young children's knowledge about visual perception

Young Children's Knowledge about VisualPerception: Projective Size and Shape

Bradford H. Pillow and John H. FlaveilStanford University

PILLOW, BRADFORD H., and FLAVELL, JOHN H. Young Children's Knowledge about Visual Percep-tion: Projective Size and Shape. CHILD DE\'ELOI'MEM\ 1986, 57, 125-135. Although recent researchindicates that an increased sensitivity to visual appearances develops around 4 or 5 years of age,evidence from perceptual studies suggests that certiun types of appearances, that is, projective sizeand shape, are not noticed or understood until at least 7. 4 experiments investigated preschoolchildren's knowledge of the projective size-.distance and projective shape-orientation relationships.In Experiment 1, 3- and 4-year-olds were asked whether an object shuuld be moved farther or nearerin order to increase or decrease its apparent size. 4-year-olds performed significantly better thanchance, but 3-year-olds did not. Experiment 2 showed that 3-year-olds are able to perceive projec-tive size changes, indicating that although they do not fully understand the projective size-distancerelationship, the necessary pereeptual information is potentially available to them. In Experiment 3,3- and 4-year-olds were asked to indicate how a circular object should be rottited to make it appeareither circular or elliptical. Again, 4-year-olds perfomied significantly better than chance, but 3-year-olds did not. Again also, the results of Experiment 4 indicate that although 3-year-olds are not awareof the projective shape-orientation relationship, the>' are capable of attending to changes in projee-tive shape. Thus, the constraints on children s knowledge of the projective size!—distance and projec-tive shape—orientation relationships seem to be at least partly cognitive rather than wholly pereep-tual. These results are interpreted as further evidence for the acquisition of level 2 perceptknowledge during early childhood.

According to Flavell's (1974, 1978) di.s- very competent at level 1 but not level 2 in-tinction between level 1 and level 2 knowl- ferences, and level 2 knowledge is usually ac-edge of visual perception, at level 1 children quired around 4 cir 5 years of age. In the ear-can infer what objects can or cannot be seen liest investigation of the level 1-level 2from another person's viewpoint, whereas at distinction, Masangkay et al. (1974) assessedlevel 2 they also know that an object or array level 2 knowledge by asking children aboutmay present different appearances to viewers the appearance of a picture from another per-at different locations. That is, level 2 knowl- son's point of view. While the experimenteredge enables children to infer the nature, as and the child sat facing each other across awell as the content, of another person's visual table, the experimenter placed a profile pic-experience. Although the basic distinction ture of a turtle horizontally between herselfbetween level 1 and level 2 knowledge is and the child, I'hen the child was askedclear conceptually and has been supported by whether the experimenter saw the turtle up-the results of a number of studies, the nature side down or rightside up. Three-year-olds re-of level 2 knowledge has not been fully sponded correctl>' on only about half of thespecified either conceptually or empirically, trials, whereas 4-year-olds performed nearand the transition from level 1 to level 2 has ceiling. Using the turtle task and variants of it,not been investigated or explained. Flavell et al. (1981) obtained similar results.

Flavell, Flavell, Green, and Wilcox (1980) in-The level 1-level 2 distinction has been vestigated another aspect of level 2 perspec-

demonstrated in a number of studies (Flavell, tive-taking knowledge, namely, knowledge of1978; Flavell, Everett, Croft, & Flavell, 1981; the effects of an object's distance from the ob-Flavell, Shipstead, & Croft, 1978; Hughes, server on the clarity of perception. They1978; Hughes & Donaldson, 1979; Masang- found that 4-year-olds were much more com-kay et al., 1974). In general, 3-year-olds are petent than 3-yeai-oIds at judging that an ob-

The authors wish to express their gratitude to the teachers, parents, and children of BingNursery School, Grace Lutlieran Preschool, and Apricot Tree Preschool, whose cooperation madethese studies possible. We also thank Dane E. Lavin for the drawings used in this study, Richard J.Gerrig for helping with the second experiment, and Maijorie E Taylor for helpful comments on anearlier draft of this paper.

[Child Development, 1986, 57, 125-135. © 1986 by the SocieW for Research in Child Development Inc.Ali rights reserved. 0009-3920/86/5701-0021$01.00]

126 Child Development

server stationed closer to a small object wouldbe able to see it better than an observerstationed farther away along roughly the sameline of sight, and that observers stationed thesame distance from the object would be ableto see it equally well.

Thus far, level 2 knowledge has beendefined only in a general way—that is, as anunderstanding of how an object's appearancediffers when it is seen from different perspec-tives or under different circumstances. Fur-ther specification is clearly possible. Visualappearances are multifaceted; an object mayhave an apparent size, shape, location, color,texture, or identity, and its features may beclearly visible or difficult to discern. Thus,level 2 knowledge could include a great vari-ety of information, ranging from specificknowledge concerning particular aspects ofappearance and particular viewing conditionsto more general knowledge about the natureof visual appearances. These latter might in-clude the realizations (a) that multiple ap-pearances may exist for a single object, (b)that appearances may be misleading, and (r)that different viewers may have different per-ceptual experiences of the same object orscene. The former might include knowledgeabout the ways that particular aspects of ap-pearance may be affected by specific factorssuch as spatial transformations of the viewer-display relationship, the quality of illumina-tion, an object's rate of movement through thevisual field, the duration of its visibility, thecontext in which an object is seen, andthe viewer's prior knowledge and expecta-tions. This detailed information concerningthe influence of viewing circumstances on vi-sual experience may be useful for inferringthe nature of another person's visual experi-ence as well as for determining when andhow an object is likely to be misperceived, byeither oneself or another.

As an initial investigation of this concep-tualization of level 2 knowledge about visualperception, the present work investigatedyoung children's understanding of the effectsof spatial transformations of the viewer-display relationship on apparent size andshape. Children's understanding of the visualconsequences of such changes is of interestfor at least two reasons. First, beginning withPiaget and Inhelder's (1956) three-mountainstask, the ability to infer how changes in loca-tion alter the appearance of an object or arrayhas been a traditional concern in the perspec-tive-taking literature. Second, it is not clearwhen this understanding should be expectedto develop. On the one hand, the classi-

fication of knowledge about spatial transfor-mations as level 2 knowledge suggests that itmay be acquired by the age of 4 or 414, theage at which the first appearance of level 2knowledge has been found in previous stud-ies (Flavell, 1978, 1981; Flavell, Shipstead, &Croft, 1978; Hughes, 1978; Hughes &Donaldson, 1979; Masangkay et al., 1974).Furthermore, because the acquisition of level2 knowledge should be facilitated by situa-tions in which (a) differences in appearanceare striking and easily perceptible, (b) the rel-evant changes occur along well-understooddimensions, and (c) there is a simple relation-ship among the apparent properties in ques-tion, relevant objective physical properties,and viewing conditions, it would seem thatthe effects of changes in distance or orienta-tion on apparent size and shape might beimderstood relatively early. On the otherhand, the natural tendency to perceive con-stancy rather than retinal projection (Hoiway& Boring, 1941), present since infancy(Bower, 1974; McKenzie, Tootell, & Day,1980), could prevent children from noticingretinal projections or discovering their sys-tematic relationships to distance and orienta-tion. Moreover, the results of previous studiesindicate that children may not perceive pro-jective size or shape easily. For example, al-though adults can voluntarily alternate be-tween the perception of objective and retinalsize (Epstein, 1963; Gilinsky, 1955), whenPiaget (1969) asked young children to matchthe projective size of t\\'() vertical rods by ad-justing the length of one of them, childrenunder 7 did not understand the task, as if theyhad no conception of projective size. In an-other study, Rappoport (1969) asked 5-, 7-,and 9-year-olds to make one of two equidis-tant triangles look farther away. The tendencyto make the triangle smaller increased greatlybetween ages 5 and 9, with 5-year-olds re-sponding at chance. Therefore, Rappoport's(1969) results suggest that knowledge of theprojective size—distance relationship in-creases with age and is virtually nonexistentbefore age 7. Similarly, in a study of formperception, Vurpillot (1964) found that 7-year-olds did not respond differentially toobjective and projective shape matching in-structions. Their responses to both t>pes of'nstructions tended toward shape constancy,again suggesting that younger children arenot aware of retinal projection.

The present study was designed to inves-tigate the development of preschool chil-dren's knowledge of the effects of spatialtransformations of the viewer-display rela-tionship on apparent shape and size. In Ex-

Pillow and Flavell 127

periment 1 we assessed 3- and 4-year olds'knowledge of the projective size-distance re-lationship by requiring them to indicatewhether an object should be moved fartheraway or nearer in order to make it look largeror smaller to either themselves or another ob-server.

Experiment 1METHOD

SubjectsThe subjects were 32 nursery school chil-

dren, 16 3-year-oIds (mean age 3-10, range 3-7to 4-0) and 16 4-year-olds (mean age 4-5,range 4-1 to 4-9). Seven of tbe 3-year-oldswere female and nine were male. Six of the 4-year-olds were female and 10 were male.

MaterialsPictures.—Line drawings on 21.5 x

27.5-cm plastic transparencies were sus-pended at eye level 1.07 m in front of thesubject. A 6.4-cm circular portion of eachdrawing was blank. The missing features fromthis region were drawn on a circular card-board cutout attached to a vertical rod thatcould be placed at various distances behindthe transparency. For example, one drawingwas a clown without a face. The clown's facewas drawn on a separate cardboard circle.When placed at the proper distance behindthe transparency drawing, the cardboard cir-cle matched the blank region of the line draw-ing in projective size and gave the appearanceof fitting into the picture like a piece of a puz-zle. The cardboard circles were of three sizes;13 cm, 18 cm, and 21 cm in diameter.

Nonsense shapes.—Three cardboardnonsense shapes with irregular contours (ap-proximately 21 X 25 cm) were used for anadditional set of questions.

ProcedurePretest.—To ensure that all children

knew the correct meanings for "big" and "lit-tle," at the beginning of the session eachchild was shown two paper squares (one 5 x5 cm and the other 23 x 23 cm) and askedwhich of them was big and which was little.

Picture questions.—Seated behind a51x71-cm screen, children viewed each pic-ture monocularly through a viewing tube(length 11.4 cm, diameter 4 cm). Only thetransparency, the vertical rod with the card-board cutout, and the plain white wall at theback of the room could be seen through theaperture. The floor, ceiling, sidewalls, andfurniture could not be seen. The test trialswere preceded by a demonstration in which

the child first viewed the picture with thecardboard cutout positioned so that it ap-peared to Ht the drawing perfectly. Then thecutout was moved nearer, making it look toobig for the picture, and farther away, makingit look too small. While moving the cutout, theexperimenter blocked the child's view of thechanges in position by standing stationary infront of the viewing hole with his back to thechild and moving tlie cutout an arm s lengthin the appropriate direction. This procedureprevented children from leaming an associa-tion between "bigness " or "smallness" andcertain directions of movement or positions inthe room. Each test trial began with the cut-out positioned so that it fitted the picture. Af-ter the child had agreed that the cutout fitted,the experimenter, blocking the child's view ofhis actions, moved it either farther away orcloser to the child and asked whether itlooked too big or too little. Then the experi-menter asked the following question: "Nowthe clown's face looks too big [little] so wewant to make it look little [big]. To make theclown's face look little [big] to you, should wemove it this way or tjhat way?" While offeringthe two choices of direction, the experimenterpointed toward the child or directly away.Children responded by pointing. No feed-back, either verbal or visual, was given re-garding the conectness of responses. Whenchildren indicated a direction, the cutout wasnot moved. Instead, the picture and cutoutwere replaced and a new trial began. Thetransparency pictures and cardboard cutoutsprovided a concrete, clearly visible demon-stration of projective size differences and thegoal of making the circular cutout appear to fitthe drawing was well defined. Thus, this pro-cedure made it possible to convey the idea ofprojective size and tci refer to changes in pro-jective size in a simple and direct manner.Moreover, the required response, pointing,was simple and nonverbal.

There were eight test trials with the pic-tures. On four trials (big trials) the cutout wasmoved away from thie child, making it looklittle, and the child was asked how it could bemade to appear big. The other four (littletrials) required the child to indicate how thecutout could be made to appear little. In addi-tion, half of the big trials and half of the littletrials were "self-trials requiring children tomake judgments about their own perspective,as described above, and half of the trials were"other" trials requiring children to make judg-ments about another person's perspective.For the "other" trials, the experimenter satbehind the screen and viewed the picturesthrough the viewing tube, while the child


stood at the opposite end of the room behindthe cardboard cutout. For "other" trials thequestion was: "Now the clown s face lookstoo little [big] to me. We want to make it lookbig [little] to me. To make the clown's iaeelook big [little] to me, should we move it thatway or that way?" While asking the question,the experimenter pointed toward and awayfrom himself and the child. Again, childrenresponded by pointing. Because the childrenstood next to the cutout, which remained sta-tionary, they had no direct access to the ex-perimenter's visual experience and receivedno verbal feedback; thus children again wereprevented from learning an association be-tween "bigness" or "smallness" and certaindirections of movement or positions in theroom. The sequence of "self and "other" and"big" and "little" trials was counterbalanced,as was the order of the direction choices(pointing away from or toward the subject) inthe test questions.

Nonsense shapes.—As an additionalmeasure of children's awareness of the projec-tive size-distance relationship, a second taskwas included. While standing in fiont of awindow, the experimenter held one of thenonsense shapes approximately 1.5 m in frontof the child and asked the following ques-tions: (a) "If I put this way far away over there[pointing across the street] will it look big toyou or will it look little to you?" (far question)and (h) "If I put this right up close to youreyes, will it look big to you or will it look littleto you?" (close question). Far and close ques-[ions were presented in a counterbalanced se-quence, and the order of the choices big orlittle was counterbalanced. One pair of farand close questions was asked for each of thethree nonsense shapes. The first nonsenseshape trial was presented immediately afterthe pretest. The last two were presented after

completion of the eight picture questions. Fi-nally, to determine whether subjects whocould predict projective changes also knewthat objective size remains constant as projec-tive size changes, after each of the last two far/close pairs an "objective size" question wasasked: "You said that when this is far away itwill look little [big]. When it's far away is itreally and truly little [big], or does it just looklittle [big]?" The order of "really and truly"and "just look" was counterbalanced. As thewording suggests, each subject's response ofbig or little to the immediately preceding pro-jective question was used as the size tenn inthe objective question.

RESULTS AND DISCUSSION

All .32 children passed the pretest on themeanings of "big" and "little." The results forthe picture questions are shown in Table 1.Whereas the 4-year-olds perfbrmed signifi-cantly better than chance on the picture ques-tions (mean number correct = 6.81), f(15) =6.24, p < .001, the .3-year-olds did not (meannumber correct = 4.:38), t(15) < 1. Moreover,the 4-year-olds performed significantly betterthan the 3-year-olds, f(30) = 3.28, p < .01.Performance on "self" and "other" trials didnot differ, nor did perfomiance on "big" and"little" questions, as indicated by sign tests.On the six nonsense shape questions, both 3-year-olds (mean number correct = 4.13), f(15)= 3.21, p < .01, and 4-year-olds (mean num-ber correct = 5.25), f(15) = 6.25, p <.OO1,perfonned significantly better than chance;again, however, the 4-year-olds performedsignificantly better than the 3-year-olds,f(30) = 2.30, p < .05. Performance on far andclose questions did not differ significantly bysign test. As indicated by diflerencc scores(number correct on last four trials - numbercorrect on first four trials), perfonnance on the

TABLE 1

P E R C E M AGE OF SuRiEcrrs MAKINC; 0-8 C;ORRE(:T RESPONSES

NUMBER OE QUESTIONS ANSWERED CORREC:TUY

EXPERIMENT AND AU.E 0 1 2 3 4 5 h

Experiment 1:3 6 6 6 19 19 6 194 0 (1 0 6 13 6 0

Experiment 2:3 0 0 8 17 8 17 50

Experiment 3:3 0 0 6 19 25 25 254 . ^ 0 0 0 0 fi - l 25

Exr^eriment 4:3 0 0 0 8 8 25 25

^'orE.— Number possible is 6 in Experiment 2.

(i19

1356

025

25

Pillow and FlaveU 129

last four trials did not differ significantly fromperformance on the first four trials for either3-year-olds (mean difterenee = -.13), t(15)<1, or 4-year-olds (mean difference = .25),f(15) = 1.46, p > .1.

On the two objective size questions, theperformance of 3-year-olds (mean numbercorrect = 1.19) and 4-year-olds (mean num-ber correct = 1.56) did not differ significantly,f(30) = 1.28, p > .2. These questions wereintended to determine whether children whocould predict projective size changes cor-rectly also understood that these changeswere apparent rather than real. Moreover,asking whether projective size changes arcapparent or real made sense only if childrenhad demonstrated an understanding of thosechanges. Therefore, the objective size-(juestion performance of children who wereat or near ceiling on the projective questionswas compared with the perfomiance of thosewho were not, collapsing across age groups.The 18 children who answered at least six ofthe eight picture questions correctly per-fonned significantly better on the two objec-tive size questions (mean number correct =1.72) than did the 14 who answered fewerthan six picture questions correctly (meannumber correct = 1.07), t{30) = 2.4, p < .05.Fuithennore, the probability of answeringboth objective size questions correctly wasgreater fbr children who correctly answeredboth of the immediately preceding pairs ofnonsense shape questions (p = .72) than forchildren who did not answer both pairs ofnonsense shape qnestions correctly (p = .43).

Whereas the 3-year-oIds perfbrmed es-sentially at chance on the picture questionsbut showed at least some awareness of theprojective size-distance relationship on thenonsense shape task, the 4-year-olds clearlyknew that objects appear smaller whenfarther away and larger when nearer, andthose who correctly predicted projective sizechanges also tended to believe tliat thesechanges were apparent rather than real.Moreover, the 4-year-olds' performance didnot depend on whether they were required tomake judgments abont their own or anotherperson's perspective, or whether they had tomake the stimuli appear larger or smaller.Thus, their understanding of the projeetivesize-.-distanee relationship seems to have thestatus of a general mle that can be appliedequally well to a variety of situations. Fur-thermore, this knowledge seems to be ac-quired around 4 years of age. Therefore, theage at which children in Experiment 1 beganto demonstrate clear knowledge of the projec-tive size-distance relationship coincides with

the age of transition fi-om level 1 to level 2knowledge found in previous studies (Flavell1978; Flavell et al, 1981; Flavell, Shipstead,& Croft, 1978; Masangkay et al., 1974). De-spite the marked difference in the perfor-mance of 3- and 4-year-olds on tlie picturequestions, the 3-year-olds' competence on thenonsense shape questions suggests that theymay have some understanding of the projec-tive size-distance relationship and that theacquisition of this knowledge may be gradual.Although Experiment 1 did not directly mea-sure children's perceptual abilities, the 4-year-(5lds' awareneiss of how apparent sizechanges with distance implies that, contraryto Piaget's earlier findings, they must havesome ability to perceive projective size;otherwise, they could not have discoveredthis relationship.

Experiment 2Despite tlie numerous opportunities to

observe the effects of distance on apparent orprojective size encountered in the course ofeveryday experience, many of the 3-year-oldsin Experiment 1 did not demonstrate anunderstanding of the relationship betweenthe two. There are at least three reasons why3-year-olds might not fully understand this re-lationship. First, an inability to consciouslyperceive projective size may prevent themfrom teaming about its relationship to dis-tance. In contrast, even if 3-year-olds cannotice changes in projective size, they maynot have discovered a systematic relationshipbetween apparent size and distance, eitherbecause they ordinarily do not attend to pro-jective size, despite their ability to do so, orbeeanse they give litde thought to changes inprojective size on those occasions when theydo in fact obsei-ve them, or both. Experiment2 investigated 3-year-oIds' ability to detectchanges in projeetive size. An inability tonotice such changes conld be the primary fac-tor limiting the acquisition of knowledgeabout the projec-tive size-distance relation-ship. However, if 3-year-olds are able to de-tect changes in proj(;ctive size, then whateverconstraints there may be on their knowledgewould appear to be attentional or conceptual.

METHOD

SubjectsThe subjects were 12 nursery school chil-

dren (mean age 3-9, range 3-5 to 4-0). Six weremale and six were female.

MaterialsThe materials were a spherical balloon, a

bicycle tire pump, gmd a bicycle.


ProcedureObjective changes.—With the child

watching, the experimenter gradually inflatedand deflated the balloon and asked, "Does itlook like the balloon is getting big or gettinglittle?" The order of the choices "big" and"little" was eonnterbalanced. The purpose ofthis procedure was to ensure that childrenknew the meanings of "big " and "little " andcould correctly identify and label Increasesand decreases in size.

Frojective changes.—While the child andexperimenter watched from the sidewalk, acyclist rode a bicycle down the middle of astreet, moving alternately away from and to-ward the child. At the beginning of each trialthe experimenter pointed to the cyclist andsaid, "See the man on the bicycle? Watch himcarefully." Then, as the cyclist rode away(away trials), the experimenter asked, "Lookat the man on the bicycle. Does it look like heis getting big or getting little?" The order ofthe choices "big " and "little" was counterbal-anced. After riding approximately 50 m, thecyclist stopped and the experimenter pointedto him and repeated the instructions. As thecyclist returned (toward trials), the experi-menter again asked whether he appeared tobe getting little or big. The cyclist made threeround trips, so each child was asked six cjues-tions about apparent size. The balloon wasinflated and deflated four times, twice at thebeginning of each session and once more aftereach of the first two ronnd trips by the bicyclerider, making a total of eight trials with theballoon. To make it clear that projective,rather than objective, size was being referredto, size changes were the only alternatives of-fered in the projeetive question. Therefore,because only projective size was changing,the question should make sense and elicitconsistendy correct responses only if inter-preted as referring to projective size changes.


All 12 children answered the eight bal-loon questions correctly, indicating that theyunderstood the words "big" and "litde" andcould use them correctly to refer to changes insize. The results for the projective ciuestionsare presented in Table 1. Perfonnance onthese six questions was signifieantly betterthan chance (mean number correct = 4.83),t(ll) = 4.16, p <.O1, and performance ontoward and away trials did not diflersignifieantly by sign test. Though group per-formance was not at ceiling, these results in-dicate that 3-year-olds have some ability toattend to changes in projective size. Thus, al-though the results of Experiment 1 suggested

that 3-year-oIds may not yet have a completeunderstanding of the projective size-distancerelationship, the results of Experiment 2 sug-gest that the pereeptual information necessary"to learn about this relationship may be poten-tially available to them.

Experiment 3Experiment 3 investigated children's

understanding of the relationship betweenprojective shape and orientation relative to aviewer's line of sight. The procedure wassimilar to that used in Experiment 1 exceptthat subjects were required to indicate howan object should be oriented to make it ap-pear either circular or elliptical to eitherthemselves or another observer.

METHOD

SubjectsThe snbjects were 32 preschool children,

16 3-year-olds (mean age 3-9, range 3-5 to 4-0)and 16 4-year-olds (mean age 4-6, range 4-1 to4-9). Nine of the 3-year-olds were male andseven were female. Six of the 4-year-oldswere female and 10 were male.

MaterialsA cardboard box with a 21.5 x 27.5-cm

rectangular opening on one side and a 4-cmcircular opening on its top was used as aviewer. Plastic transparencies with line draw-ings could be placed over the vertical open-ing on the side or they could be placed on ahorizontal frame that fit into the box near itstop. This arrangement permitted an observereither to look into the box from the side ordown into it from the top. The line drawingsdepicted animals whose bodies were repre-sented either with an empty circle or anempty ellipse. Inside the box (and below thehorizontal picture frame) there was a horizon-tal rod to which a cardboard circle (diameter,9 cm) was attached. The projective image ofthe circle could be made to appear either cir-cular or elliptical by rotating this rod. All ofthe circles had patterning on them except fora plain black circle that was used for a demon-stration, and the inside of the box was wellilluminated. Consequently, the circle's tiltwas easily visible. The transparency drawingswere positioned so that the projective imageof the cardboard circle inside the box conldbe made to fit the boundaries of the circular orelliptical region in the drawing when viewedfi'om the proper location. For example, onedrawing was a horse with an elliptical body.When a brown circle was tilted at the properangle it appeared to fit into the picture, repre-senting the horse's body.

ProcedurePretest.—To ensure that all children

knew the correct meanings of "fat" and"thin," at the beginning of the session eachchild was shown a cardboard circle and acardboard ellipse and asked which of themwas fat and which was thin. Next, to ascertainthat children understood the words "standingup" and "lying down," each child was showna pair of pencils, one vertical and the otherhorizontal. The child was asked whieh pencilwas standing np and which was lying down.

Picture questions.—Children viewedeach picture monocularly through a viewingtube either from in front of the box or from thetop of the box, depending on whether the pic-ture was attached to the front of the box (frontquestion) or placed in the horizontal frame(top qnestion). The test trials were precededby a demonstration trial. First the childviewed a picture of an elliptieal animal withthe circle positioned so that it appeared to fitthe drawing perfectly. Then, the circle wasrotated to make it appear too "fat" (eircular) tofit the picture, and rotated again to make itappear too "thin" (narrow ellipse). Whilerotating the circle, the experimenter blockedthe child's view of these changes by placing ahand in front of the viewing tnbe. This proce-dure i>revented children from learning an as-sociation between circular or elliptical projec-tive shape and specific directions of rotationor specific orientations within the box. More-over, projective shape was dissociated fromthe circle's position in the box (vertical vs.horizontal) by nsing two viewing positions,front and top, separated by a 90° angle. Whenviewed from above, a circle in a nearly hori-zontal position would appear more or less cir-cular, but when viewed from the front of thebox, a circle in this position would appear el-liptieal. However, the opposite would be tmewhen the circle was rotated toward a verticalposition. Each test trial began with the circlepositioned so that it appeared either too circu-lar or too elliptical to fit the picture. The childwas asked whether it looked too fat or toothin. Then the experimenter asked the follow-ing cjuestion: "Now the horse's body looks toofat [thin] so we want to make it look thin [fat].To make the horse's body look thin [fat] toyou, should we make it stand up like this[holding a finger upright] or lie down like this[holding a finger horizontally]?" No feedback,either verbal or visual, was given concerningthe correctness of responses. When childrenmade their responses, the circle was not ro-tated. Instead, the picture and circle were re-placed and a new trial began. There wereeight test trials. On four trials children wereasked how the circle could be made to appear

PiDow and Flavell 131

"thin" (elliptical) and on the other four theywere required to indicate how it could bemade to appear "fat" (circular). In addition,half of the trials required children to makejudgments about their own perspective, andhalf of the trials required judgments concern-ing another person's perspective. For these"other" trials, the child sat next to the boxwhile die experimenter viewed the picture.The question for the "other" trials was, "Nowthe horse's body looks too fat [thin] to me, sowe want to make it look thin [fat] to me. Tomake the horse's body look thin [fat] to me,shonld we make it stand up like this [holdingfinger upright] or lie down like this [holdingfinger horizontally]?" The picture was placedhorizontally and viewed from above on half ofthe trials and attached vertically and viewedfrom in fi-ont on the other half. The order of"fat" and "thin," "self" and "other," and"front" and "top" trials was counterbalanced,as was the order of thei choices "stand np" and"lie down" in the test question. Finally, therewere two "objective shape" questions, onefollowing each of the last two "thin" trials foreach child. The question was: "You said if wemake this lie down [stand up] it will lookthin. When we make it lie down [stand np], isit really and tmly thin, or does it just lookthin?" The order of ihe choices "really andtmly" and "just look" was counterbalanced.The child's choice of stand up or lie down forthe immediately preceding picture questionwas used in the objective shape cjuestion.


All 32 children jiassed both the preteston the meanings of "fat" and "thin" and thepretest on the meanings of "stand up" and"lie down." The results for the picture qnes-tions are shown in Table 1. Whereas the 4-year-olds performed significantly better thanehance on the picture questions (mean num-ber correct = 6.19), f(15) = 6.37, p <.OO1, the3-year-olds did not (mean number correct =4.44), t(15) = 1.35, p >.O5. Moreover, the 4-year-olds perfbrmed significantly better thanthe 3-year-olds, f(30)==5.40, p <.(K)1. Perfor-mance on "self" and "other" trials did not dif-fer signifieantly for eifher age group, nor didperfonnance on "front" ancl "top" trials, orperformance on "fat" and "thin" questions, asindicated by sign tests. Performance on thelast four trials did not differ significantly fromperfonnance on the first four trfals for either3-year-olds (mean difference = -.63), t{15)= 1.50, p >.O5, or 4-year-olds (mean difTer-enee = -.25), f(15) = 1.16, p >.2. On the twoobjective shape questions the performance of3-year-olds (mean number eonect = .81) and4-year-olds (mean number correct = 1.31) did


not differ significanUy, *(30)=1.85, p >.O5.For further analysis of perfonnance on thesecjnestions the responses of children who per-formed near ceiling on the picture questionswere compared with the responses of thosewho did not, collapsing across age groups.The 14 children who answered at least six ofthe eight cjnestions correedy performedsignificantly better on the two objective shapeciuestions (mean number correct = 1.5) thandid the 18 who answered fewer than six pic-ture questions correctly (mean number cor-rect = .72), ti30) = 3.0, p < .01. Furthennore,the probability of answering both objectiveshape questions correctly was greater for chil-dren who correctly answered the two picturec}uestions immediately preceding the objec-tive shape qnestions (p = .67) than for chil-dren who did not answer both of these picturequestions correctly (p = .25).

The pattern of results in Experiment .3was very similar to the findings in Experi-ment 1. The .3-year-olds performed nearchance, but the 4-year-olds demonstrated aclear nnderstanding of the relationship be-tween an object's projective shape and itsorientation relative to an observer's line ofsight. They conld correctly indicate how theorientation of an object shonld be changed tomake it appear either more circular or moreelliptieal, and this understanding was not lim-ited to the familiar horizontal line of sight;that is, they performed equally well whenasked qviestions about a vertical (downward)line of sight. Thus, the 4-year-olds imderstoodthat projective shape is a function of the ob-ject's orientation relative to the viewer's lineof sight rather than a function of its orientationrelative to the horizontal plane. They alsounderstood that these changes were apparentrather than real. Moreover, the 4-year-olds'performance did not depend on whether theywere required to make judgments abont theirown or another person's perspective, orwhether they had to make the stimuli appearcircular or elliptical. Therefore, their under-standing of projective shape appears to hesufficiendy general to allow them to solveproblems equally well in a variety of situa-tions. Fnrthermore, this ability seems to beacquired by the age of 4 or 4V2, the same agethat children in Experiment 1 began to showclear understanding of the projective size-distance relationship. Although Experiment 3did not directly measure children's percep-tual abilities, the 4-year-olds' understandingof the relationship between orientation andprojective shape implies that children of thisage must possess some ability to perceive pro-jective shape, contrary to Vurpillot's (1964)earlier findings.

Experiment 4Experiment 4 investigated 3-year-olds'

ability to detect changes in projective shape.An inability to notice such changes may bethe primary factor limiting the acquisition ofknowledge abont the relationship betweenprojective shape and orientation. If they areable to detect changes in projective shape,then the constraints on their knowledgewould appear to be at least partly cognitive.

METHOD

SubjectsThe snbjects were 12 nnrsery school chil-

dren (mean age 3-8, range .3-5 to 3-11). Sixwere female and six were male.

MaterialsThe materials were two plates with dif-

ferent patterns (diameter 23 em), a thin chil-dren's book (20x20 cm), a paper folder(23 X 30 cm), and a picture of a worm. Theworm picture was made by superimposing apiece of blue paper with the outline of aworm cut out of it over an orange piece ofpaper with the worm's eye drawn on it. Theblue paper was cut in half horizontally so thatthe wonn's width could be varied by adjust-ing the distance between the halves of theoutline.

ProcedureObjective changes.—The child watched

as the experimenter gradually separated thetwo halves of the worm's outline, making theworm fatter, and then gradually moved themcloser together, making the worm thinner.Each time the worm's width changed, thechild was asked whether it was getting fat orthin. The order of the choices "fat" and "thin"was eonnterbalanced. The purpose of thisprocedure was to ensure that children under-stood the terms "fat" and "thin" and coulduse them to label changes in shape. Therewere four trials at the beginning of eaeh ses-sion (two fat and two thin) and two more half-way through tlie test procedure.

Projective changes.—The child and ex-perimenter sat about 2 m apart, facing eachother. The experimenter held up an object—one of the plates, the book, or the folder—andslowly rotated it. While the object was beingrotated, the experimenter asked "Look at this.Does it look like it's getting fat or gettingthin? " There were eight trials, four eaeh withcircular stimuli and with rectangular stimuli.The order of the choices "fat" and "thin" wascounterbalanced. On half of the trials the ob-ject's projective image grew wider and on halfof the trials it grew narrower. As was the casein Experiment 2, the alternatives in the pro-


jective question were chosen so that the ques-tion would make sense only if inteii^reted asrelerring to projective, rather than objective,shape.

Rt SILTS AND DISCUSSION

All 12 children answered the objectivechange questions with the worm correctly, in-dicating that they understood the words "fat"and "thin" and could use them to refer tochanges in shape. Results tor the projectivechanges questions are presented in Table 1.Performance on the eight projective shape(luestions was significantly better than chance(mean number correct = 5.92), f(ll) =3.92, p< .01. Performance on "fat" and "thin" trialsdid not differ significantly, nor did perfor-mance with vertical and horizontiil rotation, asshown by sign tests. Though group perfor-mance was not at ceiling, these results indi-cate that 3-year-olds have some ability to per-ceive changes in projective shape. Although,as suggested by the results of Experiment 3,many 3-year-olds may not yet have discov-ered the systematic relationship between pro-jective shape and orientation, the results ofExperiment 4 snggest that the perceptual in-formation necessary to learn about this rela-tionship may be potentially available to them.

General Discussion(Contrary to the previous findings that

children under the age of 7 years are imawareof projective phenomena in vision (Piaget,1969; Vurpillot, 1964), the results of this studysuggest that children begin to notice changesin projective size and shape, and to under-stand the visual consequences for projectivesize and shape of certain spatial transfonna-tioiis of the viewer-display relationship, dur-ing the preschool years. Considering that thenahiral tendency to perceive constancy-should render changes in apparent size subtleand difficult to notice in most ordinai->' cir-CLinistances, the diseovery of the projectivesize—distance and projective shape—orien-tiition relationships by children as \xnmgas 4 years seems particularly striking. At leasttwo factors may have contributed to the dis-crepancy between the present results andthose of previous studies. First, because lealsize and shape are most salient, children maytend to interpret projective size or shape-matching instruetions as refening to real sizeatid shape, whereas the forced-choice ques-tions used in the present study may be lessambiguous because requiring subjects to indi-cate a direction of change should eliminatereal size or shape as a possible choice. Sec-ond, the transparency drawings may have

helped to convey the notions of projectivesize and shape more clearly than they wereconveyed in previous studies. As the level 2classification would suggest, knowledge ofboth the projeetive size—distance relationshipand the pnyective shape—orientation relation-ship is acquired during the fourth year. Thus,the age at which this knowledge first appearscoincides with the age of transition from level1 to level 2 found in previous studies (Flavell,1978; Flavell et aL, 1981; Flavell, Shipstead,& Croft, 1978; Hughes, 1978; Hughes &Donaldson. 1979; Masangkay et al., 1974).Moreover, 4-year-olds' understanding of thevisual eflects of changes in distance or orien-tation is not limited to specific siti.iations, suchas making judgments about their own per-spective or about familiar points of view. In-stead, their knowledge is general and abstractenough to allow them to solve a varietv- ofproblems, including those that require takinganother person's visual perspective.

Although children are not able to demon-strate a complete vmderstanding of the rela-tionships between projeetive size and dis-tance or projective shape and orientation untilapproximately tlie age of 4, 3-year-olds seemto have some ability to attend to changes inprojective size and shape. Thus, the necessaryperceptual information may be available tochildren before they construct these relation-ships, f-'erhaps 3-year-olds' knowledge is con-strained by an inability to conceptualize vari-ations in one dimension as a function ofvariations in another. According to Piaget(19701, between the ages of 4 and 6 years chil-dren begin to develop a logic consisting offunctions of the form (/ = (f)x that allowsthem to discover dependency relationshipsand covariations. A number of other theorists(Case, 1984; Fiseher, 1980, Fischer & Pipp,1984; Halford, 1982; Siegler, 1981) have alsohypothesized the development of similarcapacities at this age. For example, Fischer(1980} has proposed that at the age of 4 or 5children develop the ability/ to relate covar>-ing entities to each other, and Siegler (1981)has suggested that children do not begin toconceive of dependency relationships intenns of consistent rules before the age of 4.In the case of projective size or shape, an ob-ject's appearance is a product of its objectiveproperties and the prevailing viewing condi-tions (e.g., distance from the observer).Hence, discovering the projective size—dis-tance and jjrojective shape-orientation rela-tionships may re(inire, at least in part, an abil-ity to relate chariget on covarying dimensionsto each other. However, becanse the presenttiisks (.'ould be solved by conceptualizing therelevant dimensions as attril)vites with two


values (e.g., big and little) rather than as con-tinuous dimensions, the nnderstanding ofcovariation evidenced by our subjects may bevery rudimentary. More generally, progress-ing from level 1 to level 2 may involve acquir-ing infomiation about visual appearances,constant objective properties, and viewingcircumstances, and discovering systematic re-lationships by coordinating observations ofthe three. The finding that prior to the acqui-sition of level 2 knowledge, children cannotice changes in appearanee without havingsystematic understanding of them is eonsis-tent with this view of the transition from level1 to level 2.

Civen that 4-year-olds demonstrated aclear understanding of the projective size-distance and projective shape—orientation re-lationships, a further question concerns theexact nature of the knowledge or abilitiesthey used to solve the perspective problemsin this study. Salatas and Flavell (1976) havedistinguished between level 2 rules and com-putational procedures. As they and others(Flavell, Flavell, Green, & Wilcox. 1981;Flavell, Omanson, & Latham, 1978) haveshown, in some cases it is possible to inferhow an object appears froin another view-point or would appear if moved relative to theobserver, either by applying knowledge ofperspective niles or by using compntationalprocedures (e.g., mental rotation). Beeansethe relationship between projective size anddistance can be summarized by the simplerule that projective size decreases as distanceincreases arid vice versa, projeetive size prob-lems probably are solved by rule nse. How-ever, the projective shape—orientation rela-tionship is more diffieult to eneode in asimple rule. Inferring how a complex objectlooks from varions positions around tlie objectseems to lend itself to computational proce-dures rather than liile use because rules relat-ing different views of the object would benumerous and complex. Moreover, Marmor(1975) found evidence that 5-year-olds repre-sent rotation in their imagery and that tlieirkinetic imagery is similar to that of 8-year-oldsand adults, suggesting that the present sub-jects conld have used such processes. On theother hand, easier shape-orientation problemsemploying simple stimuli and not requiringprecise computation might be soluble by ruleuse. For example, knowing that more of a sur-face is visible when it is peri^endicular to theline of sight than when it is parallel or nearlyparallel to the line of sight might be ent)ughto solve the problems used in Experiment 3.Unfortunately, the data provide no hints as tohow children in the present stndy solvedthese problems. The two strategies seem

equally likely, and children may have dif-fered in their preferred strategy.

Taken together with the results of previ-ous studies, the results of the present investi-gation suggest that young children possessrich and detailed knowledge concerning thenature of visual experience. Knowledge of vi-sual perception is an important acquisitionnot only because of its relevance to visual per-spective taking but also because it may berelated to understanding the eoncept of ap-pearance and the distinction between appear-ance and reality (Flavell et al., 1983), as wellas to the ability to assess another person'sknowledge state. Cognitive perspective-taking studies (e.g., Mai-vin et al., 1976;Mossier et al., 1976; Wimmer & Perner, 1983)indicate that both the ability to infer what an-other person does and does not know and theunderstanding that others may ha\e false be-liefs increase around the age of four. In manysituations, m order to know what objects orevents another person has knowledge of, it isnecessary to be aware of what that person hasseen. Similarly, awareness of the nature ofsomeone else's pereeptual experience of anobject or event often may be necessaiy formaking inferenees about how that person islikely to constnie that object or event. Inother words, level 2 pereeptual perspective-taking abilities may contribute to the ability toinfer what another person knows or believesabout the nature, as contrasted with the exis-tence or occurrence, of objects or events. Inaddition, level 2 perspective knowledge mayfacilitate the realization that one's own beliefsma\' be based upon misleading percepti^ial ex-periences, and therefore may differ hom ob-jective reality, as well as from the beliefs oiothers. Recent evidence (Flavell, Creen, &:Flavell, in preparation) indicates that level 2perspective-taking ability is highly correlatedwith understanding of the appearance-realit>-distinction. Moreover, knowledge about vi-sual perception is of interest because there isa great deal that yonng children might cometo know about visual experience. As de-scribed earlier, many aspects of the appear-ance of objects or scenes can vaiy besides pro-jective size and shape, and many factoid othei-than spatial transformation of the viewer-display relationship can affect visual experi-ence. Consequently, the extent of children'sknowledge in this domain and the manner mwhich it develops seem worthy of further in-ve^stigation.

ReferencesBower, I. C. H. (1974). Development in infancy.

San Frantisco: W. U. Freeman.


Case, R. (1984). The process of stage transition: Aneo-Piagetian view. In R. J. Stemberg (Ed.),Mechanisms of cognitive development (pp. 19—44). New York; W. H. Freeman.

Epstein, W. (196.3). The inflviences of assumed sizeon apparent distance. American Journal of Psy-chology, 76, 257-265.

Fischer, K. VV. (1980). A theoiy of cognitive de\el-opnient; The eoiib ol and construction o( hierar-chies of" skills. Psychological Revieiv. 87, 447-531.

Fiseher, K. W., & Pipp, S. L. (1984). Processes of"cognitive development; Optimal level and skillacquisition. Iu R. J. Sternherg (Ed.), Mecha-nisms oj cognitive development (pp. 45—80).New York; W. H. Freeman.

Fla\ell. ]. H. (1974). The development ot inlei-enees about others. In T. Mischel (Ed.), Under-standing other persons (pp. 66-1]6). Oxford;Blaekwell.

Fiavell, j . H. (1978). The development of knowl-edge about visual perception. In C . B. Keasey(Ed.), Nebraska symposium on motivation (pp.4.3—76). Lincoln; University of Nebraska Press.

FlavoU, J, H., Green, F. L., & Flavell, E. R. (In(Jieparation). The development of knowledgeabout the appearance-realit\' distinction.

Flavell, j . H., Everett, R. A., Croft, K., & Flavell,E. R. (1981). Young ehiidren'.s knowledgeal)out visual perception; Further evidence torihe Level 1-Level 2 distinction. Develo))-inental Psychology, 17, 99-103.

Flavell, I. H., Flavell, E. R., & Green, F. L. 11983).Ue\ elopment of the appearanee-realit^v' distinc-tion. Cog7iitive P.sychology, 15, 9.5—120.

EUueil, I. fl., Flavell, E. R., Green, F. L, & Wil-cox, S. A. (1980). Young children's knowledgetibout visual perception; Effects of observer'sdistance Ironi target on perceptual C'larity oftarget. Developmental Psychology, 16, 10-12.

Flav ell, 1. H., Flavell, E. R., Green, F. L.. & Wilcox,S. A. (1981). The development of three spatialperspective-taking rules. Child Development,52, 3.56-358.

Flax ell, |. H., Omanson, R. C:., & Latham. C. (1978).Solving spatial perspective-taking problems l)\rule versus computation; A developmentalstudy. Developmental Psychology, 14, 462—473.

Flavell. J. H., Shipstead, 8. G., & Crolt, K. (1978).Young children's knowledge about visual per-ception; Hiding objects from others. Child De-velopment, 49, 1208-1211.

Gilinsky, A. S. (19.55). The effect of attitude uponthe perceptiou of size. American Journal ofPsychology, 68, 173-192.

Halford, G. S. (1982). The development of thought.Hillsdale, N'J; Erlbauui.

Hoiway, A. E., & Eloring, E,, G. (1941). Detemii-nants of apparent visual size with distance vari-ant. American Journal of Psychology, 54, 21—37.

Hughes, M. (1978). Selecting pictures of anotherpersons view. British Journal of EducationalPsychology, 48, 210-219.

Hughes, M., &: Donald.son, M. (1979). The use ofhiding games for studying the coordination ofviewpoints. Educational Review, 31, 1.33-140.

Mamior, G. S. (1975). Development of kinetic im-ages; When does the child first representmovement in mental images? Cognitive Psy-chology. 7, 548-559.

Mar\'m, R. S., Cireenherg, M. T., & Mossier, D. G.(1976). The early development of conceptualperspective taking; Distinguishing among mul-tiple perspectives. Child Development, 47,511-514.

Masangkay, Z. S., McGlusky. K. A., Mclnt>'re. G. W.,Sims-Knight, J., Vaughn, B. E., Ik Flavell, J. H.(1974). The early development of inferencesabout the visual percepts of others. Child De-velopment, 45, 3.57—.366.

McKenzie, 13. E., Tootell, H. E., & Day, R. H.(S980). Development of visual size constanc\'during the 1st year of human infancy. Develop-mental Psychology, 16, 163—174.

Mossier, D. G.. Marvin, R. S., & Greenberg, M. T.(1976). (conceptual perspective taking in 2- to6-year-()kl children. DeveAopmental Psychol-ogy, 12, 8.5-86.

Piaget. J. (1969). The mechanisms of perception.New York; Basic.

Piaget, J. (1970). Genetic epistemology. New York;Norton.

Piaget, J., & Inhefder, B. (1956). The child's concep-tion of space. London; Routledge & KeganPaul. '

Rappoport, ]. L. (1969). Size-constan<:y in childrenmeasured by a funetional size-discTiminationtiisk. Journal of Experimental Child Psychol-ogy. 7, 366-373.

Salatas, H.. t« Flavell, J. H. lT976). Perspective-taking; 1 he develnpment of t"wo eoniponents ofknowledge. Child Development, 47, 103-109.

Sieglei. R. S. (1981) Developmental sc(iuenceswithin and belrween concepts. Monographs ofthe Society for Research in Child Devclop-nunt. 46(3, Serial No. 189).

V\npill<)t. E. (1964). Perecption ct representationdans la constance de la tonne. AnnecPsijcholofiique, 64, 61-82.

Wimmer, H., & Perner, J. (1983). Beti<'ts about lie-li<'ls; Representation and constiaining tunctionot wrong beliefs in young children's under-standing oi deception. Cognition, 13, 103—128.

young children's knowledge about visual perception

Documents