaseries,atopicalreadyreviewedinthischapter.Childrenofvariousages
wereshowntenwoodensticks,alreadyarrangedinacompleteseries,fromsmallesttolargest.Eachchild
was“toldtotakeagoodlookatitandrememberwhathehasseen.’’Thenaboutaweeklater,eachchild
wasaskedtorecalltheseriesbydrawingitorbytracingitoutwithhisfingersonthetable.Afterthis,the
experimenterdeterminedthechild’sstageofdevelopmentwithrespecttoseriationbygivinghimthe
usualtests.Theexperimenteralsoobtainedacheckonthechild’sdrawingabilitybyhavinghimcopya
seriesofsticksavailabletodirectperception.Thiscopycouldthenbecomparedwiththechild’sdrawing
frommemorytodetermineifdistortionsinthelatterstemfrommeredrawingdeficiencies.Inbrief,the
experiment involved (1) determining children’s intellectual level with respect to seriation, (2)
presentingthemwithacompletedseriestoremember,and(3)measuringrecallbyfingertracingand
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drawing.Furthermore,(4)ameasureofdrawingabilitywastakensothatthisfactorcouldbecontrolled.
Whatshouldhappen insuchanexperiment?According to theclassicview, theseries impresses
itselfonthepassivesubject,andtheaccuracyofrecalldependsontheextentofthesubject’sexperience
with it and on similar factors. The child’s drawings should to some degreemirror the realitywhich
impinges on him. Piaget’s view is much different: the child actively assimilates the reality into his
intellectualsystemandthisprocessofinterpretationdeterminesthenatureandqualityofrecall.Inthe
presentinstance,astage1childmaydistorthismemoryoftheseriesinaccordancewithhisimmature
intellectualoperations,andthiswillbereflectedinhisdrawingandtracing.Notethattheresultofthisis
notadrawingwhichissimplyapalecopyofthereality.Rather,itisadrawingwhichissystematically
distortedinlinewiththechild’sintellectualoperations.
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FIGURE15Drawingsofcompletedseries.
Consider a few examples of this. One childmade a drawing like that in Figure 15A, involving
several identical long lines and several identical short ones. This drawingwas similar to the child’s
actual arrangement of the sticks during the test of seriation: hemade one bunch of large sticks and
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anotherbunchofsmallsticks,butdidnotaccuratelyseriatewithineachbunch.Anotherchildproduceda
drawinglikethatinFigure15B.This,too,wassimilartohisactualarrangementofthesticks.Hemadethe
topsofthesticksincreaseinorderofsize,buttotallyignoredthebottoms.(Whenaskedtocopyawell-
formedseriesimmediatelyinfrontofthem,thesesamechildrenproducedfarmoreaccuratedrawings.
Thisallowsustoconcludethatdrawingskillinitselfisnotatissue.)Bycontrast,childreninstage3who
couldaccuratelyseriatewereaccurateinrecall,asindicatedbyveridicaldrawingsandtracings.
ThesefindingscanbetakentosupportPiaget’stheory.Theindividual’smemoryisinfluencedand
organizedtosomedegreebyhisintellectualoperations.Thechildrecallsnotwhathehasseenbutwhathe
knows.Inthepresentinstance,stage1children’srecallisdistortedbytheirimmatureseriationschemes.
(Weshallseecaseslaterwheretheeffectisofadifferentsort.)Atthesametime,Piagetpointsoutthatthe
resultsarenotentirelyclear-cut.Somestage1childrenmakeperfectlyaccuratedrawings.Theirmental
operationsdonotseemtointervenesoforcefullyintheactofrecall. Insteadtheyseemtofocusonthe
appearanceoftheseries—onits“figurativeaspects”—andmanagetorecall itverywell,muchasthey
wouldrecall(anddraw)acircleoratreeorastaircase.Itishardtoexplainwhysomestage1children
showthedistortingeffectsofintellectualoperationswhileothersdonot.
In brief, while there is some variability, the results show that intelligence—the intellectual
operations—structures the child’s recall. Knowledge interacts with perception to produce what is
remembered.
The Development of Memory
According toPiaget, there is a generaldevelopmentalprogression from theearly appearanceof
accurate recognition to the later use of accurate recall.Memory begins in a crude fashion during the
sensorimotorperiod.Atthistime,theinfantshowsevidenceofrecognition.Throughovertorabbreviated
behavior,hedemonstratesthatatoyorapersonisfamiliar.Theinfantdoesnotseemcapableofmore
demandingformsofmemory,especiallyrecall(thisofcourseinvolvesevokingamentalrepresentationof
absentobjectsorevents).Itisonlywiththeonsetofthesemioticfunction,atabout18months,thatthe
childbecomescapableofmentalrepresentationandhencerecall.Earlier,inanothercontext,wecitedthe
exampleofJacqueline,at1;11(11),whouponreturningfromatrip,wasabletoreportoneventswhich
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hadoccurredearlier:“Robertcry,duckswiminlake,goneaway”(Play,Dreams,andImitation,p.222).
Thisisanexampleofrecallinachildwhoisjustbeginningtogiveevidenceoftheuseofthesemiotic
function.Inbrief,infantsshowsignsofrecognitionmemory,whereasrecall,asoneaspectofthesemiotic
function,beginstoappearonlyatabout18months.
Aswehaveseen,oncerecallappears,itsfunctioningisinfluencedbytheintellectualoperations.
Nowweshallseethatthisinfluencecanhavedevelopmentalaspects.Piaget’sexperimentsonmemory
foraseriesshedlightonthisissue.Wealreadyknowthatthechild’srecallafteroneweekisdistortedin
linewithhiscurrentstageofseriation.Butwhathappenstorecalloveralongerperiodoftime,say,sixto
eightmonths?Accordingtotheclassicview,thememorytracesimplyfades,andthisfadingbecomesmore
completeastimegoeson.InPiaget’sview,mattersaremorecomplexthanthat.Inmanycases,theremay
wellbesomedeteriorationofmemoryoveralongperiodoftime.Andyetthereareotherpossibilitiesas
well. Memory, which depends on intelligence, therefore exhibits developmental changes which
correspondtothedevelopmentofintelligence.Indeed,Piaget’stheoryleadstothepredictionthatunder
certaincircumstances,recallmayactuallyimproveovertime.
Inthecaseofseriation,thematterworksasfollows:thestage1childseesawell-orderedseriesand
assimilates it into his intellectual operations. Since these are immature, one week later the child
inaccuratelyrecallsthesticksasacollectionofsmallonesandacollectionoflargeones.Hisintelligence
hasorganizedrecallpoorly.Thenoveraperiodoftime,thechild’smentaloperationsdevelopandhe
enters stage 3. Now, asked to recall the sticks, he remembers a well-formed series. His memory has
improvedovertimebecausehisintellectualstructureshavedevelopedmorefully.
This is indeed precisely the result which Piaget discovered. Of twenty-four stage 1 children,
twenty-twoshowed improvedrecall (asmeasuredbydrawings)when theyadvanced toa later stage
sevenoreightmonthsaftertheinitialtesting.
Severalcommentsshouldbemadeatthispoint.First,independentinvestigatorshavehadahard
timereplicatingthisresult(forexample,Samuels,1976).Agooddealofcarefulresearch,withadequate
controls,needstobedonetopindowntheeffect.Itisparticularlyimportanttoobtaindirectmeasuresof
thechild’sassumed intellectualdevelopment.Second, it is important torecognize thatPiaget’s theory
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doesnotalwayspredictimprovementinlong-termrecall.Improvementcanbeexpectedtooccuronlyif
theinitialrecallwasdistortedbyimmatureintellectualoperationsandiftheseoperationssubsequently
improve.This isaveryspecialcase,however,andoftendoesnotoccur.Forexample, supposeachild
learns someone’snameand tries to recall it ayear later.Memory for thename is likely todeteriorate
regardlessof the child’s stageofdevelopment.The child’s advancement fromstage1 to3of concrete
operationswillhavenoparticularbearingontherecallofnames,sincetherecall ismerely figurative
withnologicaloperationsinvolved.Hereisanotherexample,whichmayseemparadoxical.Supposea
stage1childisshownabadlyformedseries.Afteroneweekheaccuratelyremembersthebadlyformed
seriesbecausehehasassimilateditintohisimmaturementaloperations.Then,overthenextyear,the
child’smentaloperationsadvanceandhehasreachedstage3.Nowwhenaskedtorecallthesticks,he
producesawell-formedserieswhichistheproductofhiscurrentintellectualstructure.Unfortunately,
this is inaccurate recall, since the initial series was badly formed. This example is a case of an
improvement in intellectualstatus leadingtoadeterioration inrecall. (SeveralstudiescitedbyLiben,
1977,actuallyobtainthiskindofresult.)ThemainpointofPiaget’stheoryisnotthatmemorynecessarily
improves over time—it seldom does— but that memory is influenced by developing intellectual
operations,andnotjustbyrealevents.
Summary
Piaget distinguishes between two types of memory. Memory in the wider sense refers to the
individual’sabilitytoretainovertimethepotentialtoexhibitlearnedschemesoroperations.Memoryin
thespecificsensereferstotheindividual’sabilitytoretainovertimeinformationconcerningparticular
events,things,orpersons.Specificmemorymaytakeoneofseveralforms,themostimportantofwhich
arerecognition(animpressionoffamiliarityonanencounterwithapreviouslyexperiencedobject)and
recall(evocationofthepastthroughmentalrepresentations).Piaget’sgeneralhypothesisisthatspecific
memory is influencedby intelligence—the intellectualoperations. Intelligenceserves toorganizeand
shape memory. Piaget rejects the classic view in which events are seen to impress themselves on a
passiveobserver,leavingatraceorasimplecopyofthereality.
Piaget’sexperimentsonmemoryforaseriesdemonstratethatafteroneweek,recallisinfluenced
bytheindividual’sstageofintellectualdevelopment.Presentedwithawell-formedseries,somechildren
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recallnotwhattheyhaveseen,butwhattheyknowabouttheseries.Itisimportanttonote,however,that
there is some variability in these results. According to Piaget, there is a general developmental
progressionfromrecognitionmemorytorecall.Infantsshowsignsofrecognition;recalldoesnotseemto
appearuntiltheonsetofthesemioticfunctionatabout18months.
After it appears, recall is influenced by the development of intellectual structures. The general
hypothesisstatesthatasintellectualstructuresdevelop,theyexertcorrespondingdevelopmentaleffects
onrecall.Indeed,undercertaincircumstances,recallmayactuallyimproveovertime.Piagethasshown
thatinthecaseofseriation,recallbecomesmoreaccurateaschildrenadvancefromoneintellectualstage
to the next. It is important to note, however, that this result is not easily replicated and that Piaget’s
theorydoesnotalwayspredictimprovementinrecallovertime.Instead,themainpointofPiaget’stheory
is thatmemory is influencedandorganized(butnotnecessarily improved)bydeveloping intellectual
operations, and not simply by real events. Memory is the result of an interaction been knower and
known.
CONSCIOUSNESS
Wehaveseenhowthechilddevelopsoperativeandfigurativeaspectsofthought.Bytheageof7or
8years,heachievessomesuccessatclassifyingandorderingobjects,atproducingmentalimages,andat
remembering.Thesecognitiveprocesses,bothfigurativeandoperative,workmainlyonanunconscious
level.NowwewillassumeadifferentlevelofanalysistoconsideranewtopicwhichPiagethasrecently
studied,namely,thechild’sawarenessandverbalizationofhisownthoughtprocesses.
In studying the issueof consciousness,Piaget’s general strategy is first tohave the child solvea
problemandsecondtodeterminehisawarenessofthemethodsofsolution(TheGraspofConsciousness,
GC,1976b).Inoneinvestigation,Piagetusedstandardseriationtasks,involvingsuchmaterialsasasetof
cardsvaryinginheightandwidth,orasetofbarrelsvaryinginbothheightanddiameter.Eachchild’s
taskwastoarrangetheobjectsinorderofincreasing(ordecreasing)size.Hewastold,forexample,to
“makeanicelineofbarrels.”Assoonasthechildbegantodothis,theinvestigatoraskedhimtodescribe
whathewasdoingorwasabouttodo.Sometimesthechildwasasked“howhewouldexplaintoafriend
whatshouldbedone”(GC,p.3OI).Afterthechildcompletedthefirstseries(successfulornot),hewas
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askedtorepeatitandtodescribeandexplainhisactionsashewentalong.Thepurposeofthisrepetition
wastoensurethatthechildknewwhatwasexpectedofhim.
Suppose that a child succeeds at the seriation tasks just described: he produces an accurate
orderingintermsoflengthoftherodsorsizeofthebarrels.Giventhis,wemayinquireintothechild’s
consciousnessorcognizanceofseriation. It is important tobeginbyclarifyingwhat ismeantbyPiaget’s
usageofconsciousnessorcognizance.Piagetuses these termstorefer to thechild’sability toproducea
coherentverbalaccountofthementalprocessesunderlyinghisbehavior.Bythisdefinition,thechildis
consciousorcognizantofhisthoughtprocessesifhesays,forexample,“Ialwayslookforthebiggestone,
then I put it aside and look for the biggest one out of all the ones that are left.” In Piaget’s usage,
consciousnessreferstoanawarenessandverbalizationofone’sownthoughtprocesses.Notonlyisthe
consciouschildabletodosomething;heisalsoexplicitlyawareofhowhedoesit.9NotethatPiagetdoes
notuseconsciousnesstorefertotheelementaryandfleetingperceptionoftheimmediatesituation.Thus
thetermisnotusedtorefertothechild’sawarenessthattherearetoybarrelsonthetableorthathis
handismovingtowardthem,andsoon.Whilesuchelementaryawarenessappearsveryearlyinlifeand
isnodoubthighlyprevalent,itisnotthesubjectofPiaget’sinvestigation.Inbrief,Piagetisinterestedin
the child’s explicit knowledge of his thought processes, and not merely in the crude awareness of
ongoingactivities.
Severalquestionsthenarisewithrespecttoconsciousness.Itisespeciallyinterestingtoinquireinto
the temporal relations between action and cognizance. There are of course several possibilities. One
alternativeisthatactionandcognizanceemergesimultaneously.Asonedevelopssodoestheother,and
it is impossible to determine the direction, or even existence, of causality. A secondpossibility is that
consciousnesscomesfirst,andthusdirectsthesubsequentaction.Perhapsthechildfirstconceptualizes
his action and this helps him to perform it. A third possibility is just the reverse. Perhaps successful
behaviorprecedescognizanceofit.Thechildmaybeablefirsttoperformcertainactions,andonlylater,
uponreflection,doeshebecomeawareofhisbehavior.
ThebehaviorofoneofPiagets’subjects,STO,at6-1,workingatseriation,shedssomelightonthese
issues.Onhisfirstattempt,STOfailedtocompleteasuccessfulseries.Hecouldnotarrangecardsinorder
ofsizeandputthesmallestonesinthecenteroftheline.Hesaid,“I’vemadeastaircasethatgoesupor
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down.”Theexaminerrespondedthatthestaircaseshouldgodownallthetime,“butfirsttellmehoware
yougoingtomakeit?”STOresponded:“I’mgoingtoputthebigone,anotherbigone,anotherbigone,the
middle-sizeone,thesmallermiddle-sizeone,thesmallermiddle-sizeone,andthesmallermiddle-size
one”(GC, p. 312). STO proceeded to produce a good series, with only onemistake, which he easily
corrected.Onsubsequent trials, thesamesortof thinghappened:STOproducedgoodseriesbutpoor
verbaldescriptions.
AccordingtoPiaget,thisexampleshowsthatSTO’sseriationwasfarinadvanceofhisconsciousness
ofit.STOcouldorderthecardsinafairlysystematicwayandyetcouldreferonlyinanimprecisemanner
to“anotherbigone,anotherbigone,”or to “thesmallermiddle-sizeone,andthesmallermiddle-size
one.”Otherchildrenexhibitsimilarbehavior.Forexample,theyuseanextremelysystematicprocedure
forseriation(likeselectingthesmallestandthenthesmallestofallthoseleft)andyetcansayonlythat
theyfirsttookasmallone,thenanothersmallone,andsoon.Piagetconcludesfromdatalikethesethat,
in general, the child’s successful activities—including operative activities like seriation—precede
cognizanceofthem.Thechildcanactandthinkeffectivelybeforehecanverbalizeorbeconsciousofhis
actionsorthoughts.
Howdoesconsciousnessofproblemsolvingdevelop?Piagetproposesthatatfirstthechildisonly
dimlyawareofgoals.Forexample,hewantstomakea“staircase.”Thechildthengraduallydevelops
variousstrategies forachievinghisgoal, forexample,randomplacementorsystematicselectionof the
largest.Atfirst,heisquiteunawareofthesestrategies,justasthe3-month-oldbabyisnotconsciousofthe
procedureswhichheusesforgettinghisthumbintohismouth.Heacts,successfullyorunsuccessfully,
but does not explicitly analyze his actions. With development, however, the child observes his own
activitiesandreflectsonthem.Heinterpretshisactions;hetriesto“reconstruct”themontheplaneof
thought.Atfirst,thisprocessofinterpretationmayleadtodistortionandmisunderstanding.Piagethas
observedmanycasesinwhichtheinitialconsciousnesswasinerror—wherethechilddidnotaccurately
seewhatinfacthehaddone.Butgradually,thereconstructionbecomesmoreandmoreaccurate.The
child’sreflectiononhisownactivitiesallowsthedevelopmentofexplicitknowledgeconcerningbothhis
problem-solving processes and the objects under consideration. In this way, the child learns about
himselfandabouttheobjectssurroundinghim.Hedevelopsabstractconceptsthatcanbeverbalized.
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Piaget’spositionhasmuchtorecommendit.Itseemsusefultomakeadistinctionbetweenatleast
twolevelsofknowledge.Theredoesseemtobeakindof“actionknowledge”or“how-toknowledge”in
whichwesolveproblemsusingmeansofwhichweareunaware.ThusSTOcouldseriate,butwithout
consciousnessofhismethod.Atthesametime,thereisalsoanotherlevelofabstractknowledge,inwhich
wecanexplicitly formulateourmethodsofsolutionandeventheprinciplesunderlyingthem.Thusa
child cannot only seriate but explicitly understands the principles which he uses. The process of
transformingactionknowledgeintoabstractknowledgemaybecrucialforhumanlearning.Thereisa
gooddealofwisdombuiltintoourbehavior,andamajortaskforlearningmayconsistinmakingexplicit
whatinasensewealreadyknowunconsciously.
While these are useful points, Piaget’s investigations in this area seem to suffer from a major
weakness, namely, an overreliance on verbalizations as a source of evidence. In these studies,
verbalizationistakenasthemain,orevenonly,sourceofevidenceforconsciousnessorcognizance.Thus
STOissaidtolackconsciousnessofhisactions,sincehislanguageisinadequate.ButSTO’srepetitiveuse
of vague terms like “the smaller middle-size one” may not accurately reflect the true level of his
consciousness.Seriation ishardtoexpress inwords,andperhapsSTOcouldconceptualize itbutwas
unabletoofferadequatedescriptionsoftheprocess.Piaget’sinterpretationseemsweakinthisregard.At
thesametime,despitethedifficulties,Piaget’sresearchraisesextremelyprovocativeissuesrequiringa
gooddealoffurtherstudy.
GENERAL CONCLUSIONS
Whilecriticismsmayandshouldbemade,andwhilerevisionsarenecessary,Piaget’stheoryisan
enormouslysignificantaccomplishment.Indeed,onreviewingPiaget’slaterworkonthechildfrom2to
11,oneisstruckaboveallbytheincrediblecreativityanddiversityofhiscontribution.Between1940
and1980,Piagetrevolutionizedthestudyof thechild.He introducedascoreof fascinatingproblems
andexperimentaltasks—conservationisonlyoneexample—whichforalongtimedominatedresearch
inchildpsychology.Moreimportant,heofferedanextraordinarilydeepandsubtletheoryofcognitive
development,whichcontinuestoinformourunderstandingofthemind’sgrowth.
Notes
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1SeeH.P.Ginsburg, “TheClinical InterviewinPsychologicalResearch:Aims,Rationales,Techniques,”For theLearningofMathematics,Vol.3(1981),pp.4-11,andS.Opper, “Piaget’sClinicalMethod,” JournalofChildren’sMathematicalBehavior, Vol. 1 (1977),pp.90-107.
2See,forexample,R.GelmanandC.R.Gallistel,TheYoungChild’sUnderstandingofNumber(Cambridge,Mass.:HarvardUniversity,Press,1978),Chap.3.
3 Our exposition of Grouping I is simplified and incomplete: for example, we have defined only one binary operator.We have kept themathematical development at a very informal level. The reader interested inpursuing thematter should see JeanPiaget,TraitedeLogique (Paris:Colin,1949),andalsoj.B.Grize’s formalizationofPiaget’s systemasdescribed inE.W.BethandJeanPiaget,MathematicalEpistemologyandPsychology(Dordrecht,Holland:D.ReidelPublishingCompany,1966).
4 Although it does not seem to help with conservation, counting is far from useless in children’s arithmetic. Hebbeler has shown, forexample,thatyoungchildrenmakeverygooduseofcountingindoingaddition.SeeK.Hebbeler,“YoungChildren’sAddition,”JournalofChildren’sMathematicalBehavior,Vol.1(1977),pp.108-21.
5Strictly speaking, in the caseofnumberPiagetusesa somewhatdifferent logico-mathematicalmodel, called theGroup. The essentialdifferencebetweentheGroupingsandtheGroupisthatthefifthGroupingoperation,tautology(e.g.,A+A=A),isnotusedintheGroup.TautologydoesnotapplytonumbersincethereA+A=2A,notA.Therefore,theGroupmustbeusedfornumber.
6Recently,GelmanandBaillargeon (1983,p.171)haveargued that thephenomenonof invariant sequence isnotas clear-cutasPiagetsuggests.Theydescriberesearchshowingthat insomeareassomechildrendonotexhibitthestagesintheorderpredictedbyPiaget.Thisseemstopresentseriousdifficultiesforthetheory.
7Therecanbeinstancesoffalserecall.Piagethimselffalselyrememberedbeingtheobjectofanabortivekidnapattemptwhenhewasachild.
8 Piaget’s exposition of the classic view probably refers to theorists like Ebbinghaus, who in the nineteenth century invented nonsensesyllablesandspentmanyyearsofhislifememorizingthemhimself.Hewashisonlysubjectanddeservessomesortofprizefor an immense capacity for boredom. In recent years, however, theorists ofmemory have given up both the inclinationthemselves tomemorize nonsense syllables (althoughmay require their subjects to do it) and theoretical accountswhichtreat thesubjectaspassive.Manymoderntheoriesare insubstantialagreementwithPiageton the issueofactivity.ForacomparisonofPiaget’s theorywithothers, aswell asanexcellent critiqueofPiaget’swork, seeL.Liben, “Memory fromaCognitive-DevelopmentalPerspective:ATheoreticalandEmpiricalReview,”inKnowledgeandDevelopment,W.F.OvertonandJ.M.Gallagher,eds.(NewYork:PlenumPress,1977),Vol.I,pp.14-9-203.
9Recently, Flavell andothershavebeen investigating a similar topic,which they term “meta cognition,” andwhich involves the child’sknowledgeabouthisownknowledge.(Forareview,seeJ.H.Flavell,CognitiveDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1985.)Anexampleiswhetherthechildisawareofusingsystematicstrategiestoaidinmemory.
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The Years 2 through 11: Piaget’s Later Work
ThischapterdealswithaspectsofPiaget’slaterwork(fromapproximately1940onward)onthe
childfromabout2to11years.AswasshowninChapter1,thisportionofPiaget’sresearchandtheoryis
voluminous and covers suchmatters as the child’s conception of chance, space, geometry,movement,
number,andother topics.Sincewecannotreviewall the laterworkhere,weshall focusonwhatwe
consider tobebasic issues and conceptswhich reappear in andapply to almost all ofPiaget’s recent
writings.We will consider (1) the revised clinical method, (2) the child’s classification of objects or
events, (3) the ability to place them in ordinal relations, (4) the concept of number (particularly its
conservationovertransformations),(5)thenatureofmental imagery,(6)thedevelopmentofmemory
andconsciousness,and(7)somegeneralcharacteristicsofthought.
THE REVISED CLINICAL METHOD
WesawinChapter3thatPiaget’soriginalclinicalmethodwashighlydependentonverbalizations.
Theexaminerposedthequestionsinwords,andthechildwasrequiredtogivetheanswersinthesame
way.Theexaminer’squestionsusuallydidnotrefertothingsoreventsthatwereimmediatelypresent,
andtheproblemsdidnotalwaysinvolveconcreteobjects
whichthechildcouldmanipulateorevensee.Forexample,theexaminermightdepictachildwho
had unwittingly broken some cups andmight then ask the subject being questioned for a judgment
concerningthechild’snaughtinessandthepunishmenttobemetedout.Insuchasituationasthis,the
subjectisrequiredtodoseveralthings.Hemustinterprettheexaminer’sdescriptionsoastopicturethe
scenetohimself;hemustmakeaspecialefforttocomprehendcertaincrucialaspectsofthequestion,like
theword“naughty”;andhemustexpresshisjudgmentinwords.
Aftersomeexperiencewiththismethod,Piagetcametofeelthatitwasinadequatebecauseitrelied
too heavily on language. The childmight not understand everything said to him, particularly if the
wordsdidnotalwaysrefertoconcreteobjects.Evenifthechilddidunderstand,perhapshecouldnot
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adequately express in words the full extent of his knowledge. Consequently, Piaget modified his
procedures, and the result iswhatwe shall call “the revised clinicalmethod” (sometimes called the
“method of critical exploration”). The new method involves several features. First, the examiner’s
questionsrefer toconcreteobjectsoreventswhichthechildhasbeforehim.No longermust thechild
imaginethesethingsmerelyonthebasisofaverbaldescription.Second,aneffortismadetoletthechild
expresshisanswerbymanipulatingtheobjects,andnotsolelyexpresshimselfthroughlanguage.
For example, let us suppose that the examinerwishes to knowwhether the child can form two
distinctclasses.Toinvestigatethematterhemightpresentthechildwithanarrayofcirclesandsquares
allmixedtogetherinnoorder,andaskhimtoputtogethertheonesthatbelongtogether,orsortouttwo
distinctpiles.Whatthechilddoeswiththeobjects—whatsortofpileshemakes—andnotwhathesays
aboutthem,constitutestheprimarydataofthestudy.Ifafterencouragementachildstillcannotforma
pileofcirclesseparatefromapileofsquares,thentheexaminermightconcludethathedoesnothavethe
classificationskillsunderinvestigation.Whilecompletelynonverbaltestsaredesirable,itisoftenhardto
inventthem.ThisisespeciallytrueforPiaget,sinceheusuallyinvestigatesthechild’sunderstandingof
abstractconceptsthatarenoteasilymanifestedinthebehavioralmanipulationofconcretematerials.The
revisedclinicalmethod, therefore,mustoftendepend for itsdataon thechild’sverbal responses.But
evenwhenthisisnecessary,thechild’sanswersrefertoaproblemstatedintermsofconcretematerials
whicharepresent.
Third, Piaget introduced the use of counterarguments or countersuggestions. These involve
presentingthechildwithapointofviewthatcontradictshisown,andaskinghimwhathethinksofthe
opposingview.Thepurposeofthesecounterargumentsistodeterminethestabilityandauthenticityof
thechild’sthinking.Childrenwhohavemasteredaconceptwillresistthecountersuggestion;thosewho
havenottendtobeswayedbythecontradictoryargument.
Afourthfeatureoftherevisedclinicalmethodisnotnew:theexaminer’squestioningisflexible.
Ratherthanemployastandardizedlistofquestions,hemodifiesthemoraddsnewonesasthesituation
demands.Asbefore,Piagetstillfeelsthatthereisnopointeitherinaskingachildaquestionthathedoes
notunderstandorinfailingtoclarifyananswer.
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To summarize, the revised clinical method involves posing questions concerning concrete
materials; allowing the child to “answer” by manipulating the materials, if this is at all possible;
introducing counterarguments; and, as in the earlier clinicalmethod, statingquestions andpursuing
answersinaflexibleandunstandardizedway.Whetherornottherevisedclinicalproceduregivesan
accurateassessmentofthechild’sabilitiesisamatterfordebate.Ingeneral,mostpsychologists(outsideof
Geneva) do not use this method in research, mainly on the grounds that it is not sufficiently
standardized.Wethink that thisattitude ismistaken,especiallysince thereareverygoodreasons for
avoiding standardization.1 In any event, the revised clinical method is less exclusively verbal than
Piaget’searlierprocedureandattemptstogiveanaccurateassessmentofthechild’sthoughtprocesses
whichinlargemeasuremaybenonverbal.
CLASSIFICATION
Piaget has used the revised clinical method to study classification in the child. The preceding
chaptershavealreadytouchedonthisandrelatedmatters,anditmaybeusefultoreviewsomeofthe
materialhere.Wesawthatthereisaprimitivesortofmotorclassificationinthesensorimotorperiod(0to
about2years)whentheinfantappliestoobjectsintheenvironmentabbreviationsoffamiliarschemes.
Forexample,Luciennesawatoyparrothangingabovehercribandkickedherfeetveryslightly.Thiswas
anabbreviationofaschemewhichshecouldquiteeasilyhaveappliedtothepresentsituation.Itseemed
asifheractionclassifiedtheparrotasa“thingtobeswung.”Moreover,theabbreviationshowsthatthe
behaviorwasbecominginternalized.Eventuallyitcouldbereplacedbythethought:“That’stheparrot;
that’s something I can swing.” But the abbreviated schemes are not yet instances of legitimate
classification.Onereasonisthattheschemesapplytoindividualobjectsoveraperiodoftimeandnottoa
collectionofobjects.Forexample,Luciennekickedfromtimetotimewhenevershesawparrotsandthus
indicatedrecognition.Butthis
recognitiondoesnotimplythatsheconsideredtheparrotstobelongtoaclass.Matureclassification,
on the other hand, involves the conception of a collection of things, whether they are immediately
presentorimagined.AsecondreasonwhyitisnotpossibletocreditLuciennewithclassificationhasto
do with inclusion relations, which will be expanded on shortly. Briefly, this refers to the ability to
constructahierarchicalclassification,suchthattoyparrotsareasubclassofalarger,moreinclusiveclass
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liketoysingeneral.
From about 2 to 4 years the child begins to classify collections of objects in away that is quite
primitive. He uses the preconcept. Sometimes he fails to see that one individual member of a class
remains the same individual despite slight perceptual changes, and sometimes he thinks that two
different members of the same class are the same individual. Between 5 and 10 years, the child’s
classificationisstillfaultyinseveralways.Thereisthephenomenonofjuxtaposition,theinabilitytosee
thatseveralobjectsareindeedmembersofthesameclass.Thereisalsosyncretism,thetendencytogroup
togetheranumberofdisparateeventsintoanill-definedandillogicalwhole.
As was pointed out, Piaget’s investigations of the preconcept, syncretism, and juxtaposition,
conductedinthe1920sand1930swerepreliminaryandtentative.First,thereexistedmethodological
defects:thedatawerealmostexclusivelyverbalsothatPiaget’sinterpretationwasbasedlargelyonwhat
the child said. Second, Piaget’s concepts—syncretism, juxtaposition, the preconcept—were somewhat
vagueandneededelaboration. Inthe1950sPiagetreturnedtothestudyofclassificationinthechild
fromabout2to12years.Theseinvestigationsmakeuseoftherevisedclinicalmethod;theyalsomodify
thenotionsofpreconcept,syncretism,and juxtapositionandsuggestnewwaysofconceptualizingthe
child’sclassificatoryactivities.
Some Properties of a Class
BeforeexaminingPiaget’sresearchintoclassification,wemustclearlyunderstandwhathemeans
byaclass.Supposewehavebeforeusanumberofobjectsallmixedtogether.Thearraycontainsalarge
red triangle, a small blue circle, a large pink circle, and a small black triangle. All the objects are
discriminablydifferentonefromtheother.Thatis,thereisnodifficultyinperceivingthatanyoneobject
isdifferentfromanyoftheothers.Forexample,thelargeredtriangleisveryobviouslylargerandredder
thanthesmallblacktriangle.Suppose,too,thatwewishtoplacetheseobjectsintotwodifferentclasses.
Onewayofdoingthisistoputinoneseparatepilethelargeredtriangleandthesmallblacktriangle.In
thesecondpilewouldgothesmallbluecircleandthelargepinkcircle.Iftheoriginalarraycontained
additionaltriangularobjects,regardlessoftheir
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sizeorcolor,theywouldofcoursegointhefirstpile.Similarlyallothercircularobjectswouldgoin
thesecondpile.Thetwopileseachrepresentaclass.Ofcourse,wemightclassifytheobjectsinanother
way.Wecouldputinonepilethetwosmallobjects(regardlessoftheircolororshape)andinthesecond
pilethetwolargeobjects.Thereareusuallymanydifferentclassesthatonemayformfromagivenarray
ofobjects.
Piagetmakesanumberofpointsabouttheclassesformedfromtheoriginalarray(forpurposesof
illustrationconsiderjustourfirstexample,theclassoftrianglesandtheclassofcircles):
1.Noobjectisamemberofbothclassessimultaneously.Forexample,thelargeredtriangleisintheclassoftrianglesandnotalsointheclassofcircles.Thus,theclassesaremutuallyexclusiveordisjoint.Thisholdseven if therearemore than twoclasses formed. (Forexample, wemight divide some animal pictures into the classes of lions, tigers, andelephants,allofwhicharedisjoint.)
2.Allmembersofaclasssharesomesimilarity.Forexample,thesmallbluecircleandthelargepinkcirclebothsharethepropertyofcircularity.Circularityisthedefiningproperty,thecrucialattribute,oftheclass;thatis,weincludeintheclassofcirclesanyobjectwhichiscircular.Anotherwayofputtingitistosaythatcircularityistheintensionoftheclass.Thedefiningpropertyorintensionoftheotherclassistriangularity.
3.Eachclassmaybedescribedintermsofalistofitsmembers.Insteadofdescribingaclassintermsofitsdefiningpropertyorintension(forexample,theclassoftriangularobjects),wemay simply list theobjects in the class (forexample, large red triangleandsmallblack triangle). Sucha list is theextensionof the class.Note that the listmay involveconcreteobjects(likelarge,bluecircles)orabstractideas,events,actions,andsoon(likethelistofthepartsofspeech).
4. The defining property of a class determineswhat objects are placed in it. Anotherway ofstatingthisisthatintensiondefinesextension,orthe“fieldofapplication”ofaconcept.Forexample,ifweknowthatoneclassistobeformedonthebasisoftriangularityandanotheronthebasisofcircularity,wecanpredictthecontentofthelistofobjectsineachclass.
Thesearesomefundamentalpropertiesofclasses,asPiagetdefinesthem.(Thereareothercrucial
attributestoo,likeinclusionrelations,whichwewilldiscusslater.)Piagetthenaskswhetherthechild
classifiesobjectsinaccordancewiththeseproperties.Whenaskedtogroupobjects,doesthechildform
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mutuallyexclusiveclasses?Dohisclasseshavedefiningpropertieswhichdeterminethelistofobjectsin
eachclass?
Piaget discovers three stages of development. The first two—both of which we may call
preoperational—occur roughlyduring theyears2 to7.The third stage—thatofconcrete operations—
occursroughlyfromtheyears7to11.
Stage 1
To investigate classification,Piagetperformedanumberof experimentswhichused the revised
clinicalmethod.Inonestudy,hetestedanumberofchildrenfromabout2to5yearsofage.Theywere
presentedwith flat geometric shapes ofwood and of plastic. The shapes included squares, triangles,
rings,andhalf-rings,allofwhichwereinseveralcolors.Theshapesweremixedtogetherandthechild
wastold:“Puttogetherthingsthatarealike.”Sometimesadditionalinstructionsweregiven:“Putthemso
thatthey’reallthesame”or“Putthemhereifthey’rethesame,andthenoverthereifthey’redifferent
fromthisonebutthesameaseachother”(EarlyGrowthofLogic,EGL,p.21).
Thechildrendisplayedseveralmethodsofgroupingtheobjects.Onemethod iscalledthesmall
partialalignment.Withthismethodthechildusesonlysomeoftheobjectsintheoriginalarrayandputs
them together in severalways apparentlywithout any overall guiding plan. For example, one child
beganbyputtingsixhalf-rings(semicircles)ofvariouscolors inastraight line; thensheputayellow
triangle on top of a blue square; later she put a red square in between two blue triangles; then put
squaresandtrianglesinnoparticularorder,inastraightline.Thereareseveralpointstonoteaboutthis
performance. Sometimes similarities among objects determine the collection. For example, the subject
whoseperformancewas just describedbeganwith a line of half-rings. At other times the same child
groupedthingsonthebasisofnodetectablesimilarity;thatis,sheputayellowtriangleonabluesquare,
oraredsquarebetweentwobluetriangles.Inbothofthesecases,thereisnosimilarityofeithercoloror
form.
Itisclearthatsmallpartiedalignmentsarenottrueclassesforseveralreasons.Oneofthemisthat
intension does not define extension; that is, no consistent defining property determined which
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geometric formswereput invariouscollections.Thechilddoesnotoperateunderanoverallguiding
plan like a system of rules (defining properties) which organize theway in which he arranges the
objects.
Otherchildrenofthisageusethegeometricfigurestoconstructaninterestingformorpicture.One
childarrangedanumberofcirclesandsquarestorepresentalongverticalobjectandthenproclaimedit
tobetheEiffelTower;anotherchildplacedanumberofhalf-ringsinbetweenseveredsquares,allina
horizontalline,anddescribedtheresultasabridge.Piagetcallstheseproductionscomplexobjects.Itis
obviousthatlikethesmallpartialalignments,andlikesomeothertypesofcollectionsnotdescribedhere,
thecomplexobject isnotatrueclass.Figuresarenotplaced inthecomplexobjectbecausetheyshare
somedefiningproperty;rather,extensionisdeterminedsolelybytherequirementsofthepictureunder
construction.
Inanotherinvestigation,Piagetpresentedchildrenofthesameagewithnongeometricfiguresfor
classification—little toyswhich included people, houses, animals, and so on. Once again, the results
showedaninabilitytoformclasses.Onechildputtwodollsinacradle,thentwowheelbarrowstogether,
thenahorse.Whentheexamineraskedthechild forall theobjects likeahorse,shegavehimall the
animalsandthenababyandtwotrees.Thisexampleillustratesthefactthatalthoughtheyoungchild
may perceive similarities among the objects, these do not fully determine what objects go into the
collection. That is, the child saw that all animalswere in some respect similar and gave them to the
examinerwhenaskedforobjectslikethehorse.Ifthechildhadstoppedthere,shemighthaveformeda
classwhichwasbasedonthedefiningpropertyof“animalness.”However,shewentontothrowinthe
babyand two trees.The similarity (intension) that she firstperceiveddidnot fullydeterminewhich
objectswere to be grouped together (extension). It is as if the child forgot about the initial defining
property(animalness)andthenswitchedtosomeother.
Wemaymakeseveral commentson these investigations.First, theymakeclear thenatureof the
revisedclinicalmethod.Theexaminergivesthechildconcreteobjectstoworkwith.Thetaskinstructions
andquestionsarestillverbal,ofcourse,buttheyrefertorealthingsthatthechildcanmanipulate.The
childisrequiredtosayverylittle.Mostofhisresponsesarenotverbalbutbehavioral.Hedoesnothaveto
saythatalloftheanimalsdoordonotgotogether;rather,hecanputthemtogetherorfailtodoso.
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Second,althoughtherevisedclinicalmethod isan improvementoverwhatwasusedbefore,we
wonderwhetherthetaskwasentirelycleartothechild.Theinstructions(e.g.,“Puttogetherthingsthat
arealike”)seemrathervagueandsusceptibletomanyinterpretations.Wesuspectthatdifferentmethods
of presenting the task to the child might produce entirely different results. Piaget considered this
objectionandtriedanessentiallynonverbalmethod.Hebegantoclassifytheobjectshimselfandasked
thechildtodothesamething.Theresultagainwasnottrueclassification,but“complexobjects,”andso
on.Whilethismethodwasnotsuccessful,itdoesnotexhaustthepossibilities.Otherinvestigatorshave
exploreddifferentprocedures,withsomesuccess.2
Stage 2
Childrenfromabout5to7yearsproducecollectionsthatseemtoberealclasses.Whenpresented
withthesituationdescribedearlier,onechildproducedtwolargecollections,onewhichcontainedall
thepolygonsand theother the curvilinear forms.Moreover, eachof these collectionswas subdivided
further. Thepolygons, for instance, contained separatepiles of squares, triangles, and so on, and the
curvilinearformsinvolvedseparatecollectionsofcircles,half-rings,andsoon.Thus,thechildnotonly
seemstoformclasses,butarrangesthemhierarchically,asinFigure2.Therearetwogeneralcollections
(polygons and curvilinear forms) at the top of the hierarchy, and these both branch out into several
subcollections below (squares, triangles, etc.). The child’s activities may be characterized in several
additionalways.(1)Heplacesintheappropriatecollectionalloftheobjectswhichwereintheinitial
array.Theyoungerchilddidnotdo this;he leftsomeobjectsunclassified. (2) Intension fullydefines
extension.Thatis,ifthechilddefinesacollectiononthebasisofthedefiningpropertyofcircularity,all
circlesgointothatpile,andnoneisplacedinanyotherpile.(3)Atagivenlevelofthehierarchy,similar
definingpropertiesareusedtodeterminecollections.Forexample,atthelowerlevelofthehierarchyin
Figure2,allthecollectionsaredefinedintermsofgeometricform—squares,triangles,andsoon.Itisnot
thecasethatsomecollectionsaredefinedbyformandsomebycolor.Tosummarize,itwouldseemthat
thechildfromabout5to7yearsproducesratherelaboratehierarchicalcollectionswhichdeservetobe
calledtrueclasses.
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FIGURE2Classificationofgeometricobjects.
Piaget feels, however, that the child of this stage fails to comprehend one crucial aspect of the
hierarchyhehasconstructed.Thechilddoesnotunderstandkeyrelationsamongthedifferentlevelsof
thehierarchy.Thisistheproblemofclassinclusionwhichwewillnowillustrate.Supposewearegivena
randomly organized array of blue and red squares and black and white circles. We construct an
arrangement(seeFigure3)suchthattherearetwomajorcollections(squaresversuscircles)andwithin
eachofthesetherearetwofurthersubdivisions(blueversusredsquaresandblackversuswhitecircles).
Thus,thereisahierarchywhosehigherlevelisdefinedbyshapeandwhoselowerlevelisdefinedby
color.Consider for themomentonlyone-halfof thehierarchy,namely, thesquareswhicharedivided
intoblueandred.Ifweunderstandinclusionrelations,thenwecanmakestatementsofthissort:(1)All
ofthesquaresareeitherblueorred.(2)Therearemoresquaresthantherearebluesquares.(3)There
aremoresquaresthanthereareredsquares.(4)Iftheredsquaresaretakenawayfromthesquares,then
theblueonesareleft.(5)Ifthebluesquaresaretakenawayfromthesquares,thentheredonesareleft.
(6)Allthebluesaresquares,butonlysomeofthesquaresareblue.These,then,aresomeofthepossible
statementsaboutinclusionrelations—therelationsofthepartstothewhole,ofthewholetotheparts,
andthepartstotheparts.Theymayseemveryobvious,butsodomanyotherprincipleswhichchildren
failtounderstand.
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FIGURE3Classificationofsquaresandcircles.
Piaget investigated the understanding of inclusion relations in children of various ages. Let us
considernowthechildfromabout5to7years.Piagetpresentedeachofhissubjectswithanumberof
picturesof flowersandotherthings.Thechildwasfirstrequiredtogroupthepicturesinanywayhe
wished, and then he was asked a number of questions concerning inclusion relations. The results
concerning spontaneous classification replicatedwhatwas found earlier: the child from5 to 7 years
constructscollectionswhichseemtoinvolveahierarchy.Onechildformedtwolargecollections:flowers
versusotherthings;thenhefurthersubdividedtheflowersintoprimulasversusotherkindsofflowers.
IntermsofFigure4,thechildseemedtohaveconstructedthetoptwolevelsofthehierarchy.(Hedidnot
makeafurthersubdivisionintermsofyellowversusotherprimulas.)Itwouldseemthattheconstruction
ofsuchahierarchyimpliestheunderstandingofinclusionrelations.Ifthesubjectdividedtheflowers
intoprimulasversusotherkinds,musthenotunderstand that therearemore flowers than thereare
primulas? The results of Piaget’s questioning, however, point to different conclusions. Consider this
protocolofachildaged6years2months:
A little girl takes all the yellow primulas andmakes a bunch of them, or else shemakes a bunch of all theprimulas.Whichwaydoesshehavethebiggerbunch?—Theonewith theyellowprimulaswillbebigger. [Hethencountedtheyellowprimulasandtheotherprimulasandfoundthattherewerefourofeachkind]Oh no,it’sthesamething....—Andwhichwillbebigger:abunchmadeupoftheprimulasoroneofalltheflowers?—They’reboththesame.(EGL,p.102)
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FIGURE4Classificationofflowersandotherthings.
Although this child had earlier constructed a hierarchical arrangement of the materials, he
maintainedthattheyellowprimulasdidnotformasmallercollectionthantheprimulasasawholeand
thattheprimulasdidnotformasmallercollectionthantheflowersasawhole.Bothoftheseanswers,of
course,arequitewrong.Inbothcases,thepartissmallerthanthewholefromwhichitderives.
What is the explanation for the child’s inability to comprehend inclusion relations? Piaget
postulates that once the child has divided a whole into two subgroupings, he cannot then think
simultaneouslyintermsofthelargercollectionandthesubdivisionswhichhehasconstructedfromit.
For example, suppose a child divides a collection of flowers (thewhole) into primulas versus other
flowers(subdivisionsofthewhole).Whenheisasked“Aretheremoreprimulasormoreflowers?”he
mustconsiderboththeoriginalcollection(flowers)andoneofhissubdivisions(primulas)atthesame
time.Hemustcomparethe“size”ofoneagainstthatoftheother.Undertheseconditions,hefocusesor
centersonthecollectionhecansee(theprimulas)andignorestheoriginalcollection(alloftheflowers),
whichisnolongerpresent in its initialstate(acollectionoftheprimulasandotherflowersallmixed
together).Andsincehecentersonthepart,ignoringthewhole,hisanswerstoinclusionquestionsare
oftenwrong.
Stage 3
Childrenfromabout7to11yearsofagearebothcapableofconstructinghierarchicalclassifications
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andofcomprehendinginclusion.Forexample,afterconstructingahierarchy,onechildof9yearsand2
monthswasasked:
Whichwouldmakeabiggerbunch:oneofalltheprimulasoroneofalltheyellowprimulas?—Alltheprimulas,ofcourse,You’dbetakingtheyellowonesaswell.—Andalltheprimulasoralltheflowers?—Ifyoutakealltheflowers,youtaketheprimulastoo.(EGL,p.109)
Thisprotocolmakesquiteclearthechild’sabilitytothinksimultaneouslyintermsofthewholeand
itsparts(e.g.,“Ifyoutakealltheflowers,youtaketheprimulastoo”).Whilehephysicallyseparatesthe
flowersintoprimulasandotherkinds,thechildisabletoreasonbothabouttheoriginalwholeandits
part at the same time.His thought hasdecentered from exclusive preoccupationwith the part or the
whole.
Piagetalsofoundthatwhenthechildofthisagewasaskedthesamequestionsabouthypothetical
objects,thesubjectoftenfailedtogivecorrectanswers.Apparently,thechild’sclassificationisconcrete:
he understands the inclusion relations of a group of real objects, but fails to comprehend the same
relationswhenimaginaryclassesareinvolved.Thegapbetweenhypotheticalandconcretereasoningis
anotherexampleofverticaldécalage.
Wemaysummarizebystatingthatthechildfrom7to11hasreachedthemostadvancedstageas
farastheclassificationofconcreteobjectsisconcerned:hecanconstructahierarchicalarrangementand
understand the relations among the levels of the hierarchy. Piaget then proposes that this
accomplishmentcanbedescribedintermsofalogicomathematicalmodel.Letusexplorethisidea.
Rationale for the Use of a Logicomathematical Model
WehaveseenthatPiagetattemptstodescribethebasicprocessesunderlyingtheclassificationof
objectsor events.Heproposes that the stage1 child (2 to4or5years) fails to constructhierarchical
arrangementspartlybecauseafterashortwhileheforgetsthedefiningproperty(intension)whichhe
hasusedtoformacollection.Thestage2child(5to7years)canconstructahierarchybecauseofthe
ability to use a defining property to determinewhich objects go in a collection, but at the same time
cannot understand inclusion relations because of the inability to simultaneously consider several
immediatelypresentcollectionsandthelargeronefromwhichtheywerederived.Thestage3child(7to
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11years)cancorrectlyanswerquestionsconcerninginclusionbecauseofhisabilitytothinkoforiginal
classesandtheirderivativesatthesametime.
Thusfar,wehavedescribedthesebasicprocesses(theabilitytothinksimultaneouslyofsubclasses
andlargerclasses)intermsoftheordinarylanguage.Manypsychologistsbelievethatthisistheproper
procedure;butothers,includingPiaget,feelthatdescriptionsofstructureshouldbephrased,asmuchas
possible,inaformallanguagelikemathematics.
Letusconsiderfirst,however,someaspectsoftheuseofthecommonlanguage.Mostpsychological
theorieshavebeenstatedinthisway.Freud,forexample,wroteexclusivelyinGermanandnotinlogic
nor mathematics, and no doubt there is not a single formula in the entire corpus of psychoanalytic
doctrine.AnotherexamplefromanotherpointonthepsychologicalspectrumisTolman,anexperimental
psychologist,whoproducedhistheoriesoflearninginordinaryEnglishandmadeuseofonlyafew(and
nonessential) symbols.TolmanandFreudarehardly isolatedexamples.Today, too, themajorpartof
psychological theorizing is done in English, or Russian, and so forth. Several advantages are usually
claimedforthisprocedure.Theordinarylanguagemaybericherandsubtlerthanformallanguages,and
alsoitisgenerallyeasiertoreadthanmathematicsorlogic.
However,anotherapproachtothisproblemispossible.Piagetfeelsthatforscientificpurposesthe
ordinary language is fundamentally ambiguous and must be supplemented by formal approaches.
Anyoneevenslightly familiarwith thehistoryofpsychologyknows thatmost, ifnotall,psychological
theories stated in the common languagehavebeenvagueandeasily susceptible tomisinterpretation.
Even today there aremany fruitless arguments over themeaningofwords like “concept” or “ego” or
“learning.”Asanexample,letusconsidertheword“thought,”whichwehaveusedwithoutdefinition
quitefrequently.Nodoubt“thought”meansquitedifferentthingstodifferentreaders.Tosomeitmay
mean “ideas,” and to some “consciousness”; to others it may mean “mental effort,” “meditation,”
“concentration,”“opinion,”andsoforth.Isitanywonderthatagivenpsychologicaltheorywhichuses
words like this will elicit a variety of interpretations and, hence, considerable argument and
misunderstanding?PerhapsaprimeexampleofthedifficultyisPiaget’sownuseofverbaltheoriesinhis
earlywork.Considerableconfusionstillsurroundstheterms“egocentrism,”“moralrealism,”andsoforth.
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Piaget feels, then, that the ordinary language produces obscure and ambiguous psychological
theorizing, andmust therefore be supplemented, if not replaced, by othermodes of description. The
physical sciences have convincingly shown that mathematics is an extremely powerful tool for
communicating certain precise ideas. Piaget—along with increasingly large numbers of other
psychologists—feelsthatitwouldbefruitfulforpsychologytoadoptasimilarapproach,andhehimself
has attempted to do so in the case of classification and othermatters. Let us now explore his formal
descriptionofthestructureofclassification.
FIGURE5Classificationhierarchy.
Grouping I
The formal description called a Grouping3 begins with this situation: we have a classification
hierarchyofthesortconstructedbythe7-to11-year-oldchildreninPiaget’sexperiments(seeFigure5).
Thisiswhatwestartwith(thatis,itisagiven)andtheGroupingdescribeswhatthechildcandowith
thehierarchy.Atthetopofthehierarchythatthechildhasconstructedarethetwoclasses,flowerswhich
weshallsymbolizeas(C)andotherthings(C').Onthemiddlelevelofthehierarchywefindprimulas
(B)andotherflowers(B').Onthelowestlevelthereareyellowprimulas(A)andprimulasofothercolors
(A').Eachoftheclasses(A,A',B,B',C,C')isanelementofthesystem.Thereisonebinaryoperatorthatmay
beappliedtotheelements,namely,combining.Wewillsymbolizecombiningby+,althoughthereader
shouldbeawarethatcombiningclassesisnotpreciselyequivalenttoaddingnumbers.Theoperator+is
binarysinceitcanbeappliedtoonlytwoelementsatatime.Justaswecanaddonlytwonumbersatany
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onetime,sowecanonlycombinetwoclassesatatime.
Given theelements and thebinaryoperator, the fiveproperties describe theways inwhich the
operatormaybeappliedtotheelements.
Thefirstpropertyiscomposition(usuallyreferredtoinmathematicsasclosure)whichstatesthat
whenwecombineanytwoelementsofthesystemtheresultwillbeanotherelementofthesystem.For
example,ifwecombinetheyellowprimulaswiththeprimulasofothercolors,wegetthegeneralclassof
primulas.ThismaybewrittenasA+A'=B.Orifwecombinetheyellowprimulaswithalltheprimulas,
wegetall theprimulas.WemaywritethisasA+B=B.Thispropertydescribesaspectsofthechild’s
abilitytounderstandahierarchy.Forexample,hecanmentallyconstructalargerclassbycombiningits
subclasses.
Thesecondpropertyisassociativity,whichmaybestbeillustratedinaconcretemanner.Suppose
we want to combine three classes such as yellow primulas, primulas, and flowers (A, B, and C,
respectively). Remember thatwe cannot just add all three of them together simultaneously since the
operator (combining) is binary; that is, it can be applied to only two elements at a time. Given this
limitation,thereareatleasttwowaysofaddingA,B,andC.Wemightfirstcombinetheyellowprimulas
andtheprimulasandgetprimulas.Thatis,wedoA+B=B.Thenwemightcombinethisresult(B)with
flowers-in-general(C)andgetflowers-in-general.Thus,wedoB+C=C.Tosummarize,wefirstperform
A+B=BandthenB+C=CsothatourfinalresultisC.Anotherwayofstatingthisis(A+B)+C=C.
There is yet a second way of combining the classes. We could start by combining the yellow
primulas(A)withthecombinationofprimulasandflowersingeneral(B+C)andfinishwiththesame
result:flowers-in-general,(C).ThuswecanwriteA+(B+C)=C.Notethatthefinedresultofperforming
theoperationbyeithermethodisC,sothatthetwomethodsmaybeconsideredequivalent.Wemaywrite
thisequivalenceas(A+B)+C=A+(B+C).Thisequationexpressesthefactthatthechildcancombine
classesindifferentordersandcanrealizethattheresultsareequivalent.
The third property is identity, which states that there is a special element in the system (the
“nothing” element), that produces no changewhen combinedwith any of the other elements. If we
combine the nothing elementwith the yellowprimulas the resultwill be the yellowprimulas. Ifwe
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symbolize nothing by 0, thenwe have A + 0 = A.More concretely, if we do not combine the yellow
primulaswithanyoftheotherclasses,then,ofcourse,westillhavetheyellowprimulas.
Thefourthpropertyisnegationorinverse,whichstatesthatforanyelement(class)inthesystem,
thereisanotherelement(theinverse)thatproducesthenothingelementwhencombinedwiththefirst
element.Thatis,ifweaddtotheclassofyellowprimulasitsinverse,thenweareleftwithnothing.The
inverseisequivalenttotheoperationoftakingawaythesameclass.Ifwestartwithyellowprimulasand
combinewiththisclassitsinverse,weareineffecttakingawaytheyellowprimulaswiththeresultthat
weareleftwithnothing.WecanwritethisasA+(-A)=0orA-A=0.Theinverserulemightapplytoa
trainofthoughtlikethis:“SupposeIcombinetheyellowprimulaswithalloftheotherprimulas.ThenI
havealloftheprimulas.ButifItakeaway[inverseornegation]alloftheotherprimulas,thenIamleft
again just with the yellow primulas. ’ ’ Note how this train of thought is reversible. First, the other
primulasareadded,butlatertheyaretakenaway,sothatthethinkerisonceagainatthepointwherehe
started.Negation,then,isonekindofreversibility.
Theinversealsomaybeusedtoexpressaspectsofclassinclusion.Supposewestartwiththeclassof
primulas (B) and take away (or add the inverse of) the primulas which are not yellow (A'). This
operationleavesuswiththeyellowprimulas(A).WemaywritethisasA=B+(-A')orA=B-A'.Thistype
ofreasoningunderliesthechild’sabilitytosaythattherearemoreprimulasthanyellowones,thatthe
yellowprimulasareincluded intheclassofprimulas,orthattheyellowprimulasareonlysomeofthe
primulas.
Thefifthpropertyactuallyencompassesseveralaspects.Oneofthemisrelatedtospecialidentity
elements.Supposewecombinetheclassofyellowprimulaswithitself.Theresultisyellowprimulas.We
maywritethisasA+A=A.Inthisequation,Afunctionsasanidentityelementlike0.AddingAtoAislike
adding0toA:theresult,A,isunchanged.Piagetcallsthistautology.Anotheraspectisresorption.Ifwe
combinetheclassofyellowprimulaswiththeclassofprimulas,theresultisprimulas.Wemaywritethis
asA+B=B.Here,too,Afunctionsasanidentityelement.AddingAtoBislikeadding0toB;theresult,B,
isunchanged.Inasense,thisisanotherwayoflookingatinclusionrelations.Theyellowprimulasmust
be includedintheclassofprimulas(ormustbesomeoftheprimulas)sinceaddingtheformertothe
latterdoesnotchangethelatter.
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These,then,aresomeoftheaspectsofGroupingIandareintendedasaformaldescriptionofthe
processes underlying the child’s classification. The model involves elements (classes), the binary
operatorofcombining,andfivepropertiesgoverningtheapplicationoftheoperatortotheelements.
Discussion of Grouping I
AfewgeneralremarksshouldbemadeconcerningGroupingI.First,Piaget’suseofmathematicsis
notatallmeanttoimplythatthechildunderstandsthelogicomathematicalmodelinanyexplicitsense.It
is obvious thatmost children have never heard of the special identity element, let aloneGrouping I.
Clearly,thechildisnotamathematicianatthislevel.Infact,heoftencannotdescribeinanyclearway,
mathematicalorotherwise,hisprocedureforsolvingaparticularproblem.Hisreportisoftenincoherent.
Piagetusesthelogicomathematicalmodel,therefore,nottocharacterizethechild’sconsciousness,butto
describetheprocessesunderlyinghisclassification.
Second,GroupingIisnotmetricallyquantitativeinthesensethatitdoesnotinvolvenumbers.The
operations involve classes whichmay be of any size. It does notmatter whether there are 5 yellow
primulasand6whiteones,or5,000yellowprimulasand300whiteones.Inbothcasestherearemore
primulasthantherearewhiteprimulas,andsoforth.
Third,wemayexpandonourearlierpointthattheGroupingisintendedtodescribethestructure
ofthechild’sclassification.Piagetisnotinterestedintheminordetailsofthechild’sperformance;thatis,
whetherheisclassifyingflowersorfishorwhetherhefirstputtheflowersinanarrangementandthen
theanimals.Piaget insteadattempts tocapture theessenceof thechild’sactivitiesand to identify the
processesunderlyingthem.TheGroupingisPiaget’swayofdescribingtheseprocessesinaclearway.
Therefore,theGroupingisnotsimplyaprotocol listingeverythingthatthechilddoes. It is insteadan
abstractionwhichdescribesbasicprocessesliketheabilitytocombinementallytwosmallerclassesintoa
largerone,ortotakeawayoneclassfromanother.
The grouping also is a comprehensive and integrated structure. It is comprehensive since it
describes the processes underlying basic classification activities. The Grouping describes the
potentialities of the child, and not necessarilywhat he does in any one task at any one time. Let us
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suppose that a child constructs a hierarchy of classes. In doing so hemay notmake use of inclusion
relations.Inthiscase,theGroupingdoesnotsomuchdescribewhatthechildactuallydoes,butwhathe
iscapableofdoingundertheproperconditions.
Also,theGroupingisanintegratedsysteminthesensethateachofthepropertiesdoesnotstand
alonebut isrelated toallof theothers.Onthemathematical level, this iseasy tosee.Thepropertyof
associativitydescribestheorderinwhichelementsmaybecombined,butthepropertyofcompositionor
closure is needed to interpret the result of the associative combination. In other words, associativity
showsthattwodifferentordersofcombiningelementsareequivalent,andcompositionrevealsthatboth
oftheseordersofcombinationresultinanotherelementwhichmustbeinthesystem.Thus,theproperty
ofassociativitywouldbemeaninglesswithoutthepropertyofcomposition.Wecannothaveoneproperty
withouttheother.ThisfeatureoftheGroupingis,ofcourse,intendedtoreflectanimportantaspectofthe
child’s activities: the child’s successful classification (including the understanding of inclusion)
presupposes an interrelatedwhole, a structure of mental operations. For example, suppose the child
recognizesthattherearemoreprimulasthanyellowprimulas.Thisachievement impliesanumberof
interrelatedmentalacts.
Thechildmustbeawarethattheprimulas(whicharenolongerpresentinasinglecollection)are
thecombinationofyellowprimulasandprimulasofother colors (A+A'=B).Thechildmustalsobe
aware thatwhenyellowprimulasare takenaway from theprimulas, there remainprimulasofother
colors(B-A=A').These, then,aresomeoftheoperationsunderlyingthechild’sanswertoaquestion
concerninginclusion.Whenthechildcorrectlyanswersthequestion,hemaynotfirstactuallyperformall
theseoperations.However,theyareimplicitinhisanswer;hecouldnotanswercorrectlyifitwerenot
possibleforhimtoperformalltheoperationsinvolvedintheclassificationsystem.Tosummarize,any
particularresponsethatthechildmakestoaclassificationproblemcannotbeconsideredinisolation.His
responsepresupposesacomplexstructure,and it is thiswhichPiagetdescribesas theGrouping.The
Grouping,inotherwords,describesthementaloperationswhichmakeitpossibleforthechildto“really”
understandclassification.
Fourth, the Grouping explains and predicts behavior. Insofar as the Grouping describes the
processes underlying the child’s classification, it may be said to explain performance. The Grouping
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statesthatthechildcancombinetwoclassestogetalargerone.Thisoperation,amongothers,underlies
thechild’sabilitytounderstandinclusionrelationsandinthissenseexplainsit.InsofarastheGrouping
isgeneral itmaybesaidtopredictbehavior.TheGrouping isnot limitedtotheobjectsPiagetusedto
studyclassification.BecausetheGroupingprovidesadescriptionofstructure,itgoesbeyondthedetails
ofanyparticularproblemandallowsustopredictwhatthechild’sperformanceislikeonothersimilar
tasks.
Fifth,PiagethasdescribedseveralotherGroupingsallofwhichareintendedtorefertothechild’s
ability(from7to11)todealwithconcreteobjectsorthoughtaboutthem.Therefore,stage3istermed
concreteoperational.
Sixth,towardtheendofhislife,PiagetbegantofeelthattheGroupingmodelisnotfullyadequate
as an account of the concrete operations. While the facts concerning children’s performance on the
classificationtasks(andothersaswell)remainaswellestablishedasever,theGroupingmodelsuffers
fromseveraldeficiencies.“[TheGrouping]model...hasgeneratedlittleenthusiasmfromlogiciansand
mathematiciansbecauseof itsunavoidable limitations . . . and consequent ‘lackof elegance’ ” (Piaget,
1977b).(Indeed,onemightevengofurtherandclaimthatthelogicofthemodelisnotonlyinelegant,
butnotentirelycoherent.)“[TheGroupingmodel]...wastoocloselylinkedtothetraditionalmodelof
extensional logic and truth tables” (Piaget, 1980, p. 5, quoted in Beilin, 1985). In view of these
limitations, Piaget felt it is necessary to develop new formal models to characterize the essence of
concrete operational thought. “Abetterway, I nowbelieve, of capturing thenatural growthof logical
thinkinginthechildistopursueakindoflogicofmeanings”(Piaget,quotedinBeilin,1985b).While
Piagetdidnothave the time todevelopsuchmodels indetail,hebegan theeffortby introducing the
notion of “correspondences,” which we describe in our discussion of pre-operational strengths. It is
importanttorealize,asBeilinpointsout,“thatPiagetwasnotirrevocablycommittedtoaparticularlogic
or abstract model; consequently, following Piaget’s example, others are free to [select] the logical or
mathematicalmodelsthatbestexplainthedataofcognitivedevelopment”(Beilin,1985,p.112).
Inbrief,Piagetbelievedthatwhilethinkingisbestdescribedintermsof logicalmodels,hisown
effortsinthisareawerenotentirelysuccessful.Henceitisnecessarytoexpandthetheorybydeveloping
newmodels.AsPiagetclaimed,hehimselfwasthechief“revisionist”ofPiagetiantheory.
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Summary and Conclusions
Piaget’searlywork(inthe1920sand1930s)dealtwithclassificationinapreliminaryway.Inthe
1950shereturned to theproblem,using therevisedclinicalmethod.Hepresented2- to11-year-old
childrenwithanarrayofobjectstobeclassified.Thefindingswerethatinstage1(2to5years)thechild
fails to use consistently a clear rule or defining property to sort the objects into different classes. He
insteadconstructsgraphiccollectionswhicharesmallpartialalignmentsorinterestingforms.Instage2
(5 to 7 years), the child sorts the objects by a reasonable defining property and even constructs a
hierarchical classification, but fails to comprehend inclusion relations. Stages 1 and 2 are termed
preoperational.Instage3,whichisconcreteoperational(7to11years),thechildhasamaturenotionof
class, particularly when real objects are involved. The child sorts them by defining properties,
understands the relations between class and subclass, and so forth. To describe clearly the processes
underlyingthechild’sactivities,PiagetproposesalogicomathematicalmodelwhichhecallsGroupingI.
ThisGroupinginvolvessomeelements,abinaryoperator,andfivepropertiesrelatingtheoperatortothe
elements.Also,theGroupingisnotmetricallyquantitativeinthesensethatitdoesnotmatterhowbigor
small(innumericalterms)arethevariousclassesinvolved.Thechild,ofcourseisnotconsciousofthe
Grouping; rather theGrouping is intended todescribe thebasic structuresofhis activities. Inhis last
years,Piagetrecognizedtheshortcomingsof theGroupingmodelandproposedthedevelopmentofa
new“logicofmeanings.”
Piagetstressesthattheagenormsdescribingclassificationareonlyapproximate.Aparticularchild
maypassfromstage1tostage2at6yearsandnotnecessarilyat4or5years.Onechildmayspendthree
years in stage 1while another childmay spend four years in the same stage. Piaget doesmaintain,
however,thatthesequenceofdevelopmentisinvariant.Thechildmustfirstbecharacterizedbystage1
before he can advance to stage 2 and then to stage 3. Piaget also points out that a child may not
necessarilybe inthesamestageofdevelopmentwithrespecttodifferentareasofcognition.That is,a
childmaybeinstage1withrespecttoclassification,andinstage2ofnumberdevelopment.Thus,achild
maybeslightlymoreadvancedinsomecategoriesofthoughtthaninothers.
Oneimportantissueregardingclassification,andindeedalltheconceptsstudiedbyPiaget,isthe
generalityofthefindingsforchildrenindifferentcultures.Recently,muchcross-culturalworkhasbeen
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carriedouttodeterminewhetherchildrenindifferentculturesemploythetypesofreasoningdescribed
byPiaget, andwhether the sequenceof stages is invariant across cultures, asPiagetproposes.Opper
(1971;andinDasen,1977)hasexaminedanumberofPiagetianconcepts,includingclassification,in
rural and urban children in two Southeast Asian countries, Thailand andMalaysia. Likemany other
investigators(forareview,seeDasen,1977),Opperfindsthatalthoughtheagesmayvary,thesequence
ofdevelopmentisthesameindifferentcultures:first,Thaichildrenarecharacterizedbystage1,then
stage2,andsoon.
Moreover, Opper finds that Thai andMalaysian children present responses similar to those of
Swisschildren.Forexample,whenaMalaysiangirlinstage2ofclassificationwasaskedwhetherthere
aremorerosesorflowersinabunchofsevenrosesandtwoorchids,sheresponded,“Therearemore
roses than flowers.” The examiner said, “Show me the flowers.” The child then pointed to the two
orchids.
AThaiboy,inthesamestage,waspresentedwithsevenrosesandtwolotus.He,too,maintained
thattherearemorerosesthanflowers.Moreroses.—Morethanwhat?—Morethanflowers.—Whatarethe
flowers?—Roses.—Are there any others?—There are.—What?—Lotus.—So in this bunch, which is
more,rosesorflowers?—Moreroses.—Thanwhat?—Thanlotus.
Turningtothestage3child,wealsofindthesameresponsesastheSwisschildren.Forexample,a
Malaysiangirlsaid:Therearemoreflowersbecauseifit’sroses,it’sonlythese[pointingtoroses],butthe
flowersareplus thesealso [pointing to orchids].We see then that inmany casesThai andMalaysian
children’sargumentsarevirtuallyidenticaltothoseofSwisschildren.
How can we evaluate Piaget’s work on classification? On the one hand, Piaget has been very
successfulatwhathehasattemptedtodo.Anumberofindependentinvestigatorshaveconfirmedthat
stage1classificationtakesunusualforms(e.g.,Vigotsky,1962),thatyoungchildrenexperiencegenuine
difficulty with class inclusion (Klahr andWallace, 1972), and that the course of development with
respecttoclassificationisgenerallyasPiagethasdescribed(Kofsky,1966).Ontheotherhand,itshould
bepointedoutthatPiaget’sapproachtoclassificationisofaveryspecificsort.Hefocusesmainlyonthe
hierarchicalstructureofclasses,forexample,classinclusion.Heisnotparticularlyconcernedwithother
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aspectsof conceptswhichnowseemtobequite important.ThusNeisser (1967)haspointedout that
everyday concepts are often vague and difficult to define, and Rosch (1973) has developed a new
approachfocusingonnonlogicalaspectsofchildren’sconcepts.Thedefiningpropertyorintensionofa
classisoftenquitevague,aparticularobjectmayfitintoseveralclassessimultaneously,theboundaries
betweenclassesmaybe fuzzy,and itmaynotbepossible to formasimplehierarchy. Inbrief,Piaget’s
approachfocusesononlyoneofmanyimportantaspectsofclasses.
RELATIONS
In Chapters 2 and 3 we have already reviewed several aspects of relations, a problem (like
classification)withwhichPiagethasbeenconcernedsincehisearliestworkinpsychology.Wesawthat
in the sensorimotor period the infant displays precursors of relations. He can broadly discriminate
withinthedimensionsofnumerosity,intensityofmusculareffort,andloudnessofsounds(amongother
dimensions).Inthecaseofnumerosity,youwillrecallthatLaurentsaid“papa”whenPiagetsaid“papa,”
thatLaurentsaid“bababa”whenPiagetsaid“papa-papa,”andthatLaurentsaid“papapapa”inresponse
to “papapapapapapa.” Laurent’s imitation, although not exact, nevertheless implies an ability to
discriminateorhearthedifferenceamongseveralsoundswhichdifferedinnumberofrepetitionsofone
syllable.Similarly,inthecaseofmusculareffort,Laurentappearedabletodetectthedifferenceamong
thevariationsinvigorwithwhichheswungachain,andalsohewasabletodiscriminateamongsounds
ofdifferentdegreesofloudness.Thus,theinfantcandifferentiategradationswithindifferentkindsof
stimuli:somethingsarelouderthanothers,ormorenumerous,orbigger,andsoforth.Hecanperceive
differencesinvariousaspectsofhisworld.Theabilitytomakesuchdiscriminationsisaprerequisitefor
reasoningaboutdifferences.
Piaget’s early research on the child from about 5 to 10 years investigated reasoning about
differences, but not the perception of differences. He presented children with this verbal problem
(amongothers):“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichisthe
darkest,Edith,Suzanne,orLili?”{JudgmentandReasoning,p.87).Theresultsshowedthatchildrenfrom
5to10yearsareunabletodealwithproblemsofthissort,calledtransitivity,ataverballevel.
Asinthecaseofclassification,Piagetreturnedtotheproblemofrelationsinhislaterwork.Using
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therevisedclinicalmethod,heperformedseveralinterestingstudiesonordinalrelations,whichwewill
nowcharacterizebriefly.
Some Properties of Ordinal Relations
Piaget’sdefinitionofordinalrelationsinvolvesseveralfeatures.Supposewehaveseveralnumbers,
suchas17,65,25,3,and1,0OI.Itispossibletoarrangetheminorderofincreasingsize.Wemayusethe
symbol<tostandfor“isasmallernumberthan”andwrite3<17<25<65<1,0OI.Thesequenceisan
orderingofthenumberswiththesmallestbeingfirst,thenextsmallestsecond,andsoforth.Notethatthe
absolutesizeofthenumbersmakesnodifference.Thesecondnumberdoesnothavetobeexactlyone
morethanthefirstorexactlytwiceasbigasthefirst.Thelastnumber,solongasitislargerthan65,may
beofanysizewhatsoever.Also,wedonotneedtohavezeroas thebeginningof theseries.Theonly
requirements forordering thenumbersare that theyaredifferent fromoneanother, thatat leastone
numberissmallerthantherest,thatanotherislargerthanalltherest,andthatanynumberinbetween
thesmallestandthelargestisbothlargerthantheoneimmediatelyprecedingitintheseriesandsmaller
than the one immediately following it. Of course, orderings are not limited to numbers.Wemay also
ordersoundsonthedimensionofloudness.Supposesoundaisverysoft,bismuchlouderthana,andc
isslightlymoreloudthanb.Thenwehavea<b<c,where<means“issofterthan.”Againtheprecise
degreeofloudnessdoesnotaffecttheordering.
Piaget’s work deals with such matters as the child’s ability to construct orderings or ordinal
relationsandtomanipulatetheminvariousways.Thesestudies,involvingchildrenfromabout4to8
yearsofage,usuallydetectthreedistinctstagesofdevelopment:stage1lastingfromabout4to5,stage2
fromabout5to6,andstage3fromabout7andabove.Thefirsttwostagesarepreoperational,andthelast
isconcreteoperational.Whiletheagenormsareapproximate,thesequenceiscrucial.
Stage 1
Onestudywasconcernedwiththeabilitytoconstructanorderingofacollectionoftenstickswhich
differedonly insize.Wewillcall theshortestof thesticks(about9centimeters in length)A, thenext
largerB,andsoonthroughJ,thelargest(about16centimetersinlength).AdifferedfromBbyabout.8
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centimeters,andthisalsowastrueofBandC,andsoon.Piagetpresentedthechildwiththesticksina
randomlyorganizedarrayandaskedhimtoselectthesmallestofthelot.Afterthiswasdone,Piagetgave
aninstructionlikethis:“Nowtrytoputfirstthesmallest,thenonealittlebitbigger,thenanotheralittle
bitbigger,andsoon”(Child’sConceptionofNumber,CCN,pp.124-25). Inanotherstudythechildwas
askedtomakeastaircasefromthesticks.
Whenconfrontedwiththisproblem,childreninstage1showedseveredreactions,noneofwhich
wassuccessful. Somechildrenproducedrandomarrangementsof the sticks, likeH,E,B, J, and so on.
Otherchildrenmanagedtoorderafewofthesticks,butnotallofthem.AnexampleofthisreactionisA,B,
C,D,H,F,E,andsoon.
Anotherstrategywastoplacethelargersticksinonecollectionandthesmallersticksinasecond
collection.Withineachofthesecollections,however,thestickswereinarandomorder.Amoreadvanced
reactionalsoappearedwhichmaybeconsideredatransitiontothenextstage.Thechildstartedwith
somestick,likeB,apparentlyselectedatrandom;thenhetookanotherstick,likeH,andmadethetopofit
extendslightlyabovethetopofB;athirdstick,forexample,A,wasmadetoextendslightlybeyondthe
topofB;andsoforth.Theresultwasthatthetopsofthesticksformanordering;Hisslightlyhigherthan
B,andAslightlyhigherthanH,andsoforth,asinFigure6.Butthebottomsofthesticksalsodifferedina
randomway,andfailedtolieonastraightlineastheyshould.Thus,thechildconstructsanordering,but
onlybyignoringthelengthofeachstick.Thisprocedurefreeshimfromthenecessityofcomparingeach
stickwiththeoneimmediatelyprecedingitandwiththeonetofollow.Onewayofcharacterizingthese
activitiesistosaythatthechildfocuses(centers)ononeaspectoftheproblem(puttingthetopsinorder)
butignoresanother,equallyimportantaspect(arrangingthebottomsinastraightline).Tosummarize,
thechildatthisstagefrequentlycannotformasystematicorderingofanynumberofobjectsalthoughhe
issometimesabletoorderafewofthem.
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FIGURE6Orderingofsticks.
Stage 2
Presentedwiththesameproblem,childreninthesecondstagegenerallysucceedinconstructing
theordinalarrangementofsticks,sothatA<B<C<D<E<F<G<H<I<J.Butthechilddoesnotbuildthe
orderingswithout difficulty. Sometimes he begins by ignoring the bottomsof the sticks, as in stage 1.
Sometimeshemakesmanyerrors,likeA<D<B,andsoon,andtakesalongtimetorecognizeandcorrect
them.Thechildcontinuallyrearrangeshisordering,andshiftsthesticksfromonepositiontoanother.
Essentiallythechild’sprocedureisoneoftrialanderror,lackinganoverallplanorguidingprinciple.
Forexample,ifhehaschosenAasthesmallest,hemightthenchooseanothersmallone,like
D,andlineitupnexttoA.Thenhemightchooseanothersmallone,likeC,andplaceitnexttoDand
seethatitissmallerthanD.Sincethisisso,hemightrearrangethesticksplacingCafterAbutbeforeD.
AfterbeginningwithA,thechildfailstolookforastickthatislongerthanAbutsmallerthanalltheones
remaining. If this rule is followed, then each step of the ordering can be constructed without any
difficulty.However, thechildat this stagedoesnotemploysucha logicalprocedure.He fails tomake
systematic comparisons between a given stick and the one immediately preceding it and all those
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following.
This tendencywas furtherrevealedby theadditionofonemoreproblem.Afterconstructing the
orderingAthroughJ,thechildrenweregivenanewcollectionoftensticks,a,b,c,d,e,f,g,h,i,j.Eachof
thesenewstickscouldfitinbetweenapairofsticksofthefirstseries.Thatis,ifthenewsetofstickswere
orderedcorrectlyalongwiththefirstset,thearrangementwouldbeA<a<B<b<C<c<D<d<E<e<F<
f<G<g<H<h<I<i<J<j.Thechild’staskwastodopreciselythis;tofitthenewsticksintotheordering
alreadyconstructed(AthroughJ),soastomakeanewordinalarrangementinvolvingalltwentysticks.
Childrenofthisstagehadgreatdifficultywiththeproblem.Infact,manyfailedtosolveit.Partof
one child’s orderingwasC e d D, and another producedH g G I h j c, and so forth. Other children
succeededinproducingthecorrectordering,butonlyafterconsiderabletrialanderror.
Thesedifficultiesseemduetoseveralfactors.Onefactorappearstobethatthechildperceivesthe
originalseriesasawholeandfindsithardtobreakuptheseriesintosmallerunits.Also,childrenofthis
stagedonotapproachtheproblemwithaguidingprinciple.Theyfailtousearulelike,“Startwiththe
smallestofa-j)insertitinbetweenthepairofthesmalleststicksinA-J)thentakethesmallestofb-jand
insertitbetweenthesmallestpairofsticksinB-J)andsoforth.”Notonlydidthechildrenfailtousearule
likethis,buttheyalsohaddifficultyindecidingthatagivenelementofa-jwasatthesametimebigger
thanonestickinA-JandsmallerthanthenextlargerstickinA-J.Toplacedproperly,thechildmustsee
thatd<EandthatD<d.Hemustcoordinate thesetworelationsbutfailstodosoconsistently.That is,
somechildrenwouldtakeeand,seeingthatitwaslargerthanB,wouldplaceitrightafterB.Theyfailed
toconsiderwhetherewasatthesametimesmallerthanC,andthereforemadeanerror.
Afterinvestigatingthechild’sabilitytoconstructanorderingandplacenewelementsinit,Piaget
wenton to study the child’s ability to construct equivalencesbetween two separateorderings (which
involveequalnumbersofelements).Toillustratethis,letustakeaclasswithfifteenboysandfifteengirls
andordereachofthesegroupsintermsofheight.Wefindtheshortestboy,thenext-to-shortestboy,and
soon,andwedothesameforgirls.Wecanseethatthetwoorderingsareequivalentinsomewaysand
differentinothers.Somedifferencesarethattheheightoftheshortestboymaybe48inches,whereasthe
height of the shortest girl is 44 inches. Also, the second shortest boymay be 4 inches taller than the
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shortestone,whereasthesecondshortestgirlisonly1inchtallerthantheshortestgirl.Despitethese
realdifferences,thereareimportantsimilaritiesbetweenthetwoorderings.Theboywhois48inches
tallandthegirlwhois44inchestall,despitetheirdifferenceinheight,areequivalentintermsoftheir
positionintheordering.Theyareboththeshortest.Thesameholdstrue,ofcourse,forthetallestboyand
girl,thenexttotallest,andsoforth.
Piagetthenraisesthe issueofwhethertheyoungchildcanrecognizetheequivalencesbetween
twodistinctorderings.Doesheunderstandthattwoobjects,whiledifferinginheight,forexample,canat
thesametimebeequivalentintermsoftheirrelativepositioninanordering?Tostudythematterhefirst
presentedchildrenwithtendolls,A-J,whichwerepresentedinarandomdisplayandwhichcouldbe
arrangedinorderofheight;andwithtensticks,A'-J',alsorandomlyarranged,whichcouldbeorderedin
size.Thesticksweresmallerthanthedolls,andthedifferencesbetweenadjacentpairsofstickswere
smallerthanbetweenpairsofdolls.Thechildwastoldthatthedollsaregoingforawalkandthateachof
themmust have the proper stick. The intention of the instructions, of course,was to get the child to
produceanorderingofthedollsandofthesticksandtomakeeachmemberofoneorderingcorrespond
totheappropriatememberoftheotherordering.Thus,dollAshouldhavestickA',dollBshouldhave
stickB',andsoon.Piagetcallsthisprocesstheplacingoforderingsintoone-to-onecorrespondence.
Theresultsshowedthatchildrenofthisstagecanproduceaone-to-onecorrespondenceofdolls
andsticks,butonlyinatrial-and-errorfashion.Themostcommonprocedureistoorderthedolls(bytrial
anderror)andthentoorderthesticks(bytrialanderror).Onlyaftertwoseparateorderingshavebeen
constructedaretheelementsofeachputintoone-to-onecorrespondence.Thatis,thechildfirstidentifies
thelargestdoll,thenexttolargestdoll,andcompletestheorderingofdolls;thenhegoesontoorderthe
sticks.Itisonlyafterthisisdonethatthechildplacesthelargeststickwiththelargestdoll,thenextto
largest stick with the next to largest doll, and so forth. While this procedure works, it is somewhat
cumbersome.Aneasiermethodistobeginbyidentifyingthelargest(orsmallest)dollandthelargest(or
smallest)stickandimmediatelyplacingthetwotogether.Thesecondstepistochoosethe largestdoll
andstickofallthoseremainingandtoplacethemtogether,andsoforth.Inanyevent,thechildinthis
stage does succeed in setting the two orders into one-to-one correspondence. He seems to have
establishedthattheorderingsareequivalent.
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FIGURE7Theequivalenceofrelativeposition(dollsandsticks).
The next problem concerns the stability of the equivalence established by one-to-one
correspondence.Letussupposethatthesticksareplacedveryclosetogetherwiththeirorderpreserved
(asinFigure7).Theshorteststickisclosesttothethirdtallestdoll,thesecondstickisclosesttothefourth
tallestdoll,andso forth.Doesthechildrecognizethat thesecondtalleststick isstill equivalent to the
secondtallestdoll,eventhoughtheformerisnowclosesttothefourthtallestdoll?Thatis,doesthechild
conservetheequivalenceofrelativepositionwhentheovertone-to-onecorrespondenceisdestroyed?
Piaget presented this and similar problems to a number of children. He placed the sticks close
togetherandaskedwhichstick“goeswith”whichdoll.Piagetdiscoveredseveredmethodsofattacking
theproblem.Themostprimitivereactionistoassertthatadollisequivalenttothestickclosesttoit.Thus,
thesecondlargeststickandfourthlargestdollareconsideredtobelongtogethersimplybecauseoneis
belowtheother.Thechild’sjudgmentisdominatedbyspatialrelations.Otherchildrentrytosolvethe
problembycounting,buttheyfailtodosoproperly.Forexample,onechildsaidthatthefourthlargest
stickwasequivalenttothethirdlargestdoll.Thereasonforhismistakewasthathenoticedthatthere
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werethreesticksprecedingthefourthlargeststick;hethencountedoutthreedolls,stoppedthere,and
identifiedthethirddollwiththefourthstick.Thismethodisquitefrequentamongchildrenofthisstage;
thatis,theyfindadollcorrespondingtothenthstick,countingtheprecedingn-1sticks,thencountthe
dolls,stoppingatthen-1thelement.Thechildconfusesthepositiontobefound(say,stick4)withthe
numberofprecedingelements(3).
Stage 3
Afterabouttheageof6-7years,thechildissuccessfulinallofthetaskswehavedescribed.When
askedtoconstructasingleorderingofsticksdifferinginsize,thechilddoessoquiteeasily.Theordering
isguidedbyanoverallplan.Thechildusuallybeginswiththesmallest(orsometimes,withthelargest),
then thenext smallest, and so forth, in sequenceuntil theordering is complete.This strategymaybe
characterizedasstartingwiththesmallestandcontinuingtotakethesmallestofeverythingthatisleft,
untilthestickshavebeenexhausted.Whenaskedtoplaceadditionalsticks(a-j)intheirproperpositions
within the ordering (A-J) already constructed, the child does so with almost no errors. The process
underlyingthisachievementisthecomparisonofoneofthenewsticks(say,d)withtwointheoriginal
orderingsimultaneously.That is, toascertaind'sproperposition, thechilddeterminesthat it isat the
sametimebiggerthanDbutsmallerthanE.Tophrasethematterdifferently,hecoordinatestwoinverse
relations—biggerandsmallerthan.
Inasimilarwaytheconcreteoperationalchildeasilyplacestwoseparateorderingsintoone-to-one
correspondence.Onechildimmediatelyputthebiggestdollwiththebiggestball(ballsweresometimes
usedinplaceofsticks),thenexttobiggestdollwiththenexttobiggestball,andsoforth.Hisstrategywas
to identify thebiggestdollandballofall thoseremainingand toplace the twotogetheratonce.This
procedureismoreeconomicalthanthatoftheyoungerchildwhofirstordersthedolls,thentheballs,
and finallybegins toput them together.When thisone-to-onecorrespondence isdestroyed, thechild
conservestheequivalenceofrelativeposition.Herealizesthatthesmallestdollisstillequivalenttothe
smallestballandnottotheballtowhichithappenstobeclosestinspace.
Insummarizingthematerialontheconcreteoperationalchild,then,wecanstatethatheisadeptat
understanding and manipulating ordinal relations. However, as in the case of classification, one
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limitation applies: he can deal with relations on a concrete level only; that is, when real objects or
thoughtsaboutthemareinvolved.Nevertheless,histhoughtisfarmoreadvancedthanthatofthechild
in stages 1 and 2. The child can construct orderings, put two such orderings into one-to-one
correspondence,andconservetheresultingequivalences.Asinthecaseofclassification,theprocesses
underlying the child’s ability tomanipulate relations form integrated and comprehensive structures.
Each of his mental operations cannot be understood without reference to the others of which he is
capable. These processesmust be interpreted in terms of complex systemsof operations. To describe
thesesystems,Piagethasdevelopedseverallogicomathematicalmodels,similartoGroupingI(although
they,of course,deadwithrelations,notclasses).Also,Piagethas investigatedseveralotheraspectsof
ordinalrelations,suchastransitivity(ifa>bandb>c,thena>c),whichwewillnotcoverhere.
NUMBER
Theabilitytounderstandclassesandrelations,accordingtoPiaget,isbasictomatureconceptsin
many areas. The several groupings which describe the processes underlying the older child’s
performance in problems of classes and relationsmay also be used to characterize concepts of space,
chance,geometry,andsoforth.Sincewecannotreviewall theseconcepts,wewillconcentrateonone
thatisparticularlyinterestingandthathasreceivedconsiderableattentionintheAmericanandBritish
researchliterature,namely,theconceptof(whole)number.
First,wemustunderstandwhatPiagetdoesanddoesnotmeanbytheconceptofnumber.Hedoes
notmean and isnot interested in computational abilities as taught in the first few grades of school.
Whetherthechildcanadd2and2,orsubtract3from5,isnottheissue.ThereasonforPiaget’slackof
interest in thesematters is that simple addition and subtraction of whole numbers, aswell as other
manipulationsof them,canbecarriedoutentirelybyroteandwithoutunderstanding.Thechildcan
simply memorize the addition and subtraction tables and fail to comprehend the basic concepts
underlyingthem.Piagetdoesnotdenythatitisusefultomemorizethefactsofadditionandsubtraction;
for purposes of computation, we all find it helpful to do so. He asserts, however, that for mature
understanding of number, such rotememorization is not sufficient andmust be accompanied by the
masteryofcertainbasicideas.
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Amongthese ideasareone-to-onecorrespondenceandconservation.Letus firstconsiderone-to-
onecorrespondence.SupposewearepresentedwithacollectionorsetofdiscreteobjectsasinFigure8.
Thesizeoftheobjects,theircolor,andsofortharecompletelyirrelevant.Allthatisrequiredisthattheset
contain a finite number of discrete objects. We are then given a box of objects and are required to
construct from it another setwhich has the same number property as the first set. It does notmatter
whethertheobjectsinthesecondset(whichwewillcallsetB)arethesamecolor,size,andsoonasthose
inthefirstset(setA).WhethersetAcontainselephantsandsetBcontainsgeraniumsisirrelevant.The
onlyrequirementisthattheyhavethesamenumber.OnewayofconstructingasetBsothatitwillhave
thesamenumberpropertyasAisbycountingtheobjectsinA(say,therearefive)andthentakeoutofthe
boxthesamenumberofobjects.Thisprocedure,whichofcourseisquiteadequate,probablyoccursfirstto
adults.Butsupposewecannotcount.SupposewedonotknowthenumberofobjectsinsetA.Evenwith
theselimitationsthereisasimplewayofconstructinganewset,B,whichwillhavethesamenumber
propertyasA.ThismethodmerelyinvolvesputtingnexttoeachmemberofsetAone,andonlyone,new
object.Thesenewobjects,aftertheone-to-onecorrespondencehasbeenestablished,formaset,B,with
thesamenumberasA.Ofcoursewedonotreallyhavetophysicallyplaceeachnewobjectnexttoonein
A;wecannotetheone-to-onecorrespondencementally.That is,wecan“saytoourselves,”“Thisnew
object corresponds to the first in the lineof setA,” and soon.The important idea is not thephysical
placingtogetherofthesets,butthepairingofonememberinsetAwithoneinsetB,howeverthisisdone.
FIGURE8Collectionofobjects.
Althoughverysimple, the ideaofone-to-onecorrespondence isbasicandpowerful,andmaybe
usedinavarietyofsituations.Ifwewanttodeterminewhethertherearethesamenumberofseatsas
peopleinanauditorium,allwehavetodoisaskeveryonetositdown(withnooneallowedtositon
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anyoneelse’s lap!). Ifall thepeopleare inseats(inone-to-onecorrespondencewith theseats)and if
noneoftheseatsisempty,thenthenumbers(whatevertheymaybe)ofpeopleandseatsareequal.If
therearepeoplestanding,thenthisdefinestherelationofmorepeoplethanseats.Ifthereareempty
seats, then this defines the relation of more seats than people. In brief, one-to-one correspondence
establishesthatanytwosets—regardlessofthenatureoftheobjectscomprisingthem—areequivalentin
number.Countingorotherproceduresarenotneeded.Lackofone-to-onecorrespondenceestablishes
thatonesetislargerthantheother(andonesmallerthantheother).
FIGURE9Conservationofnumber.
ThesecondbasicideawhichPiagetinvestigatesisconservation.Supposethatwehaveestablished
thatsetsAandBareequalinnumber,asinFigure9A.Thatis,wehaveputsetAinaline,andbeloweach
memberofsetAwehaveputanewobject.The lineofthenewobjects issetB.Supposethatwethen
compress themembers of set B, as in Figure 9B, so that the perceptual one-to-one correspondence is
destroyed.NoweachmemberofsetBisnotdirectlybelowadifferentmemberofsetA.Theproblemis
whetherthetwosetswhichnowdifferinphysicalarrangementstillareequalinnumber.Inotherwords,
istheequivalenceestablishedinFigure9AconservedwhentherearrangementshowninFigure9Bis
performed?Toadults,thismayseemlikeafoolishquestion.Ofcourse,theequalityofnumbershasnot
changed!Buttheproblemiswhetherchildrenacceptthissimpleandbasicidea,too.Iftheydonot,then
theirworldofnumbermustbeverychaoticindeed.Ifquantityisseentochangewhenevermerephysical
arrangement isaltered, thenthechild fails toappreciatecertainbasicconstanciesor invariants in the
environment.
Piagethasconductedanumberof investigationsonthechild’sunderstandingofthesetwobasic
ideas: one-to-one correspondence and conservation of the equivalence of twonumbers.He finds that
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youngchildrenfailtounderstandthesetwonotionsandthataperiodofdevelopmentisrequiredbefore
thechildachievesthementaloperationsnecessaryforthoroughcomprehensionofnumber.Letusnow
reviewtheexperiments.
Stage 1
Tostudytheabilitytoconstructsetsofequivalentnumber,Piagetpresentedchildrenwithavariety
ofproblems.The simplestof these involvedplacingbefore the childa rowof sixor sevenpenniesor
buttonsorsweets,andsoon.Theexaminerthenaskedthechildtopickoutthe“samenumber”or“as
many” from a large collection of similar objects. Thus the childwas given set A andwas required to
constructasecondset,B,whichwasequivalentinnumber.Thechildrenwere,ofcourse,nottoldhowto
constructsetB.Hereisaprotocoldescribinghowastage1child,4yearsand7monthsofage,dealtwith
theproblem.Piagethadplacedsixsweetsinarowandtoldthechildthattheybelongedtohisfriend
Roger:
“Putasmanysweetshereastherearethere.Those...areforRoger.Youaretotakeasmanyashehas.”(Hemade a compact row of about ten,whichwas shorter than themodel.)—“Are they the same?”—“Not yet”(addingsome).—“Andnow?”—"Yes.”—“Why?”—“Becausethey’relikethat”(indicatingthelength).(CCN,p.75)
FIGURE10Failuretoconstructequalsets.
The example makes clear the predominant tendency of this stage. The child does not use the
methodofone-to-onecorrespondence.Instead,hethinksthatthetwosetsareequivalentinnumberif
theyhavethesamelengths.InPiaget’sterms,thechildcentersononedimension—thelength—ofsetA
(Roger’ssweetsorthemodel)andbaseshisconstructionofsetBsolelyintermsofthatonedimension.
TheresultispicturedinFigure10.Thelengthsofthetworowsareequal,buttheirnumbersarenot.The
newrowisdenser;thatis,therearesmallerspacesbetweenthesweets,thanRoger’srow,butthechild
ignoresthisfactandconcentratesonlyonthelengths.Sincehefailstocoordinatethetwodimensionsof
lengthanddensityatthesametime,hecannotconstructsetsequivalent innumberexceptwhenvery
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smallnumbersareinvolved,orexceptbyaccident.
In another investigation, Piaget tried tomake the child understand the principle of one-to-one
correspondence,andthenperformedtheconservationexperiment.Inthisstudy,setAwasarowoften
vasesandsetBconsistedofflowers.Onechild,4yearsand4monthsofage,
put13flowersclosetogetherinarowopposite10vasesrathermorespacedout,althoughhehadcountedthevases from 1 to 10. Since the rowswere the same length, he thought that the flowers and vaseswere “thesame.”—“Thenyoucanputtheflowersintothevases?”—“Yes.”—Hedidso,andfoundhehad3flowers[left]over.(CCN,p.50)
Thechild,then,initiallyconstructedsetBsoastomakeitthesamelengthassetAandthoughtthat
thetwosetswerethereforeequalinnumber.Theexaminerthenmadethechildconstructaone-to-one
correspondencebetweentheflowersandvases;thatis,thechildputeachflowerinavase.Theresult
was ten flowers in ten vases (or two sets equivalent in number), and the three extra flowers were
discarded. The question now iswhether the child realizes that the two sets are really equivalent in
number.Doesthechildconservetheequivalencedespiteamerephysicalrearrangementoftheobjects?
Tofindout,Piagetcontinuedtheexperimentwiththesamechild.
The flowerswere taken out andbunched together in front of the vases. [That is, they formed a shorter rowthan did the vases.] “Is there the same number of vases and flowers?”—“No.”—“Where are there more?”—“There are more vases.”—“If we put the flowers back into the vases, will there be one flower in eachvase?”—“Yes.”—“Why?”—“Becausethereareenough.”(Thevaseswereclosedupandtheflowersspacedout.)—“Andnow?”—“Therearemoreflowers.”(CCN,p.50)
Notethatafterthechildhadhimselfestablishedaone-to-onecorrespondencebetweentheflowers
andvases,hefailedtoconservethenumericalequivalenceofthetwosets.Whentheflowerswereput
intoashorterrowthanthevases,thechildbelievedthatthenumberswerenolongerequalandthatnow
thereweremorevases.Hemaintainedthiseventhoughherealizedthattheone-to-onecorrespondence
couldbereestablished;that is, that theflowerscouldbereturnedtothevases.Thenwhentherowof
vaseswasmadeshorterthanthatoftheflowers,hechangedhismindonceagain.Heassertedthatnow
thereweremore flowers. Clearly, this child centered on the lengths of the rows and used only this
informationtomakejudgmentsofequivalenceorlackofequivalenceofnumber.Whentherowswerethe
samelength(aswhentheflowerswereinthevases),hesaidthattheywereequalinnumber.Whenthe
rowsdifferedinlength,hebelievedthatthelongerlinehadthegreaternumber.
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Piagetalsoinvestigatedtheroleofcounting,questioningthewayinwhichcountingthetwosets
affectsthechild’sjudgment.Onechild,5yearsand3monthsofage,failedtheconservationproblem.He
saidthatsetA(sixglasses)wasgreaterthansetB(sixbottles)becauseonewaslongerthantheother.
Thentheexaminersaid:
“Can you count?”—“Yes.”—“Howmany glasses are there?”— “Six.”—“And how many bottles?”—“Six.”—“Sothere’sthesamenumberofglassesandbottles?”—“Therearemorewhereit’sbigger[thatis,longer].”(CCN, p.45)
This examination shows thatwhile the child can count, the act ismeaningless in deedingwith
conservation.Althoughhecanreciteastringofnumbers,hedoesnotcomprehendwhattheysignify.The
fact that he counted six bottles and also six glasses does not imply to him that the sets are equal in
number. For him, equality of number is determined solely by equality of lengths, and counting is an
extraneousandirrelevantact,whichdoesnotassureeithertheequivalenceofsetsoritsconservation.4
Stage 2
The child of this stage easily constructs two sets equivalent innumber, but fails to conserve the
equivalencewhenthesetsarerearranged.Per,achildof5years,7months,
hadnodifficultyinmakingarowof6sweetscorrespondingtothemodel.[Piagetuses“model”torefertosetA, the row to be copied, and “copy” to refer to set B.] The model was then closed up: “I’ve got more.”—“Why?”—“Becauseit’salongerline.”(Theprocesswasreversed.)—Nowtherearemorethere,becauseit’sa big line.” But a moment later, Per said the opposite: “Are there more here [referring to the longerrow]?”—“No.”—“Why not?”—“Because it’s long.”—“And there [the shorter row]?”—“There are more there,becausethere’salittlebundle”[Thechildmeantthattheshorterrowwasdenser].—“Thenaretheremoreinalittlebundlethaninabigline?”—“Yes.”AfterthisPerwentbacktousinglengthasthecriterion,madethetworowsthesamelengthagainandsaid:“Nowthey’reboththesame.”(CCN,p.79)
Theprotocolshowsthatthechildofthisstageeasilyconstructsasetequalinnumbertoanother.He
also establishes the equivalence by the method of one-to-one correspondence. That is, in order to
constructsetB,heplacesanewsweetjustbeloweachinsetA.Buttheone-to-onecorrespondenceisnot
fullyunderstood;itisjust“perceptual.”WhensetBismadeshorterthansetA,thechildfailstoconserve
the equivalencewhich he so easily constructed. The protocol also shows that the child is ambivalent
about thecriteriaused toestablishequalityor inequalityofnumber.Sometimeshemaintains that the
longerrowhasmorebecauseitislonger;atothertimeshebelievesthattheshorterrowhasmorebecause
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it is denser. In Piaget’s terms the child sometimes centers on the lengths (ignoring densities) and
sometimes centers on the densities (ignoring lengths). This tendency is an improvement over what
occursinthepreviousstage,sincetheyoungerchild(instage1)consistentlycentersononlyoneofthe
twodimensions,usuallylength,anddoesnotconsidertheother,usuallydensity,atall.Bycontrast,the
childinstage2haswidenedthesphereofhiscentrations.Henotices,albeitatdifferenttimes,thatboth
dimensionsmayberelevantandusestheinformationfromeitherofthesedimensionsseparatelytomake
ajudgment.Thisuseofpartialinformationiscalledregulations.Wewillseenexthowthechildinthe
periodofconcreteoperationscoordinatesthetwodimensions.
Stage 3
The results of this stage are easy to describe. The child can now construct a set numerically
equivalenttoanothersetandcanconservetheirequivalencedespitechangesinphysicalarrangement.
Hereisaprotocolillustratingthisstage:
“Takethesamenumberofpenniesastherearethere[therewere6 insetA],Hemadearowof6underthemodel,butputhismuchclosertogethersothattherewasnospatialcorrespondencebetweentherows.Bothendsof themodel extendedbeyond thoseof the copy. “Haveyougot the samenumber?”—"Yes.”—“Are youandthatboy[referringtothehypotheticalownerofsetA]justasrichasoneanother?”—“Yes.”—(The penniesof the model were then closed up and his own were spaced out.)—“And now?”— “Thesame.”—“Exactly?”—“Yes.”—“Whyaretheythesame?”—“Becauseyou’veputthemclosertogether.”(CCN,p.82)
Thisprotocolcontainsseveralinterestingfeatures.OnefeatureisthatinmakingsetBequaltosetA,
theconcreteoperationalchilddoesnotbothertoplaceeachelementinBdirectlyundereachelementin
A.Hedoesnotneedtorelyontheperceptionofspatialproximitybetweentheelementsofeachset.How
thendoesheconstructnumericallyequivalentsets?Onemethod,ofcourse,issimplytocountthenumber
ofobjectsinsetA,andthenmerelycountoutthesamenumberforsetB.Probablysomechildrenusedthis
method,butPiagetconcludedfromhisclinicalexaminationsthatotherchildrendidnotusecounting.
Theyseemedtousethemethodofone-to-onecorrespondence,butinamoresophisticatedwaythanthe
youngerchild.Theconcreteoperationalchild’stechniquemaybedescribedasfollows:toconstructsetB
equaltosetA,heputsoutonepennyforthefirstpennyinsetA,andsoforth.Itdoesnotmatterwherehe
putsthemembersofsetB.TheonlycrucialrequirementisthathematcheachmemberinsetAwithone
andonlyonememberinsetB(anonspatialone-to-onecorrespondence).Thechildmustnotforgettoput
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outapennyforeachmemberofsetA(thatis,hecannotskipanymemberofsetA)andmustnotputout
morethanonepennyforeachmemberofsetA(thatis,hemustnotcountanymemberofsetAtwice).
Theprocessofestablishingsetsequalinnumbermaybedescribedintermsofclassesandrelations.
Asfarasrelationsareconcerned,thechildusesthemethodofvicariantordering.SupposethatsetA(the
model)isalineofpennies,andthechildmustconstructasetB(thecopy)fromalargesupplyofcandies.
Hebeginsbypointingatthepennyontheextremeleftandputsoutasweet.Thenhepointstothesecond
pennyfromtheleft,putsoutasweetforit,andcontinuesuntilthelineofpennieshasbeenexhausted.
Thisprocessofpointingtoonepennyatatime,beingcarefultocounteachpennyonceandonlyonce,is
anordering. It isequivalent tosaying: “Thispennycomes first, thisonesecond, thisone thirdandso
forth.Inaway,theorderingofpenniesislikearrangingaseriesofsticksordollsinorderofheight.There
is a first stick, a second stick, and so forth, just as there is a firstpennyanda secondone.Therefore,
something like the ability to construct ordinal relations underlies the child’s construction of sets
equivalentinnumber.
Despite theevident similarity, the twoprocesses—constructingordinal relations (as inordering
thesticks)andvicariantordering(thepennies)—arenotidentical.Inthecaseofthesticks,thereisone
andonlyoneshorteststickwhichmustcomefirst intheseries,oneandonlyonesecondshorteststick
whichmustcomesecondintheseries,andsoforth.Inthecaseofthepennies,itdoesnotmatterwhich
pennyisconsideredfirstintheseries,whichcomessecond,andsoon.Onecouldstartcountingatthe
extremeleft,attheextremeright,inthemiddleorwhereveronepleased,justsolongasoneiscarefulnot
toomitpointingtoeachofthepenniesandnottopointtoanyofthemmorethanonce.Theorderingof
penniesiscalled“vicariant”forthisveryreason:theorderinwhichthepenniesarecounteddoesnot
matter.
Other aspects of relations are involved too.When putting out one and only one sweet for each
penny,thechildiscoordinatingtwoorderings.Thisissimilartotheproblemofdollsandsticks.Justasthe
childcangivetotheshortestdolltheshorteststick,tothesecondshortestdollthesecondshorteststick,
andsoforth,socanheplacethefirstsweetwiththefirstpenny,thesecondsweetwiththesecondpenny,
andsoforth.Ofcourse,theone-to-onecorrespondenceofpenniesandsweetsisvicariant,whereasthe
one-to-onecorrespondenceofdollsandsticksisnot.Inthelatterinstance,thereisoneandonlyonestick
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(theshortest)whichgoeswiththeshortestdoll,andsoforth.Inthecaseofpenniesandsweets,itdoes
notmatterwhichsweetisplacedintocorrespondencewithanypenny,solongasoneandonlyonesweet
isusedforeachpenny.
Theconstructionofequivalentsetsalsoinvolvesclassification.Tothechild,thepenniesinsetA,for
instance,areinsomewaysallthesameandinsomewaysdifferentfromoneanother.Theyaredifferent
inthatacertainpennyiscountedfirst,anotheronesecond,andsoforth.Theyarethesameinthatitdoes
notmatterwhichiscountedfirst,whichsecond,andsoforth.Inotherwords,itisonlythechild’sactof
pointingtoeachinturnthatdifferentiatesthepennies;otherwise,theyareallequivalent.Insofaraseach
ofthepenniesisanelementequivalenttoalltherest,theyareallmembersofthesameclass.Thesameis
true,ofcourse,ofthesweetsinsetB.
Thus far we have seen how the child’s ability to construct sets equivalent in number may be
analyzedintoanumberofcomponentskills.Underlyingthechild’sovertperformance(e.g.,placingona
table seven sweets corresponding to seven pennies) are a number of concrete operations: vicariant
ordering, one-to-one correspondence of two vicariant orderings, and classification. Some of the
operations involveclassesandothers relations.Thus,number isaunionof classesandrelations.The
operationsareconcretesincethechildcanapplythemonlytoimmediatelypresentobjectsorthoughts
about them.Theyareoperations since theyare actionswhich the childperformsmentally andwhich
have the added property of being reversible. This means that for each particular mental action, for
instanceaddition, thechildcanperformitsoppositeaction, in thiscasesubtraction,which leaveshim
wherehestarted.Asoperations,theymayalsobedescribedintermsofoverallstructuresorsystems,that
is,intermsoftheGroupings,anexampleofwhichwehavegiveninthecaseofclassification.5
Inthestageofconcreteoperations,thechildcanalsoconservenumber.Afterconstructingtwosets
equivalent in number, the child recognizes that the sets remain equivalent despite mere physical
rearrangementofthesets.Ifthesevensweetsarecompressedtomakeashortlinewhilethelineofseven
penniesremainsthesame,thetwosetsareneverthelessstillequalinnumber.Theequivalencehasbeen
conserved.
Whatenablestheconcreteoperationalchildtoconservewhilethepreoperational(stages1and2)
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childfailstodoso?Recallthemechanismunderlyingthepreoperationalchild’sfailure:centration.The
youngerchildcentersononlyalimitedamountoftheinformationavailable.Whentherowofsweetsis
compressed,henoticesonlythatthelineofpenniesisnowlongerthanthelineofsweets.Heignoresthe
fact that the line of sweets is denser (has smaller spaces between adjacent elements), and bases his
judgmentonlyonthelengths.Thepreoperationalchildknowsthatempiricalreversibilityispossible:he
realizesthatifthesweetswerereturnedtotheiroriginalpositions,therewouldbeonesweetforeach
penny.Thisknowledgedoesnothelp,however;despite it, he feels that thenumberof a set changes
whenitsappearanceisaltered.Perceptualfactorshavetoostrongaholdonthechildatthisstage.They
arenotyetsufficientlycontrolledbymentalactionswhichcancompensateformisleadinginformation.
Bycontrast,theconcreteoperationalchilddecentershisattention.Heattendstoboththerelevant
dimensionsandusesthisinformationinseveralways.
1.Henoticesthatthelineofpennieshasbecomelongerthanthelineofsweetsandthatthelineofsweetshasbecomedenserthanthelineofpennies.Moreover,hecoordinatesthetwodimensions. He mentally manipulates the visual data available to him. This mentalactivity leads him to realize that while the length of the line of pennies increases(relativetothesweets)byacertainamount,thedensityofthelineofsweetsincreasesbyanequivalentamount.Inotherwords,thechildconceivesthatthepennies’increaseinlengthisbalancedby,orcompensatedfor,bythesweets’increaseindensity:thereisarelation of reciprocity or compensation between length and density. In effect, oneincreasecancelsouttheotherwiththeresultthatthesetsremainequivalentinnumber.Thisreciprocityisoneformofreversibility.Sincetheincreaseinlengthcounteractstheincreaseindensity,theresultisareturn,orareversal,totheoriginalsituation,whichisequalnumber.
2.Theconcreteoperationalchildalsocomestousetheoperationofnegation.Wehavealreadyseenthatwhentherowofsweetsiscompressed,theconcreteoperationalchildrealizesthatthesweets’ increaseindensityisreciprocatedbythepennies’ increaseinlength,and that, as a result of these reciprocal transformations, the number of the two setsremains equivalent. The concrete operational child is also able to imagine that thesechangescanbeannulledornegated.Hereasonsthattheactionofcontractingthesweetscanbenegatedbytheinverseactionofspreadingthemout.Theoneactionisannulledby theother. Suchannulmentornegation isanother formof reversibility; that is, thechild mentally reverses the action of contracting the row of sweets. As a result heattributesequalnumberstothetwosets.Notethatthestage3childbothreversestheactofcontractingandrecognizesthatthefinalresultistheoriginalarrangementofsweets
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andpennies.Thestage2child,whoiscapableofempiricalreversibility,recognizesthatthesweetscanbereturnedtotheiroriginalpositionbutdoesnotfocusonorappreciatetheactofrearrangement.Heattendstostates,nottransformations.
3. The concrete operational child sometimes uses an identity argument, reasoning that thenumbersmustbethesamesincethesameobjectsareinvolved:nothinghasbeenaddedortakenaway.
Thestage3child’s thought isconcrete inaspecialsensewhichSinclair(1971),oneof themost
importantGenevaninvestigators,expressesquiteclearly:“Concreteoperations...doesnotmeanthatthe
childcanthinklogicallyonlyifhecanatthesametimemanipulateobjects....Concrete,inthePiagetian
sense,meansthatthechildcanthinkinalogicallycoherentmanneraboutobjectsthatdoexistandhave
realproperties,andaboutactionsthatarepossible;hecanperformthementaloperationsinvolvedboth
whenaskedpurelyverbalquestionsandwhenmanipulatingobjects....Theactualpresenceofobjectsis
nointrinsiccondition”(pp.5-6).
Tosummarize, thestage3child,havingenteredtheperiodofconcreteoperations,canconstruct
two sets equivalent in number, and can conserve this equivalence despite changes in appearance.
Underlyingtheseachievementsareanumberof thoughtprocesses.Theability toconstructequivalent
setsrequiresvicariantorderingandclassification.Theabilitytoconserve,whichisacquiredasaresultof
thedecentrationofthechild’sattention,issupportedbythreetypesofoperationswhicharesometimes
explicitlyexpressedinthechild’sjustificationofhisresponse:reciprocity,negation,andidentity.These
areaspectsofconcreteoperations,whichmaybedescribedbythegroupings.Thechilddoesnotalways
performallofthethoughtprocesseswhenpresentedwithaproblemofconstructingequalsets,nordoes
herefertoallthreeargumentswhenaskedforajustificationofconservation.Hemightonlyrefertoone
or perhaps two of them. The child is, however, capable of performing all the concrete operations,
althoughhemaynot alwaysdo so. In fact, after a periodof time the concrete operational child takes
conservation for granted.He immediately recognizes that number is conserved anddoes not need to
proveconservationtohimselfbymeansofnegationorreciprocity.Whenaskedwhynumberisconserved,
hethinksthatthequestionissillyandthatthefactofconservationisself-evident.Forhim,conservation
has become amatter of logical necessity. This is evidence that the child has acquired an underlying
structureofmentaloperations inwhicheach isdependentupon theotherandnone isperformed in
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isolation.Thestage3child’sthoughtisconcreteinthespecialsensethathecanthinkcoherentlyabout
anddealwithrealobjectsbutnothypotheticalentities.
In conclusion, Piaget’s work on number has been extraordinarily productive. It has stimulated
volumes of research on children’s number, and many of Piaget’s findings have been successfully
replicated,eveninnon-Westernsocieties(seeDasen,1977).AsweshallfindinChapter6,theworkhas
alsohadimplicationsforeducationalcurricula.Likemanymajorcontributionstopsychology,thework
has aroused a good deal of controversy, and several alternative views have been proposed (see, for
example,GelmanandGallistel,1978;andGinsburg,1982).
CONSERVATION
Thus far, we have described only the conservation of number—that is, the child’s ability to
recognize that thenumericalequivalencebetween twosets remainsunchangeddespitealterationsof
physical arrangement. Piaget has also investigated severed other conservations which include
continuous quantity, substance, weight, and volume. The conservation of continuous quantity may be
definedbythissituation.Thechildispresentedwithtwoidenticalbeakers(AandB),eachfilledwith
equalamountsofliquid(seeFigure11),andisaskedwhetherthetwoglassescontainthesameamount
ornotthesameamounttodrink.Afterheagreestotheequivalenceofquantities,theliquidispouredby
either the experimenter or the child from one of the two identical beakers (say, B) into a third,
dissimilarlyshapedbeaker(C).Thecolumnoftheliquidinthethirdclass(andtheglassitself)isboth
shorterandwiderthanthatintheremainingoriginalglass(A).Thechildisnowaskedwhetherthetwo
beakers(nowAandC)containequalamounts.Ifheassertsthattheydo,heisaskedtoexplainwhy.The
liquid inC is then returned to theoriginalbeakerB, and the child is againasked ifA andB contain
identicalamounts.Themanipulationisrepeated,thistimewithaglass(D)whichistallerandthinner
thantheoriginalbeakers.Finally,theliquidofeitherAorBispouredintoaset(E)ofaboutthreeorfour
smallerglassesandthesamequestionsareaskedofthechild.Ifthechildcontinuouslyassertsineach
casethattheamountthathasbeenpouredfromBintothedifferentbeakersisalwaysthesameasthe
amountremaining in theoriginalbeaker(A), thenhehasconservedcontinuousquantity.That is, the
childrecognizesthatmerelypouringtheliquidfromBtoCorDorE,doesnotincreaseordecreasethe
quantity;the“amount”ofliquidremainsthesame(orisconserved)whetheritisinBorinC.Sincethe
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quantitiesAandBwereequal,andsincepouringtheliquidofBintoCdoesnotchangeitsquantity,then
thequantitiesinAandCmustalsobeequal.Ifthechilddoesnotconsistentlyassertthisequality,thenhe
hasfailedtoconserve.
FIGURE11Conservationofcontinuousquantities.
Inthecaseofconservationofsubstance,thechildispresentedwithtwoidenticalballsofPlasticine
(orclay,etc.).HeisfirstaskedwhetherthereisthesameamountofPlasticineinbothballs.Ifhedoesnot
think so, he is asked to take away or add some clay tomake them identical. Then, the experimenter
changesoneoftheballstoasausageshape,whilethechildwatches.Thechildmustnowdecidewhether
ornottheballandthesausagehaveequalamountsofsubstance.As inthe liquidsituation, theball is
changed into a varietyofdifferent shapes. If the child consistently asserts that thebelli and thenew
shapesdohaveequalamountsofsubstance,thenhehasconservedsubstanceandhasrecognizedthat
merelychangingtheshapedoesnotaltertheamountofmatterinvolved.
To test theconservation ofweight, the experimenter again presents the childwith two identical
ballsofPlasticineandplacesthemonabalance.Thechildseesthatthetwoballsweighthesame.Then
theyareremovedfromthebalanceandoneballistransformedintotheshapeofasausage.Thechildis
askedtoanticipatetheresultsofplacingtheballandthesausageonthetwosidesofthebalance.Will
theystillremainbalancedorwillonesidebeheavierthantheother?Thequestioniswhetherthechild
recognizesthatweightisconserveddespitechangesinshape.Hereagainaseriesofchangesaremadeto
oneoftheballsandthequestionastotheidentityofweightisrepeated.
Inthecaseofconservationofvolume,twoballsofPlasticineareplacedintwoidenticalbeakers,each
filledwithequalquantitiesofliquid.Thechildseesthattheballsdisplaceanequalvolumeofliquidin
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bothbeakers.Or,inthechild’sterms,theliquidgoesupanequaldistanceinbothcases.Thentheballs
areremovedfromthebeakers,andoneballischangedintotheshapeofasausage.Thequestionnowis
whetherthechildrecognizesthatbothballandsausagecontinuetodisplaceequalvolumes,orwhether
thewatergoesupanequalamountinbothcases.
All theseconservationsaresimilar.Theyinvolvea firstphase inwhichthechildmustrecognize
thattwoamounts—liquidquantity,substance,weight,orvolume—areequal.Mostchildrenabovetheage
of 4 years are quite successful in this task. All the conservations also involve a visible transformation
whichmaybedonebyeitherthechildortheexperimenter.Whilethechildwatches,orasaresultofhis
ownactions,theliquidispouredfromonebeakertoanother,ortheballischangedintoasausage.Itis
quiteapparentthatnoliquidorPlasticineisaddedortakenaway.It isalsoapparentthatthingsnow
lookdifferent.Thecolumnofliquidisshorterandwider,andtheballisnowasausage.And,finally,all
theconservationsinvolveasecondphaseinwhichthechildmustonceagainjudgewhethertheamounts
inquestion are still the same.Of course, they are equivalent, and the issue iswhether the childwill
recognizethisorbemisledbytheobservedchangesinappearance.
Piaget’sgeneral findingsare that there isasequenceofdevelopmentwithregard toeachof the
conservations.Childrenbeginbyfailingtoconserveandrequireaperiodofdevelopmentbeforetheyare
able to succeedat the task.Forexample, in the caseof continuousquantities, childrenarenotable to
conserveuntilabouttheageof6or7years.Inthefirstphaseoftheproblem(twoidenticalbeakers,each
filledwithequalamountsofliquid),theyoungestchildren,around4or5yearsofage,correctlyconclude
that theamountsof liquidareequal.Since thechildhaseitherpouredout the liquid into thesecond
beaker,orhastoldtheexperimenterwhentostoppouring,thisisnotsurprising.Ifaskedtojustifythe
identity,thechildwillsaythatthewatercomesuptothesamelevelineachglasssothattheamountsare
equal.Whentheliquidinonebeakerispouredintoathirdglasswhichisdifferentinshapefromthefirst
two,thechildnowmaintainsthattheamountsarenolongerequal.Oneglasshasmoretodrinkthanthe
other.Askedtoexplainhisanswer,hesaysthattheglasswiththetallercolumnofliquidhasthegreater
amount.Thisjudgmentofamountsistiedexclusivelytotheheightsofthecolumnsofliquid:whenthe
heightsare the same (as inphase1), the child thinks that theamountsare the same;when theyare
different(asinphase2),thentheamountsmustbedifferenttoo.
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Instage2,thechildof5or6yearsvacillatesinhisresponsestotheconservationproblem.Whilehe
usuallyfailstoconserve,hisapproachtotheproblemvariesfromtimetotime.Inthesecondphaseofthe
experiment(whenonebeaker isshorterandwiderthantheother), thechildsometimessaysthatthe
tallerbeakerhasmore todrink,andsometimesmaintains that thewideronehas thegreateramount.
Unlikethestage1child,hedoesnotconcentrateexclusivelyontheheightsofthecolumnsofliquid,but
sometimesbaseshisjudgmentsonthewidthsaswell.
Instage3,thechildiscapableofconservation.Whenaskedwhytheamountsdonotchangeafter
thepouring,hegivesatleastoneofseveralreasons.OneisthatiftheliquidinCwerereturnedtoits
originalcontainer,B, thenthetwoinitialbeakers,AandB,wouldcontain identicalcolumnsof liquid.
Thisisthenegationargument.Asecondreasonistheidentityargument:it’sthesamewater.Youhaven’t
addedanyortakenanyaway.Athirdargument,involvingcompensationorreciprocity, isthatthethird
glass,C,isshorterthantheoriginalbeaker,A,butwhatClostinheightwascompensatedbyC’sgainin
width;therefore,theamountinCmustbeequaltotheamountinA.
Towardtheendofhislife,Piagetreturnedtotheproblemofconservationandstressedtheroleof
commutability. Inoneexperiment,Piaget (1979)presentedchildrenwithaconservationofsubstance
problemofthefollowingtype.Aballofclayispresentedandthenapieceisremoved.Thechildisasked
iftheballhasthesameamount,andsaysno,sincesomethinghasbeentakenaway.Thepiecethathad
beenremovedfromonesideoftheballwasplacedontheothersideandthechildwasagainaskedifthe
ballhasthesameamountnow(withthepieceaddedtotheotherside)asdidtheoriginalball.Piaget
findsthatundertheseconditions,childrenassertconservationataveryyoungage.Theysayessentially
that“It’sthesamething,youtookitawayandthenputitbackandit’salwaysthesame”(p.21).Inother
words,thechildrenhaveunderstood“thatthereisdisplacement,andthatwhenonedisplaces,whatis
addedatoneplacehasbeentakenawayfromanotherplace”(p.21).ThisPiagetcalls“commutability”
andclaimsthatitisoneimportantfactorinconservation.Commutabilitybearsasimilaritytothenotionof
compensation.
In the case of conservation of substance, weight, and volume, a similar progression to that of
quantityappears.Inthefirststage,thechildfailstoconserveapparentlybecauseofaconcentrationon
onlyoneofthestimulusdimensionsinvolved.Thatis,inthecaseofweighthemaysaythatthesausageis
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heavier than the ball because the former is longer. In the second stage, he again fails to conserve,
although now he vacillates between the two dimensions involved. For instance, he may sometimes
believethattheballisheavierbecauseitiswiderandatothertimesassertthatthesausageisheavier
because it is longer. In the third stage, the child conserves, for reasons similar to those cited for
continuousquantities.
Whilealltheconservationsfollowasimilarcourseofdevelopment,thereisastrikingirregularityas
well—thephenomenonofhorizontaldécalage.Thisreferstothefact,whichhasbeenwellsubstantiated,
thatthechildmasterstheconservationofdiscontinuousquantityandsubstanceataboutage6or7;does
notachievestage3oftheconservationofweightuntilage9or10;doesnotunderstandtheconservation
ofvolumeuntilapproximately11or12.Ineachcasetheargumentsusedarethesame,sometimeseven
involvingthesamewords.Buthavingmasteredconservationinonesubstantivearea,likesubstance,the
child is not able to generalize immediately to another area like that of weight. First, he acquires
conservationofdiscontinuousquantityandsubstance,andthenweight,andthenvolume.Thedécalage,
orlackofimmediatetransfer,illustrateshowconcreteisthethoughtofthechildduringtheagesofabout
7to11years.Hisreasoningistiedtoparticularsituationsandobjects;hismentaloperationsinonearea
maynotbeappliedtoanother,nomatterhowusefulthismightbe.
GENERAL CHARACTERISTICS OF THOUGHT
Wehavereviewedthedevelopmentofvariousaspectsofthought:classes,relations,number,and
conservation.Itwouldseemusefulatthistimetotakeabroaderlookatsomegeneralcharacteristicsof
cognitivedevelopment.
Underlying Patterns of Thought
There are striking regularities in the child’s cognitive development. In each of the two major
periodsofdevelopmentdiscussedinthischapter(preoperationalandconcreteoperational),thechild
usesdistinctivepatternsofthoughttoapproachdifferentsubstantiveproblems.Thereappeartobesome
generalpatternswhichcharacterize the thoughtof thepreoperational childandsomeotherpatterns
manifestedintheconcreteoperationalchild’scognition.
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Consider,first,thechildfromabout4to7yearsinthepreoperationalperiod.(Rememberthatthis
age designation is only approximate, since a child as old as 9 or 10 years typically shows a
preoperationalapproachtotheconservationofvolume.)Onegeneralcharacteristicofcognitiveactivity
duringthisperiodiscentration.Thechildtendstofocusonalimitedamountoftheinformationavailable.
In the conservationofnumber, he judges two sets equalwhen they are the same length and ignores
anotherrelevantvariable,thedensity.Intheconservationofcontinuousquantity,thechildjudgestwo
amountsequalwhen theheightsof thecolumnsof liquidare thesameand ignores thewidth. In the
constructionofordinalrelations(theproblemoforderingtensticksintermsofheight),hesucceedsonly
byconsideringthetopsof thesticksand ignoringthebottoms,orviceversa. Inall theseproblems, the
preoperational child deploys his attention in overly limitedways. He focuses on one dimension of a
situation,failstomakeuseofanother,equallyrelevantdimension,andthereforecannotappreciatethe
relationsbetweenthetwo.(Thenotionofcentration issomewhatsimilar toPiaget’searlierconceptof
juxtapositionwhichisthetendencytothinkintermsofthepartsofasituationandnotintegratethem
intoawhole.)
Bycontrast, theconcreteoperational child is characterizedbydecentration. He tends to focus on
severeddimensionsofaproblemsimultaneouslyandtorelatethesedimensions.Intheconservationof
number,hecoordinateslengthanddensity:twosetshavethesamenumberwhenthefirstislongerthen
the second but the second is denser than the first. In the conservation of continuous quantity, he
recognizes thatamountsareequalwhenonecolumnof liquid isat thesametimetallerbutnarrower
than a second. In the construction of ordinal relations, he determines whether a given object is
simultaneously bigger than some objects and smaller than others. In all these problems, the concrete
operational child attends to severed aspects of the situation at once. Centration anddecentration are
generalpatternsofthought,underlyingstructures.
Thetwomajorperiodsofdevelopmentcanbecharacterizedinotherwaysaswell.Thethoughtof
thepreoperationalchildisstaticinthesensethatitcentersonstates.Intheconservationofsubstancehe
focuses on the shape of Plasticine (sometimes a ball and sometimes a sausage) and ignores the
transformation,thatis,thechangefromonestatetotheother.Intheconservationofcontinuousquantity
he focuses on the heights of the columns of liquid and not on the act of pouring. He lacks adequate
representationsofanobject’sshiftfromonepositiontoanother.Ingeneral,heconcentratesonthestatic
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statesofasituationandnotonitsdynamictransformations.
Theconcreteoperationalchild,ontheotherhand,isattunedtochanges.Intheconservationshe
concentratesonthetransformation:theactofpouringtheliquid,orspreadingapartasetofobjects,or
deformingaballintoasausage.Heformsmoreorlessaccurateimagesofthechangeswhichhavetaken
place,and,therefore,canreason,forexample,thatasasetexpandsinlengthitsimultaneouslydecreases
indensity.
The preoperational child’s thought lacks reversibility. He may be able to predict an empirical
reversibility as, for instance, in the case of the liquidswhere hewould agree that if thewaterwere
pouredbackintoB,therewouldbethesamequantityasbefore.Butthisempiricalreversibilitydoesnot
changethefactthatnowhebelievesthereismore(orless)waterinthenewglassC.Itisasifpouring
fromBtoC,andfromCtoBweretotallyunrelatedactions.Theolderchild,ontheotherhand,realizes
thatpouringfromCtoBreversesornegatestheactionofpouringfromBtoCandisawarethatitisthe
sameactionperformedinanotherdirection.Bycarryingouttheactionmentally,thatis,byreversingthe
pouringinhismind,heisabletoascertainthatthequantityofwaterinC(thelowerwiderglass)isthe
sameasinB.Hecanperformamentaloperationwhichleadshimtoacertainconclusion,andthendothe
reverseofthisoperationwhichenableshimtoreturntohisoriginalstartingpoint.
Theconcreteoperationalchildcanalsoperformanothertypeofreversibilitywhenoperatingon
relations.Thisisreciprocity.Forinstance,intheexampleofliquidquantity,whenthechildsaysthatone
glassislongerandthinner,whereastheotherisshorterandwider,heiscancelingoutthedifferences
betweenthetwoglassesbyanactionofreciprocity.Onedifferencebalancesouttheother,withtheresult
thattheyhaveareciprocalrelationship.
Tosummarize,thepreoperationalchild’sthoughtisirreversibleandattentivetolimitedamountsof
information, particularly the static states of reality. The concrete operational child focuses on several
aspects of a situation simultaneously, is sensitive to transformations, and can reverse the direction of
thought. Piaget conceives of these three aspects of thought— centration-decentration, static-dynamic,
irreversibility-reversibility—asinterdependent.Ifthechildcentersonthestaticaspectsofasituation,he
isunlikelytoappreciatetransformations.Ifhedoesnotrepresenttransformations,thechildisunlikelyto
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reversehis thought.Bydecentering,he comes tobeawareof the transformations,which thus lead to
reversibilityinhisthought.Inconclusion,wecanseethatoneaspectofthoughtisnotisolatedfromthe
rest.Eventhoughthenatureofthesystemmayvarywiththedevelopmentofthechild,thoughtprocesses
formanintegratedsystem.
Invariant Sequence
Another striking regularity in cognitive development involves invariant order: the sequence of
activities (for example in classification, partial alignments, collections, class inclusion) assumes an
invariantorderdespitewidevariationsinculture.Cross-culturalresearchprovidesrelevantevidenceon
thisissue.WithinWesterncultureschildrenprogressthroughthevariousstagesintheorderdescribed
byPiaget.Inthecaseofconservationofcontinuousquantities, forexample,researchshowsthatSwiss,
British,American,andCanadianchildrenfirstfailtoconserve,thenvacillateintheirresponse,andlater
conservewithstability.Whilechildrenintheseculturesdonotnecessarilyachievethevariousstagesat
thesameaverageages, thesequenceofdevelopment—theorderof thestages—seems identical inall
cases.Eveninotherandverydifferentcultures,liketheThaiorMalaysian,thesamesequenceofstages
andtypeofresponsesappear.ChildreninThailand,forexample,exhibitclassificationactivitieswhich
arevirtuallyidenticaltothoseusedbyWesternchildren,andproceedthroughthesequenceofstagesin
theorderdescribedbyPiaget(Opper,inDasen,1977).Thereisgreatcross-culturalgeneralityinPiaget’s
findings.Atthesametime,wemustmakeonequalification:apparently,membersofsomeculturesdonot
advanceasfarinthesequenceofstagesasdoWesterners.Thus,forwhateverreasons,insomecultures,
individualsmaynot complete the stageof formaloperations.Not everyoneachieves thehighest level
possible in terms of Piaget’s stages. Yet, until their progress terminates, these individuals proceed
throughthesequenceofstagesinthestandardorder.Whiletheultimatelevelofdevelopmentmaydiffer
amongcultures, thesequenceseemstobe invariant,asPiagetproposes.Thephenomenadescribedby
Piagetarethusnearlyuniversal,occurringacrossextremevariationsincultureandenvironment.Piaget
hassurelycapturedsomethingverybasicinhumancognition.6
Irregularities
Piaget has gone to great lengths to dispel some misinterpretations concerning his theory. In
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particular,heshowsthattherearecertainirregularitiesindevelopment.Hepointsout,first,thattheages
atwhichthestagesoccurvaryconsiderablybothwithinandamongcultures.NotallGenevanchildren
attainstage3ofnumberdevelopmentat6or7years,andchildreninMartiniquelagbehindGenevans
byapproximatelyfouryears.InThailand,urbanchildrenattainstage3atthesametimeaschildrenin
Geneva,but ruralThai children lagbehindbyapproximately threeyears. InMalaysia, rural children
attainthenumberconceptoneyearaheadofurbanchildren,whointurnlagbehindSwisschildrenby
twoyears.Thus therateofdevelopmentseems tovary fromgroup togroup.Second, thecourseofan
individual’sdevelopmentiscontinuous.
Thechildisnotcharacterizedbystage1onedayandbystage2thenextday.Rather,thetransition
is gradual, occurring over a long period of time, and the child exhibits many forms of behavior
intermediary between the two stages. Indeed, an individual child’s behavior takes many forms in
addition to those Piaget describes as being typical of the various stages. Piaget’s stages are idealized
abstractions;theydescribeselectedandsalientpointsonanirregularcontinuumofdevelopment.Third,
thechildisnotalwaysinthesamestageofdevelopmentwithregardtodifferentareasofthought.The
childmaybe characterizedby stage2 in the case of classes, and stage1 in the case of relations. It is
unlikely,however,thathewillbeinstage1forclassesandstage3forrelations.Onlyinfrequentlydoes
onefindextremediscrepanciesbetweenstagelevelsindifferentareas.Fourth,aswehavealreadyseen,
there exists the phenomenon of horizontal décalage, in which the child displays different levels of
achievementinregardtoproblemsinvolvingsimilarmentaloperations;forexample,hemaybeableto
conservesubstancebutnotnumber.
Preoperational Strengths
Piaget (On the Development of Memory and Identity, 1968) tries to correct a widespread
misconception concerning preoperational thought. Typically, we characterize the young child as
intellectuallyincompetentsincehecannotconserve,cannotusereversibility,andcannotdecenter.Piaget
feelsthatthisviewisexaggerated;asaresultofrecentresearch,Piagetproposesthatthepreoperational
childpossessesanumberofimportantintellectualstrengthswhichmustnotbeoverlooked.Inparticular,
theyoungchildiscapableofidentity,functions,andcorrespondences.
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While unable to conserve, the young child nevertheless appreciates certain basic identities. For
example, in the standard conservation problem, the young child recognizes that the same liquid is
transferredfromonebeakertoanothereventhoughonelooksquitedifferentfromtheother.Heseesthat
thebasicsubstancedoesnotchange,eventhoughitsappearanceisalteredandeventhoughhefalsely
believesthattheamountofliquidhaschanged.Heappreciatesidentitybutfailstoconservequantity.
Piagetproposesthatthenotionofidentitymayderivefromthechild’sperceptionofhisownbody’s
growth.WithGilbertVoyat,Piagetaskedchildrentodrawthemselveswhentheywerebabies,whenthey
were a little bigger, and so on; then the experimenters questioned the children concerning the
maintenanceof their identitydespiteobviousphysicalchanges.Theexperimentersalsoposedsimilar
questions concerning the identityofotherobjects, includingplants.The results showed that children
easily appreciated their own identity despite changes in size, and were less likely to accept the
continuing identity of a plant over its various changes in appearance. Perhaps, then, the notion of
identity derives from the child’s perception of his ownbody’s growth and later is generalized to the
worldofobjects.
Thepreoperationalchildcanalsoperceivefunctionalrelationsintheenvironment.Oneexample
ofsuchfunctions(givenbySinclair,1971)involvestheopeningofacurtain:“thechildunderstandsthat
whenonepulls thecordofacurtain, thecurtainopens; the fartheronepulls, the farther thecurtain
opens”(p.4).Inotherwords,thereisafunctionalrelation,aco-variationbetweenpullingandopening,
and the child perceives that the two factors are positively related. (Theremay evenbe precursors of
functionsin infancy:thisexampleisreminiscentoftheinfantLaurentwhoseemedtorealizethatthe
morevigorouslyheshookachain,thelouderwouldbethesoundproducedbytheattachedrattles.)Itis
veryimportant,ofcourse,forthechildtorecognizesuchfunctionalrelationsintheenvironment:they
pervadeit.Thetallertheperson,thestrongerheislikelytobe;theharderonehitsanotherchild,the
more likely is the child to protest and even cry; the bigger the glass, themoremilk it holds. Despite
limitations in other areas of thought (for example, centration), the preoperational child has some
appreciation for basic functional relations, and this is of great value to him in coping with the
environment.
At the same time, Piaget points out that these functions are incomplete: they constitute only a
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semilogic.Foronething,thechild’sappreciationoffunctionsisimprecise.Toreturntotheexampleofthe
curtain, thechilddoesnotrealizeexactlyhowthepullingof thecord isrelatedto theopeningof the
curtain and cannot quantify the results with any degree of precision. Another Piagetian experiment
makes this clear. Children were presented with three toy fish, 5, 10, and 15 centimeters long,
respectively,andweretoldtofeedeachfishitsproperdietofmeatballs.Themiddle-sizedfishshouldget
twiceasmanymeatballsasthesmallest,andthelargestfishthreetimesasmany.Preoperationalchildren
understoodthefunctionalrelationbetweensizeof fishandnumberofmeatballsonly inanimprecise
way.Theyrealizedthatthelargerthefish,themoreitneedstoeat.Buttheywerenotabletoworkoutthe
functioninaprecisemanner(forexample,bygiving2,4,and6or3,6,and9meatballstotherespective
fish).
Toward the end of his life, Piaget (1979) stressed the role of “correspondences.” He used this
notiontorefertothechild’stendencytocompareobjectsorevents,todeterminethewaysinwhichthey
“correspond,” or are similar and different. This tendency appears at all levels of development, from
infancyonward,althoughittakesdifferentformsatdifferentlevels.
Forexample,aninfantfirsthitsatoyparrottomakeitswingandthenappliesthehittingschemeto
otherhangingobjectsaswell.Inasensehehascomparedthenewobjectwiththefamiliarparrotand
notedthesimilaritybetweenthem(thecorrespondenceofoneobjecttoanother).
Note:Ablackmarbleandawhitemarblearegluedtoaplate,withthewhiteoneabovetheblack
one(asinFigure12A).Thentheplateisrotatedsothatblackoneisabovethewhiteone(asinFigure
12B).
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FIGURE12CorrespondenceofMarbles.
The preoperational child displays different forms of correspondence. For example, in one
experiment,Piaget(1979)showedchildrentwoobjectsonarotatingdisk.Imaginethattheobjectsarea
whitemarbleandablackmarble,gluedtoadish,as inFigure12A.Whenthemarblesareon the left
(Figure12A),thewhiteisabovetheblack.Whenthedishisrotatedsothatthemarblesareontheright
(Figure12B),thentheblackisabovethewhite.Thepreoperationalchildobservesthesituations—the
marblesontheleftandontheright—andgraduallynotesthecorrespondencesbetweenthem.Thechild
seesthatwhenthemarblesareontheleftside,thewhiteishigher,butwhentheyareontheright,the
whitebecomesthelower.Atfirst,thechild’sapproachissimply“empirical”:torecordthefactswithout
interpreting them. But “the child discovers suddenly that there is a general order” (p. 24). He
determines,inotherwords,thatthereisareversalofposition.It’snotjustthatthewhiteishigherinone
situationandlowerintheother,butthatthewhitehasswitchedpositions.This insight thengradually
leadsthechildtoanother:thepositionswereswitchedbecauseatransformationtookplace.Therotation
ofthedishcausedtheswitchinposition.
We see then that the child begins by comparing two states, noting some basic similarities and
differences(theswitchinposition).Thesecorrespondencesareimportantbecausetheypavethewayfor
thechild’sappreciationoftransformations.Andaswehaveseen,anappreciationoftransformationsisat
theheartofconcreteoperationalthinking.
In brief, preoperational thought is not characterized solely by incompetence. Young children
appreciatecertainbasicaspectsofidentity,perhapsasaresultofexperiencewiththeirownbodies.They
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alsounderstand,albeitinanimprecisemanner,varioussimplefunctionalrelationsintheenvironment.
Theydetectcorrespondences,andthisleadsthemtoanappreciationoftransformations.Indealingwith
youngchildrenonemustbeawareof these strengthsaswell asof the commonly cited limitations, as
GelmanandGallistel(1978)andothercontemporarywritersconcurinmaintaining.
The Concept of Stage
Piaget’s theory describes a sequence of stages. For example, in the case of the conservation of
numberwehavereviewedthetransitionfromcentrationtodecentration.Nowitisimportanttoconsider
thenatureofsuchstages.WhatdoesPiagetmeanbystageandhowusefulaconceptisit?
AccordingtoPiaget(BiologyandKnowledge, 1971a,p. 17) thenotionof stage isusedwhen the
followingthreeconditionsarefulfilled.First,theremustbeaninvariantsequenceofactivities.Thus,in
thecaseofconservation,thereis,first,afailuretorecognizeequivalence;thenthereisvacillation;and,
finally,thereissuccess.Theorderofappearanceoftheactivitiesisthesameforallchildren.Second,each
stageinthesequenceischaracterizedbyanunderlyingstructure,acoresystemdeterminingthechild’s
overt behavior. Thus, underlying the child’s failure to conserve is the strategy of centration—the
tendencytofocusonlimitedamountsofinformation.Third,eachofthestructurespreparesthewayfora
succeedingone.Thus,inthecaseofconservation,theinitialcentrationpreparesthewayforavacillation
amongtheavailabledimensions,andthisinturnleadstothesubsequentdecentration.Inbrief,Piaget
proposes that stages are characterized by invariant sequence, underlying structures, and successive
integrations.
Piagetalsoemphasizedthatdespitetheexistenceofstages,developmentiscontinuous.Thechild
doesnotenteranewstageovernight;instead,thechangesaregradual,andindeedbarelyperceptible
fromclose-up.Piagetexplainedthisintermsofthescaleofmeasurement.Ifwelookcloselyatachild’s
development,observingeverydayandthususinga finescaleofmeasurement, it ishardforustosee
dramaticchanges;fromonedaytothenextwewillnotnoticedifferencesinstages.Butifwestandback,
observing the child infrequentlyand thususinga crude scaleofmeasurement,wewillbe impressed
withchanges;fromoneyeartothenextwewillseeprogressfromonestagetothenext.
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Wehavealreadyreviewedresearchconcerningthenotionsofinvariantsequenceandunderlying
structure. Cross-cultural study demonstrates that the sequence described by Piaget is extremely
widespread,ifnotuniversal.Also,thereseemtobedistinctunderlyingpatternsorstructuresineachof
the major periods under consideration—preoperational and concrete operational. Consider next
Piaget’sthirdconditionfortheexistenceofastage—therequirementthateachstagepreparethewayfor
thenext.Whileitishardtoadduceevidencesupportingthisnotion,itseemstohaveacertainamountof
facevalidity;forexample,afocusontwodimensionsseemsnaturallytofollowfromafocusonone.In
brief, the evidence concerning invariant sequence, underlying structures, and successive integrations
seemstosupportPiaget’spropositionconcerningtheexistenceofmajorstagesofdevelopment.
Atthesametime,thestagenotionsuffersfromanumberofdifficulties.One,alreadyalludedto,is
theexistenceof irregularities indevelopment.Wehaveseen that thechild isnotalways in thesame
stagewithregardtodifferentareasofthought.Thus,hemaybeinstage1withrespecttoclassesand
stage2inthecaseofrelations.Also,thephenomenonofhorizontaldécalageisverystriking:thechildmay
displaydifferentlevelsofachievementinregardtoverysimilarareasofthought.Thus,hemayconserve
substance but not number. The existence of these irregularities seems dissonant with the notion of
distinctunderlyingpatternsorstructuresofthoughtcharacterizingthemajorstagesofdevelopment.If
thepatternsaresostrongandpervasive,whyarethedécalagessostriking?
Anotherdifficultywiththestagenotionisthatthestructurespresumablyunderlyingastagemay
alsobeimplicatedinstagesoccurringearlierinthesequence.ThuswehaverecentevidencebyTrabasso
(1975), for example, to the effect thatunder certain conditions, preoperational children canperform
concreteoperationaltasks.Ifthesamestructuresunderliebehavioratdifferentstages,dowenotthen
have toalterournotionof stages?The issueof stages isextremely complexand isnow the subjectof
considerablerethinking(foranexcellentdiscussionseeFlavell,1985).
Indeed,towardtheendofhislife,Piagetseemstohaverethoughtthestagenotionhimself.Thelast
tenyearsofPiaget’sresearchrevolvedlargelyaroundissuesofcognitivechangeanddevelopmentand
did not employ stage notions to any significant degree. In this sense, Piaget became less of a
“structuralist”(onewhodealswiththeanalysisofmentalstructuresunderlyingthestages)andmoreof
a“functionalist”(onewhodealswiththefactorsdeterminingdevelopment).AsweshallseeinChapter
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6,Piaget’stheoryofequilibrationplacedtheemphasisongradualchangesorineffectonmanyfleeting
substages.WhatwasimportantforthelaterPiagetwasnotaconceptofbroad,stablestages,butatheory
ofthecontinuouschangeanddevelopmentofthechild’sintellectualstructures.
MENTAL IMAGERY
Afterhisbriefexaminationduringthe1920softhecontentofthought,Piaget’smainconcernhas
beenwiththeoperativeaspectofcognition.Thisreferstoactionsusedtodealwithorevenchangethe
world. These actions may be either overt or internal. Examples of overt actions abound in the
sensorimotorperiod.Theinfantkickstoshakearattle,orusesasticktodrawanobjectclose.Thepresent
chapterhascoveredtwomajorsubdivisionsofinternalizedactions:theisolatedandunrelatedactionsof
preoperationalthoughtandthestructuredandcoordinatedonesofconcreteoperationalthought.
Piaget has also shown an interest, albeit a lesser one, in the figurative aspect of cognition. This
referstothreewaysinwhichthechildproducesanaccountofreality.Oneisperception,asystemwhich
functionsbymeansofthesensesandoperatesonanimmediatelypresentobjectorevent.Itisthrough
perceptionthatthechildachievesarecordofthethingsinthesurroundingworld.Thisrecordisoften
inexact, as in the case of the visual illusions. A second subdivision is imitation, by which the child
reproducestheactionsofpersonsorthings. It is truethat imitation involvesactionsonthepartof the
child,buttheseactionsneverthelessfallunderthefigurativeaspectsincetheyproduceacopyofreality
butdonotmodifyit.Athirdportionofthefigurativeaspectismentalimagery.AswesawinChapter3,
mentalimageryreferstopersonalandidiosyncraticinternaleventswhichstandfororrepresentabsent
objectsorevents.Whenwe“picture”toourselvesourfirstbicycle,orthestrollwetooklastweek,thenwe
areusingmentalimagery.Asweseefromthislastexample,thetopicofmemoryiscloselyboundupwith
thefigurativeaspectofthought.Memory(recall)typicallyinvolvesretainingknowledgegainedthrough
thefigurativemode.
In recent years, Piaget has conducted important investigations into two important aspects of
figurative cognition, specifically imagery and memory. His theory stands in stark contrast to the
traditionalempiricistviewofthesematters.Thelatterassumesthatperceptionstampsontheindividual
a literal copy of reality. Given sufficiently frequent repetition of the initial event, a mental image
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mirroring the reality is formed and is stored in memory. If there is no further experience with the
originalevent,thememoryimagegraduallyfades,losingitsfidelitytothereality;itisforgotten.Piaget
criticizesthistraditionalviewonseveralgrounds.Mostimportant,hebelievethatrealitydoesnotsimply
imposeitselfonapassiveorganism.Rathertheindividualassistsintheconstructionofhisownreality.
Hisintellectualactivities—theoperativemodeofthought—servetoshapetheresultsofencounterswith
theenvironment.The resulting figurativeknowledge isnot simplya copyof reality.This theme—the
influence of operative structures on figurative knowledge—dominates Piaget’s discussion of mental
imageryandmemory.Wewillnowconsiderthesetwotopicsinsuccession.
History
Mentalimagerywasoneofthefirsttopicsstudiedbyexperimentalpsychologists.Attheendofthe
nineteenthcentury,theschoolofWundtusedtheintrospectivemethodtoanalyzethenatureofmental
imagery.TheWundtiansbelievedthatimageswerecomposedofabundleofsensationstiedtogetherby
meansofassociation.Atthebeginningofthetwentiethcentury,thestudyofimageryfellintodisrepute
fortworeasons.First,theWurzburgpsychologistsfoundthatmuchofthoughtdidnotseemtoinvolve
imageryatall,andsecond,thebehavioristrevolutionwhichoccurredintheUnitedStatesmaintained
thattheintrospectivemethodwasapoorone.Thebehavioristsfeltthatthedataofintrospection—one’s
impressions of one’s own consciousness—were not public enough. How could another psychologist
determine if an introspectionwere reliable and accurate?As a result of the behaviorist attack on the
methodofintrospection,thestudyofimagerywasconsidered“unscientific”andwaslargelyabandoned.
Recently,however,psychologistshaveshownarenewedinterestintheancientproblemofimagery,and
thetopicisonceagainbecomingcentraltoexperimentalpsychology(Neisser,1976).
Incontrasttomoderninvestigators,Piagethasbeenstudyingimagerysinceatleastthe1930s.In
Chapter3wediscussedPiaget’sworkonimageryintheyoungchilduptotheageof4years.Ifyouwill
recall,thistheoryproposedthatmentalimagesdonotoccuruntilaboutthemiddleofthesecondyear.
Before this timethechilddidnotpossessmentalrepresentationsof theenvironmentand,asaresult,
reactedmainly to events occurring in the present. After imagerymakes its appearance the child can
represent tohimselfbothevents thatoccurred in thepastandobjects thatareno longerperceptually
present. Also, according to Piaget’s theory, imagery results from imitation. At first, the child overtly
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imitatestheactionsofthingsorpeople; later,hisimitationbecomesinternalizedandabbreviated.It is
through this internalactivity that imagesarise.Clearly,Piaget’sviewscontrast stronglywithWundt’s.
Imagesarenotmerelybundlesofsensations,imposedbytheenvironmentandconnectedbyassociation;
rather,theconstructionofimagesinvolvestheactivityofinternalizedimitation.
Later,with Inhelder, Piaget returned to the studyof imagery (1971).His laterworkdealswith
childrenabovetheageof4,andposesanumberofinterestingquestions.Forexample,aretheredifferent
typesof imagesatdifferentstagesof intellectualdevelopment? If so,what is therelationbetweenthe
imagesandthementaloperationsofagivenstage?
Method
Whilethesequestionsareinteresting,thestudyofmentalimagesisverydifficult,especiallyinthe
caseofchildren.Imagesarepersonal,idiosyncraticeventswhichcannotbevieweddirectly.Onecannot
“see”anotherperson’simagery;theinvestigatormust,therefore, infertheirexistenceandnaturefrom
otherphenomena,suchasaverbalreport.Piagethasusedavarietyofmethodstostudyimagery.Oneof
thesemethodsistoaskapersontodescribehisownimages.Butlanguageisnotfullyadequateforthis
task,orevenfordescribingsomethingasconcreteastheimmediateperceptionofanobject.Wearenever
able to convey bywords the precise nature of whatwe see. In our attempt to describe percepts, we
inevitably emphasize certain features and neglect others.We have difficulty in describing shades of
colors,orgradationsof textures.Wecannotgivean impressionof theentireperceptatonce,butmust
describeitsdetails insequence,andtherebyoftenlosetheessenceofthewhole.If languagesopoorly
conveysperceptualeventswhichcontinuetoremainbeforeoureyesforfurtherinspection,howmuch
moredifficultisittodescribementalimageswhichoftenarefleetingandunstable?
Anothermethodof studyingmental images isbydrawing.Here theperson is asked todrawan
objectpreviouslypresented.Sincetheobjectisnolongerpresent,hemustproduceanimageofittoyield
the drawing. The drawing, therefore, gives some insight into the nature of the image, which is the
internal “picture” of the object. The method of drawing, however, presents several shortcomings.
Drawingisnotasimpleanddirectreflectionofimages; italsoinvolvesotherprocesses.Somepersons
havepoormemory.Iftheyhaveforgottentheirimageofanobject,theycannotverywelldrawit.Other
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personssimplycannotdrawwell.Itisnottheirimagethatisatfault,buttheirartisticskill.
A thirdmethodattempts tobypass theshortcomingsoforiginaldrawings.Thesubject isgivena
collection of drawings made by the experimenter, and must select from them the one most closely
correspondingtohisimageofwhathehadpreviouslyobserved.Thismethod,ofcourse,isnotaffectedby
variationsinsubjects’artisticabilitiesandreducesthedifficultiescreatedbyapoorevocativememory.
Buteventhemethodofselectionfromacollectionofdrawingsisnotaltogethersatisfactory.Oneproblem
is that the drawings presented are not likely to be exact copies of the person’s mental image. The
drawingsmayomitdetailsoftheoriginalimageoraddnewfeatures.Ineitherevent,thesubject’schoice
doesnotgiveafullyaccurateindicationofhisimage.
To study imagery, Piaget has used all thesemethods—verbal report, drawing, and selection of
drawings—either alone or in combination. As is customary with the explorations carried out by the
Genevaschool,themethodsweresupplementedbyverbalquestioningcarriedoutintheclinicalmanner.
Major Findings
One experiment was concerned with kinetic images, or the imagery of an object’s movement.
Childrenfromabout4to8yearsofagewerepresentedwithtwoidenticalblocks,oneontopoftheother
(seeFigure13A).Eachsubjectwasaskedtodrawthesituation,andgenerallydidthisquitewell.Then
thetopblockwasmovedsothatitslightlyoverlappedthebottomone,asinFigure13B.Afterthechild
hadhadachancetolookatthisforawhile,thetopblockwasreturnedtoitsoriginalposition(Figure
13A).Thechildwasthenaskedtodrawtheblockinitsdisplacedposition(Figure13B),whichwas,of
course, no longer visible. After this, a collection of drawingswas presented. This contained a correct
rendering of Figure 13B as well as an assortment of incorrect drawings which represented errors
typicallymadebychildrenofthisage.(Thistechniqueissimilartotheuseofcountersuggestionsinthe
interview.)Thechildwasaskedtoselectthedrawingwhichhefeltcorrespondedmostcloselytowhathe
hadseen.Inthefinalstepanothercontrolwasadded.Thetopblockwasonceagaindisplaced,andthe
childwasaskedtodrawthesituationwhileitwaspresent.Ifthechildcouldaccuratelydrawtheblocks
whenpresent,thenanyofhispreviouserrorsofdrawing(whentheblockswereabsent)mustbedueto
faultyimageryormemoryandnottofaultydrawingability.
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FIGURE13Movementofblocks.
Tosummarize,thechildFirstdrewthedisplacedblocksaftertheywerenolongervisible;thenhe
selectedfromagroupofdrawingsoneresemblingthedisplacedblocks;andfinally,whenthedisplaced
blockswereonceagainbeforehim,hedrewthem.
The findings show that before the age of 7 years, children candraw the displacedblocks quite
correctlywhentheyarepresent,butnotwhentheyareabsent;norcanthechildrenchooseadrawing
whichcorrespondstothesituation.Ingeneral,childrenofabout4and5yearsproducedandselected
drawingsofthetypesAthroughE(seeFigure14),whereaschildrenof6yearsmadeerrorslikethoseof
typesFandG.Itwasonlyat7yearsthatover75percentofthesubjectsbothdrewandchosethecorrect
drawings.
FIGURE14Drawingofblocks.
Across-culturalstudyofthisprobleminThailand(Opper,1971)showsthatThaichildrenmake
thesametypesoferrorsasdoSwisschildren,althoughitisnotuntil10yearsofagethat75percentof
theThaisubjectsmakecorrectdrawingsofthetwoblocks.
The responses of the younger child would seem to indicate that he forms only a very general
pictureofthesituation,thatis,thatoneblockhasbeenmoved.Whenaskedtodrawtheexactdetails,heis
unabletodoso.Thechildthereforereproducesthisgeneralimpressionofmovementbydetachingthe
topblockfromthebottom(cf.C),byasymmetricalmovementofshrinkingorenlargementofoneofthe
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twoblocks(cf.DandE),or,finally,bytheretentionofonecommonboundaryoridenticallineforthetwo
blocks, inadditiontomakingchangesontheothersideof theblocks(cf.FandG).His imagedoesnot
appeartocorrespondtotheactualsituation.Thechildseemstocenterononedimension,thatis,onone
particularaspectofthesituation—forexample,theoverlappingofthetopblockindrawingsEandF,or
theoverlappingof thebottomblock indrawingsDandG.However, thechilddoesnotcoordinate the
movementofoneblockwiththefinalstateofthetwoblocks.Apparentlythechilddoesnotanalyzethe
situationinsufficientdetailbutmerelyformsaglobalimpressionofwhathashappened.Heisawarethat
theblockhasmoved,but the intimatedetailsof themovementandtheensuingdisplacementseemto
haveescapedhisattention.Asaresult,hismentalimageisinadequate.
A second typeof imagery is static imagery. In this instance the image reproduces a collectionof
objects,ascene,orapicture—inbrief,anysituationinwhichtheelementsremainunchangedineither
shape or position. Piaget finds that the child is able to produce adequate static imagery earlier than
kinetic.
We have reviewed only a small sampling of Piaget’s experiments on imagery. Their results,
together with those of a great many more studies, have led Piaget to draw the following general
conclusionsconcerningimageryanditsrelationtointelligenceasawhole.First,imagerydevelopsina
gradualmanner.Theevolutionofimageryisnotasdramaticasthatofthecognitiveoperationswhich
display a clear-cut sequence of stages. There appears to be only one major turning point in the
developmentof images.Thisseemstooccurataroundtheageof7or8yearsandcorresponds to the
onsetoftheperiodofconcreteoperations.Beforethebreak,thatis,fromtheageof11/2toabout7years,
thechildseemscapableofproducingwithanydegreeofaccuracyonlystaticimages,andeventheseare
farfromperfect.Thechildcannotrepresentcorrectlythemovementsofanobjectorevensimplephysical
transformations;theimagesproducedforsuchsituationsaregrosslydeformed.
Piagetbelieves that thereason for thisdeficiency isoneaspectofoperativecognition,namely,a
tendencytoconcentrateontheinitialandfinalstatesofagivensituationandtoneglecttheintervening
events which are responsible for the changes. We have already seen this tendency, which is called
centration, operating in the case of conservation. If youwill, recall the situationwhere the childwas
presentedwitha lineofvases,eachofwhichcontainedaflower.Theflowerswereremovedfromthe
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vasesandspreadapart.Whenthisoccurs,theyoungchildusuallybelievesthattherearemoreflowers
thanvases,sincethelineofflowersisnowlongerthanthelineofvases.Hehascenteredonthelengths
andignoredanumberofotherfactors.Hehasfailedtodecenterandtoconsiderthedensityofthelines,
aswellastheirlength,andhehasignoredtheintermediarytransformation(theremovalandspacingof
theflowers).Thus,thechildfocusesmainlyontheinitialandfinalstates(theflowersinthevasesand
the flowersspacedout)and fails to integrate these impressionswithallelse thathasoccurred.Thus,
beforetheageof7or8imageryisextremelystatic.Asaresult,thechildproducesadistortedpictureof
realitycharacterizedbyanemphasisonsuperficialfeatureswhichareeachisolatedfromothersandnot
coordinatedintoacoherentwhole.
Fromabout theageof7yearsonward,however, thechildbecomescapableofproducing images
whichcanreproducekineticsituations.Thisimprovementisduetothefactthathecannowimaginenot
onlytheinitialandfinalstates,butalsotheintermediarytransformations.Hisimageryhasbecomeless
static.Ofcourse,itisneverpossibletoreproducealltheinterveningevents,sinceinsomecases(likethe
pouringofliquid),theyoccurrapidly.Butthechildrecognizesthatasequenceisinvolvedandthatthere
hasbeenaseriesofinterveningstepsbetweentheinitialandfinalstates.
Afinalquestionconcernstherelationbetweendynamicimagesandtheconcreteoperations.Kinetic
imagesoccuratapproximatelythesametimethatthechildbecomescapableoftheconcreteoperations;
whatthenistherelationbetweentheoperativeandfigurativeaspectsofthoughtatthisstage?Onthe
onehand,wehavealreadyseenthatoperativecognitioninfluencesthenatureofthechild’s imagery.
Thus,theconcreteoperationalchild’sdecentrationcontributestothedynamicnatureofhisimagery.In
Piaget’s theory, figurative cognition (here, imagery) is dominated by operative cognition (here, the
concrete operations).On the other hand, images canplay an auxiliary role in thinking. For example,
considerthenumberconservationtaskinvolvingflowersandvases.Theconcreteoperationalchildcan
formaccuratetransformational imagesofthedisplacementoftheflowers.Afterthetransformationhas
beendone,hecorrectlypicturesthewayinwhichtheflowershavebeenremovedfromthevases.The
ability to form imagesof this sortdoesnotguarantee that the child can conservenumber; aswehave
alreadyseen,theprocessesunderlyingconservationarenotsolelyperceptualorimaginal.Nevertheless,
thechildwhohasacorrectimageofthetransformationiscertainlyaheadofthechildwhodoesnot.In
otherwords, images are a useful andnecessary auxiliary to thought during the concrete operational
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stage. By providing relatively accurate representations of the world, images assist the process of
reasoningalthoughtheydonotcauseit.
Summary and Conclusions
Images represent absent objects or events. They are “symbols,” in the sense of bearing some
resemblance to the object represented, and are personal and idiosyncratic. Images do not give as
completeanddetailedareproductionoftheobjectasisprovidedbydirectperception.Imagesfirstmake
theirappearancearoundthemiddleofthesecondyearoflife,andtheyarisefromaprocessofimitation
whichgraduallybecomesinternalized.Untiltheageofapproximately7years,thechildisonlyableto
produceapproximatelycorrectmentalimagesofstaticsituations.Heconcentratesonstatesratherthan
ontransformations.Thelimitedimageryofthechildispartlytheresultofimmatureoperativestructures.
Asthesestructuresdevelop,sodoeshisimagery.Aftertheageofabout7years,thechildbecomescapable
ofcorrectkineticimagery.Thisnewabilitypermitsafurtherunderstandingofreality:thechildnowhas
availableamoreaccurateanddetailedrenderingoftheeventsonwhichtofocushisreasoning.
MEMORY
Memory,too,isinfluencedbyoperativecognition.Beforeexploringthis,itisnecessarytobeginby
clarifyingsometerminology.
Definitions
Inordinarylanguage,weusethewords“memory”or“remember”inseveraldifferentsenses.Here
isananecdotetoillustratethepoint.Anadulthasnotriddenabicyclesincechildhood,someyearsago.
Nowhis own child gets a bicycle and askswhether the adult “remembers” how to ride. “Of course, I
rememberhow to rideabicycle,” says theadult.Asked (skeptically) toprove it, theadult geton, and
pedals around a bit. Despite the lack of practice over a long period of time, he is able to ride very
smoothly,muchtothesurpriseofthechildwhoownsthebicycleandwhonowwonderswhetherhewill
gettorideit.Astheadultispedalingdownthestreet,he“remembers”ridingthebicyclewhichheowned
asachild.Hehasafairlyclearmentalpictureofitsoverallshapeandform,aswellastheplacesinwhich
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herode.
This example illustrates two very different kinds of “memory.” In the first kind, the adult
remembers how to do something. Although there has beennopractice formany years, he hasnot lost
general bicycle-riding skills. He “remembers” how to ride not just a specific bicycle, but any bicycle.
Through experience, he has acquired a physical skill of a general nature, and remembers it. In this
instance,weusethetermmemorytoindicatethatthepaststillexertsaninfluenceonthepresent.The
adult’s ability to ride a bicycle, acquired through a set of earlier learning experiences,was somehow
preserved within him. Note that after childhood this ability existed as a potential, since until this
incident hedidnot actually engage in thebehavior.Note, too, that the element of earlier learning is
crucialtothedefinition.Itwouldnotmakesensetosay,“Irememberhowtosneeze,”sincesneezingwas
neverlearned.Yetitwouldmakesensetosay, ‘‘Irememberhowtokeepfromsneezing”sincethatwas
learned.Inbrief,thisisonevaliduseofmemory:apersoncanretain,overaperiodoftime,abehavioral
potentialwhichistheresultofpreviouslearning.
Theothersenseofmemory isquitedifferent.When theadult ‘‘remembers”ridinghischildhood
bicycle,heisreferringtoaspecificeventandthinginthepast.Hehasaholdonaparticularsliceofhis
own history. He ‘‘remembers” a bicycle with wide tires, and a heavy frame—a Schwinn, in fact. He
remembers riding it up Commonwealth Avenue to a park with a certain kind of path. This kind of
memoryismorespecificandconcretethanthefirst.Inthiskindofremembering,theadultretainsspecific
eventsorthingsfromthepast;intheotherkindofremembering,hepreservesthegeneralskillsacquired
in the past. Often the two types of memory occur together. A person remembers how to type (thus
preservingthegeneralability)andalsoremembersthespecifictypewriterusedinhisearlylessons(thus
retaininginformationconcerningaspecificthingfromthepast).Butthetwotypesofmemorydonothave
tocoexist.Apersonmayrememberhowtotypeandyetmayhavetotallyforgottenthespecifictypewriter
orhisearlylessons.Similarly,apersonmayrememberthetypewriterandlessons,butnotrememberhow
totype.Thus,wehaveusedsomeexamplesofphysicalskillstoillustrateadistinctionbetweentwotypes
ofmemory.
In the intellectual domain, Piaget’s theory (Piaget and Inhelder,Memory and Intelligence,MEM,
1973)proposesasimilardistinctionbetween“memoryinthewidersense”and“memoryinthespecific
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sense.”Theformerrefersto“theconservationoftheentirepast,oratleastofeverythinginthesubject’s
pastthatservestoinformhispresentactionorunderstanding”(MEM,p.1).Moreprecisely,memoryin
thewidersensereferstothe“conservationofschemes,”totheretentionofacquiredpatternsofbehavior
orthought,liketheconcreteoperations.Bycontrast,memoryinthespecificsense“refersexplicitlytothe
past,” to specific eventsor thingsorpersons in an individual’shistory.Anotherwayof lookingat the
distinctionistosaythatmemoryinthewidersenseinvolvestheoperativeaspectofthought:itistheway
inwhichgeneraloperationsorwaysofdoing thingsarepreservedover time.Memory in the specific
senseisgenerallyfigurative: itpreserves information concerning specific things—a face, anobject, an
activity. (These “things” include actions, but only specific actions that are thought to have actually
occurred,notthepotentialforactionsofageneraltype.)
Piagetgoesontoproposesomefurtherdistinctionsconcerningmemoryinthespecificsense.This
typeofmemory—andweshallnowsimplyusethewordmemorytorefertoit—maytakeoneofseveral
forms.Perhapsthemostprimitiveisrecognition.Thisoccurswhenapersonencountersthings(anevent,
person, thing, etc.)previously experiencedand “has the impressionofhavingperceived thembefore
(rightlyorwrongly,fortherearefalserecognitions)”{MEM,p.5).Thus,weseesomeoneknownbefore,
and“saytoourselves”thatthepersonisfamiliar,eventhoughhisnamemayeludeusandwecannot
recallwhereweknewhim.Similarly,thebabyinthesensorimotorperiodrecognizesfacesandplaces
whentheyareencountered.Orthebabyshowsthroughhisabbreviatedschemesthatherecognizesatoy
he has played with. Recognition, then, is one form of (specific) memory, involving an impression of
familiarityuponanencounterwithapreviouslyexperiencedobject.
Recall isamuchmoresophisticatedanddifficultformofmemory.Itinvolvesproducingamental
account of a previously experienced thing in the total absence of that thing. One examplewould be
remembering your childhood bicycle or your first grade teacher.Recall sometimes involves a mental
picture,sometimeswords,sometimesanodor.Thecrucialaspectofrecallisthattheindividualproduces
some kind ofmental representation of the previously experienced event.7 It is evident that recall is
closely linkedwith the semiotic function, alreadydiscussed, since the latter involves the formationof
mentalrepresentationsforabsentthingsorevents.
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The General Hypothesis
Piaget’smaininterestisinthefunctioningofmemoryinthespecificsense—recognitionandrecall.
Howdoesspecificmemoryoperate?
According to some empiricist views, memory works in the following manner. An individual
perceivesanobjectandstoreswithinhimitsreplicaortrace.Themorefrequentlyorrecentlytheobjectis
perceived,thestrongerthetrace,andhencethestrongerandmoreaccuratethememory.Inthisclassic
view,memoryissimplyacopyofsomethingreal,andtheaccuracyofthecopydependsonsuchfactorsas
frequency,recency,andthe like.Notethat intheclassicview,theindividual ismainlypassive:things
imposethemselvesonhim;theymakeanimpressiononhim;theyformatraceinhimasapieceofchalk
leavesarecordonaslate(hencetheexpressiontabularasa,orblankslate).8
Piaget’sview isdifferent.Heproposes that the childdoesnot simply record reality inapassive
manner,storingacopyinthewarehouseofmemory.Instead,asPiagetseesit,thechildassimilatesand
interpretsreality,sothatmemoryisinpartafunctionofthechild’sintellectualoperations.Memorystems
notonlyfromexperiencebutfromintelligence.This,then,isthegeneralhypothesiswithwhichPiaget
beginshisempirical investigations.Giventhis theoretical framework,Piagetgoesonto investigate the
specificwaysinwhichmentaloperationsaffectmemory,especiallyrecall.
Experiments on Memory of a Series
Tostudytheinfluenceofknowingonremembering,Piagetconductedseveralexperiments,oneof
whichinvolvedmemoryforaseries,atopicalreadyreviewedinthischapter.Childrenofvariousages
wereshowntenwoodensticks,alreadyarrangedinacompleteseries,fromsmallesttolargest.Eachchild
was“toldtotakeagoodlookatitandrememberwhathehasseen.’’Thenaboutaweeklater,eachchild
wasaskedtorecalltheseriesbydrawingitorbytracingitoutwithhisfingersonthetable.Afterthis,the
experimenterdeterminedthechild’sstageofdevelopmentwithrespecttoseriationbygivinghimthe
usualtests.Theexperimenteralsoobtainedacheckonthechild’sdrawingabilitybyhavinghimcopya
seriesofsticksavailabletodirectperception.Thiscopycouldthenbecomparedwiththechild’sdrawing
frommemorytodetermineifdistortionsinthelatterstemfrommeredrawingdeficiencies.Inbrief,the
experiment involved (1) determining children’s intellectual level with respect to seriation, (2)
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presentingthemwithacompletedseriestoremember,and(3)measuringrecallbyfingertracingand
drawing.Furthermore,(4)ameasureofdrawingabilitywastakensothatthisfactorcouldbecontrolled.
Whatshouldhappen insuchanexperiment?According to theclassicview, theseries impresses
itselfonthepassivesubject,andtheaccuracyofrecalldependsontheextentofthesubject’sexperience
with it and on similar factors. The child’s drawings should to some degreemirror the realitywhich
impinges on him. Piaget’s view is much different: the child actively assimilates the reality into his
intellectualsystemandthisprocessofinterpretationdeterminesthenatureandqualityofrecall.Inthe
presentinstance,astage1childmaydistorthismemoryoftheseriesinaccordancewithhisimmature
intellectualoperations,andthiswillbereflectedinhisdrawingandtracing.Notethattheresultofthisis
notadrawingwhichissimplyapalecopyofthereality.Rather,itisadrawingwhichissystematically
distortedinlinewiththechild’sintellectualoperations.
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FIGURE15Drawingsofcompletedseries.
Consider a few examples of this. One childmade a drawing like that in Figure 15A, involving
several identical long lines and several identical short ones. This drawingwas similar to the child’s
actual arrangement of the sticks during the test of seriation: hemade one bunch of large sticks and
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anotherbunchofsmallsticks,butdidnotaccuratelyseriatewithineachbunch.Anotherchildproduceda
drawinglikethatinFigure15B.This,too,wassimilartohisactualarrangementofthesticks.Hemadethe
topsofthesticksincreaseinorderofsize,buttotallyignoredthebottoms.(Whenaskedtocopyawell-
formedseriesimmediatelyinfrontofthem,thesesamechildrenproducedfarmoreaccuratedrawings.
Thisallowsustoconcludethatdrawingskillinitselfisnotatissue.)Bycontrast,childreninstage3who
couldaccuratelyseriatewereaccurateinrecall,asindicatedbyveridicaldrawingsandtracings.
ThesefindingscanbetakentosupportPiaget’stheory.Theindividual’smemoryisinfluencedand
organizedtosomedegreebyhisintellectualoperations.Thechildrecallsnotwhathehasseenbutwhathe
knows.Inthepresentinstance,stage1children’srecallisdistortedbytheirimmatureseriationschemes.
(Weshallseecaseslaterwheretheeffectisofadifferentsort.)Atthesametime,Piagetpointsoutthatthe
resultsarenotentirelyclear-cut.Somestage1childrenmakeperfectlyaccuratedrawings.Theirmental
operationsdonotseemtointervenesoforcefullyintheactofrecall. Insteadtheyseemtofocusonthe
appearanceoftheseries—onits“figurativeaspects”—andmanagetorecall itverywell,muchasthey
wouldrecall(anddraw)acircleoratreeorastaircase.Itishardtoexplainwhysomestage1children
showthedistortingeffectsofintellectualoperationswhileothersdonot.
In brief, while there is some variability, the results show that intelligence—the intellectual
operations—structures the child’s recall. Knowledge interacts with perception to produce what is
remembered.
The Development of Memory
According toPiaget, there is a generaldevelopmentalprogression from theearly appearanceof
accurate recognition to the later use of accurate recall.Memory begins in a crude fashion during the
sensorimotorperiod.Atthistime,theinfantshowsevidenceofrecognition.Throughovertorabbreviated
behavior,hedemonstratesthatatoyorapersonisfamiliar.Theinfantdoesnotseemcapableofmore
demandingformsofmemory,especiallyrecall(thisofcourseinvolvesevokingamentalrepresentationof
absentobjectsorevents).Itisonlywiththeonsetofthesemioticfunction,atabout18months,thatthe
childbecomescapableofmentalrepresentationandhencerecall.Earlier,inanothercontext,wecitedthe
exampleofJacqueline,at1;11(11),whouponreturningfromatrip,wasabletoreportoneventswhich
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hadoccurredearlier:“Robertcry,duckswiminlake,goneaway”(Play,Dreams,andImitation,p.222).
Thisisanexampleofrecallinachildwhoisjustbeginningtogiveevidenceoftheuseofthesemiotic
function.Inbrief,infantsshowsignsofrecognitionmemory,whereasrecall,asoneaspectofthesemiotic
function,beginstoappearonlyatabout18months.
Aswehaveseen,oncerecallappears,itsfunctioningisinfluencedbytheintellectualoperations.
Nowweshallseethatthisinfluencecanhavedevelopmentalaspects.Piaget’sexperimentsonmemory
foraseriesshedlightonthisissue.Wealreadyknowthatthechild’srecallafteroneweekisdistortedin
linewithhiscurrentstageofseriation.Butwhathappenstorecalloveralongerperiodoftime,say,sixto
eightmonths?Accordingtotheclassicview,thememorytracesimplyfades,andthisfadingbecomesmore
completeastimegoeson.InPiaget’sview,mattersaremorecomplexthanthat.Inmanycases,theremay
wellbesomedeteriorationofmemoryoveralongperiodoftime.Andyetthereareotherpossibilitiesas
well. Memory, which depends on intelligence, therefore exhibits developmental changes which
correspondtothedevelopmentofintelligence.Indeed,Piaget’stheoryleadstothepredictionthatunder
certaincircumstances,recallmayactuallyimproveovertime.
Inthecaseofseriation,thematterworksasfollows:thestage1childseesawell-orderedseriesand
assimilates it into his intellectual operations. Since these are immature, one week later the child
inaccuratelyrecallsthesticksasacollectionofsmallonesandacollectionoflargeones.Hisintelligence
hasorganizedrecallpoorly.Thenoveraperiodoftime,thechild’smentaloperationsdevelopandhe
enters stage 3. Now, asked to recall the sticks, he remembers a well-formed series. His memory has
improvedovertimebecausehisintellectualstructureshavedevelopedmorefully.
This is indeed precisely the result which Piaget discovered. Of twenty-four stage 1 children,
twenty-twoshowed improvedrecall (asmeasuredbydrawings)when theyadvanced toa later stage
sevenoreightmonthsaftertheinitialtesting.
Severalcommentsshouldbemadeatthispoint.First,independentinvestigatorshavehadahard
timereplicatingthisresult(forexample,Samuels,1976).Agooddealofcarefulresearch,withadequate
controls,needstobedonetopindowntheeffect.Itisparticularlyimportanttoobtaindirectmeasuresof
thechild’sassumed intellectualdevelopment.Second, it is important torecognize thatPiaget’s theory
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doesnotalwayspredictimprovementinlong-termrecall.Improvementcanbeexpectedtooccuronlyif
theinitialrecallwasdistortedbyimmatureintellectualoperationsandiftheseoperationssubsequently
improve.This isaveryspecialcase,however,andoftendoesnotoccur.Forexample, supposeachild
learns someone’snameand tries to recall it ayear later.Memory for thename is likely todeteriorate
regardlessof the child’s stageofdevelopment.The child’s advancement fromstage1 to3of concrete
operationswillhavenoparticularbearingontherecallofnames,sincetherecall ismerely figurative
withnologicaloperationsinvolved.Hereisanotherexample,whichmayseemparadoxical.Supposea
stage1childisshownabadlyformedseries.Afteroneweekheaccuratelyremembersthebadlyformed
seriesbecausehehasassimilateditintohisimmaturementaloperations.Then,overthenextyear,the
child’smentaloperationsadvanceandhehasreachedstage3.Nowwhenaskedtorecallthesticks,he
producesawell-formedserieswhichistheproductofhiscurrentintellectualstructure.Unfortunately,
this is inaccurate recall, since the initial series was badly formed. This example is a case of an
improvement in intellectualstatus leadingtoadeterioration inrecall. (SeveralstudiescitedbyLiben,
1977,actuallyobtainthiskindofresult.)ThemainpointofPiaget’stheoryisnotthatmemorynecessarily
improves over time—it seldom does— but that memory is influenced by developing intellectual
operations,andnotjustbyrealevents.
Summary
Piaget distinguishes between two types of memory. Memory in the wider sense refers to the
individual’sabilitytoretainovertimethepotentialtoexhibitlearnedschemesoroperations.Memoryin
thespecificsensereferstotheindividual’sabilitytoretainovertimeinformationconcerningparticular
events,things,orpersons.Specificmemorymaytakeoneofseveralforms,themostimportantofwhich
arerecognition(animpressionoffamiliarityonanencounterwithapreviouslyexperiencedobject)and
recall(evocationofthepastthroughmentalrepresentations).Piaget’sgeneralhypothesisisthatspecific
memory is influencedby intelligence—the intellectualoperations. Intelligenceserves toorganizeand
shape memory. Piaget rejects the classic view in which events are seen to impress themselves on a
passiveobserver,leavingatraceorasimplecopyofthereality.
Piaget’sexperimentsonmemoryforaseriesdemonstratethatafteroneweek,recallisinfluenced
bytheindividual’sstageofintellectualdevelopment.Presentedwithawell-formedseries,somechildren
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recallnotwhattheyhaveseen,butwhattheyknowabouttheseries.Itisimportanttonote,however,that
there is some variability in these results. According to Piaget, there is a general developmental
progressionfromrecognitionmemorytorecall.Infantsshowsignsofrecognition;recalldoesnotseemto
appearuntiltheonsetofthesemioticfunctionatabout18months.
After it appears, recall is influenced by the development of intellectual structures. The general
hypothesisstatesthatasintellectualstructuresdevelop,theyexertcorrespondingdevelopmentaleffects
onrecall.Indeed,undercertaincircumstances,recallmayactuallyimproveovertime.Piagethasshown
thatinthecaseofseriation,recallbecomesmoreaccurateaschildrenadvancefromoneintellectualstage
to the next. It is important to note, however, that this result is not easily replicated and that Piaget’s
theorydoesnotalwayspredictimprovementinrecallovertime.Instead,themainpointofPiaget’stheory
is thatmemory is influencedandorganized(butnotnecessarily improved)bydeveloping intellectual
operations, and not simply by real events. Memory is the result of an interaction been knower and
known.
CONSCIOUSNESS
Wehaveseenhowthechilddevelopsoperativeandfigurativeaspectsofthought.Bytheageof7or
8years,heachievessomesuccessatclassifyingandorderingobjects,atproducingmentalimages,andat
remembering.Thesecognitiveprocesses,bothfigurativeandoperative,workmainlyonanunconscious
level.NowwewillassumeadifferentlevelofanalysistoconsideranewtopicwhichPiagethasrecently
studied,namely,thechild’sawarenessandverbalizationofhisownthoughtprocesses.
In studying the issueof consciousness,Piaget’s general strategy is first tohave the child solvea
problemandsecondtodeterminehisawarenessofthemethodsofsolution(TheGraspofConsciousness,
GC,1976b).Inoneinvestigation,Piagetusedstandardseriationtasks,involvingsuchmaterialsasasetof
cardsvaryinginheightandwidth,orasetofbarrelsvaryinginbothheightanddiameter.Eachchild’s
taskwastoarrangetheobjectsinorderofincreasing(ordecreasing)size.Hewastold,forexample,to
“makeanicelineofbarrels.”Assoonasthechildbegantodothis,theinvestigatoraskedhimtodescribe
whathewasdoingorwasabouttodo.Sometimesthechildwasasked“howhewouldexplaintoafriend
whatshouldbedone”(GC,p.3OI).Afterthechildcompletedthefirstseries(successfulornot),hewas
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askedtorepeatitandtodescribeandexplainhisactionsashewentalong.Thepurposeofthisrepetition
wastoensurethatthechildknewwhatwasexpectedofhim.
Suppose that a child succeeds at the seriation tasks just described: he produces an accurate
orderingintermsoflengthoftherodsorsizeofthebarrels.Giventhis,wemayinquireintothechild’s
consciousnessorcognizanceofseriation. It is important tobeginbyclarifyingwhat ismeantbyPiaget’s
usageofconsciousnessorcognizance.Piagetuses these termstorefer to thechild’sability toproducea
coherentverbalaccountofthementalprocessesunderlyinghisbehavior.Bythisdefinition,thechildis
consciousorcognizantofhisthoughtprocessesifhesays,forexample,“Ialwayslookforthebiggestone,
then I put it aside and look for the biggest one out of all the ones that are left.” In Piaget’s usage,
consciousnessreferstoanawarenessandverbalizationofone’sownthoughtprocesses.Notonlyisthe
consciouschildabletodosomething;heisalsoexplicitlyawareofhowhedoesit.9NotethatPiagetdoes
notuseconsciousnesstorefertotheelementaryandfleetingperceptionoftheimmediatesituation.Thus
thetermisnotusedtorefertothechild’sawarenessthattherearetoybarrelsonthetableorthathis
handismovingtowardthem,andsoon.Whilesuchelementaryawarenessappearsveryearlyinlifeand
isnodoubthighlyprevalent,itisnotthesubjectofPiaget’sinvestigation.Inbrief,Piagetisinterestedin
the child’s explicit knowledge of his thought processes, and not merely in the crude awareness of
ongoingactivities.
Severalquestionsthenarisewithrespecttoconsciousness.Itisespeciallyinterestingtoinquireinto
the temporal relations between action and cognizance. There are of course several possibilities. One
alternativeisthatactionandcognizanceemergesimultaneously.Asonedevelopssodoestheother,and
it is impossible to determine the direction, or even existence, of causality. A secondpossibility is that
consciousnesscomesfirst,andthusdirectsthesubsequentaction.Perhapsthechildfirstconceptualizes
his action and this helps him to perform it. A third possibility is just the reverse. Perhaps successful
behaviorprecedescognizanceofit.Thechildmaybeablefirsttoperformcertainactions,andonlylater,
uponreflection,doeshebecomeawareofhisbehavior.
ThebehaviorofoneofPiagets’subjects,STO,at6-1,workingatseriation,shedssomelightonthese
issues.Onhisfirstattempt,STOfailedtocompleteasuccessfulseries.Hecouldnotarrangecardsinorder
ofsizeandputthesmallestonesinthecenteroftheline.Hesaid,“I’vemadeastaircasethatgoesupor
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down.”Theexaminerrespondedthatthestaircaseshouldgodownallthetime,“butfirsttellmehoware
yougoingtomakeit?”STOresponded:“I’mgoingtoputthebigone,anotherbigone,anotherbigone,the
middle-sizeone,thesmallermiddle-sizeone,thesmallermiddle-sizeone,andthesmallermiddle-size
one”(GC, p. 312). STO proceeded to produce a good series, with only onemistake, which he easily
corrected.Onsubsequent trials, thesamesortof thinghappened:STOproducedgoodseriesbutpoor
verbaldescriptions.
AccordingtoPiaget,thisexampleshowsthatSTO’sseriationwasfarinadvanceofhisconsciousness
ofit.STOcouldorderthecardsinafairlysystematicwayandyetcouldreferonlyinanimprecisemanner
to“anotherbigone,anotherbigone,”or to “thesmallermiddle-sizeone,andthesmallermiddle-size
one.”Otherchildrenexhibitsimilarbehavior.Forexample,theyuseanextremelysystematicprocedure
forseriation(likeselectingthesmallestandthenthesmallestofallthoseleft)andyetcansayonlythat
theyfirsttookasmallone,thenanothersmallone,andsoon.Piagetconcludesfromdatalikethesethat,
in general, the child’s successful activities—including operative activities like seriation—precede
cognizanceofthem.Thechildcanactandthinkeffectivelybeforehecanverbalizeorbeconsciousofhis
actionsorthoughts.
Howdoesconsciousnessofproblemsolvingdevelop?Piagetproposesthatatfirstthechildisonly
dimlyawareofgoals.Forexample,hewantstomakea“staircase.”Thechildthengraduallydevelops
variousstrategies forachievinghisgoal, forexample,randomplacementorsystematicselectionof the
largest.Atfirst,heisquiteunawareofthesestrategies,justasthe3-month-oldbabyisnotconsciousofthe
procedureswhichheusesforgettinghisthumbintohismouth.Heacts,successfullyorunsuccessfully,
but does not explicitly analyze his actions. With development, however, the child observes his own
activitiesandreflectsonthem.Heinterpretshisactions;hetriesto“reconstruct”themontheplaneof
thought.Atfirst,thisprocessofinterpretationmayleadtodistortionandmisunderstanding.Piagethas
observedmanycasesinwhichtheinitialconsciousnesswasinerror—wherethechilddidnotaccurately
seewhatinfacthehaddone.Butgradually,thereconstructionbecomesmoreandmoreaccurate.The
child’sreflectiononhisownactivitiesallowsthedevelopmentofexplicitknowledgeconcerningbothhis
problem-solving processes and the objects under consideration. In this way, the child learns about
himselfandabouttheobjectssurroundinghim.Hedevelopsabstractconceptsthatcanbeverbalized.
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Piaget’spositionhasmuchtorecommendit.Itseemsusefultomakeadistinctionbetweenatleast
twolevelsofknowledge.Theredoesseemtobeakindof“actionknowledge”or“how-toknowledge”in
whichwesolveproblemsusingmeansofwhichweareunaware.ThusSTOcouldseriate,butwithout
consciousnessofhismethod.Atthesametime,thereisalsoanotherlevelofabstractknowledge,inwhich
wecanexplicitly formulateourmethodsofsolutionandeventheprinciplesunderlyingthem.Thusa
child cannot only seriate but explicitly understands the principles which he uses. The process of
transformingactionknowledgeintoabstractknowledgemaybecrucialforhumanlearning.Thereisa
gooddealofwisdombuiltintoourbehavior,andamajortaskforlearningmayconsistinmakingexplicit
whatinasensewealreadyknowunconsciously.
While these are useful points, Piaget’s investigations in this area seem to suffer from a major
weakness, namely, an overreliance on verbalizations as a source of evidence. In these studies,
verbalizationistakenasthemain,orevenonly,sourceofevidenceforconsciousnessorcognizance.Thus
STOissaidtolackconsciousnessofhisactions,sincehislanguageisinadequate.ButSTO’srepetitiveuse
of vague terms like “the smaller middle-size one” may not accurately reflect the true level of his
consciousness.Seriation ishardtoexpress inwords,andperhapsSTOcouldconceptualize itbutwas
unabletoofferadequatedescriptionsoftheprocess.Piaget’sinterpretationseemsweakinthisregard.At
thesametime,despitethedifficulties,Piaget’sresearchraisesextremelyprovocativeissuesrequiringa
gooddealoffurtherstudy.
GENERAL CONCLUSIONS
Whilecriticismsmayandshouldbemade,andwhilerevisionsarenecessary,Piaget’stheoryisan
enormouslysignificantaccomplishment.Indeed,onreviewingPiaget’slaterworkonthechildfrom2to
11,oneisstruckaboveallbytheincrediblecreativityanddiversityofhiscontribution.Between1940
and1980,Piagetrevolutionizedthestudyof thechild.He introducedascoreof fascinatingproblems
andexperimentaltasks—conservationisonlyoneexample—whichforalongtimedominatedresearch
inchildpsychology.Moreimportant,heofferedanextraordinarilydeepandsubtletheoryofcognitive
development,whichcontinuestoinformourunderstandingofthemind’sgrowth.
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Notes
1SeeH.P.Ginsburg, “TheClinical InterviewinPsychologicalResearch:Aims,Rationales,Techniques,”For theLearningofMathematics,Vol.3(1981),pp.4-11,andS.Opper, “Piaget’sClinicalMethod,” JournalofChildren’sMathematicalBehavior, Vol. 1 (1977),pp.90-107.
2See,forexample,R.GelmanandC.R.Gallistel,TheYoungChild’sUnderstandingofNumber(Cambridge,Mass.:HarvardUniversity,Press,1978),Chap.3.
3 Our exposition of Grouping I is simplified and incomplete: for example, we have defined only one binary operator.We have kept themathematical development at a very informal level. The reader interested inpursuing thematter should see JeanPiaget,TraitedeLogique (Paris:Colin,1949),andalsoj.B.Grize’s formalizationofPiaget’s systemasdescribed inE.W.BethandJeanPiaget,MathematicalEpistemologyandPsychology(Dordrecht,Holland:D.ReidelPublishingCompany,1966).
4 Although it does not seem to help with conservation, counting is far from useless in children’s arithmetic. Hebbeler has shown, forexample,thatyoungchildrenmakeverygooduseofcountingindoingaddition.SeeK.Hebbeler,“YoungChildren’sAddition,”JournalofChildren’sMathematicalBehavior,Vol.1(1977),pp.108-21.
5Strictly speaking, in the caseofnumberPiagetusesa somewhatdifferent logico-mathematicalmodel, called theGroup. The essentialdifferencebetweentheGroupingsandtheGroupisthatthefifthGroupingoperation,tautology(e.g.,A+A=A),isnotusedintheGroup.TautologydoesnotapplytonumbersincethereA+A=2A,notA.Therefore,theGroupmustbeusedfornumber.
6Recently,GelmanandBaillargeon (1983,p.171)haveargued that thephenomenonof invariant sequence isnotas clear-cutasPiagetsuggests.Theydescriberesearchshowingthat insomeareassomechildrendonotexhibitthestagesintheorderpredictedbyPiaget.Thisseemstopresentseriousdifficultiesforthetheory.
7Therecanbeinstancesoffalserecall.Piagethimselffalselyrememberedbeingtheobjectofanabortivekidnapattemptwhenhewasachild.
8 Piaget’s exposition of the classic view probably refers to theorists like Ebbinghaus, who in the nineteenth century invented nonsensesyllablesandspentmanyyearsofhislifememorizingthemhimself.Hewashisonlysubjectanddeservessomesortofprizefor an immense capacity for boredom. In recent years, however, theorists ofmemory have given up both the inclinationthemselves tomemorize nonsense syllables (althoughmay require their subjects to do it) and theoretical accountswhichtreat thesubjectaspassive.Manymoderntheoriesare insubstantialagreementwithPiageton the issueofactivity.ForacomparisonofPiaget’s theorywithothers, aswell asanexcellent critiqueofPiaget’swork, seeL.Liben, “Memory fromaCognitive-DevelopmentalPerspective:ATheoreticalandEmpiricalReview,”inKnowledgeandDevelopment,W.F.OvertonandJ.M.Gallagher,eds.(NewYork:PlenumPress,1977),Vol.I,pp.14-9-203.
9Recently, Flavell andothershavebeen investigating a similar topic,which they term “meta cognition,” andwhich involves the child’sknowledgeabouthisownknowledge.(Forareview,seeJ.H.Flavell,CognitiveDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1985.)Anexampleiswhetherthechildisawareofusingsystematicstrategiestoaidinmemory.
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Learning, Development, and Education
LEARNING AND DEVELOPMENT
We have now described the major periods of intellectual development— sensorimotor,
preoperational, concrete operational, and formal operational—and the stages within them.We have
postponeduntilnowconsiderationofthetransitionmechanisms.Whyisitthatthepreoperationalchild’s
thoughtadvancestoahigherlevel?Whydoestheadolescentdevelopformaloperations?Inshort,what
factorsproducethetransitionfromonestagetothenext?Piagetfeelsthatmentalgrowthinvolvestwo
processes:learninginthenarrowsenseandlearninginthebroadsense,ordevelopment.Thefirstofthese,
learninginthenarrowsense,isprovokedbyexternaleventsandlimitedtocertainsituations;thesecond,
development, is a much wider phenomenon, with broad implications. We will begin by discussing
learninganddevelopmentandthenturntothefourfactorsunderlyingtheprocessofdevelopment.
The Nature of Learning and Development
ForPiaget,theterm“learning”maybeusedintwosenses.Learninginthenarrowsenseinvolvesthe
acquisitionofnewinformationornewresponsesrestrictedtoaspecificsituation.(Notetheparallelwith
memoryinthespecificsense.)Forexample,inschoolgeography,thechildlearnsthenamesandlocations
ofthestatesandtheircapitols.Thiskindoflearningisobviouslyspecifictoparticularculturedcontexts
andisoflittlegenerality.Byvirtueofanaccidentofbirth,theAmericanchildlearnsaboutthefiftystates;
if transported to Canada, the child would then have to learn the names of the provinces and their
capitols.Learningofthistype,then,isimportant—butitisspecificandcannotbegeneralized.
Bycontrast,learninginthebroadsense,ordevelopment,involvestheacquisitionofgeneralthought
structures which apply to many situations. (Note the parallel withmemory in the wider sense.) For
example,thechildacquiressomegeneralwaysofthinkingaboutthestatesandtheircapitols.Learningin
the wider sense is involved when the child develops such notions as that a state cannot be in two
locations at the same time or that the United States must be larger than any individual state (class
inclusion). Learningof this type involves structureswhich are general andwhich canbe transferred
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fromonesituationtoanother.Theyarenottaughtthroughspecificinstruction.
Totakeanotherexample,iftheyoungchildobservesthataballofclayrepeatedlyweighsthesame
despite changes in shape, hemay learn that theweight of this particular clay ball remains constant
(conservationofweight).Thechildmayevenpredictthattheweightwillcontinuetobethesameforany
newchangeinthesameball.Inotherwords,asaresultofrepeatedempiricalobservationsorexternal
reinforcements, the childwillhave learneda law foraparticular situation.Thisdoesnotnecessarily
mean,however,thathehasunderstoodwhytheweightremainsconstant.Also,thechildmaybeunable
to generalize the law to other situations with other objects. It is only when the child develops the
structuresofconcreteoperationalthoughtthatheunderstandsthereasonsfortheconservationofweight
andcangeneralizetonewsituations.Tosummarize,specificlearningmayenablethechildtodealwitha
particularprobleminvolvingweight,butlearninginthewidersense,ordevelopment,isnecessaryfor
him to acquire thought structures capable of generalization. We see, then, that there are important
differencesbetweenlearninginthespecificsenseanddevelopment.
Piagetproposesthat,ofthetwoprocesses,development(learninginthewidersense)isthemore
fundamental.First,aswehavealreadyseen,developmentresultsintheacquisitionofgeneralcognitive
structures as opposed to specific information or responses. Second, development makes possible
meaningful learning in the specific sense. The child can appreciate the meaning of an external
reinforcementorofnewexperiencesingeneralonlywhenhisstructureshavereachedacertainstageof
developmentthroughtheprocessofequilibration.Thechildcanprofit fromexternal information—for
example, reinforcement or an adult’s explanation— only when his cognitive structure is sufficiently
preparedtoassimilateit.
Thus,informationconcerningthestatesandtheircapitolswillonlybearoterecitationunlessthe
childunderstandswhatacapitolisandhowastaterelatestothecountryofwhichitisapart.Similarly,
thespokennumberwords“one, twothree ...”areonlymeaninglesssoundsunless thechildpossesses
somegeneralstructuresofthoughtenablinghimtounderstandthat“one”islessthan“two,”andsoon.
Genuinelearningoccurswhenthechildhasavailablethenecessarymentalequipmenttomakeuseof
newexperiences.When the requisite cognitive structure ispresent,he can learn from theworldand
cometounderstandreality;whenthestructureisabsent,newexperiencehasonlysuperficialeffects.If
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thereistoogreatadisparitybetweenthetypeofexperiencepresentedtothechildandhiscurrentlevel
ofcognitivestructure,oneoftwothingsislikelytohappen.Eitherthechildtransformstheexperience
intoaformwhichhecanreadilyassimilateandconsequentlydoesnotlearnwhatisintended;orelsehe
merelylearnsaspecificresponsewhichhasnostrengthorstability,cannotbegeneralized,andprobably
willsoondisappear.Itisforthisreasonthatthechild’slearning,inschoolorout,cannotbeaccelerated
indefinitely.Therearesomethingsheisnotreadytolearnbecausethenecessarycognitivestructureis
notyetpresent.Ifforcedtodealwithsuchmaterial,thechilddoesnotachievegenuinelearning.
Finally,Piagetmaintainsthatlearninginthespecificsensecannotaccountfordevelopment.Aswe
shallsee, thegeneralcognitivestructuresdevelopthroughacomplexprocess involving four factors—
maturation,experience(physicalandlogicomathematical),socialtransmission,andequilibration—and
consistsoffarmorethanthemechanicalacquisitionofnewinformationorresponses.ForPiaget,learning
inthespecificsensecannotexplaindevelopment.Instead,developmentexplainslearning.
Piaget and his colleagues in Geneva (Inhelder, Sinclair, and Bovet, 1974) have conducted a
number of studies into children’s learning in the broad sense and the possibility of accelerating the
acquisitionofvariouslogicalstructures.Thefindingsshedsomelightontheprocessesofdevelopment.
Thegeneralplanofthesestudieswasfirsttoadministeradiagnosticpretesttodetermineeachchild’s
developmentallevel.Afterthis,thechildrenwentthroughaseriesoftrainingsessionswhichpresented
arangeofproblems,eachofwhichwasdesignedtoelicitadifferentcognitiveoperation.Theaimwas“to
arouse a conflict in the child’s mind” so that he might attempt a coordination among the various
operationsandtherebyachieveahigherlevelofdevelopment.Theinvestigatorscarefullyobservedand
questionedchildreninconflictsituationstoseewhetherandhowlearningoccurred.Sometimelater,the
childrenweregiventwodiagnosticpost-tests,thesecondaboutfourtosixweeksafterthefirsttoidentify
theeffectsoftraininganddeterminewhetherthechangesobservedwerelong-lastingandstable.
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FIGURE16Sticksandhouses.
ConsideroneoftheGenevanstudies.Childrenwerepresentedwithtwostraightlinesofstickswith
smallhousesgluedontoeach(seeFigure16).Thelines(AandB)wereidenticalinlengthandhadthe
samenumber.Eachchildeasilyrecognizedthat lengthandnumberwerethesame.Thenasthechild
watched, line B was rearranged into configuration C, which obviously looks much different. The
experimenterthenaskedaseriesofquestionsconcerningbothlengthandnumber:‘‘Aretherethesame
numberofhouseshereasthere?Isthisroadjustaslongastheother?”Theaimwastoplacethechildin
conflictwithrespecttodifferentaspectsoftheproblem;thechildmightrealize,forexample,thatnumber
doesnotchangewhentheconfigurationistransformed,butatthesametimehemayfailtoconservethe
length.Ifsuchaconflictisproduced,howdoesthechilddeedwithcompetingschemes?Doestheconflict
producelearning?
Throughstudieslikethese,Inhelder,Sinclair,andBovetwereabletodiscoverfinedistinctionsin
thelearningprocess.Inparticularitappearsthatthelearningprocessinvolvesfoursteps.Inthefirst,the
childkeepsthetwomodesofreasoningseparateanddoesnotrealizethataconflictisinvolved.Hesays
thatthereisthesamenumberofhousesinAandCbutthatAismuchlonger.Repeatedquestioningdoes
nothelpthechildtoseethecontradiction.Inthesecondphase,thechildbeginstoappreciatetheconflict.
Heseesthatthetworoads,AandC,whichhethinksareofdifferentlengths,neverthelesshavethesame
numberofsticksineach;nowthechildunderstandsthatthispresentssomethingofaproblem.Oncethe
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childperceivesadiscrepancy,hetriestoreconcileitinsomeway.Thethirdstepinvolves‘‘compromise
solutions.”Here, the childuses an inappropriatemethod to resolve the conflict. For example, hemay
breaka stick inhalf so that the longer row in facthasmore sticksaswell!The fourth step involvesa
legitimatecoordinationof the twoschemes. In thesituationcited, thechildsees thathemustperform
certaincompensations;hesees,forexample,thatalthoughtheendpointsofrowAgobeyondthoseof
rowC,rowChasmorezigzagsthandoesAandthatthesecompensatefortheoverlapofA.
Inhelder, Sinclair, and Bovetmake several general points about their findings. One is that the
child’s ability to profit from training depends on his initial developmental level. These investigators
foundthatchildreninstage1generallyprogressedverylittleornotatallinresponsetotraining;while
thoseat a transitional level showedconsiderableprogress.The reason for thediscrepancy is that the
stage1childrencouldnotperceivetheconflictwhichthetrainingwas intendedto induce,while the
transitional childrenwereable to see it.According to this view, the childwill not experience conflict
unlesshisschemesaresufficientlydeveloped.Iftheyarenot,thennoamountofquestioningthechildor
demonstrating different arrangements of objects will produce conflict and hence intellectual
development.Conflict(andtheresultinglearning)canbeprovokedonlywhenthechildisreadyforit.
Thisperspectivehasimportantimplicationsforeducationandweshallreturntoitlater.
A second point is that amajor form of conflict occurswhen different cognitive subsystems—for
example, lengthandnumber—operatesimultaneouslyandwhenoneof theseschemeshasreacheda
moreadvancedstatethantheother.
Third,thestudieshighlightthecentralroleofthechild’sactivityandinitiative.Inparticular,the
phenomenonofcompromisesolutionsshowsthatstrategiesarenotsimplyimposedonthechild;rather
heplaysamajorroleininventingthem.
Fourth,theinvestigatorssummarizetheirfindingsasfollows:
[Atfirstthereis] . . .anapplicationofexistingschemestoanincreasingvarietyofsituations.Soonerorlater,this generalization encounters resistance,mainly from the simultaneous application of another scheme; thisresults in two different answers to one problem and stimulates the subject seeking a certain coherence toadjust both schemes or to limit each to a particular application, thereby establishing their differences andlikenesses.Thesituationsmostlikelytoelicitprogressarethosewherethesubjectisencouragedtocomparemodes of reasoningwhich vary considerably, both in nature and complexity, but which all, individually, are
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alreadyfamiliartohim.(Inhelder,Sinclair,andBovet,1974,p.265)
Wesee,then,thatdevelopmentinvolvesaconflictamongexistingschemes,thechild’sassimilation
ofnewproblemsintothoseschemes,andaself-regulatedadjustmentorprogressionofthecurrentmodes
ofthought.Piagetreferstothisasequilibration,whichconstitutesoneofthefourfactorsofdevelopment
thatweshallnowdiscuss.
Factors Underlying Development
Maturation.Asyouwillrecall,Piaget’stheoryproposesthatspecificheredityequipsthechildwith
various physical structures which affect intellectual development. Some of these physical structures
resultinautomaticbehavioralreactions.Forexample,whenthelipsarestimulated,thebabysucks;this
occurs because the appropriate reflex is activated through a “prewired” physical mechanism. The
automaticbehavioralreaction isakindof“innateknowledge”;becauseofheredity,whichreflects the
evolutionoftherace,thebabyimplicitly“knowswhattodo”inthefeedingsituation.Reflexes,however,
play aminor role in intellectual development. Inhumanbeings, physical structures givenby specific
hereditytypicallyexertindirecteffectsonintellect.Thus,thebabyisbornwitheyesthatpermithimtosee
only certain frequencies of light, to perceive depth, and to detect objects in front of the body but not
behind.Theeyesdonotprovidethebabywithapreviouslywrittenencyclopediaofknowledge—witha
stockofinnateideas.Instead,theygivethebabywaysofknowing;theybothsetlimitsonandprovide
opportunitiesforintellectualfunctioning.Inbrief,thephysicalstructuresprovidedbyspecificheredity
areorgansofknowingwhichdeterminetheroughoutlinesofintellectualgrowthbutdonotspecifyits
content.
Considernowhowmaturationenters thepicture.Thephysical structures, including the central
nervous system, take time to reach their highest level of development. The brain of the newborn, for
example,issmallerandlighterthanthatoftheadolescent.Itisobviousthatimmaturephysicalsystems
oftencontributetodeficitsincognitivefunctioning.Thesimplestexampleinvolvesmotorcoordination.
Thenewborn’smusclesandotherstructuresarenotsufficientlydevelopedtopermitwalking.Sincehe
cannotgetaround in theworld, thenewbornobviouslycanknowvery littleabout it.Otherexamples
abound. One of the factors underlying the newborn’s inability to speak is undoubtedly an
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underdeveloped articulatory apparatus. One of the variables producing his weakness at abstract
reasoning is in all probability an insufficientlymature brain. It is clear, then, that immature physical
systemscanretarddevelopment.
It is also obvious that the healthy growth of physical systems contributes, at least indirectly, to
intellectual advance, although the details of the process are largely unknown. When leg muscles
develop,thebabybecomesmobileandcanlearnaboutpreviouslyinaccessiblethingsandevents.Alsoin
infancy, “the coordination between grasping and vision seems to be clearly the result of the
myelinizationofcertainnewnervepaths in thepyramidal tract” (Piaget, “Problems inEquilibration,”
1977b,p.7).Inthemostgeneralsense,asthebrainandthecentralnervoussystemmature,theymakeit
possible for the child to use thought and language. In Piaget’s view, the question is not whether
maturationhasaneffect,buthowimportanttheroleofmaturationisandhowitoperates.Someyearsago
Gesellproposedthatmaturationisthechieffactorexplainingdevelopment.Accordingtothishypothesis,
the process of physical maturation is the most important and direct influence on all aspects of
psychologicalfunctioning.Piagetfeelsthatthispositionistooextremeforseveralreasons.
Oneisourlackofunderstandingofthematurationofthecentralnervoussystem.Howcanonebase
a theory onmaturationwhen so little is known about it? Second, it is clear thatmaturation does not
explaineverything.Forexample,childreninMartiniquereachtheconcreteoperationalstageaboutfour
yearslaterthandochildreninSwitzerland.ItwouldseemunlikelythatSwisschildren’sbrainsarefour
yearsmoremature than those of the children inMartinique. Amuchmore likely explanation is that
culturalfactorscontributeheavilytothedifferencesindevelopment.InPiaget’sview,then,physiological
maturationundoubtedlyaffectscognitivedevelopment—ofteninwayswedonotunderstand—butitis
nottheonlyfactor.1
Experience.A second influenceondevelopment is contactwith the environment.To acquire the
notion of object permanence, the infant must obviously experience things disappearing and
reappearing.Toclassifyobjects,thechildmustfirstperceivethem.Tospeakalanguage,theinfantmust
hearpeople talking. Piaget feels that contactwith the environment leads to two types of knowledge:
physical and logicomathematical. On the one hand, physical experience leads to the knowledge of
observables.Observablesreferstothepropertiesandcharacteristicsofobjects,suchasshape,color,size,
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andsoon,thatareperceivedbyaperson.Physicalknowledgeofobservablesisobtainedbyaprocessof
empiricalabstraction(calledsimpleabstraction inPiaget’searlyworks).Thechildencountersanapple
and,throughperceptualactivity,“pullsout”orabstractssomeofitsproperties.Nowthechild“knows”
that it is round and that it is red.Or he lifts a block, and in the process discovers that it is heavy. If,
however,heliftstwoblocksandnotesthatoneisheavierthantheother,thiswouldnolongerbepurely
physicalknowledge.Bycomparingthetwoblocks,hehascreatedarelationshipof“more”or“less”heavy
thatisnotgivendirectlyintheblocksthemselves.Thissecondtypeofknowledgeislogicomathematical.
In physical experience, then, a child uses empirical abstraction to extract directly from the objects
themselvesaknowledgeoftheirphysicalproperties.
Piaget makes several points about physical knowledge.2 One is that it is a major influence on
development: there isa “vast categoryofknowledgeacquiredbymeansof theexperienceofexternal
objects”(BiologyandKnowledge,BK,p.335).Agoodpartofintellectualdevelopmentislearningwhat
thingsarereallylike.
Second,theprocessofobtainingphysicalknowledgeinvolvesmorethanjustempiricalabstraction.
Piagetmaintainsthat“Itisimpossiblefortheretobedirectandimmediatecontactbetweensubjectand
objects....Anykindofknowledgeaboutanobjectisalwaysanassimilationintoschemes”(BK,p.335).
Thedataofexperiencearealways interpreted in termsofa larger intellectual frameworkofschemes,
concepts,andrelationships.Thechilddoesnotsimplyperceivethepropertiesofaparticularapplein
isolation.Rather,heperceivesandunderstandstheminrelationtoalltheotherappleshehasknown.A
particularappleisperceivedas“red”asaresultofitsassimilationtotheconceptualschemeofapples,of
which redness is one characteristic. Implicit comparisons with other (more or less red) apples
experiencedinthepastgivemeaningtotherednessofthisparticularapple.Buttheactionofcomparing
similaritiesanddifferencesbetweenapresentobjectandaschemethathasbeenconstructedonthebasis
ofpastexperiencescallsformorethanempiricalabstractionalone.
Theabstractionofanyinformationfromanobject...requirestheuseoftoolsofassimilationofamathematicalnature:relationships,oneorseveralclasses(oraction“schemes”atthesensorimotorlevel,whicharealreadyatype of practical concept), correspondences, functions, identities, equivalences, differences, etc. . . . Clearly,these tools . . . are not extracted from the objects. They are therefore due to the person’s own activities.(AdaptationVitaleetPsychologiedeL'Intelligence,AV,p.82,trans.bytheauthors)
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Inbrief,physicalknowledge,ortheknowledgeofobservables,isessentialtodevelopment,butcan
onlybebuiltupwithina larger frameworkbecause it requires certainmental toolswhichhavebeen
createdbymeansofpreviouslogicomathematicalexperience.
Logicomathematicalexperienceinvolvesknowledgeacquiredfromreflectiononone’sownactions,
notfromtheobjectsthemselves.Theconceptoflogicomathematicalexperienceisadifficultone,andwe
shallnowtrytoexplainitbymeansofanexample.
FIGURE17Twosets.
Supposethatachildencounterstwosetsofobjects,asinFigure17.SetAisarrangedinastraight
lineandsetBinacircle.Thechildexaminesthesets,accuratelyperceivingthateachelementisasquare,
thatonesetisarrangedinaline,andtheotherinacircle.Thisisthechild’sphysicalexperienceofthe
sets, and it yields accurate knowledge concerning certain properties of shape, form, and layout. But,
whileessential,physicalknowledgealonedoesnottellthechildsomethingverycrucialaboutthesets:
regardlessofsurfaceappearance,theyhavethesamenumber.Togainthisknowledge,thechildrequires
adifferentkindofexperience,logicomathematicalexperience,inwhichknowledgeisnotadirectresultof
perceiving objects, but of reflecting upon actions performed on objects. To illustrate the
logicomathematicalfactor,Piagetcitesafriend’schildhoodexperience.Attheageofabout4or5years,
hewas seated on the ground in his garden andhewas counting pebbles.Now to count these pebbles he puttheminarowandhecountedthemone, two, threeupto10.Thenhe finishedcountingthemandstartedtocount them in the other direction. He began by the end and once again found he had 10. He found thismarvelous....Soheputtheminacircleandcountedthemthatwayandfound10onceagain.(Piaget,1964,p.12)
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Throughrepetitionsofcountingandrecounting,ofarrangingandrearranging,thechildgrasped
an important property of number: it stays the same despite different orders of counting and despite
differingphysicalarrangements.
HowdidthislearningtakeplaceHowdidthechildcometoknowsomethingabouttheequivalence
ofnumber?Piagetmaintainsthatempiricalabstractionwasnotsufficienttoproducethisknowledge.Ina
sense, the child learned nothing about pebbles: he already knew that they are small, dark, smooth
objects.Thephysicalpropertiesofthepebbleswereknown,andtheydidnot“say”anythingtothechild
aboutnumber.
InPiaget’sview,thechildlearnedaboutnumbernotthroughdirectphysicalexperiencewiththe
pebblesthemselves,butbyconsideringhis
ownactions.Aprocessofreflectiveabstraction(asopposedtoempiricalabstraction)isinvolved.The
childfirstnoticesoneofhisownactions.Inthiscase,heseesthathehascountedtherowinonedirection,
getting10,andthathehascountedtherowintheoppositedirection,alsogetting10.Thisperceptionof
hisownactionsintereststhechild;itsurpriseshim.Next,“theactionnotedhastobe‘reflected’(inthe
physicalsenseoftheterm)bybeingprojectedontoanotherplane—forexample,theplaneofthoughtas
opposedtothatofpracticalaction”(BK,p.320).Thechildreflects(transposes)hisactionofcountingto
theplaneofthought.Thisisonewaythattheprocessisreflective.
Itisreflectiveinanotherwaytoo.Reflectinganactionontoanotherlevelcallsforareorganization
ofmentalstructurestointegratethenewactionwiththosealreadyexistingatthislevel.Thisprocessof
reorganization establishes new relationships and new meanings not found at the lower level. For
example,thechildhastorelatethecountingofthepebblestotheactionofincreasingquantity.Counting
to 10 always gives more objects than counting to 9. He has to relate the counting to the concept of
sequencing: 5 is always counted after4 andbefore6. Countingmust alsobe related to thenotionof
invarianceofnumber.Heseesthatifhecancounttheobjectsinvariouswaysandalwaysgetthesame
result,theymustbethesamenumber.Inasense,thechilddefinesnumericalequivalenceintermsofhis
ownactions.Inreorganizinghisactionsofcounting,hereflectsonthem,orcontemplateshisownactions,
and comes to appreciate their wider implications and significance. In sum, reflective abstraction is
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“reflected”intwoways.Thefirstconsistsofaprojection,orreflection,ofactionsontoahigherlevel,and
the second consists of a reflection upon and reorganization, or reworking, of both the projected and
previousactionsintoanewandbroaderunderstanding.
In his later work, Piaget introduces a third type of abstraction, pseudoempirical abstraction.
Pseudoempirical abstraction is found during the initial stages of the formation of logicomathematical
knowledge,whentheyoungchildneedstouseconcreteobjectsasasupportforsuchknowledge.The
countingofpebblesisanexampleofpseudoempiricalabstraction.Heretheknowledgeisnotabstracted
fromthepebbles,andthusisnotphysicalexperience,butisattributedtothem.Thechildcouldjustas
wellhavegainedtheunderstandingofnumberconservationfromanothersetofobjects,althoughsome
typeofobjectisnecessaryatthisbeginninglevel.Later,whenthechildhasgainedsufficientmasteryof
counting, he will not need the pebbles, or his fingers, or any other objects as a support, and the
abstractionwill become truly reflective. Pseudoempirical abstraction is, therefore, a primitive form of
reflectiveabstractionthatoccursduringtheearlypartoftheconcreteoperationalperiod.
There are several notable aspects of logicomathematical experience. First, it relies on physical
experience,althoughitgoesbeyondit.Intheexamplecited,achildcouldnothavediscoverednumerical
equivalence if he had not accurately perceived the pebbles. Yet perception of the pebbles—physical
experience—initselfwasnotsufficient,andhadtobesupplementedbyreflectionofandontheactions
of counting. Second, logicomathematical experience results in harmonywith the environment. As the
child’s physical knowledge becomes more accurate, his actions, and hence his logicomathematical
knowledge,constructan increasinglyobjective interpretationoftherealworld.Whiletherichness“of
thesubject’sthoughtprocessesdependsontheinternalresourcesoftheorganism,theefficacyofthese
processesdependsonthefactthattheorganismisnotindependentoftheenvironment,butcanonlylive,
act,orthinkininteractionwithit”(BK,p.345).
Althoughdifferentinnature,physicalandlogicomathematicalknowledgearecloselyintertwined,
particularly during the early years. In physical knowledge, the source of knowledge is exogenous or
externaltotheperson.Itisintheobject,oratleastthoseaspectsoftheobjectthatareperceivedbythe
person. Piaget calls these aspects theobservables. Observables, such as shape, color, or size, form the
content of physical knowledge. However, this type of knowledge is extracted within a framework of
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mental instruments—schemes, concepts, and so on—that have been created by an endogenous or
internal source, that of reflective abstraction. These instruments constitute the form of physical
knowledge.Inlogicomathematicalknowledge,thesourceofknowledgeisendogenousandisfoundin
thecoordinationsoftheperson’sownactions,althoughatfirsttheobjectsoftheexternalworldserveas
the basis for this knowledge, as in the process of pseudoempirical abstraction. With development,
logicomathematicalknowledgebecomesmoreandmoreremoved fromreality,asreflectiveabstraction
continuallyleadstotheconstructionofnewoperations,andofoperationsuponoperations.Theformal
theoriesoflogic,mathematics,orphysicsareexamplesoflogicomathematicalknowledgeasitfunctionsin
a“pure”state.But,atthesametimeasbecomingmoredetachedfromphysicalreality,logicomathematical
knowledge provides conceptual tools which are able to grasp a deeper and more profound
understandingofthephysicalenvironment.
Bothphysicalandlogicomathematicalexperienceareimportant,butPiagetfeelsthattheyarenot
sufficienttoexplaindevelopment.Onereasonisbecausetheyomitsocialfactors.
Socialtransmission. A third factor influencing cognitive development is social transmission. This
phraseisusedinaverybroadsensetorefertotheinfluenceofthecultureonthechild’sthought.Social
transmission may refer to a parent explaining some problem to a child, or to a child’s obtaining
information by reading a book, or to a teacher giving instruction in a class, or to a child discussing a
questionwithapeer,ortoachild’simitationofamodel.Certainly,thesocialtransmissionofknowledge
promotescognitivedevelopment.Theaccumulatedwisdomofaculturepassesdownfromgenerationto
generation, and enables the child to learn through the experience of others. Because of social
transmission,thechildneednotcompletelyreinventeverythingforhimself.Thecultureprovideshim
withextraordinarycognitivetools—thecountingnumbers,alanguage,analphabet.Thesetoolsenable
him to do mathematics, to speak, to write—in sum, to participate in higher intellectual activities,
particularlythoseofaliteratenature.
But social transmission itself is not sufficient. Unless the child is prepared to understand the
culturalwisdom,socialtransmissionwillnotbeeffective.Inotherwords,toappreciatetheknowledge
passedonbyotherindividuals,thechildmustpossesscognitivestructureswhichcanassimilateit.The5-
year-old cannot learn the calculus, however well it is transmitted, because he does not have the
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prerequisitestructures.
SomeAmerican andRussian psychologists have proposed that one specific type of social factor,
namely,thechild’sownlanguage,isvitalforthedevelopmentofbehaviorandthought.Inverygeneral
terms,theirthesisisthatatabouttheageof4or5yearsthechildusesinternalspeechtocontroland
organizehisactivities.Language“mediates”betweenexternaleventsandthechild’sresponse.Without
aninternallinguisticsystem,thechild’sresponsesaredirectlycontingentuponexternalevents;butwith
suchasystemthechildcanrepresentexternalevents,delayrespondingtothem,andcantherebycontrol
hisownbehavior.
Piaget’sview,verydifferentfromtheforegoing,attributesalesserroletolanguage.Piagetdoesnot
accept the proposition that language is the sole or primary device by which the child formsmental
representationsof external events.Representation takesmany forms—mental imagery, symbolic play,
drawing—inadditionto language.Thus,mental imagesareoftennonverbal.At18monthsofage, the
infanthasimagesofthingsandeventseventhoughhecanhardlyspeak.AccordingtoPiaget,theinfant’s
imagesandotherrepresentationsderivefromimitatingpersonsandthingsandnotfromlanguage.In
brief,therepresentationalfunction,andgenerally,thefigurativeaspectofthought,neednotinvolveor
dependonlanguage.3
Piagetbelievesthattheoperativeaspectofthoughtalsoneednotinvolvelanguage.Inthecaseof
classification, we have seen that the preoperational child in stage 1 cannot produce a hierarchical
arrangementofobjectsanddoesnotunderstandinclusionrelations.Thisissodespitethefactthatthe
childcanusealloftherelevantwordsinvolved.Hecansay“bluetriangles,”or“redcircles,”or“moreof
these,” or “some of these.” Even though the language is available, the preoperational child cannot
classify.Thisisnot,however,toassertthatlanguageplaysnoroleinthedevelopmentofclassificationor
othermentaloperations.Forexample,thepresenceofnounsinthelanguagemaystimulatethechildto
thinkintermsofdiscreteclasses.Also,theabilitytoverbalizeathoughtstructure,likeclassinclusion,may
helptoconsolidateandgeneralizeit.Nevertheless,forPiaget,thoughtinvolvesmorethanlanguageand
isnotdependentuponit.
ThispropositionisreinforcedbytheresearchofSinclair(reportedinInhelder,Sinclair,andBovet,
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1974).Shebeganbyexaminingthelanguageoftwoseparategroupsofyoungchildren,someofwhom
wereunabletosolveconservationproblemsandsomeofwhomweresuccessful.Shefoundacorrelation
between theability to conserveand theability to talkabout it.Theconservingchildrenusedphrases
comparingthevariables,saying,forexample,thatoneglassofwateris“tallandthin,”whiletheotheris
“short and fat.” The nonconserving children, on the other hand, used “undifferentiated terms” to
describe the situation; they said, forexample, thatoneglassofwater is “big”and theother is “fat.” It
would appear then—perhaps contrary to Piaget’s views—that conservers and nonconservers are
characterizedbydifferenttypesoflinguisticability.
Butdoestheuseofcomplexlanguagecausetheabilitytoconserve?Todiscovertheanswertothis
question,Sinclairtaughtthenonconservingchildrentousethelanguageoftheconserversindescribing
thevariousproblems.Iflanguageiscrucialforconservation,thesechildrenshouldthenhavebeenable
to conserve. Yet the results showed that they could not: the benefits of language trainingwere quite
limited.Itappears,then,thatlanguagedoesnotenablethechildtoconserve.Infact,theoppositeseems
true: thedevelopmentof the thought structuresunderlyingconservationenables thechild toemploy
sophisticatedformsoflanguagetodescribewhathedoesandunderstands.
FurtherevidencesupportingthispropositionderivesfromOpper’s(1979)researchinThailand.
TheThailanguagecontainscertainbuilt-intermscalled“classifiers,”whichsignifythatanobjectispart
ofahigher-order class.Thus theword for lotus specifies both that the object is that particular flower
knownasalotusandthatitbelongstothelargerclassofflowers.Thelanguageitselfvirtuallyannounces
classinclusion.Thequestionthenbecomeswhetherchildrenexposedtosuchalanguageacquireclass
inclusionatayoungeragethanusual.Opperfoundthattheydidnot.Despitethepresenceoflinguistic
mechanisms which would supposedly facilitate this development, Opper’s work showed that Thai
children did not acquire class inclusion earlier than Swiss children, whosemother tongue does not
containsuchmechanisms.ThisevidencealsoseemstosupportPiaget’spropositionthatthoughtinvolves
morethanlanguageandthattheformerisnotfullyshapedbythelatter.4
Considernowtheroleofformalschooling:Isthiskindofsocialtransmissioncrucialforintellectual
development? Some psychologists believe that it is. Some years ago, on the basis of research inWest
Africa,Greenfield(1966)proposedthattheWesternstyleofschoolingisnecessaryforthedevelopment
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ofthestagesofthoughtasdescribedbyPiaget.Themainevidenceforthisassertionwasthediscovery
thatschoolchildreninSenegaldidachievetheperiodofconcreteoperations,as judgedfromatestof
conservation,whereasthosechildrennotinschoolremainedatalowerlevelofthought.Whilethisisan
intriguing finding, the evidence in this area is by no means clear-cut. Some studies are directly
contradictory, showing that schooling is not necessary for the development of concrete operations
(Ashton, 1975; Dasen, 1972). At the present time, the weight of the evidence seems to support the
Piagetian view that schooling, like other forms of social transmission, may accelerate intellectual
development but is not necessary for it. Apparently, individuals growing up in “primitive” societies
without schools nevertheless develop the basic thought structures described by Piaget. Perhaps the
failureofsomeresearcherstoobtainthisfindingcanbeattributedtoproblemsofmeasurementinstrange
cultures,whereWesterntestingtechniquesandtestingmaterialsareofteninappropriate.Inanyevent,
Piaget’sviewisthatschoolingandotherformsofsocialtransmissioncancontributetointellectualgrowth
butdonotfullydetermineit.
Equilibration.Afourthfactoraffectingdevelopmentisequilibration,5whichinawayintegratesthe
effects of the other three factors, none ofwhich is sufficient in itself to explainmental development.
Equilibration refers to the child’s self-regulatory processes, bywhich he progressively attains higher
levels of equilibrium throughout development. The equilibration process is the backbone of mental
growth.
Letusbeginbyreviewingtheconceptofequilibrium.Piagethasborrowedthisnotionfromphysics
andbiologyandhasmodifiedittoapplytohumanintelligence.Theconceptofequilibrium,whichisnot
novelinpsychology,referstoastateofbalanceorharmonybetweenatleasttwoelementswhichhave
previouslybeeninastateofdisequilibrium.Freud,forexample,makesuseofasimilarprinciplewhen
hestatesthatapersontendstowardareleaseoftension.ForPiaget(unlikeFreud)equilibriumdoesnot
have the connotationof a static state of reposebetween a closed systemand its environment.Rather,
equilibrium,whenappliedtointellectualprocesses,impliesanactivebalanceorharmony.Itinvolvesa
systemofexchangesbetweenanopensystemanditssurroundings.Thechildisalwaysactive,anddoes
notmerelyreceiveinformationfromhisenvironmentlikeaspongesoakingupwater.Rather,thechild
attemptstounderstandthings,tostructureexperience,andtobringcoherenceandstabilitytotheworld.
Acognitivesystemisneveratrest,itcontinuallyinteractswiththeenvironment.Thesystemattemptsto
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dealwithenvironmentaleventsintermsofitsstructures(assimilation),anditcanmodifyitselfinline
with environmental demands (accommodation).When in equilibrium, the cognitive system need not
distorteventstoassimilatethem,nordoesitneedtochangeverymuchtoaccommodatetonewevents.
Although the concept of equilibrium was taken from physics, Piaget stresses that physical and
cognitiveequilibriumareverydifferent.Physicalequilibriumseekstomaintainthestabilityofthesystem
withoutchange.Disequilibriumisovercomebyamovementintheoppositedirectionwhichrestoresthe
original state of equilibrium. A thermostat, for example, maintains equilibrium by compensating for
increases or decreases in heatwith actions that restore the system to the original temperature.With
intellectual development, however, there is both stability and change. Cognitive systems, as they
progress, preserve past intellectual achievements but at the same time create new actions and novel
responseswhichallowthepersontogainmoreunderstanding.Equilibriumresultsfromregulationsthat
tendtowardbetter formsofknowledge.There isan increase inknowledgeratherthanareturntoan
originalstate,andthisrequiresadynamicmodelofequilibrium.“Itwouldnotdo,then,toconceiveof
equilibration as a simple process toward equilibrium since it always involves construction oriented
towardbetterequilibrium’’(EquilibrationofCognitiveStructures,ECS,p.26).
For Piaget, cognitive development consists of a succession of alternating equilibria and
disequilibria. Each successive level of equilibrium reaches a better form of knowledge through the
additionandreorganizationofcognitiveelements.Thesequantitativeandqualitativechangesresultin
new relationships, new understandings, and the solving of certain problems, but also open up the
possibilityofnewquestionsandproblems,ofnewimbalancesanddisequilibria.Toreconcileboththe
stabilityandthechangesthatoccurincognitivedevelopmentandtoemphasizethedynamicaspectof
this process, Piaget refers to it as optimizing equilibration (équilibration majorante). Optimizing
equilibration is the process that leads to the successive improvements in equilibrium that occurwith
development.Eachnewequilibriumbecomesmorepowerful in itsabilitytocomprehendthephysical
characteristicsandrelationshipsoftheobjectsintheenvironment,andalsotoattributecausal, logical,
andmathematicalpropertiestothem.
Piaget describes three types of equilibrium, all ofwhich contribute toward achieving a balance
betweenthepersonandhisenvironment.Thefirstistheequilibriumbetweenapersonandanobjector
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event of the environment. Here the person encounters an object, assimilates it to a scheme, and
accommodatestheschemetotheparticularobject.Iftheschemeisappropriate,thereisequilibrium;if
not,therewillbedisequilibrium.Achildwhoonlyhasschemesforappleandorangeswouldhaveno
troublewhenencountering instancesof these fruits,butwouldbe indisequilibriumwhenpresented
withherfirstexperienceofapineapple.Thistypeofequilibriumdependsupontheinteractionbetween
apersonandtheenvironment,thatis,betweenassimilationandaccommodation.
Anothertypeofequilibriumisbetweenthevariouscognitivesubsystems.Here,theequilibriumis
internalratherthanexternal.ExamplesofthiscanbefoundintheresearchbyInhelderandcolleagues
into learning, discussed in the previous section, which indicated that very often the lack of
understandingofaproblemiscausedbyanimbalanceduetodifferencesinthespeedofacquisitionof
differentcognitivesubsystems.Forexample,atacertainstageofdevelopmentthechild’sacquisitionof
thesubsystemofnumberisinadvanceofthatoflengthandthiscreatesadisequilibrium.Onlywhenthe
twosubsystemsreachthesamelevelandareinequilibriumisthechildabletounderstandconservation
oflengthproblems.Assimilationandaccommodationarealsoinvolvedinthissecondtypeofequilibrium,
buttheyarecarriedoutinternallybymeansofreciprocalassimilationandaccommodationofthevarious
cognitivesubsystems.
Athirdtypeofequilibriumisbetweenanoverallcognitivesystemanditscomponentsubsystems,
thatis,betweenthewholeanditsparts.Theoverallsystem,byintegratingthevariouselements,assumes
variouspropertiesofitsownwhicharenotfoundintheindividualsubsystems.Thesesubsystemsdonot
ceasetoexistbyvirtueofbeingintegrated,butcontinuetoretaintheirownspecificcharacteristicsand
thusbedifferentiatedfromeachother.Oneexampleisthehierarchicalclassinclusionofanimals.The
category of animals integrates the various subcategories of lions, tigers, cats, dogs, and so forth. It
incorporatescertaincharacteristicsofeachofthese,buthasabroaderapplicationthananyofthem.The
subcategories are clearly differentiated from each other even though they may have certain
characteristicsincommon.Theintensionandextensionoftheclassofanimalsdoesnotduplicateentirely
thoseofanyofthesubclasses,justastheintensionandextensionofeachoftheseisdistinctfromthoseof
any other subclass. Another example is the coordination at the level of formal operations of the two
earliertypesofreversibility,negationandreciprocity,withintheoverallINRCsystem.TheINRCgroup
provides more possibilities than either of the two types of reversibility encountered earlier in
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development although these continue to exist as distinct processes even when they have become
integratedintotheINRCsystem.Thisthirdtypeofequilibriumisbetweentheprocessesofintegration
anddifferentiation,butalso involvesassimilationandaccommodation. Integration isaccomplishedby
assimilation,whereasaccommodationisresponsiblefordifferentiation.
One fundamentalquestion regarding thedynamicsof thisprocessofoptimizingequilibration is
this:Whatarethetransitionmechanismsthatenable theprogression fromone levelofequilibriumto
another more powerful type of cognitive structure? Piaget believes that a major factor is reflective
abstractionin itsdual formsofprojectionandreorganization.Piagetalsoproposessomemorespecific
principles to explain conceptual development: differentiation and integration, the relativization of
concepts,andthequantificationofrelations.
Differentiation and integration are two complementary processes that play a major role in
conceptualdevelopment.Differentiationistheprocessofconstructingnewschemesorelementsonthe
basisofexistingonessoastomeettherequirementsofexperience.Asaresult,finerandfinerdistinctions
aremadebetweenandwithin schemesor concepts. Integration is theprocessof establishing linksor
connectionsbetweentheseelementssoastomaintaintheirunity.
Whenfacedwithafamiliarobjectorexperienceforwhichhealreadyhasaschemeavailable,the
childusesthisschemetoassimilatethefamiliarexperience.If,however,heencountersanovelobjector
event,forwhichexistingschemesareinadequate,anewschemewillneedtobeconstructed.Thisnew
schemewilleitherbederivedfromanexistingonethatbearssomesimilaritytothenewexperience,or
may result from the reciprocal assimilation of two or more schemes that separately contain the
characteristics of this experience. The new differentiated schemes that are created do not exist in
isolation, but become related to, or integrated with, existing schemes into higher-order ones. By
introducingnewrelationshipsandcharacteristicstoconcepts,differentiationandintegrationallowfor
thesubsequentassimilationofmorevariedexperiencesandhenceopenupthepossibility for further
differentiationandintegration.
Differentiationandintegrationarecloselyrelatedtotheintensionandextensionofconcepts.Recall
thattheintensionofaclassorconceptreferstothecharacteristicsorpropertiesofthatclass.ForPiaget,
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thismeanstheactionsthatapersoncancarryout,ortheschemesthatapersonhasavailable,relatingto
thatclass.Theintensionofanapplereferstotheavailableschemesofred,round,orsweet.Extension
referstothemembersoftheclass,itsfieldofapplication,ortheobjectstowhichtheseschemesapply.In
thechild,orinanadultforthatmatter,intensionandextensionarenotstatic.Onthecontrary,theyare
constantlychangingastheresultofexperience,anditistheprocessesofdifferentiationandintegration
that underlie these changes. The first characteristics to be differentiated are the obvious superficial
aspectsofthephysicalenvironmentthatcanbedirectlyperceived.Theserefertophysicalexperience.
Gradually,asthechildreflectsonhisexperiencesoftheseobjects,hegoesbeyondmerelyapprehending
observable characteristics to draw inferences from them. Since inferences are processes of a
logicomathematical nature, differentiation and integration now occur within a logicomathematical
framework. Thus, knowledge moves from the periphery to the center of objects, from exogenous to
endogenousprocesses.Inthiswaydifferentiationandintegrationleadtoanincreasinglycomplexand
deeperunderstandingoftheworld.
Thedevelopmentof the “cat” concept can serveas an illustration. For theveryyoung child, the
conceptof “cats” initially refers to theactualcats thatheencountersathome, inhisneighborhood,or
even in stories. At this stage his cat scheme is very general, and indeed there is often an
overgeneralizationofschemes. Its intensionmightbesomethingwith four legs,a tail,and fur,and its
extensionmayevenincludesquirrels,badgers,orotherfour-leggedcreatureswithatailandfur.With
additionalexperienceofcatsofdifferentcolorssuchasginger,black,ortabby,orwithdifferenteyecolors,
blue, green, or yellow, he will construct or differentiate subschemes of cats to account for these
differences. Each subscheme has its own characteristics distinct from the others, but they are all
interrelatedandintegratedwithintheoverallschemeofcats.
Suchdifferentiationandintegrationcouldcontinueindefinitely,dependingupontheexperiences,
interests,andmotivationoftheperson.Thechildstartswiththeirphysicalcharacteristicsortheactions
thatcanbetakenwithcats,suchasstrokingorfeeding.Later,thepersonconsidersfeaturessuchasbreed,
personalitytraits,orgenesthatarenotdirectlyobservableandrequireinferences.Thusajudgeatacat
show,whoneedstogofarbeyondjustasuperficialknowledgeoftheobservablecharacteristicsofcats,
wouldhaveahighlydifferentiatedandintegratedconceptofcats.
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Piagetreferstothis increasinglywidenetworkofrelationsor linksthatareestablishedbetween
schemesandtheirelementsbymeansofdifferentiationandintegrationastherelativizationofconcepts.
The child initially understands objects, situations, or events in terms of a limited number of broad,
undifferentiated categories or schemes. As she begins to create additional subschemes or elements to
account for new differentiated characteristics, she establishes relationships and interdependencies
between these elements.With an increased number of elements comes an increase in the number of
compositions,andhenceofpossibleinterrelationshipsbetweenthem.Theserelationshipsmaycoverthe
observablecharacteristicsofactionsandobjects,theirphysicalfeaturessuchasshape,size,orcolor.Or
theymaycovercoordinations, that is, inferencesdrawnfromtheperson’sactionsthatconstructspatial,
causal,andlogicomathematicalrelationshipswithotherobjectsintheenvironment.Therelativizationof
conceptsunderliesamovement froman initial, superficial,andundifferentiatedunderstandingofan
objecttoadeeperandmorevariedgraspofitsvariousproperties,functions,andrelationships.
Considertheseriationofstickstaskasanexampleofrelativization.Theveryyoungchilddivides
thesticksintothetwobroadundifferentiatedschemesof“large”and“small.”Relationshipsbothwithin
and between the schemes are somewhat limited. The slightly older child begins to distinguishmore
characteristicsoflengthandcreatesanewschemeof“mediumsize.”Alreadymorerelationsneedtobe
constructedbecauseofthelargernumberofschemes.Laterthechildwillbeabletoseriatethesticks,first,
in a tried-and-error fashion, and thenmore systematically.When the seriation is finally grasped, the
childisabletosetuprelationsandinterdependenciesbetweeneveryelement.Eachofthesticksbecomes
linkedor related toeveryotherone inanordered systemof graded lengths ranging fromshortest to
longest.
Onetypeofrelationthatthechildslowlyconstructsisquantification.Thequantificationofrelations
refers to the child’s progressivemove from an initial focus on the qualitative features of a concept to
reasoning on its quantitative aspects. For example, in seriation, the young child first focuses on the
qualitiesof“bigness”or“smallness.”Alltheelementsinthe“large”categoryareviewedasbeingsimilar
toeachother,theyarealllargeanddifferentfromthoseinthe“small”one.Theconstructionofathird
“middle-sized”categoryisstillaqualitativeapproach,althoughitisamovetowardquantification.The
additionofthemiddlecallsforcomparisonsamongthethreecategoriesinwhichthechildfocusesmore
specificallyon,andbecomesmoresensitiveto,thedifferencesinlengthbetweenthesticks.
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Withincreasingsensitivitytothesedifferences,thechildcomestorecognizethat,evenwithineach
category,thesticksareperhapsnotquiteassimilarasfirstbelieved.Indeed,therearedifferencesamong
the various “large” sticks. Eventually, the child understands that all the sticks are related in a
quantifiablemanner.Eachstick,whencomparedwiththeothers,isalittlemore,orless,“long”or“short.”
Theyareallnowviewedasvariationsalongthesingledimensionoflength.Theimplicationisthatthe
childhasnowconstructedacontinuumwithunlimitedpossibilitiesofincludingnotonlyactualobjects
presented,butalsoanyotherpossiblevariationalongthatsamecontinuum.Forexample,thechildcould
envisagethepossibilityof includingsticksthatwillneveractuallybepresentedbutareonlymentally
conceived.
Thiscontinuumisalogicomathematicalconstructionofwhichtheactualstickspresentedformonly
onepart.Furthermore,atthispoint,thechildalsounderstandsthat“more”and“less”arereciprocally
related.Asthesticksbecomelonger,or“morelong,”theyalsobecome“lessshort.”Amoveinthepositive
directionof“morelong”implicitlyinvolvesacorrespondingmoveintheopposite,negativedirectionof
“lessshort.”
Forpurposesofsimplicity,thepresentexamplehasconcentratedonthequantificationofasingle
property,the“long-short”dimensionoflength.Inreallife,ofcourse,thesituationisfarmorecomplex.
Objectsvaryalonganumberofdimensions.Applesarenever identical.Each individualapplecanbe
quantifiedalonganumberofdimensions:size,color,texture,sweetness,tonamebutthemostobvious
characteristics.All thesedifferences canbeplacedalongquantifiable continua thatdonotnecessarily
develop at the same pace. As quantification proceeds for these various differences, it allows for the
possibilityofanincreasingnumberofrelationships,andinthiswaynotonlycontributestowardamore
objectiveunderstandingofreality,butalsotowardbetterandbetterformsofequilibrium.
Inevitably, the study of equilibration and the successive levels of equilibrium along the path of
development leads to the reverse of the coin, disequilibrium. As Piaget states, the existence of any
positiveinstancenecessarilyimpliestheexistenceofitsnegation.Consequentlythestudyofequilibrium
leads to the study of disequilibrium. Piaget holds that disequilibrium is of crucial importance in the
processofequilibration,sinceitistheprimemotorofintellectualdevelopment.Disequilibriummotivates
thesearchforbetterformsofknowledge,andthusprovidesthelinkbetweenonelevelofequilibrium
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andthenext.
Disequilibrium,orimbalance,occurswhenapersonencountersanobjectoreventthatheisunable
toassimilateduetotheinadequacyofhiscognitivestructures.Insuchsituations,thereisadiscrepancyor
aconflictbetweenthechild’sschemesandtherequirementsoftheexperience.Thisisaccompaniedby
feelings of unease. Piaget refers to this situation as a disturbance, perturbation, or conflict. Generally
speaking, a disturbance is anything that prevents the person from assimilating an experience or
achievingagoal.Sinceassimilationisinvolvedindisturbances,andassimilationalwaysoccursrelativeto
anassimilatoryscheme,theconceptofdisturbanceisarelativeone.Whatmaybeadisturbancetoone
person,becauseof thenatureandtypeofschemesavailable,maynotbeso foranotherperson,either
becausehisschemesarenotsufficientlydevelopedforhimeventoperceivetheeventasdisturbing,or
becausehisschemesaresowellorganizedthataparticulareventorexperienceisrapidlyassimilated.In
theconservationofliquidstask,theveryyoungchildstateswithnofeelingofuneaseorconflictthatthere
ismoreliquidwhenitispouredintoatallthincontainerthanwhenitisinashortfatone.Forhim,the
situationisnotdisturbing.Thissamesituationwill,however,produceconflictintheslightlyolderchild,
who feels unease at stating that the same water is more, or less, depending upon the shape of the
container.Theevenolderchildagainfeelsnoconflictbecausehecanexplainthesituationinalogical
way.
When faced with a disturbance, the person reacts with responses that attempt to regulate the
conflict.Theseresponses,orregulations,willdifferdependinguponwhatschemesareavailable.Inmost
ofthestudiescarriedoutinGeneva,threetypesofreactionstodisturbanceshavebeenfound,andPiaget
callsthemalpha,beta,andgamma.
Alphareactionsaregenerallyfoundintheveryyoungpreoperationalchildwhooften,becausehe
doesnotperceivetheeventasdisturbing,simplyignoresit.Ifheperceivesitatall,itwouldbeasaminor
disturbancethatrequiresonlyslightmodificationofhisstructures.Ontheotherhand,hemaydeformthe
eventcompletelysoastofithisschemes.Inbothcases,verylittlechangeoccurstothecognitivesystem.
Alpha reactions, therefore, either modify the disturbing element so as not to interfere with existing
cognitivestructuresorignoretheconflictaltogether.Theyoungchildwhohasonlyschemesforsquares
andcirclesmayassimilateanovelshapesuchasatriangleintothesquarescheme,therebycompletely
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deforming the experience. Similarly, a child who, during the early stages of language development,
refers to all animals as “dogs,” is not disturbed by feelings of unease. She assimilates all four-legged
creaturesintoherunderlyingschemeofdogs,regardlessoftheextenttowhichrealityisdeformedtodo
this.
With beta reactions, which are usually found during the later preoperational and concrete
operationalstages,thechildseekstoincorporatetheconflictingeventintohiscurrentcognitivesystem.
Todothis,hemodifiesandreorganizesthissystemsoastotakeaccountofthedisturbance.Thechildof
thislevelnotonlydistinguishescirclesfromsquares,butwillcreatenewschemeswhenheencounters
triangles,rectangles,andsoon.Thedisturbance introducesvariations intothesystembycausingnew
schemestobecreatedthatwillexistalongsidetheoriginalones.Thevariationsarepartialbecausethe
child is able to create only a limited number of new schemes or subcategories. Beta reactions are
neverthelessanimprovementonalphaonesbecausetheyattempttoadaptthesystemtodisturbances
perceivedintheenvironment.
Finally,gammareactions are foundat the formaloperational level.Here theperson constructs a
systemthatallowshimtoanticipateallpossiblevariationsbymeansofinferences.Thesystembecomesa
closedoneandthelikelihoodofdisturbanceisreduced.Theoriginaldisturbingelementbecomesone
possible variation within a whole system of possible transformations. The child at this level can
anticipate the possibility of all sorts of shapes, both regular and irregular, even before he actually
perceivesthem.
The alpha, beta, and gamma reactions are not necessarily confined to particular stages of
development.Piagetbelievesthatthesametypesofreactionsaretobefoundinanyareaofknowledge,
sothatifanadultwereexposedtoatotallynewtopic,shetoowouldexhibitthesamesequenceofalpha,
beta,andfinallygammareactionswhenshemasterstherelevantknowledge.
In sum, disequilibrium, a major cause of cognitive development, is caused by disturbances,
perturbations,or conflicts thatoccurwhen there isadiscrepancybetween thechild’s schemes,which
determinewhatsheisabletoassimilate,andtherequirementsofcertainexperiences.Disequilibriumis
relativetothechild’sdevelopmental level.ThechildreactstotheconflictbyregulationswhichPiaget
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categorizesasalpha,beta,orgamma,dependingupontheschemesavailable.
Contradictions.Closelyrelatedtocognitiveconflictanddisequilibriumisthenotionofcontradiction
(seePiaget,ExperimentsinContradiction,1981a).Oneexampleistheconservationofliquidstask,where
liquid appears to bemorewhen in a tall thin container than in a short fat one. The person starts to
question this contradiction and, to resolve it, tries to discover its reasons or causes. In an attempt to
explorethenatureofcontradictionandrelateittotheequilibrationprocess,Piagetandhiscolleagues
havecarriedoutanumberofstudiesinthisarea.
Inoneofthetasks,thechildrenwerepresentedwithaseriesofsevendisks,referredtoasAtoG,
eachofwhichwasimperceptiblylargerthanthepreviousone.Thediskswereattachedtoaboardsothat
anysingleonecouldonlybecomparedwiththoseimmediatelybeforeandafterit.ThusdiskAcouldbe
comparedwith B, Bwith C, and so on. The last and largest disk, G, was not attached, and could be
compared with any other disk of the series. Since each disk was only very slightly larger than the
previousone,thedifferencebetweeneachofthesixattacheddiskswasimperceptible,althoughitwas
evident that G was larger than A. The child was asked to explain the contradictory situation of an
apparentequalitybetweenthefirstsixdisks,A=B,B=C,andsoon,andthenonequalitybetweenGand
A.
Inthisandotherstudiesofthesamenature,threestageswerefoundinthechild’sunderstanding
of contradiction. During an initial stage, the young child is not aware that there might be any
contradictioninthesituation,inthiscaseofadmittingthatthefirstsixdisksareequal,thatFisequaltoG,
andthatGislargerthanA.HealsoappearstofeelnouneaseatstatingatonepointintheinterviewthatF
is the same size as G and later at another point that G is larger than F. Either he forgets his former
statement, or he does not relate the two statements together, and thus does not recognize the
contradiction.Childrenwhoremembertheirpreviousstatementsattempttoreconcilethecontradiction
butdosowithinappropriateactions.SomeofthemsaythatGisthesameasF,thatFisthesameasA,and
thatGislargerthanA.Aswehaveseenintheprevioussection,thesearealphareactions.
Atthesametimeasexhibitingalackofawarenessofmanycontradictions,theyoungchildofthis
initial stage provides examples of what Piaget calls pseudocontradictions, that is, he interprets as
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contradictory certain relationships or situations that are not so to the person at a higher level of
development.Forexample,intheseriationtask,ayoungchildfindsitcontradictorythatastickcanbe
simultaneously larger(thanprevioussticks)andsmaller(thantheonestofollow)orthatahalf-filled
glasscanbehalffullaswellashalfempty.Hebelievesthatastickiseitherlargeorsmall,aglasseither
emptyorfull,butnotbothatthesametime.
Duringasecondstage,thechildbeginstobeawareofthecontradictionsinhisstatements.Hewill
search for solutions, but since he does not yet have the ability to overcome these contradictions, his
solutionswillbecompromiseones.Intheearlierdisksexperiment,hewillsetuptwodistinctclasses:the
“small”disks,A,B, andC, and the “large”ones,E, F, andG, but thenhemighthave troubledeciding
whether theboundarydisk,D,shouldbe in the“small”or“large”categoryandwillmove itbackand
forthbetweenthetwo.SomechildrenbelievethatdiskGchangesinsize,andfirstsayitisthesamesize
asF,butthenthatitbecomeslargerwhencomparedwithA.Otherchildreninthisstagemaycreatethree
classes,withanintermediatesizebetweenthesmallandlargecategories.Forexample,AandBwouldbe
small,C,D,andEintermediate,andFandGlarge.Allthesedifferentreactionsconstitutebetabehavior,
orthecreationofvariationswithinthesystem.
Finally,ataround11to12years,thestage3childunderstandsthatthedisksformaseriation,with
imperceptible differences between each successive disk. He has quantified the size relationship. By
doingthishehascreatedanewcognitivestructurethatisabletoassimilatethedisturbingelement.This
understanding of the situation resolves the imperceptible differences problem. It allows the child to
explaintheapparentcontradictionandtoanticipatethepossibilityofanunlimitednumberofdisks.
Piaget states that the child’s initial unawareness of contradiction occurs because he first
concentrates on the observable features of a situation or the results of an action, onaffirmations, and
neglectsthenonobservables,orwhathasbeenexcludedbytheaction,thenegations.Thecommonfeature
oftillcontradictionsisanincompletecompensationbetweenaffirmationsandnegations.Fortheyoung
child,affirmationspredominateovernegations.Thisisbecauseitiseasiertoapprehendpositivesthan
negatives.Theperceptionofanabsentobjectorcharacteristicinvolvesexpectations thatgobeyondthe
informationactuallyprovidedbytheobjects.Wecanspontaneouslythinkofredobjects(affirmations),
but we need to construct or infer the category of nonred ones (negations) since they are not given
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perceptually.Negationrequiresinference,thatis,aninternalconstruction,andthechildneedstimeto
buildtheseinternalconstructions.
Onlywhen the intension and extension of a concept have become sufficiently differentiated to
cover negations will the child be able to overcome contradiction. The awareness of contradiction
presupposes theability todraw inferences. In the foregoing task, theyoungchildconcentrateson the
observablesoraffirmationsthat“AisthesameasB,”“BisthesameasC,”andsoon,until“Fisthesameas
G”and“GislargerthanA.”Tofeelcontradictionandtoovercomeit,thechildmustbeabletoinfertwo
things.First,hemustrealizethattherelationship“GislargerthanA”(affirmation)impliesthat“Aisnot
equaltoG”(negation).Second,andmorecomplex,thechildmustbeabletoinfer,byusingaschemeof
transitivity,that“AisthesameasF.”Sinceonlyadjacentdiskscanbecompared,thiscannotbeobserved
directlyandisalsoanegation.Itisonlyatquiteanadvancedstageofdevelopmentthatthechildacquires
transitivityandhencebecomescapableofconstructingthisnegation.
All this may seem contrived, artificial, and irrelevant to the study of normal intellectual
development, but that is not so. On the contrary, Piaget believes that the concepts of affirmation and
negationareof tremendous importance to thewholeof cognitivedevelopment.This isbecauseevery
actionnecessarilyandimplicitlycontainsbothapositiveandanegativeaspect,bothanaffirmationanda
negation.Theclassofredobjectsimpliesalltheobjectsexcludedfromthisclass,ortheclassofnonred
objects.Additionimpliessubtraction,andsoon.Affirmationsandnegationsarefoundateverylevel,in
perception, sensorimotor actions, and mental operations. Initially, the young child grasps only
affirmations.Onlyslowlyandlaboriouslydoesheconstructnegations.Hisnegationsaresystematically
graspedonlywhen thechild is able to construct reversibleoperational structures inwhich there is a
completecompensationofaffirmationsandnegations.
AlthoughPiagetreachedtheseconclusionsonaffirmationsandnegationsduringthelatterpartof
hiscareer,hefeltthattheyweresuchanimportantexplanatoryframeworkforintellectualdevelopment
asawhole thathe returned tomanyofhis earlier studies, inparticular the conservation tasks, inan
attempttoexplainpastfindingsintermsofthechild’sinitialprimacyofaffirmationsandhissubsequent
constructionofnegations.
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Toendthissectiononequilibration,letuslookathowPiagetincorporatestheconceptsofempirical
and reflective abstraction, optimizing equilibration, equilibrium, and disequilibrium, into a model of
cognitivedevelopmentwhichhecallsthespiralofknowing.Thisspiralofknowingissymbolizedbyan
invertedcone,asshowninFigure18.Theinnerspiralofthecone,A,representsinternalconstructionsin
theformofreflectiveabstractionwithitssuccessiveprojectionsandreorganizationsthatarecarriedout
withintheoptimizingequilibrationprocess.Theouterlayers,EandE',representinteractionswiththe
environmentintheformofempiricalabstractionwithintheframeworkofpreviousreflectiveabstraction.
These two processes, A and E/E', are in constant interaction as new projections and reorganizations
result from interactions with the environment. Three vectors, a, b, and c, determine the progress of
cognition.Vectorarepresentsthehierarchicalsuccessionofcognitivestructures,startingwithreflexes,
moving throughsensorimotorschemes,preoperational structures, concreteoperations, finally toreach
prepositionaloperations.Vectorbrepresentsthemodificationsofthestructuresanddis-equilibriathat
result from interactions with the environment. Vector c represents explorations of the environment
whichleadtopartiedorcompletereorganizationofthestructures.
FIGURE18The spiral of knowing. From Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique etPhénocopie,byJ.Piaget.Copyright1974byHermann,Paris.ReprintedbypermissionofHermann,Paris.
Theever-wideningbutopencirclesofspiralArepresentthreemajorcharacteristicsofequilibrium.
First,thereistheunderlyingpoweroftheequilibrium.Thisreferstothenumberofactionsthatcanbe
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carried out and hence to the number of schemes available, or the field of application of the cognitive
structures. As the field of application extends and schemes becomemore differentiated,more actions
becomepossible,andequilibriumbecomesmorepowerful.This increase inschemes,or in the fieldof
application,isreflectedinthewideningofthecircles.
Theyoungchild’sclassificationsystem,forinstance,wouldberelativelyundifferentiatedwithfew
classesandsubclasses.Withonlyafewschemesandsubschemesavailable,itwouldnotbepossiblefor
himtocarryoutmanyactions,ortoestablishmanylinksorrelationshipsbetweenthem.Thisequilibrium
wouldnotbeverypowerful.Fortheolderchildwhohasalreadyconstructedahierarchicalclassification
system with numerous subclasses, the possibility of links and relationships becomes boundless. The
equilibriumisthereforeinfinitelymorepowerful.
Thepowerofaparticularlevelofequilibriumisdirectlyrelatedtothedegreeofrelativizationand
quantification of concepts as well as to differentiation and integration. Understanding becomes
increasingly coherent as relationships and connections between schemes increase. Consequently an
increaseinpowerofequilibriumisaccompaniedbyagrowthincoherence.
Anothercharacteristicofequilibriumisstability,whichisdefinedasthecapacitytocompensateby
actions ormental operations for changes in the environmentwithout disturbing thewhole structure.
When a system is stable, the introduction of new elements does not destroy it. The structure easily
incorporates the new elements and does not change. Stability is achieved when any action in one
direction (affirmation) can be compensated for or canceled out by an action in an opposite direction
(negation).Withastableequilibrium,affirmationsarebalancedbynegations.Inseriation,forinstance,
the young child who is able to construct a series only by trial and error will, when presentedwith
additional sticks to insert, find it necessary to destroy thewhole series and start from the beginning
again, whereas the child with amature seriation structure can incorporate an unlimited number of
additionalstickswithoutdistortingtheseries.Thelatterhasamorestableequilibrium.Perfectstabilityis
achieved when the person is able to anticipate disturbances or conflict before they are actually
encountered.
Athirdcharacteristicofequilibriumisitsopenness,whichreferstotheabilitytoincorporatenew
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ideasandraisenewquestionsandproblems.Thesewill lead tonovelactionsandresponses to solve
theseproblems.Thisopennessisreflectedintheupwardmovementofthespiral.Eachsuccessivelevelof
equilibrium in the equilibration process solves previous problems and provides answers to previous
questions,butat thesametimeopensupthepossibilityofnewproblemsandnewquestions. It is this
opennessthatensuresthatcognitioniscontinuallydeveloping.Thesethreecharacteristicscombined—
power, stability, and openness—ensure that the equilibration process continually conserves past
understandingandconstructsnewknowledge.
POSSIBILITY
Piagetwasgreatlyconcernedwiththeconstructionofnewknowledge,aproblemunderlyingthe
equilibrationprocessand thespiralofknowing.Howdoes thechildcreatenewresponsesoractions?
What accounts for the openness of the spiral toward new possibilities of disequilibrium and re-
equilibration?
In a number of studies designed to investigate the development of the concept of possibility,
childrenwererequiredtocomeupwithasmanysolutionsaspossibletocertainproblems.(SeePiaget,Le
PossibleetleNecessaire,1981b,1983.)Forexample,theywereaskedtoindicateallthedifferentways
theycouldthinkoftoplacethreediceonapieceofcardboard,tomakeatoycargofrompointAtopointB,
ortocutupapapersquare.
Findingsof this typeofstudyshowedthreemainstages inthedevelopmentofpossibilities.The
youngchildof4 to5yearscomesupwitha limitednumberofpossiblesolutions,oneor twoatmost.
These few possibilities are often accompanied by a strong feeling of necessity, which Piaget calls
pseudonecessity.Thisisthefeelingthatitisimpossibletochangerealityortheimpressionthatbecause
this is how things are, this is how they necessarily have to be. Reality, as given in the few solutions
suggested,isfeltofnecessitytobetheonlypossibility.
Inthestudywiththethreedice,theveryyoungchildrenof4to6yearswereabletocomeupwith
onlyafewsuggestions,andthesewereoftengeneratedbyaprocessofanalogy.Forexample,onechild
placedthethreediceinthethreeanglesofthesquarepaper.Whenaskediftherewereotherways,he
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movedoneofthedicetothefourthangle, thenmovedthethreedicearoundthevariousangles,each
timeleavingadifferentanglewithoutadie.Childrenofthislevelalsobelievethatthebestsolutionsare
thosethataresimilartothefirstoneproposed.
Atthenextstagetheolderchildrenareabletoincreasethenumberofpossiblesolutionssuggested,
andcomeupwitharangeof“co-possibles,”thenumberofwhichincreasewithage.Childrenof7to8
yearsproducefourtofivepossiblesolutions,whereasby9to10yearstheycanenvisagethirtyormore
solutions,eventhoughtheythemselvesarenotalwaysabletodescribeallthesepossibilities.Withthe
dice problem, children of 7 to 10 years suggested numbers ranging from twenty to ten thousand,
althoughwhentheexperimentersuggestedtenthousand,onechildfeltthatthisnumberwastoohigh.
Theyrealizethatthesemanysolutionsexistasabstractco-possibleswhichsomeoneelsemaybeableto
describe,eventhoughtheythemselvescannot thinkofallof them.At thisstage, thebestsolutionsare
consideredtobethosethatdifferthemostfromtheonesthathavealreadybeensuggested.
Finally, around 11 to 12 years, children infer more or less immediately that the number of
possibilitiesisunlimited.Thechildrealizesthatanysolutionproposedisonlyasampleofsuchavast
numberofsolutionsthatitwouldnotbepossibletothinkofthemall.Atthispoint,anunlimitednumber
ofpossibilitiesisconceptuallydeducedratherthanactuallyobserved.
The idea of an unlimitednumber of possibilities is obviously not something the child is able to
observe in theenvironment,but is something thatheconstructs internallybymaking inferences from
whatisactuallygiveninasituation.Aswehaveseen,inferencesrequireaninternalconstructionthat
goes beyond observables. This explains why it takes so long for a child to acquire the concept of
possibility.
Piaget maintains that the conquest of possibilities is a crucial mechanism of the equilibration
process.Eachnewpossibilityopensupafieldofvirtualorpotentialnewpossibilities.Asthechildsolves
problemshebeginstodiscoverothers,andtorealizethateachproblemcangenerateahostofpossible
solutions,notallofwhichheisabletodescribe.Itisthiscreationandmultiplicationofpossibilitiesthat
providestheopennessofequilibration,andexplainstheproductionofnoveltywhichisoneofthebasic
questionsraisedbyPiagetinhisgeneticepistemology.
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Studies were also conducted into the feeling of necessity in the child. Their results show that
necessity follows a parallel development to possibility. Young children start with the feeling of
pseudonecessity,whichwasfoundinthestudiesofpossibility.Olderchildrenproduceasmallnumber
ofco-necessitiesandgrasptheideathateachoftheco-possibilitiesorsolutionstoaproblemisequally
necessary.Finally,around11to12years,thechildexplainsthatthereareanunlimitednumberofco-
necessities.
Inhisdiscussionsontherelationshipamongpossibility,necessity,andreality,Piagetstatesthatin
the early stages of development, there is a lack of differentiation among these threemodalities. The
youngchild,owingtohislimitednumberofschemes,believesthattheonlypossibilitiesarethosethatare
observable.Moreover,theseareconceivedofasbeingnecessary,whichisinfactapseudonecessity.Asthe
child’sschemesmultiply,andasmoreconnectionsbetweenthemareestablished,hebecomescapableof
goingbeyondobservablesandofdrawinginferencesaboutreality.Itistheseinferencesthatleadtothe
construction of a larger number of co-possibilities. Possibilities are the result of the differentiation of
schemes. At the same time, with development, the initial regulations are changed into reversible
operations.Operationsareaccompaniedby feelingsofnecessity.Aswehaveseen in theconservation
tasks,necessityisonecharacteristicoflogicalreasoningprocesseswhichresultsfromtheintegrationof
schemes and their transformation into operatory structures. Operations represent a synthesis of the
possible and the necessary, as well as a synthesis between integration and differentiation which is
characteristicofthethirdtypeofequilibrium.
Summary and Conclusion
Piaget distinguishes between development and learning in the narrow sense. Development is
influencedby four factors.Physical structuresboth limit certain aspects of cognitive development and
make others possible, butmaturation in itself is not sufficient to explainmental development, partly
becausethereareobviousculturaleffectsoncognitivefunctioning.Asecondfactorisexperience.Physical
experience involves gaining knowledge of objects by observing them directly. Logicomathematical
experience involves an internal coordination of the individual’s actions which at the outset are
performedon theobjects, but laterdonot require this physical support.However, these two typesof
experiencearenotsufficienttoexplaindevelopment,becausetheyomit,amongotherthings,theeffects
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of social influences. A third factor, socialtransmission, refers to the acquisition of knowledge by such
techniques as reading or instruction. This factor is also insufficient to explain development, partly
becauseitignorestheroleofthecognitivestructureswhichmakesocialinfluencesefficientorinefficient.
Afourthfactorisequilibration.Thisconceptinvolvesthechild’sself-regulatoryprocesseswhichleadhim
throughprogressivelymoreeffectivestatesofequilibrium.Thenotionofequilibriumreferstoasystemof
exchangesbetweenanopensystemand its surroundings. It impliesasystemthat is inactivebalance
withitsenvironment.Thedegreeofequilibriumisdefinedbyasystem’spositiononthreedimensions:
fieldofapplication,stability,andopenness.Thegreaterthedegreeofthesequalities,themoreperfect
the equilibrium. Research stresses the central role of internal conflict in promoting equilibration. As
equilibrationproceeds,thechildcomestoappreciatetherolesofpossibilityandnecessity.
Piagetdistinguishesbetweenlearninginthenarrowsenseandlearninginthewidersense.The
former involves the mere acquisition of specific responses to particular situations. Such learning is
superficial:itisunstable,impermanent,andunlikelytogeneralize.Learninginthewidersenseinvolves
theacquisitionofgeneralcognitivestructures.Indeed,theseareusedtogivemeaningtospecificlearning
andoftenmakeitpossible.Thus,developmentexplainslearning.Further,developmentoccursthrougha
self-regulatoryprocessinvolvingthefourfactors,notthroughtheacquisitionofspecific informationor
responses.Learningthereforecannotexplaindevelopment.
Piaget’s theory makes an enormous contribution in focusing on the processes of self-regulated
development.Piagetcontinuallystressesthechild’scontributiontothedevelopmentalprocess.Itisthe
childwhotriestoassimilatetheconservationproblemintoalreadyavailablestructures,anditisthechild
who feelsa subjective lackof certaintyabouthis solution.Thechilddoesnot simply react toexternal
events,buttakesanactivepartinhisowndevelopment.Piaget’snotionofself-regulationisextremely
valuable. It seems to capture a goodpartof the realityof children’sdevelopment. It also serves as an
alternative to human engineering views which stress the external shaping of responses and the
modificationofbehavior.
EDUCATION
Inthepresentsection,wewillconsidersomeimplicationswhichPiaget’sviewsholdforeducation.
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WhilePiagethasdevoted relatively little attention toproblems in this area,hiswork canmake three
typesofcontributionstoeducationalpractice.First,Piaget’stheoryprovidessomegeneralprinciplesfor
theconductofeducation.Second,Piaget’sstudiesof thedevelopmentofspecific logical,mathematical,
andphysicalconceptsinthechildcanassistthedevelopmentofcurriculaandteachingpracticesinthese
areas.Third,Piaget’sclinicalinterviewingtechniquecanproveavaluablediagnosticandevaluativetool
fortheteacher.ThissectionthereforewilldescribePiaget’sthoughtswithrespecttoeducationandwill
discuss these three types of potential contributions. The section closes by considering possible future
directionsforaPiagetianapproach.
Itshouldbeemphasizedattheoutsetthatour intentionisnottoproposeparticularcurriculaor
instructionalpracticesonthebasisofPiaget’swork.AsSinclair(1976,p.11)putsit,
I’m not sure thatmuch can be donewith application of Piaget’s theory in a detailedway by the Piagetianpsychologist. . . .Thereareabsolutelyno [direct]practical indications in theworkofPiagetwith respect toeducation....Piagethasverylittletosaywithrespecttospecificproblemssuchashowtoteachreadingandwriting,andvariousothereducationaltechniques.
Hence,wewillbeconcernedwiththemajorguidingprincipleswhichemergefromPiaget’swork.
LikePiaget,wefeelthattheimplementationoftheseprinciplesrequiresthespecialskillsoftheeducator,
whounderstandsthedistinctiveconditionsoftheschoolsetting,ratherthanthepsychologist.
A Child-Centered Approach
OneofPiaget’smostsignificantcontributions ishisnotionthat theyoungchild isquitedifferent
fromtheadultinseveralways:inmethodsofapproachingreality,intheensuingviewsoftheworld,and
intheusesof language.Piaget’s investigationsconcerningmatterssuchastheconceptofnumberand
verbal communication have enabled him to produce a change—indeed, one might almost say a
metamorphosis—in our ways of understanding children. As a result of his work we have become
increasingly aware that the child isnot just aminiature although lesswiseadult, but abeingwith a
distinctivemental structure that is qualitativelydifferent from the adult’s. The child views theworld
fromauniqueperspective. For example, the childbelow the ageof7 years trulybelieves thatwater,
whenpouredfromonecontainertoanother,gainsorlossesinquantity,dependingontheshapeofthe
secondcontainer.Orinthecaseofnumber,theyoungchild,althoughabletocountto20ormore,hasno
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conception of certain fundamental mathematical ideas. He may think, for example, that a set of five
elements is largerthanasetofeightelements if thephysicalarrangementof thesetstakesoncertain
forms.
Theseandmanyotherunexpecteddiscoveries leadtothesurprisingrecognitionthatthechild’s
worldisinmanywaysqualitativelydifferentfromthatoftheadult.Onereasonforthechild’sdistinctive
viewofrealityisadistinctivementalstructure.Theyoungchild(belowabout7or8yearsofage)centers
hisattentiononlimitedamountsofinformation;heattendstostatesratherthantransformations;heis
egocentric,failingtotakeintoaccountotherpointsofview;hisconceptsarerelativelyundifferentiated;
andheisincapableofformsofthought,suchasreversibility,whichallowsymbolicmanipulationofthe
dataofexperience.Eventheolderchild(between7and11years)isstronglytiedtoconcretesituations
although he is capable of fairly subtle mental operations. The child reasons best about immediately
presentobjectsandfailstoappreciatethecontradictionsorpossibilitiesinherentinasituation.
Oneresultofthechild’scognitivestructureisaviewofrealitywhichtotheadultseemschaoticand
unnatural.Anotherconsequence is that theyoungchild’suseof language isdifferent fromthatof the
adult.That is, thewords that thechildusesdonothold thesamemeaning forhimas theydo for the
adult. Adults often overlook this point. We usually assume that if a child uses a particular word, it
automaticallyconveysthesamemeaningthatitdoeswhenanadultusesthatword.Adultsoftenbelieve
thatonceachildhaslearnedthelinguisticlabelforanobject,hehasavailabletheunderlyingconcept.
ButPiagethasshownthatthisoftenisnotthecase.Thechilddoeslearnhiswordsfromtheadult,but
assimilates them into his ownmental structure,which is quite different from the adult’s. Thewords
“sameamounttodrink,”forexample,areinterpretedinonewaybythe4-year-old,andinanotherway
by the adult. Only after a period of cognitive development does the child use these words and
understandtheminthesamewayasthemorematureperson.
Theimplicationofthisverygeneralproposition—thattheyoungchild’sthoughtandlanguageare
qualitativelydifferentfromtheadult’s—isalsoverygeneral:theeducatormustmakeaspecialeffortto
understandtheuniquepropertiesofthechild’sexperienceandwaysofthinking.Theeducatormusttry
to adopt a child-centered point of view, and cannot assume that the child’s experience or modes of
learningare thesameashisown.Forexample,while theeducatorhimselfmay learnagreatdealby
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readingabookorlisteningtoalecture,similarexperiencesmaybefarlessusefulfortheyoungchild.The
educatormayprofit froman orderly sequence ofmaterial, but perhaps the child does not.While the
educatormayfeelthatagivenideaissimpleandindeedself-evident,thechildmayfinditdifficult.In
short, it is not safe to generalize from the adult’s experience to that of the child. The educator’s
assumptions,stemmingastheydofromanadultperspective,maynotapplytochildren.Theeducator
needstoimprovehisowncapacitytowatchandlisten,andtoplacehimselfinthedistinctiveperspective
ofthechild.Sincethemeaningexpressedbythechild’slanguageisoftenidiosyncratic,theadultmusttry
tounderstandthechild’sworldbyobservinghisactionsclosely.Therearenoeasyrulesorproceduresto
usetounderstandthechild.Whatisnecessaryisconsiderablesensitivity—awillingnesstolearnfrom
thechild,tolookcloselyatthechild’sactions,andtoavoidtheassumptionthatwhatistrueorcustomary
fortheadultisalsotrueforthechild.Theeducatorneedstointeractwiththechildinaflexiblewayto
gaininsightintothelatter’scurrentleveloffunctioning.Withthisattitude—awillingnesstoobservethe
childandtolearnfromhimtheeducatorcanbegintounderstandthechildandtotailortheeducational
experiencetothechild’sneeds.Educationmuststemfromachild-centeredperspective.
Activity
Theconceptthatchildren—orindividualsofanyage—learnbestfromself-initiatedactivityisvital
fortheguidanceofeducation.ThroughoutthisbookwehaveseenthatPiagetplacesmajoremphasison
theroleofactivity—bothphysicalandmental—inintellectualdevelopment.InPiaget’sview,“toknow
anobject,istoactonit”(Piaget,“DevelopmentandLearning,”1964,p.8).Almostfrombirth,theinfant
touchesobjects,manipulatesthem,turnsthemaround,looksatthem,andthroughsuchactivitiesgains
an increasingunderstandingof their properties. It is through action, notpassiveobservation, that he
developsanunderstandingoftheworld.Indeed,thereisasenseinwhichthechildconstructsreality.
For the older child, too, the essence of knowledge is activity. Thus, when the preoperational child
attempts to remember (retain his knowledge over time), he actively organizes the material by
assimilatingittoavailableschemes.Often,thechild’sunderstandingisnotonaverballevel,whichinfact
usually takes a long time to develop. The adolescent’s knowledge also involves activity: in trying to
understandphysicalphenomena,heactivelygenerates combinationsofhypotheticalpossibilitiesand
transformstheminthought.Hedoesnotsimplyrespondtotheimmediatepresent.Tosummarize,inall
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cases—whetherbehavioralschemes,concreteoperations,orformalstructuresareinvolved—theessence
ofknowledgeisactivity.
Topromotegenuineunderstanding, the teacher should therefore encourage the child’s activity.
Whentheteacherattemptstobypassthisprocessinvariousways—forexample,bylecturingataclassof
youngchildren—theresultisoftensuperficiallearning.Perhapsthisisonereasonwhysomuchofwhat
is taught in school is immediately forgotten after the school year ends. By contrast, genuinely active
learningcanleadtoamoresolidandlong-lastingunderstanding.
Awordofcautionisneededinconnectionwiththisemphasisonactivity.Sometimesteacherstakeit
to refer solely tophysicalactivity; theybelieve that themanipulationofobjectsautomatically leads to
learning. This may be true in some situations, but it is not always the case. Take, for example, a
preschooler who is actively engaged in playing with the toys provided at school—swinging on the
swings,orbuildingcastlesinthesandpit.Thischildwillprobablylearnsomethingabouttheproperties
oftoys,swings,orsand,andabouthisownrelationshipstotheseobjects.Thisisimportantknowledgefor
the child at this stage.Take, on theotherhand, the caseof ahigh school student following a science
lesson.First, the teachercarefullydemonstratesaparticularexperiment to theclass.Theteacher then
asks thepupils to carryout the sameexperiment, forwhich theprocedure is given stepby stepona
certainpageofthetextbook.Isthepupilwhocarriesoutthecorrectphysicalactionsasdescribedinthe
bookreallylearning?Notnecessarilyso,oratleastheisnotalwayslearningthethingsthattheteacher
intendedhim to learn. If thepupil’sphysicalactionsarenotaccompaniedbyparallelmentalactivity,
suchasthinkingofalternativetypesofresultsandtheirmeaning,itisunlikelythatmuchrealandlasting
learningwill occur. At this stage, simply tarrying out physicalmanipulationswill not producemuch
learning.
AsPiaget(ScienceofEducationandthePsychologyoftheChild,1970c)putit,“althoughthechild’s
activity at certain levels necessarily entails the manipulation of objects, ... at other levels the most
authenticresearchactivitymaytakeplaceinthespheresofreflection,ofthemostadvancedabstraction,
andofverbalmanipulation(providedtheyarespontaneousandnotimposedonthechild)”(p.68).
Acceptance of the principle of active learning requires a considerable reorientation of beliefs
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concerningeducation.Teachers(andthepublicatlarge)usuallyconsiderthattheaimofeducationisto
impartexistingknowledge,oftenofafactualtype,asefficientlyaspossibletothepupil,whowillthen
absorb it in the form presented. In this view, if students were allowed to design and conduct
experiments, there would not only be chaos in the classroom, but there would also be no learning.
AccordingtoPiaget’stheory,thesebeliefsandattitudesareerroneousforseveralreasons.Teacherscan
infactimposeverylittleknowledge.Itistruethattheycanconvincethechildtosaycertainthings,but
these verbalizations often indicate little in the way of real understanding. Moreover, it is seldom
legitimate to conceiveofknowledgeas a thingwhich canbe transmitted.Certainly the childneeds to
learnsomefacts,andthesemaybeconsideredthings.Sometimes,drillorprogrammedinstructionmay
assistinlearningofthistype.Butoftenthechilddoesnotlearnevenfactswhenimposed;thestudent
mayhavetodiscoverthemhimself.
Inaddition,factsarebutasmallportionofrealknowledge.Trueunderstandinginvolvesaction,on
boththemotoricandconceptual levels.Consider forexampletheunderstandingofclassproperties.A
traditional viewmightpropose that the child can simplybe taught some facts about classification, for
instance,thatasquareisageometricform.Piaget’sview,ontheotherhand,arguesthatunderstandingof
classificationconsistsofasequenceofactivities.First,thechildphysicallysortsorotherwisemanipulates
objects.Hefeelsvariousformsandinthisway(amongothers),perceivesthedifferencesamongthem.He
mayputdifferentformsindifferentplaces.Later,hecansorttheobjectssolelyonamentallevel;nowthe
child does not need to separate things physically. Later still, he can perform inclusion operations on
imaginedclassesofobjectsandcanconsiderthatahypotheticalclass includesand is“largerthan” its
constituentsubclass.Thus,knowledgeofclassificationdoesnotmerelyinvolvefactsbutactionsaswell:
physical sorting, mental sorting, mental inclusion operations. Furthermore, most of these actions are
nonverbal.
Since learning occurs through the child’s activity, structured teaching methods, such as
programmedlearningoraudiovisualaids,shouldbedeemphasizedinfavorofmore“active”methods.
Instead of attempting to impart truths, teachers should set up situationswhichwill lead the child to
question,toexperiment,andtodiscoverfactsandrelationships.Childrenneedtobeencouragedintheir
exploratory frame of mind. This occurs naturally in the very young child, who is constantly
experimentingwithobjects,language,andsituationstounderstandmoreabouttheworld.Yetoncehe
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startsgoingtoschool,heseemstoceasebeinganexperimenter.Whathashappenedtoextinguishthis
desirefordiscovery?Inschool,explorationisoftendiscouragedentirely.Andwhenitdoestakeplace,the
teacher—notthechild—isusuallytheexperimenter.Underthesecircumstances, thechild learnsvery
little, becomes disinterested, and losesmotivation. Teachers should therefore present the child with
materialsandsituationsthatencouragethedesignofhisownexperiments.Thiswill inturnleadtoa
deeperandmorelong-lastingknowledgethanwillarotememorizationoffactspresentedbyteachersor
intextbooks.
WehaveseenthatPiaget’stheorystressestheroleofactivityineducation.Itshouldbeclearthat
Piaget’sintentionisnottoglorifyactivityforitsownsake.Instead,it istopointoutthatactivity,when
channeledincertaindirections,leadstothegoalofgenuinelearning.Asweshallseenext,thenotionof
reinventionprovidesanunderstandingofthegoal,genuinelearning.
Reinvention
Supposethatthechildhasbeenencouragedtoengageinactiveexplorationandthattheeducator
has taken pains to guide the process of equilibration in a manner sensitive to the child’s cognitive
abilitiesandneeds.Thegoadofallthisactivityistoproducegenuineunderstanding.Aswehaveseen,
thisdoesnot involve themere repetitionof simple facts.Genuineunderstanding is insteada process of
reinvention.AsPiagetputsit,“readcomprehensionofanotionortheoryimpliesthereinventionofthis
theorybythesubject”(Piaget,“CommentsonMathematicalEducation,”1977a,p.731).
Piagetdescribesthereinventionprocessasfollows.Atfirst,thechildengagesinconcreteactivities
involvinganotionlikecardinalnumber.Forexample,hemayspontaneouslycountalineofobjectsfirst
from left to right and then from right to left.Activities suchas these, spontaneously generatedby the
child,leadtotheunderstandingofkeyprinciples.Hefinds,forexample,thatifyoucountasetfromright
toleft,yougetthesamenumberaswhenyoucountfromlefttoright.
In thePiagetian view,we can say that the child has reinvented a key aspect of the principle of
cardinality.Thenotionofreinventionisusedsincetheconceptwasnotsimplytransmittedfromteacher
tochild;instead,thechildwasputinapositionwherehisownspontaneousactivityledtothecreationof
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the concept. Thus, when the child gets the same number regardless of the direction of counting, he
concludesonhisownthatdirectionalitymakesnodifferenceforcounting.This“concludingonhisown”is
theessenceofreinvention.
The understanding which results from reinvention, Piaget maintains, is more genuine and
powerfulthanisthatprovidedthroughstructuredteachingandpassivelearning.Oneindicationofthe
reinventedconcept’spoweristhatthechildspontaneouslyusesitinnewsituations,asifheistestingits
generality. The childwho receives the concept in a passive fashion is less likely to engage in active
generalizationofthistype.
Atthesametime,Piagetpointsoutakeylimitationtothechild’sreinventedunderstanding:“the
pupilwillbefarmorecapableofdoingandunderstandinginactionsthanofexpressinghimselfverbally
... a large part of the structures the child uses when he sets out actively to solve a problem are
unconscious”(Piaget,1977a,p.731).Sothechild’sreinventionleadstoagenuineunderstanding,but
onethatisnotyetcapableofexpressiononaconscious,verballevel.
Theachievementofahigherlevelofunderstandingshouldbedelayeduntilalatertime.AsPiaget
putit,“formalization[inmathematics]shouldbekeptforalatermomentasatypeofsystematizationof
thenotionsalreadyacquired.Thiscertainlymeanstheuseofintuitionsbeforeaxiomatization”(inPiaget,
1977a, p. 732). In otherwords, formalization should be introduced only after the child has become
comfortablewithhis“informalnotions”andonlywithmuchassistanceonthepartoftheteacher.Indeed,
one of the teacher’s main responsibilities is to help the child achieve an explicit consciousness,
expression,andformalizationofhis“intuitiveknowledge.”Inalatersection(oncurriculum),weshall
explore the process of helping the child to make a transition between these different levels of
understanding.
Individualized Learning
Piaget’s theory stresses that current cognitive structuresandnewexperiences interact toarouse
interest and stimulate the subsequent development of understanding. Interest and learning are best
facilitatediftheexperiencepresentedtothechildbearssomerelevancetowhathealreadyknows,butis
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atthesametimesufficientlynoveltopresentincongruitiesandconflicts.Inotherwords,Piagetproposes
thatthechild’sinterestisarousedwhenanexperienceismoderatelynovel(recallthediscussionofthe
moderatenoveltyprincipleduringinfancy).Thismeansthattheexperienceisnotsoradicallynovelthat
the child cannot assimilate it into current cognitive structures, and it is not so familiar as to be
immediatelyandeffortlesslyassimilated,andthusoflittleinterest.Theprincipleisrelativistic:byitself
an event does not possess some degree of interest. Rather, interest is derived from the interaction
between the state of the child’smind and theproperties of the thing to be known.At the same time,
moderatelynovelexperiencespresentthechildwithcognitiveconflict.Andaccordingtothetheoryof
equilibration,theseconflictsserveasthebasisforreorganizationofcognitivestructuresandsubsequent
development.
The situation with regard to interest and conflict is complicated by the fact that there is
considerablevariationamongchildrenofthesameageintheirrateofdevelopment.Wehaveseenthat
somechildrenwithinagivencultureacquireconservation,forexample,atage5andothersnotuntil8.
Consequently,inanyclassofthirtytofiftychildren,therearewidedifferencesamongchildreninlevels
ofcognitivefunctioning.Becausetheselevelsvary,thechildren’sinterests,whicharedeterminedbyan
interactionbetweenthecurrentlevelofcognitivefunctioningandexperience,willalsovary.Theteacher
isthereforeinevitablyfacedwithawidevariationamongstudentsinbothcognitivelevelandinterest.
Todealwiththis,theremustbeextensivechangesinclassroompractice.First,teachersshouldbe
aware of the child’s current level of functioning. To some extent the teacher can rely on Piaget’s
discoveriesforthisinformation.ButPiaget’sworkcoversonlyalimitednumberofthosetopicsusually
studiedinschool.Therefore,theteacherhimselfmustmakeanassessmentofhisstudents’capabilities.
Onceobtained,thisknowledgewillhelptheteachertocreatesituationsintendedtoprovokethechildto
questionandexperiment.Theteachermayalsoselectsuitablecounterargumentswhichwillencourage
thechildtoclarifyhisthinking.Knowledgeofstudents’functioningwillalsohelptheteachertopresent
theconflictsituations that,aswehaveseen fromthe trainingresearchcarriedout inGeneva,areone
importantmechanismofconceptualgrowth.
Theassessmentofintellectuallevelisnotaneasytask.Theevaluationmustbedifferentfromthe
usualstandardachievementtestswhichoftenmeasureonlysurfaceknowledge,rotememory,andother
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superficial aspects of learning. The teacherwill have to evaluate not only the products of thought—
correct or incorrect answers—but the process of students’ thinking aswell. The teacherwill need to
observethechildrencarefullyandattempttodiscoverboththeircompetenciesandtheirweaknessesin
anyarea.Withoutsuchevaluation,theteacherwillfinditdifficulttojudgebetweenwhatismoderately
novelandthuslikelytoarouseinterest,betweenwhatisalreadyknownortooadvancedforthepupilat
thisstageofdevelopment,andbetweenwhatisorisnotaconflictsituationforeachindividualstudent.
Oncetheteacherrecognizesthechild’scurrentleveloffunctioninghecancreateexperienceswhichwill
promoteinterest,arouseconflict,andfacilitatedevelopmentforthestudent.
Second,teachingshouldbeorientedmoretowardtheindividualstudentthantheoverallgroup.
Sincetherearegreatindividualdifferencesinalmostallareasofcognitivedevelopment, it isunlikely
thatanyonetaskorlessonwillarousetheinterestoforpromotelearninginallmembersoftheclass.For
somechildren,aspecifictaskmaybetooeasilyassimilatedintocurrentmentalstructures,whileforother
studentsthesameproblemmayrequiretoogreatadegreeofaccommodationforthemattheirpresent
stage of development. The result is boredom for the first group and confusion for the second. Third,
childrenmustalsobegivenconsiderablecontrolovertheirownlearning.Somemayneedmoretimethan
otherstodealwiththesamematerial;similarly,childrenmayapproachthesameproblemindifferent
ways.
Topromoteinterestandlearning,then,theteachershouldtailorthecurriculumtothelearnerand
trytoindividualizeteachingasmuchaspossible.Thismeansthatthelargegroupshouldeffectivelybe
disbandedasthesoleclassroomunit,thatchildrenshouldoftenworkonindividualprojects,andthat
theyshouldbeallowedadegreeoffreedomintheirownlearning.Severalobjectionsareusuallyraised
tothissortofaproposal.Underanindividuallearningarrangement,wouldnotchildrenwastetheirtime
orengage inmereplay?Onemaycounter thisargumentbynotingthat the teachermaydependona
certainamountofspontaneousintellectualmotivationinchildren,particularlyyoungerones.Piagethas
shownthatthechildisquiteactiveinacquiringknowledge,andthathelearnsaboutimportantaspectsof
realityquiteapart frominstruction in theschools. In the first twoyearsof life, forexample, the infant
acquiresaprimitiveunderstandingofcausality,ofthenatureofobjects,ofrelations,oflanguageandof
manyotherthings—largelywithoutthebenefitofformalinstructionoradult“teaching.”Oneneedonly
watchaninfantforashortperiodoftimetoknowthatheiscurious,interestedintheworldsurrounding
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him,andeagerto learn.Thesamecanalsobesaidofolderchildrenandissupportedbythefactthat
someschoolsmanagetooperateindividualizedprogramswithagooddeadofsuccess.Inaddition,one
mustrememberthatindividualizedinstructiondoesnotrequiretheabrogationofresponsibilityonthe
partoftheteacher.Indeed,themoreindividualizedthelearning,theheaviertheburdenontheteacher.
The teacher must assess the student’s level, assign relevant learning experiences, and generally
supervisetheentirelearningprocess.Gettingchildrentowork“ontheirown”requiresaconsiderable
contributiononthepartoftheteacher.
Indeed, the burden is so heavy that teachers often feel that the provision of individualized
instructioninlargeclasses(betweentwentytofiftychildren)isanentirelyunrealisticandimpractical
solution.It istruethat in largeclassesnosingleteachercaneffectivelytailoracurriculumtomeetthe
specificcognitiveneedsofeverypupilateverymomentoftheteachingday.Andfromanotherpointof
view,itmightnotevenbeagoodideatohavetwenty,thirty,orfiftyindividuallearners,all“doingtheir
own thing’ ’ since some of the advantages of group learningwould be lost in the process. Yet,when
covering topics where there are obvious differences among children in their understanding of the
material,teacherscandividetheclassintosmallgroupsofchildrenatapproximatelythesamelevel.For
othertopics,allchildrencanworkindividuallyattheirownlevel,whileforstillothertopicstheentire
class canbe joined together.Theessentialpoint is that teachingneeds tobe flexible; the teacher can
employacombinationofgroupandindividualinstruction.
What the student needs, then, are opportunities to learn in a rich environmentwhich contains
manypotentiallyinterestingelements.Thestudents’needsateacherwhoissensitivetohisaffectiveand
cognitiveneeds;whocanjudgewhatmaterialswillchallengehimatagivenpointintime;whoisableto
evaluate his level of functioning and present new ideas at a level consistent with the student’s
intellectual and linguistic development; who can present this knowledge in a way that arouses the
child’s interestandactivity;andwhocanhelpthestudentswhennecessaryandwhohasfaith inthe
child’scapacitytolearn.
Social Interaction
InPiaget’s view, physical experience and concretemanipulation are not the only influences on
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learning.Anotherfactorthatleadstothedevelopmentofknowledgeissocialexperienceorinteraction
withotherpersons.WhilePiagethasnotwrittenextensivelyonthistopic,hisworkcontainsanumberof
importantimplicationsconcerningtheroleofpeersintheeducationalprocess.
The effects of social experience, although almost negligible during the first fewmonths of life,
become increasingly important as the child grows older.Wehavepointed out earlier that one of the
primedeterrents toanobjectiveunderstandingofreality is thechild’segocentric thought.At first, the
childcannotviewpeople,objects,orevents inthesurroundingworldobjectivelybecausehecanonly
perceivethemastheyrelatetohimself.Theveryyoungchildassimilatesexternaleventsdirectlyintohis
ownactionschemes.Objectsoreventsareonlyrelevanttotheextentthattheyconcernthechild’sown
privatepreoccupations.Hecannotviewobjectsoreventsfromanyperspectiveexcepthisown,andthis
egocentrismofcoursepreventshimfromgaininganobjectiveviewofobjectsorofpersons.Gradually,as
thechildbecomescapableofdecenteringhisattention,ashebeginstofocussimultaneouslyonvarious
aspectsofreality,andashecomestounderstandanotherperson’spointofview,thenhegainsamore
objectiveknowledgeofreality.
Onemethodwhich promotes the relinquishment of egocentrism is social interaction.When one
childtalkstoanother,hecomestorealizethathiswayofviewingthingsisnottheonlyperspective.The
childseesthatotherpeopledonotnecessarilysharehisopinions.Socialinteractioninevitablyleadsto
arguments and discussion: the child’s views are questioned, and he must defend and justify his
opinions. This action forces the child to clarify his thoughts, for if hewants to convince others of the
validityofhisownviews, thechildmustpresentthemclearlyand logically. Inaddition,otherpeople
maynotbeastolerantofhisinconsistenciesasisthechildhimself,andtheydonothesitatetopointthem
out.Thussocialinteractionhelpsthechildtorecognizetheshortcomingsinhisthinkingandforceshim
toseeotherpointsofviewwhichmayconflictwithhisown.Suchconflictsinschemesorideasareoneof
themechanismsofprogress.Therefore,weseethat,inadditiontothemorecommonlystressedaffective
sideofsocialinteraction—theneedtogetalongwithotherpeople—thereisalsoanimportantcognitive
component.Socialexperiencenotonlyhelpspeopletoadjusttoothersatanemotionallevel,butitalso
servestoclarifyaperson’sthinkingandultimatelyhelpshimtobecomemorecoherentandlogical.
Itshouldbemadeclearthatsocialexperience isnot independentofphysicalexperience.Verbal
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exchangeofopinions,forexample,isnotfeasibleoncertainsubjectsuntilthechildhastheexperienceof
manipulatingobjects.Duringtheearlystagesofdevelopment,physicalexperienceisespeciallycrucial.
Yet once the child has acted on an object or a situation, language can then serve as amajor tool to
internalizetheexperienceintoacompactcategory.Thechildcanalsouselanguagetocommunicatean
understandingof experience to others. Indeed, the very attempt to communicatepermits the child to
makeexplicitcertainaspectsofexperiencewhichwereatfirstunderstoodonlyatthelevelofaction.The
child’s activity andexperience areofparamount importanceduring the early stagesofdevelopment;
laterverbalcommunicationandsocialinteractionhelptodefineandconceptualizethisexperience.
TheimplicationofPiaget’sview,therefore,isthatsocialinteractionshouldplayasignificantrolein
theclassroom.Childrenshouldconverse,shareexperiencesandargue,fortheseareallmajortoolsinthe
acquisitionofknowledge.
Curriculum
Intheprecedingsections,wehavereviewedvariouseducationalprinciples.Mostrefertogeneral
aspects of the learning process and in themselves do not represent a completely novel approach to
education.Manyofthesepointshavealreadybeenemphasizedbyeducationalphilosophers.Theroleof
activityinlearningwasdiscussedbyRousseauandDewey,andtheprincipleofindividualizedlearning
hassomecommonalitywithSkinner’sconceptsofprogrammedinstruction.Piaget’sresearchaddsnew
empiricaldatainsupportoftheseprinciples,buttheeducationalprinciplesthemselvesarenotnew.The
uniqueness of Piaget’s contribution to education lies in other areas, particularly in his detailed
descriptionof thedevelopmentofnumerousphysical, logical, andmathematical concepts inchildren,
andinhisaccountofthegeneraldevelopmentofthinking.Thistypeofknowledgewasnotavailableto
other educational theorists such as Rousseau or Dewey. A number of the concepts which Piaget has
investigatedareparticularlyrelevanttoeducation,sincetheyaretaughteitherdirectlyorindirectlyin
schools.Forexample,whileconservationoflengthisnotusuallytaughtinschools,itisaprerequisitefor
theunderstandingofmeasurement,whichistaught.Knowledgeofthechild’scognitivelevelandofthe
child’sunderstandingofparticularconceptscanbeusedtofacilitateeducationinseveralways.
Limits.Ontheonehand,researchconcerningthechild’scognitiveleveldemonstratesthatthereare
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limitationsonwhat the child can learn.Thechild’s thoughtdevelops througha seriesof stages, each
showingbothstrengthsandweaknesses.Anyonestageischaracterizedbytheabilitytoperformcertain
actionsand,ontheotherhand,bythepropensitytocommitparticularerrors.Oneimplicationofthestage
theoryisinaway“pessimistic.”Sinceintellectualdevelopmentseemstofollowanorderedsequence—a
sequencewhich,untilproof to the contrary, appears tobeuniversal—theyoungchild is incapableof
learningcertainkindsofconcepts.Itwouldservenopurpose,forinstance,totrytoteachachildofthe
preoperationalperiodtheprincipleofinertia,oranyotherabstractnotionwhichrequirestheexistence
ofreasoningataformaloperational level.Somethingscannotbetaughtatanylevel,regardlessofthe
methodadopted.Itisofcoursepossibletoacceleratesometypesoflearningthroughtheuseofsuitable
environmentalstimuli.Forinstance,ifachildofthepreoperationalperiodisfairlyclosetoachievingthe
structureofconcreteoperations,suitablephysicalexperiencemayexpeditetheprocess,withtheresult
thatthestructuremaybeacquiredsomewhatearlierthanifnosuchexperiencehadbeenpresented.But
aswehaveseen,suchaccelerationispossibleonlyifthechildisinatransitionalstage.
Given these limitations on children’s learning, the educator can respond in several ways. One
strategyistodelaytheteachingofcertainsubjectsuntilchildrenarepresumed“ready”tounderstand
them.Tosomeextent,thisstrategyisobviouslyreasonable:itmakesnosensetoteachcalculustothe5-
year-old.Ontheotherhand,thisapproachcanbeappliedinanoverly-zealousmanner.Thus,onemight
proposethatsinceelementaryschoolchildrencannotemployformaloperations,scienceshouldnotbe
taught until adolescence, when it is possible to reason in a hypothetico-deductive manner. Such a
practicewouldbeunfortunatebecauseevenyoungchildrencanunderstandsomethingofscienceona
level appropriate to their own cognitive abilities. For the concrete operational child, science could
involveagooddealofphysicalexperiencewhichmightleadtoformaloperationalthought.Similarly,in
mathematics,whilepreoperationalchildrencannotfullyunderstandequivalence,theycanprofitfrom
considerableexperienceinthecountingofconcreteobjects.Oftensuchconcreteactivityisaprerequisite
formoreabstractunderstanding.Inbrief,whilelimitationsinchildren’scognitiveabilitiespreventthem
fromlearningcertainconcepts,oneshouldnotforgetthatpreparatorywork,usuallyofaconcretenature,
isoftendesirableandevennecessaryforlaterunderstanding.Hence,despitethelimits,oneshouldnot
giveuponyoungchildren’s learningof certain concepts,but should searchoutappropriateways for
themtoengageinpreparatoryactivities.6
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Strengths. At the same time, there is amore “optimistic” side to Piaget’s theory. At each stage of
development,thechildiscapableofcertainformsofthought,ofspecificconcepts.Forexample,Piagethas
found that concepts of topological geometry (distinctions between closed versus open figures, etc.)
develop in the childbefore thoseofEuclideangeometry (measurementof angles, distances, etc.) and
projective geometry (measurement of perspectives, coordinates, etc.). Understanding of topological
notionsappearsfairlyearlyinlife,whereasthechildonlybeginstounderstandthenotionsofEuclidean
and projective geometry at around 7 years of age. Thus, while the 5-year-old may be incapable of
learning projective concepts, he has already developed an intuitive understanding of topological
notions.Eachstageofdevelopmentischaracterizedbystrengthsaswellasweaknesses.Knowledgeof
thestrengthsaswellasofthelimitationscanbeusedtoimproveeducationinseveralways.Onepossible
improvementisadetailedevaluationandmodificationofexistingcurricula.Thistypeofworkisbeing
carried outmore andmore extensively in several countries. For example, Shayer (1972; 1974) has
workedwithanumberof science courses (chemistry,physics, biology) commonlygiven in theUnited
Kingdom.Hehas tried, for each topic covered, to assess theminimumconceptual level required for a
pupiltobeinterestedinandtograsptheparticularconceptinvolved.Shayerattemptstodeterminehow
suitablethecoursesandspecificconceptsareinrelationtothedevelopmentallevelsofthestudents.Asa
result of these investigations, he suggests that many learning problems may be due to a mismatch
betweentheconceptuallevelofthemajorityofpupilsandtheconceptsbeingpresented.Suchwork—
assessingstudents’strengthsandweaknessesinrelationtothematerialtaught—caneventuallyleadto
thedevelopmentofnewandmoreeffectivecurricula.
Knowledgeofstudents’ intellectualstrengthscan leadto the improvementofeducation inother
ways,too.Inparticular,itcanproduceanoptimisticviewconcerningstudents’potentialandthecreation
of new learning opportunities. Piaget’s theory shows that by the age of 5 or 6, when they are
simultaneously entering school and theperiodof concrete operations,most childrenhavedeveloped
remarkably sophisticated intellectual processes. By this age, most children already possess the
intellectual prerequisites for understanding a good deal of what is taught in elementary school. For
example,children’sspontaneousconceptofnumberissuchthattheyshouldhavenoparticulardifficulty
withthemostnotoriousofschoolsubjects,namely,arithmetic.Asaresultofnaturaldevelopment,they
understand ideasofone-to-onecorrespondence,equivalence,additivity—that is, theconcepts forming
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thefoundationforagooddealofschoolarithmetic.Inotherwords,Piaget’stheorysuggeststhatvirtually
allchildrenpossessthecognitiveequipmentfordoingstandardacademicwork.Whatistaughtinschool
should easily be assimilated into the existing cognitive framework. Piaget feels that it is difficult to
understandhowstudents“whoarewellendowedwhenitcomestotheelaborationandutilizationofthe
spontaneous [patterns] of intelligence can find themselves handicapped in the comprehension’’ of
academicsubjects(Piaget,
ScienceofEducation,1970c,p.4).Theteachershouldthereforeseriouslyconsiderthenotionthat
theeducationofchildrencanrelyonsomealreadyexistingintellectualassets.Problemsinlearningare
notlikelytostemfromfundamentalintellectualdeficitsinthechild.Giventhisnotion,theeducatorcan
devisecurriculawhichattempttoexploitthechild’sstrengths.If,forexample,thepreoperationalchildis
capableofunderstanding“functions,” thentheeducatormayelaborateonthisconcept. If theconcrete
operationalchildcandealwithcomplexformsofequivalence,thentheeducatormaytrytoexploitthis
informalknowledge.Thenaturalcourseofdevelopment—thespontaneousappearanceof intellectual
capabilities—provides important opportunities for the fostering of academic knowledge and should
therefore exert a strong influence on the nature of curriculum. The educator should also expect that
children will have little difficulty in mastering school work because of their natural intellectual
strengths.
Intuitionandconsciousness.Weallknowthatdespitechildren’sintellectualstrengths,theteaching
ofcertainsubjectsdoesnotgoassmoothlyasitmight.Arithmeticisaprimeexample.Althoughchildren
already possess spontaneous notions of basic mathematical ideas, they usually have a terrible time
learningschoolarithmetic.Whyshouldthisbeso?Thereare,ofcourse,manydifferentkindsofreasons,
butperhapsPiaget’snotionofdifferentlevelsofunderstandingcanshedsomelightontheissue.
Thefirstoftheselevelsismotoricorpracticalunderstanding.Thisisthelevelofaction.Thechild
canactdirectlyonobjectsandmanipulatethemcorrectly,makingtheobjectsdowhattheyaresupposed
to do. All this indicates that the child has “understood” objects at the level ofmotor responses. This
knowledge is preserved in the form of schemes, which allow the actions to be repeated in identical
situationsandgeneralized tonewones.Another levelofunderstanding isconceptualization.Here the
childreconstructsinternallytheactionsthatwerepreviouslyperformeddirectlyonobjects,andatthe
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same time adds new characteristics to these actions. He organizes themental activities and provides
logicalconnections.Atthesametime,muchofthechild’sintellectualworkremainsunconscious.Aswe
sawinreviewingPiaget’sworkonconsciousness,thechildisoftencapableofmentaloperationsthathe
isnotawareofandcannotexpress.Athirdlevelofknowledgeinvolvesconsciousnessandverbalizations.
Now the child can dealwith concepts on an abstract level and can express hismental operations in
words.Thechildcanreflectonhisownthought.
At all stages of intellectual development, children find it easier to act—either behaviorally or
mentally—thantoachieveconsciousnessoftheiractions.Consciousnessandverbalizationarerelatively
latedevelopments,andtheiremergencemaydependonpriorunderstandingatthelowerlevels.
The existence of different levels of understanding—practical, conceptual, and conscious—has
importantimplicationsforeducation.Wehavealreadyseenthatateverystageofcognitivedevelopment
thechildpossessesbasicintellectualstrengths.Usuallytheseinvolveunderstandingattheunconscious
levels,thatis,motoricandconceptualunderstanding.Bycontrast,schoollearningtypicallyoperatesatan
exclusively verbal and formalized level. The child’s spontaneous mathematics is informal and
unconscious;thearithmetictaughtinschoolisformalandhighlyverbalized.ForPiaget,then,oneofthe
key problems of education involves “finding the most adequate method for bridging the transition
between these natural but nonreflective structures [that is, understanding of the first two types] to
consciousreflectionuponsuchstructuresandtoatheoreticalformulationofthem”(ScienceofEducation,
1970c,p.47).Piagetrecommendsgraduallybuildingonwhatthechildalreadyknows—onthechild’s
actionsorunverbalized“intuitions”—toachieveasubsequentformalization.
Perhaps there is a paradox here: to foster true abstraction and consciousness, one must first
encourage the concreteandunconscious.Of course, thisdoesnotmean that all learningmustalways
involvethemanipulationofconcreteobjects.Theadolescentinthestageofformaloperationsmayprofit
fromverbalorwrittenmaterial,providedthatinthecourseofdevelopmenthehasalreadyacquireda
gooddealofmotoricandconceptualknowledgecorrespondingtotheabstractioninquestion.If,however,
theformaloperationallearnerencountershighlyabstractmaterialwithwhichhehashadnorelevant
previousexperience,thenforhim(liketheyoungerchild)lowerlevelsofunderstandingmayhelpto
serveasafoundationforconsciousness.Formostofus,trulyabstractunderstandingcanbeachievedonly
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throughimmersionintheconcrete.Inbrief,oneofthechieftasksofeducationistheeliminationofthe
gapbetweenthechild’sinformedmodesofunderstanding,whichPiagethasdescribedinsomedetail,
andtheformalitiestaughtinschool.
A caution. A word of caution is necessary with regard to the use of actual Piagetian tasks or
experiments in the school curriculum.Since conservation is an indicator that the childhas reacheda
certainstageofdevelopmentorhasacquiredacertaincognitivestructure,someeducatorsbelievethat
thedirectteachingofconservationwillautomaticallypromotethedevelopmentofthechild’sunderlying
cognitivestructure.Piaget’stasksarethereforebeingusedasteachingdevices,asbasicsubjectmatterin
thecurriculum.Thisseemstomakelittlesense.Learningthecorrectresponsestocertainspecifictasks
doesnotmeanthatachildwill reach thesame intellectual levelasanotherchildwhospontaneously
gives the correct responses to the same task. The only result of instruction in Piagetian concepts is
generally that the child acquires some very localized learning in the narrow sense, which does not
promotegeneralprogressinotherareasofcognition.Suchinstructionisthereforeofratherlimitedvalue,
especiallysincethecognitivestructuresnormallydevelopinaspontaneousfashion,quitewithoutthe
“benefit”ofeducation.
Clinical Method
AswehaveseeninChapter1,itwasveryearlyinhiscareerthatPiagetrejectedstandardtestsasa
useful tool for the studyof cognitivedevelopment. Such tests, he felt, fail to give a good indicationof
underlying cognitive processes. Piaget now feels that standard tests are not particularly useful for
educational purposes, either. Indeed, he considers the tests to be a “veritable plague on education”
(quoted by Elkind, 1976, p. 192). For Piaget the preferred method is the clinical interview. This
technique isnotmerelypreliminary, nor is it sloppyorunscientific. It is instead themostuseful and
“valid”methodcurrentlyavailableforthestudyofthinking.Theclinicalmethodhasanimportantroleto
play in education, too, particularly in the areas of assessment and diagnosis. By the use of suitable
probing questions that attempt to reveal the underlying reasons for a child’s initial statement or
judgment, by presenting countersuggestions to the child’s arguments, and by providing conflict
situations, the teacher who employs this method can discover a great deal about a child’s cognitive
functioning. In theclinicalmethod, the interviewermustobserveand listento thechildcarefullyand
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mustadaptboththepaceandthelevelofthequestioningtotheindividualchildwhois interviewed.
Standardizationmustbeavoided.Itisnotthepurposeoftheinterviewtofindoutonlywhetherachildis
abletoansweracertainquestioncorrectlyornot,buttouncoverunderlyingcognitiveprocesses.Incorrect
answers in particular provide the interviewer with an indication of the child’s current state of
knowledge.
Theclinicalmethodneednotbe restricted toPiagetian tasks, likeconservationor seriation.The
method can be used in any situation inwhich the objective is the exploration of the child’s thought
processes.Hence,itisquiteappropriate,andwethinkveryuseful,toemploythemethodtoexaminethe
child’s understanding of academic subject matter. For example, clinical interviewing has proved
successfulintheinvestigationofelementaryschoolchildren’sproblemsinlearningarithmetic(Ginsburg,
1982).Teachersattemptingtoassesstheirpupils’functioningmightthereforefindthemethodauseful
diagnostictoolinmanyareasofclassroomlearning.Thetechniqueisparticularlyvaluableinidentifying
theintellectualdifficultieswhichunderlielearningproblems.
Anotherandmoreindirectuseofthemethodmightbemadeinprogramswhichattempttotrain
prospective teachers in questioning skills for use in teaching situations. There aremany similarities
betweentheclinicalinterviewandthe“Socratic”questioningtechniqueintheclassroom.Forinstance,in
agrouporindividualsetting,askillfulteacherdoesnotsimplyaskquestionswhichrequiretherecallof
correctanswers;evenmoreimportant,heasksprovocativequestionsthatstimulatethepupil tothink,
and to become aware of underlying causes. This requires questions that probe into the “whys” of
situations.Inaddition,teachersneedtoadaptthelevelandpaceoftheirquestionstotheunderstanding
ofpupils;teachersneedtobeabletolistenandobservetounderstandthemeaningofaresponse.These
skillsofquestioning,sensitivity,andinterpretationareallstressedintheclinicalinterview.
These, then,are twoways inwhichPiaget’sclinicalmethodcanbeused ineducation: first,asa
meansofassessmentdifferentfromstandardtestsinbothitsflexibleprocedureanditsaimofassessing
cognitivestructure,and,second,asameansofdevelopingintheprospectiveteacherasensitivitytoward
learnersandthequestioningskillsessentialforinstruction.
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Future Directions
During the period from 1960 to 1980, psychological and educational researchers carried out
numerous studies based on the structural aspects of Piaget’s theory, that is, the stages of cognitive
development,conceptsofconservation,classification,orseriation.Educatorsinparticularbelievedthat
anoveralltheoryofhumanintellectualdevelopmentshouldbeabletoprovideinsightsthatwouldhelp
them in their teaching in the classroom.These studies have resulted in a certain amount of perhaps
predictabledisenchantmentanddisappointment.Expectationsweretoohigh.Itisdifficulttoseehowa
theorythatemphasizesfourbroadstagesofdevelopmentcouldprovideusefulinsightsforateacherwho
teaches childrenover the relatively shortperiodofoneyear, just as it isdifficult to imaginehow the
studyofconservation,whichisnotaconcepttaughtinschool,couldbeofanydirectbenefittotheteacher.
Piaget’s laterworkintotheprocessesofcognitivedevelopmentandthemechanismsof learningoffers
more scope for both cognitive psychology and education. This later functional approach to cognitive
development, however, like the early structuralwork, doesnothavedirect applications to education.
Beforeitcanhelptheteacherintheclassroomsetting,agreatdealofresearchisneeded.Butitprovidesa
frameworkforthestudyandanalysisoftheprocessesbywhichlearnersacquirewhatitisteachersare
tryingtoteachandcouldresultininsightsintoclassroomteachingandlearning.Threemainareasofthis
laterworkhavepotentialapplicationstoeducation.
The first is related to Piaget’s distinction among three types of knowledge: social, physical, and
logicomathematical.Thedifferentnatureofeachtypecallsfordifferenttypesofteachingmethods.Social
knowledgecallsfordidacticmethods;physicalknowledgeisbestpromotedthroughthemanipulation,
exploration, and discovery of objects; and logicomathematical knowledge requires construction,
reinvention,andreflectiononactionsandcoordinations.Atpresent,teachershaveatendencynotonlyto
treat all knowledge as if it were of the same type, but in many cases to treat it as if it were social
knowledge and best promoted through errorless learning. While this type of learning may be
appropriateforsocialknowledge,itmaynotnecessarilybesuitablefortheothertwotypes.If,asPiaget
claims, it is disequilibrium, disturbance, or conflict that motivates the search for better forms of
knowledge, thenthe learningofphysicaland logicomathematicalknowledgewouldcall forsituations
withsomeelementofconflict.
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Ifaparticularsubjectmattercouldbeanalyzedintermsofthesethreetypesofknowledge,andthe
kindsofconflictlikelytoleadtolearning,thenteachingappropriatetoeachtypecouldbedesigned.This
mightresultinmorevaried,interesting,andeffectiveteachingmethodsthanthosecurrentlyadopted.
AnotherareaofPiaget’stheorywithindirectapplicationtoeducationisthatofthealpha,beta,and
gamma reactions to disturbances. Here again, specific subject matters could be analyzed with these
concepts in mind and appropriate teaching methods and situations designed for each level. Alpha
reactions would require situations which enable the learner to become more aware of disturbing
elements.Learnersatthebetalevelneedsituationsthathelpthemtoexploreandconstructvariations
and compromise solutions,whereas learners at the gamma levelneed tobehelped to integrate their
morematureunderstandingofoneparticularareaofknowledgewithotherareas.
ThethirdareainwhichPiaget’sworkcanprovideaheuristicframeworkforeducationalresearch
coversspecificprinciplesof theequilibrationprocess, suchasdifferentiationand integration,and the
relativization and quantification of concepts. For any specific area of academic learning, researchers
couldidentifytheprocessesinvolved,suchasthetypeofdifferentiationsandintegrationsthatoccur,the
sequenceandnatureofrelativizations,thecharacteristicsthatarequantifiedforanyparticularconcept,
theinterrelationshipsbetweenthesequantifications,andsoon.Understandingofthedynamicsofthese
processes for an academic subject could then help educators to set up appropriate teaching-learning
situations.
Thisapproachtoteachingandlearningwouldbearadicalchangefrompastpractices.Ifadopted,
theeducator,ratherthanlookingatteachingfromthepointofviewoftheacademicsubjecttobelearned
oratwhathasprovedsuccessfulinthepast,wouldapproachtheteaching-learningsituationfromthe
pointofviewofthe learnerandhowthis learnerspontaneouslyacquiresknowledge.Webelievethat
this constructivist, genetic epistemological approach to the classroom setting, based on the functional
aspects of Piaget’s theory, could prove to be an extremely fruitful method of collaboration between
psychologyandeducationandcouldleadtoimportantcurriculumdevelopmentsinthefuture.
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Summary and Conclusions
WehavereviewedsomeofthemajorimplicationsofPiaget’sviewsforeducationalpractice.While
Piagethasnotbeenmainlyconcernedwithschools,onecanderivefromhistheoryanumberofgeneral
principleswhichmayguideeducationalprocedures.Thefirstoftheseisthatthechild’slanguageand
thoughtaredifferentfromtheadult’s.Theteachermustbecognizantofthisandmustthereforeobserve
childrenverycloselyinanattempttodiscovertheiruniqueperspectives.Second,childrenneedtoacton
thingstolearn.Formedverbalinstructionisgenerallyineffective,especiallyforyoungchildren.Activity
constitutesamajorportionofgenuineknowledge;themerepassivereceptionoffactsorconceptsisonly
aminorpartofrealunderstanding.Third,childrenaremostinterestedandlearnbestwhenexperience
ismoderatelynovel.Whenanewevent isboth familiarenoughso that itmaybeassimilatedwithout
distortionintocurrentcognitivestructure,andnovelenoughsothatitproducessomedegreeofconflict,
theninterestandlearningarepromoted.Sinceatagivenagelevelchildren’scognitivestructuresdiffer,
allchildrenwillnotfindthesameneweventinteresting,norwilltheylearnfromit.Thisimpliesthat
successfulgroupinstructionisalmostimpossible.Childrenshouldworkindividually,withfreedom,at
tasks of their own choosing. Piaget finds, too, that an important aspect of learning is self-regulation.
Beforeenteringschool,andwithoutadult instruction,thechildlearnsinmanyways.Fourth,children
shouldhavetheopportunitytotalkwithoneanotherinschool,toargueanddebate.Socialinteraction,
particularlywhenitiscenteredonrelevantphysicalexperience,promotesintellectualgrowth.
Fifth,oneofPiaget’smajorcontributionstoeducationliesintheprovisionofextensivedataonthe
developmentinchildrenofbasicmathematical,logical,andscientificconcepts,andthusonthegeneral
developmentof thinking.This informationcanbeusedtodeterminethe limitsonchildren’sability to
learn, toevaluatecurricula, todevelopnew learningexperiences, and toeliminate thegapsbetween
intuitionandconsciousness.Sixth,Piaget’sclinicalmethodcanbeusedasaneffectiveaidindiagnosis
and assessment, and in helping teachers acquire thequestioning skills useful for promoting genuine
learning in the classroom. Finally, Piaget’s theory of equilibration has implications for the conduct of
teaching.
It should be clear that these views are at variancewithmany of the assumptions of traditional
education.According toPiaget’sevidenceandtheory,studentsofagivenage leveldonotandcannot
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learn essentially the same material; they learn only in a minor way through verbal explanation or
writtenexposition(concreteexperiencemustcomefirst);theycananddoexertcontrolovertheirown
learning;andtheyshouldtalktooneanother.Itshouldalsobeclearthattheseideasarenotparticularly
new.The “progressive”educationmovementhasproposedsimilarprinciples formanyyears.Piaget’s
contributionisnotindevelopingneweducationalideas,butinprovidingavastbodyofdataandtheory
whichprovideasoundbasisfora“progressive”approachtotheschools.
Wewouldalsoliketopointoutthattheseeducationalideasarenotonly“idealistic,”butpracticalas
well.ManyprimaryschoolsinGreatBritainandintheUnitedStateshavebeenapproachingeducationin
linewiththeprinciplesdescribedabove,andhavedrawndirectlyonPiaget’sworkfortheirinspiration.
These schools represent a very promising experiment in educational innovation and have already
achievedagoodmeasureofsuccess.
Wewill close this section on education, and this book,with a quotation fromPiaget, stating his
educationalgoalsandatthesametimedescribinghisownaccomplishment.
Theprincipalgoalofeducationistocreatemenwhoarecapableofdoingnewthings,notsimplyofrepeatingwhat other generations have done—menwho are creative, inventive, and discoverers. The second goal ofeducation is to formmindswhichcanbecritical,canverify,andnotaccepteverythingtheyareoffered.Thegreatdangertodayisofslogans,collectiveopinions,ready-madetrendsofthought.Wehavetobeabletoresistindividually, to criticize, to distinguish betweenwhat is proven andwhat is not. Sowe need pupilswho areactive,wholearnearlytofindoutbythemselves,partlybytheirownspontaneousactivityandpartlythroughmaterialwesetupforthem;wholearnearlytotellwhatisverifiableandwhatissimplythefirstideatocometothem.(Piaget,“DevelopmentandLearning,1964,p.5)
Notes
1Lenneberghasproposedasophisticatedtheoryofmaturationtoexplainthedevelopmentoflanguage.Thistheory,whichisfarsuperiortoGesell’s, is in many respects congruent with Piaget’s and deserves to be taken seriously indeed. See E. H. Lenneberg,BiologicalFoundationsofLanguage(NewYork:JohnWiley&Sons,Inc.,1967).
2 Piaget himself has given relatively little attention to physical experience, despite his estimate of its importance. In developmentalpsychology, this topic isusually treatedunder the rubricofperceptualdevelopment,and themost important theory in theareaisE.J.Gibson’s.SeeE.J.Gibson,PrinciplesofPerceptualLearningandDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1969).
3Today,manypsychologistsarecomingtoagreewithPiaget’sthesisthatthoughtshapeslanguagefarmorethanlanguageshapesthought.See,forexample,J.McNamara,“CognitiveBasisofLanguageLearninginInfants,’’PsychologicalReview,Vol.79(1972),pp.1-13.
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4Theseassertionsconcerningtheroleoflanguagehavenotgoneunchallenged.Beilin(1977)inparticularhasdemonstratedthattraininginverbal rules can accelerate the pace of conservation, and in an address (“Language and Thought: Thistles Among theSedums,”PiagetSociety,1977)haselaboratedontheroleoflanguageinthedevelopmentofthinking.
5Piagetrevisedhisconceptofequilibrationonseveraloccasions.Thepresentdescription isbasedonhis last revisioncontained inworkswrittenbetween1970to1980andinparticularinTheEquilibrationofCognitiveStructures(1985).
6Oneimportantissueregardstheteachingofreadingtotheyoungchild.OnthebasisofPiaget’stheory,whatcanoneconcludeconcerningthedesirabilityof teaching4-or5-year-oldstoread?Webelieve that the theoryhas little ifanythingtosayaboutreading,since Piaget has not studied it directly and since it is not clear how the intellectual skills which he has studied relate toreading. Our own experience is that there is no cognitive limitation which would prevent preoperational children fromlearningtoreadiftheyaremotivatedtodoso.
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