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AcomputationalthinkingrequirementforMITundergraduates

Reportoftheworkinggrouponcomputationalthinking

January2017Summaryoffindings:Duringthespringof2016,ChairoftheFacultyKrishnaRajagopalandDeanforUndergraduateEducationDennyFreemanassembledagroupoffaculty,representingallfiveschoolsoftheInstitute,toconductanin-depthstudyoftheroleof“algorithmicreasoning/computationalthinking”inthecontextoftheeducationofMITundergraduates.Thegroupwasaskedtoconsiderasetofquestionsrelatingtothistopic,includingwhetherformalexposuretoalgorithmic/computationalthinkingshouldberequiredofallMITundergraduatestudents.Asummaryofthekeyfindingsoftheworkinggroupincludes:

• ComputationalthinkingshouldplayanexplicitroleintheformaleducationofallundergraduatestudentsatMIT.Computationalthinkingprovidesadistincttypeofrigorousthoughtofimportantintellectualvalue;itrequiresanddevelopsimportantmodesofcommunication;itacknowledgestheneedtounderstandthetransformationalimpactofcomputationinotherdisciplines;anditcreatesopportunitiesandaccessforourstudentsandgraduates.

• Inresponsetovariedcommunityinterpretationsofthetopic,theworkinggroupdevelopedanotionofcomputationalthinkingandalgorithmicreasoning,definingthembothinandofthemselvesandinrelationtoothermodesofthought.Thisnotionincludestheassertionthatcomputationalthinkingisbroaderthanaproficiencyincomputerprogramming,althoughprogramminglanguagesprovideaparticularlyusefulframeworkforunderstandingthefundamentalsandapplicationsofcomputationalthinking.

• Whileasignificantportionofthestudentbodycurrentlytakesarelevantcourseincomputation,coverageisnotuniversal.Theworkinggroupbelievesthatjustaseverystudentlearnscriticalthinkingandinductiveanddeductivereasoningaspathwaystoanalysis,understandinganddiscoverythroughtheirhumanities,artsandsocialsciencesubjectsandthroughthecurrentscienceGeneralInstituteRequirements,sotooshouldeverystudentlearncomputationalthinking.Thus,theworkinggrouprecommendsthatallundergraduatesberequiredtotakeatleastonesubjectofferingincomputation.

• Computationalthinkinginvolvesmorethantheskillofcomputerprogrammingortheabilitytousecomputertools;itincludesfundamentalmodesofreasoningabouttherenderingofphysicalorsocialsystemsina

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mannerthatenablescomputationalexperimentstocomplementphysicalorsocialones.Formalexposuretotheseconceptsisimportantforallstudents.

• TheworkinggrouprecommendsthattheInstituteproceedwithaconsiderationofmechanismsbywhichacomputationrequirementcouldbeinstitutedforallundergraduatestudents,whileaddressingtheimpactaddinganadditionaldegreerequirementorsubstitutingacurrentrequirementwouldhaveonstudentloadandwhileaddressingtheneedtoconnectcomputationalthinkingtodomain-specificcontextsacrossdifferentintellectualdisciplines.TheworkinggroupalsorecommendsthatthisconsiderationexaminetheimpactofpotentialchangesinrequirementsonABETaccreditationofengineeringdegrees.

• Theworkinggroupreportoutlinesseveralwaysinwhicharequirementincomputationalthinkingmightbeimplemented,andexplorestheadvantagesandchallengesofeachapproach.OptionsforincorporatingacomputationalrequirementmustcarefullyconsiderthetightconstraintsimposedonstudentsbythecurrentInstitute-widerequirementsandbyadditionaldepartmentaldegreerequirements,andshouldavoidaddingasignificantburdenonourstudents.

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Background:Duringthespringof2016,ChairoftheFacultyKrishnaRajagopalandDeanforUndergraduateEducationDennyFreemanassembledagroupoffaculty,representingallfiveschoolsoftheInstitute,toconductanin-depthstudyofthemeaningofthephrases“algorithmicreasoning”and“computationalthinking”inthecontextoftheeducationofMIT’sundergraduatesacrossallfiveschools.Theirchargetothisgroupincludedthefollowingquestions: 1)Howdofaculty,studentsandalumniindifferentfieldsofendeavor,acrossthefullbreadthrepresentedbyMIT’sfiveschools,usecomputationalthinking?2)What,ifany,isthecommonintellectualframeworkthatpeopleacrossMITemploywhentheyspeakofcomputationalthinkingandalgorithmicreasoning?3)Towhatextentarealgorithmicreasoningandcomputationalthinkingalreadybeingtaught?4)Shouldweacknowledgealgorithmicandcomputationalthinkingasanexplicitexpectationofallourgraduates?5)Ifyes,whatarethekeyelementsofalgorithmicandcomputationalthinkingandwhataretheassociatedlearningobjectivesandmeasurableoutcomesforknowledge,skillsandattitudes?6)Ifyes,doesitmatterwhenduringtheircareersatMITourstudentsareexposedtocomputationalthinkingandalgorithmicreasoning?7)Whatareourpeerinstitutionsdoing?Forallofthesequestions,theworkinggroupwaschargedtoconsiderthediversityofmeanings,ofmodesofknowledge,andoflearningobjectivesacrossMIT’sschoolsandtherangeofendeavorsofourstudentsandalumni.Thisreportsummarizesthefindingsofthegroupinresponsetothesequestions.Basedonthegroup’sfindings,thereportarticulatessomepotentialactionsandchangesinrequirements,anyofwhichwouldadvancethegoalofimprovingthecomputationalthinkingskillsofMITundergraduates.Thereportdoesnotspecifyanyparticularchangeinpolicynorthespecificdetailsnecessarytoimplementanyoftheseimprovements,sincetheserecommendationswerenotpartofthecharge.Process:TheworkinggroupengagedinaseriesofactivitiestosolicitinputfromacrosstheInstitute,includingthefollowing:

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• TheChairoftheFacultyandtheDeanforUndergraduateEducationsentanemailtoeveryfacultymembersolicitinginput.Theworkinggroupdiscussedthe17responsesreceivedbyemail,aswellasadditionalcommentsandsuggestionsprovidedinpersonbyothers.

• TheChairandDeansentasimilarmessagetothestudentbodyofMIT.Thoughweexpectthatstudentinterestinthetopicishigh,only2responseswerereceivedanddiscussed,perhapsbecauseofthetimingoftheworkinggroup’sactivities.

• Membersoftheworkinggroupcontactedeveryacademicdepartmenthead,andeitherengageddirectlywiththedepartmentheadorwithadesignatedrepresentative,solicitinginputonthequestionsposedinthechargetothegroup.

• TheworkinggroupsoliciteddatafromtheRegistraronrecentenrolmentsofundergraduatestudentsinclassesthatteachandcultivatecomputationalthinking.

• Theworkinggroupexaminedthecurriculaandrequirementsofpeerinstitutions.

• Meetingextensivelyoverthelatespringandsummerterms,theworkinggroupdebatedanddiscussedissuesandoptionsrelatedtothecharge.

• Theworkinggroupissuedadraftreportearlyinthefalltermof2016,andsolicitedcommentsonthisreportfromtheentireMITcommunity.Commentswerereceivedfromindividualfaculty,studentsandalumni.CommentswerealsoreceivedfromtheCommitteeontheUndergraduateProgram,andfromtheAcademicAdvisoryCounciloftheUndergraduateAssociation.Allcommentswerethendiscussedbytheworkinggroupandappropriaterevisionstothereportbasedonthatdiscussionwereincorporatedintothefinalreport.

Whatis“computational/algorithmicthinking”andisitrelevanttotheeducationofeveryMITundergraduatestudent?Theworkinggroupspentconsiderabletimediscussingtheconceptsofcomputationalthinkingandalgorithmicreasoning.Theterm“computationalthinking”datesatleastbacktoSeymourPapertin1980,althoughacommonlyacceptedformaldefinitionofthetermisstillunderdebate.Onecommondefinitionofcomputationalthinking,attributedtoJeannetteWing,is:

thethoughtprocessesinvolvedinformulatingaproblemandexpressingitssolution(s)insuchawaythataninformationprocessor–humanormachine–caneffectivelycarryoutthatsolution.

Suchadefinitionclearlyoverlapswithseveralotherformalizedmodesofthinking(suchasmathematicalorlogical);however,thefocusonadetailed,orderedsequenceofoperationsthatcanbeexecutedinadisciplinedmanner(i.e.,algorithmicdesign)byaninformationprocessordistinguishesthisapproachfrom

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others.Thisdefinitionalsodistinguishescomputationalthinkingfromcomputerliteracy(theabilitytousecomputationaltoolsasblackboxabstractions)ortheknowledgeofaspecificprogramminglanguage.Whiletheterms“computationalthinking”or“algorithmicreasoning”mayhavedifferentconnotationsindifferentdisciplines,thereisaclearsenseacrosstheInstitutethatthereisacommonexperienceofusingcomputationasamodeofthought,andthatthisismorethanacquisitionofprogrammingskills.Thisperspectivehasbeenarticulatedinthepast,forexample,inthe2010NationalResearchCouncil’sreportonComputationalThinking:

Astheuseofcomputationaldeviceshasbecomewidespread,thereisaneedtounderstandthescopeandimpactofwhatissometimescalledtheInformationRevolutionortheAgeofDigitalInformation…[H]owever,mosteffortshavenotfocusedonfundamentalconcepts.

Thereportcontinuesbylistingthreecommonapproaches(computerliteracy,particularprogramminglanguages,andprogrammingapplications)beforedistinguishingcomputationalthinkingasindependentfromanyofthem:

Butintheviewofmanycomputerscientists,thesethreemajorapproaches—althoughusefulandarguablyimportant—shouldnotbeconfusedwithlearningtothinkcomputationally.Inthisview,computationalthinkingisafundamentalanalyticalskillthateveryone,notjustcomputerscientists,canusetohelpsolveproblems,designsystems,andunderstandhumanbehavior.Assuch,theybelievethatcomputationalthinkingiscomparabletothemathematical,linguistic,andlogicalreasoningthatistaughttoallchildren.Thisviewmirrorsthegrowingrecognitionthatcomputationalthinking(andnotjustcomputation)hasbeguntoinfluenceandshapethinkinginmanydisciplines—Earthsciences,biology,andstatistics,forexample.Moreover,computationalthinkingislikelytobenefitnotonlyotherscientistsbutalsoeveryoneelse—bankers,stockbrokers,lawyers,carmechanics,salespeople,healthcareprofessionals,artists,andsoon.

Theviewsexpressedinthatsummaryloudlyechowhattheworkinggroupfoundinitsowninvestigationsanddiscussions–thatcomputationalthinkinginvolvesmorethantheskillofcomputerprogrammingortheabilitytousecomputertoolssuchasspreadsheetsorvisualizationprograms,andthattheimportanceofagroundingincomputationalthinking,especiallyforMITundergraduates,isbroaderthanspecificdisciplinaryneedsforcomputerprogrammingskills.Whiletheremaynotbeauniversallyaccepteddefinitionofcomputationalthinking,whiletheparticularinstantiationofthatideamayvarywiththespecificsofadiscipline,andwhiletherearecleartiesbetweencomputationalthinkingandotherformsofreasoning(mathematical,logical,linguistic),thereisalsoawidelysharedsenseamongthefacultyacrosstheInstitutethatanunderstandingofthe

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foundationsandtoolsofcomputation–e.g.,abstraction,modularity,recursionanditeration,divide-and-conquer,approximationandconvergence–isacriticaltoolforanystudent.Theworkinggroupthusbelievesthatcomputationalthinkingismorethanjusttheskillofcomputerprogramming.Itinvolvesunderstandinghowtomodellargescalesystemsusingappropriatelevelsofabstractionandmodularity,itutilizesmechanicaldescriptionsofinferencetoanalyzecomplexdatacollections,anditprovidesacomputationalcomplementtophysicalexperimentsonreal-worldproblems.Itis,however,hardtograsporarticulateconceptsofcomputationalthinkingabsentfacilityinadistinctandunambiguouslanguageinwhichtodescribethem.Andthisrequirestheuseofacomputerprogramminglanguageasaframeworkwithinwhichtoexplorecomputationalconcepts.Afewstudentssuggested,inreactiontothedraftreport,thatonecouldacquirefacilityincomputationalthinkingwithoutlearningaspecificprogramminglanguage;insteadfocusingontheoreticaldescriptionsandformalproofs.Theworkinggroupdoesnotsupportthisposition.Asarticulatedabove,knowinghowtoprogramacomputer(asopposedtomerelyunderstandingthesyntaxofacomputerlanguage)isarequisiteskillforcomputationalthinking.Inaddition,theabilitytoprogramacomputerisanimportantlifeskill,forseveralreasons:

• Knowledgeofcomputerprogramming(i.e.,theabilitytowritecode)enablesapersontosiftthroughvastamountsofinformation.Italsopermitsapersontocombineinformationfrommultiplesourcesinusefulways.

• Whilecomputationalreasoningintheabsenceofprogrammingwouldindeeddemonstratethatananswerprovidedbytheprogramwouldbecorrect,programmingknowledgeallowsthecorrectanswertobedetermined,accordingwithMIT’smissionofprovidingsolutionstotackletheworld’sgreatchallenges.

• Computerprogrammingskillsarecloselyrelatedtotheskillsneededtocreatelarge,complexmodelsofsocial,physical,orbiologicalsystems.

Theconceptsofcomputationalthinking,especiallyasaframeworkforrigorousreasoningaboutphysicalandsocialsystems,canprovideabasisforaugmentingotherintellectualframeworks.Manyfacultymembersconsidercomputationalmodelstobeimportantcomplementstotheoreticalandexperimentalmodels.Justashistoricallyscientistsandengineersusedtheoreticalmodelstoguidethedesignofexperimentalvalidations,andexperimentalobservationstoinformthecreationoftheoreticalmodels,todayengineers,naturalscientistsandsocialscientistsalsousecomputationalmodelsofphysicalorsocialsystemstoenhanceunderstandingofobservedorpredictedphenomena.Forthesecolleagues,theincreasingrelianceonusingcomputationalmodelstofurthertheirresearch(inbasicscience,indevelopmentoftechnology,orinmodelingofsocialsystems)requiresa

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fundamentalunderstandingofcomputation–notjustasaprogrammingtool,butalsoasafoundationalsubstrateonwhichtobuildandtestmodels.Thus,theysuggestthatstudentsshouldexperienceasubjectthatusescomputationtounderstandphysicalandsocialsystems,andthatsuchasubjectshouldincludesignificantprogrammingexperience.Inthisview,computationcanbecomeaframeworkinwhichtounderstandphysicalandsocialsystems,tocomplementtheoreticalandexperimentalmodelswithcomputationalones,andtouseprogrammingasatooltogroundthatunderstandingofasystemandtodevisecomputationalexperimentstocomplementphysicalones.Whatelementsareessentialtocomputationalthinking?Givenaperspectiveoncomputationalthinkingas“thethoughtprocessesinvolvedinformulatingaproblemandexpressingitssolution(s)insuchawaythataninformationprocessor–humanormachine–caneffectivelycarryoutthatsolution”,onecanthenaskwhetherthereareessentialconceptsthatwouldformthebasisforproficiencyincomputationalthinking.Whilesuchadiscussionmayvaryacrossdisciplines,theworkinggroupfoundthatthefollowingbasicconceptsarewidelyacceptedaskeyelementsincomputationalthinking:

• Abstractionofprocesses:capturingcommonpatternsofoperationinanalgorithmicdescriptionthatcanbegeneralizedandappliedtomultipleinstancesofaproblem.Thisabstractionincludesthesuppressionofdetailsoftheprocedurefromusers(whetherhumansorothercomputationalprocesses),sothatsubsequentcomputationalprocessescanutilizethebehaviorofanabstractionwithoutregardforthespecificsofhowitproducesresults.

• Abstractionofdata:capturingpatternsofassociationwithincomplexcollectionsofdatatostructureitsothatitcanbeappropriately/efficiently/accuratelyprocessed.Thisincludesidentificationofassociatedelementsofdata,andabstractingoutspecificdetailsofrepresentationofdataelementsfromtheuseofsuchdata.

• Decomposition:reducingacomputationaltaskintoasequenceofsimplertasks,togetherwithmechanismsforintegratingtheresultsofthatdecompositionintothesolutiontotheoriginalproblem.

• Modularity:understandinghowtocharacterizethesolutionofacomputationalproblemasasequenceofoperations,eachofwhichcanberepresentedasaseparate,abstract,computationalproblem;togetherwithdefinedoperationsforintegratingtheresultsofeachsub-operationintoasolutionfortheoriginalproblem.

• Iterationandrecursion:understandingfundamentalapproachesforsuccessivelyreducingthesolutiontoacomplexproblemintosimplerversionsofthesameproblem.

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Theseconceptscanbeunderstoodabstractly;however,theworkinggroupbelievesthatsuchconceptsarebestunderstoodwithinthespecificsofalanguageofdescription–aprogramminglanguagethatprovidestheprimitivesandmeansofcombinationinwhichtodescribeanddeploytheseconceptsonrealproblems.Asaconsequence,theworkinggrouphasusedthefollowingdescriptionasaframeworkinitsdeliberations:

Oncomputationalthinking:Whenourworkinggroupusestheterm“computationalthinking”,wemeansomethingmorethanlearningthesyntaxofacomputerlanguage.Wewantstudentstodevelopskillsandmodesofthinkingsothattheycanconstructorrecognizeuseful,wellwrittenalgorithms,canimplementthem,andcanusethemtomodelphysical,biological,orsocialsystems.Eveninthislimitedsense,anyproposedrequirementincomputationalthinkingshouldnotrequirethatMITstudentsdevelopallofthemanyskillsthatareusefulinthisarea.Rather,anyproposedrequirementshouldaskthemtolearnsomeofthefundamentalskills,andtopracticetheseskillsbydevelopingalgorithmsandwritingcomputerprograms.Suchanexperienceshouldprovideasolidfoundationonwhichsubsequentexplorationofcomputation,inawidevarietyofdisciplines,canbeundertaken.

Withthatperspective,andbasedontheinformationgatheredfromacrosstheInstitute,theworkinggroupbelievesthatcomputationalthinkingshouldplayaroleforstudentsinallpartsoftheInstitute.Thisroleisbasedonthenewintellectualmodeofthoughtthatcomputationalthinkingprovides,ratherthanpurelyonthepragmaticadvantagesthesetoolsmightgiveatMITorinprofessionallife,althoughweacknowledgethatoftenonemustuseaprogramminglanguageasaframeworkwithinwhichtodescribeaspectsofcomputationalthinking.WefurtherbelievethatthereareseveralimportantreasonswhyeveryMITundergraduatestudentshouldbearticulateintheroleofcomputationasamodeofthoughtandameansofcommunication:

1. Computationalthinkingisadistincttypeofrigorousthinkingthatisofintellectualvalue.Computationalthinking,similartomathematicalorlogicalthinking,combinesstructuredreasoningwithcreativeexplorationofpathstoreacharesult.Computationalthinkingdiffersfrommathematicalthinking,however,intheemphasisitplacesonmanagingcomplexity,limitingresources,andeffectivenessinmodelingphysicalandsocialsystems.Italsodiffersinthatitstressesimperative(or“howto”knowledge)ratherthandeclarative(or“whatistrue”knowledge).Forexample,axiomaticstatementsaboutpropertiesofsquarerootsaredifferentfromalgorithmicmethodstocomputespecificsquareroots.Additionally,computational

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thinkingofteninvolvesmakinginformeddecisionsabouttradeoffs,suchasbetweenmodeldetailandcomputationalspeed,andunderstandinghowthesetradeoffsmayhaveconsequencesfortheaccuracy,oreventhesocialandethicalimplications,ofresults.Inthisway,computationalthinkingadoptsauniformsetofprinciplesandclearlyestablishedtestsofconsistencythatprovideadistinctintellectualframeworkforthinkingaboutphysicalandsocialmodels.

2. Computationalthinkingrequiresanddevelopsimportantmodesofcommunication.Mostpeoplehavehadtheexperiencewheretheirbeliefthattheyunderstandhowsomethingworksisshatteredthemomenttheytrytodescribethatsysteminwritingorteachitclearlytoothers.Writtenandoralexpressioncrystallizesvaguethoughtsintoconcreteideas.Computationallyrigorousthought,expressedincode,leadstoaclarityofdesignthatcommunicatesthebeliefsofthecode’sauthortoothers.Computationalthinkinginvolvesmakingexplicithierarchicalandmodularrelationships;algorithmsandcodecommunicatetheserelationshipstoothers.Articulationofideasinamannerthatiscomprehensibletoothersrequiresprecision,clarity,andlogicalrigor,andthuscomputationalexpressioncancomplementnaturallanguageasameansofcommunicatingsomeideaseffectively.

3. Computersaretransformationalagentsinthe21stcentury.Theyarechangingthewaythatworkiscarriedout.Theyarechangingalmosteveryfieldofendeavor.Theyhaveenormousimpactsonourpersonallives–throughnovelsocialinteractionsaswellasindisruptingindustriesandprofessions.Itisimportantforeverystudenttodevelopanunderstandingofcomputersandwhattheycando.Eveninfieldswherenotallstudentsuseprogrammingintheircoursework,studentsshouldbecognizantoftheimpactofcomputationontheirfield.Inthisway,aknowledgeofparadigmsofcomputingisasimportantastheknowledgeoftheparadigmsof,forinstance,biology:justasastudentmaynotusebiologicalconceptsintheirareaofinterest,theyshouldbecognizantofquestions,challenges,andopportunitiesthatariseinbiology(orinphysics,chemistry,mathematics,orthehumanities,arts,andsocialsciences).

4. Computationaltrainingcreatesopportunitiesandaccessforourstudentsandgraduates.Therearemanyopportunitiesavailableonlytothosewhounderstandcomputationalthinkingandcomputerprogramming.TheseopportunitiesareavailablebothtoourstudentswhiletheyareatMIT(e.g.UROPsinvirtuallyanydisciplineatMIT)andintheirfuturecareers.ByincreasingexposuretocomputationalthinkingtoincludeallmembersoftheMITundergraduatestudentbody,accesstosuchopportunitiescanbeexpandedtostudentsfromabroaderrangeofbackgrounds,experiences,andpointsofview.Thisbothopensnewcareerpossibilitiesforstudentsandhelpstoincreasediversityincomputation-relatedfieldsinindustry.Further,ascomputationcontinuestopermeateotherdisciplines,knowledgeofand

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abilitytousecomputationaltoolswillbecomeevenmoreessentialtosuccessinawiderangeoffields.Toensurethatourgraduatesarewellpositionedtoassumeleadershiprolesinavarietyofdisciplinesandindustries,itiscriticalthattheyhaveadepthofunderstandingofcomputationalissuesandmethods.

Elementsofcomputationalthinking:Whiletheworkinggroupbelievesthateveryundergraduateshouldgainexposuretocomputationalthinking,itishesitanttocreatealistoftopicsinaformlikeasyllabus.Developmentofappropriatesubjectsincomputationmayrequirespecificsensitivitytodisciplinaryneeds,aninvestigationthatisbeyondthescopeoftheworkinggroup’scharge.However,thereiswideagreementontheusefulnessforallstudentstodevelopastrongunderstandingofthefollowingtopics:

1. Thefundamentalconstructsofcomputerprogrammingandtheirrolesinabstraction.Thesewouldincludetheuseofloopsforiteration,aswellastheuseofrecursionforalgorithmdesignandimplementation.Itwouldalsoincludetheuseofbasicdatastructuressuchaslistsandarrays,andtheuseofobjectclassesasanabstractionmechanismforencapsulatingdataandassociatedmethodsofmanipulationandinference.Itwouldincludetheuseofproceduredefinitionandspecificationasanabstractionmethod.Anditwouldincludetheimportanceoftestinganddebugginginthecreationofrobustalgorithmsandimplementations.

2. Elementsofdesignforcomputerprogramming.Theseincludetheimportanceofmodulardesignandtheroleofabstractionmechanismsasameansofsuppressingdetailandsupportingsystemdesign.Itwouldalsoincludemethodsforcreatingprogramsthatmakethemeasiertoshare,understand,test,anddebug.

3. Developingskillsinatleastonemodernprogramminglanguage.Thiswouldincludefundamentalskillsinwritingandreadingcode,debugging,andrelatedtopics.Whileitistheoreticallypossibletoapplyalgorithmicthinkingwithoutusingprogramming,theabilitytoexpresssuchthinkingthroughprogrammingandtounderstandhowcomputationactuallyworksinsocietyandindustryisvaluableinitself.

4. Understandingandextendingbasicclassesofalgorithms.Thisincludesgeneral-purposeapproachesforsolvingdifficultproblems.Someexamplesinclude:(i)greedyalgorithms,(ii)divideandconqueralgorithms,(iii)theuseofrandomizationandstochasticsamplingincomputeralgorithms,(iv)hillclimbing(orneighborhoodsearch)algorithms,(v)intervalbisectionmethod,andothers.

5. Modelingourphysicalandsocialworlds.Thiswouldincludetheabilitytocreatemathematicalandcomputationalmodelsthataidinunderstandingourphysicalandsocialworlds.Itwouldalsoincludelearningthemeritsas

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wellasthelimitsofthistypeofmodeling.Thiswouldalsoincludegroundinginmethodsforpresentingandunderstandingresultsofcomputationalexperiments,suchasvisualization,andstatisticalanalysisofuncertainty.

Inadditiontotheseelementsatthecoreofanyfundamentalcomputationalthinkingrequirement,theworkinggroupfeelsstronglythatstudentsshouldreceiveinstructioninextensionsofbasiccomputationelements,anddisciplinaryapplicationstoplacethecoreconceptswithindiversecontexts.Somepossibleexamplesofsuchextendedtopicsmightinclude:

1. Applicationofcomputationalmodelingwithindomain-specificcontexts.Forexample,theuseofsearchalgorithmsinanalyzinggenomicdata;modelingthemechanicalpropertiesofobjectsandtheirphysicalinteractions;predictingpatternsofbehaviorinlargescalesystems(transportation,communication,energy,social);andothers.

2. Understandingthelimitsofcomputers.Partofunderstandingwhatcomputerscandoisalsounderstandingwhattheycan’tdo(orcan’tdoyet).Itisalsousefultouseone’sownknowledgeandcommonsensetoaidinknowingwhencomputeroutputisnotmakingsenseorisnotrealistic.(Thisisanextensionofrecognizingwhenacalculatorresultdoesnotmakesense.)

3. Visualizationandnon-textualinteraction.Whilemanyresultsofcomputationalexperimentsarecapturedbynumericalvalues,oftentheinterpretationofthoseresultsisbestdonethroughothermeans.Visualizationofastatisticaldistributionoftrialsofacomputationalexperimentisanimportantaspectofunderstandingcomputationalresults.

4. Computationalcreativity.Theuseofcomputationtoengageandaugmenthumancreativityinnewways,enhancingexpressioninartanddesignthroughthecreativeapplicationofalgorithmsandcode.

Thus,theworkinggroupunanimouslybelievesthatallMITundergraduatestudentsshouldhavesomemasteryofcomputationalthinking,astheydowithphysical,mathematical,biologicalandchemicalthinking,andastheydowiththecriticalthinkingembeddedinthehumanities,artsandsocialsciences.PerceptionacrosstheInstitute:Althoughnotunanimous,theworkinggroupfoundverybroadsupportacrosstheInstituteforamechanismbywhichallMITundergraduateswouldgaincompetenceincomputationalthinking,andinusingcomputation(especiallythroughprogramdesignandimplementation)asacomplementtootherformsofintellectualinquiry.Thissupportcamefromfacultyandstudentsinallfiveschools,althoughthereweresomedissentingviews(concernsarediscussedbelow).Notsurprisingly,therewas

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strongsupportthroughouttheSchoolofEngineering;however,therewasalsosupport(thoughnotuniform)withintheotherfourschools.ColleaguesfromdisciplinesasvariedasEconomics,BrainandCognitiveSciences,Physics,Biology,Music,andArchitectureallexpressedsupportfortheroleofcomputationalthinking,althoughwenotethattherewerealsosomegroupsthatdidnotseetheneedforinclusionofcomputationalthinkingforstudentsintheirsub-discipline.Currentcoverage:Althoughthereisnorequirementforcomputationthatcurrentlyappliestoallundergraduatestudents,thereisalreadywidecoverageofcomputationalconceptsformanyofourstudents:

• All8departmentsintheSchoolofEngineeringhaveanexplicitdegreerequirementofaclass(oraportionofaclassinonecase)oncomputation.Whilethespecificsofthesubjects(suchastheirunderlyingprogramminglanguageandtheirparticularfocusonalgorithmdevelopment)differacrossdepartments,andnotallmaycoverallelementsofcomputationalthinking,allsubjectsrequirestudentstotreatcomputationnotjustasatoolbutasanabilitytotranslatealogicaldescriptionofamethodintoanalgorithmicprocess.

• Currently,onedepartmentintheSchoolofScience(BrainandCognitiveSciences),oneadditionaldegreeprogramintheSchoolofScience(MathematicswithComputerScience),andonenewlycreateddegreeprogramwithintheSloanSchoolofManagement(BusinessAnalytics)alsohaveanexplicitdegreerequirementofasubjectoncomputation.(PreviouslytheManagementSciencedegreealsohadarequiredsubjectoncomputation.)

• Inadditiontocoveragethroughdegreerequirements,manystudentstakeelectiveclasseswithcomputationalconcepts.Toprovideasenseofthenumberofstudentsalreadygainingexperienceincomputationalthinking,weconsideredseniorswhograduatedintheyears2012to2016.Ofthatgroup,4017outof5429receivedaprimarydegree(notcountingdoublemajors)inadepartmentthatcurrentlyhasacomputationalrequirement.Thisrepresents74%ofthetotalcohort.Oftheremaining1412students,646(or46%)tookatleastoneof6.0001/6.0002or6.01or1.000or1.00or2.086,eventhoughnotrequiredfortheirdegreeprogram(thesefourcoursesarenottheonlyoptionsforgainingexperienceincomputation,butrepresentthefourlargestsuchoptions).Thus,outof5429students,only766werenotrequiredtotakeacomputationcourseanddidnottakeoneofthefourlargeones(theremaybeothercoursestheydidtakethatcouldbeconsideredtosatisfythisconstraint),meaningthatatmost14%ofthegraduatingseniorsinthiscohortdidnotseecomputationalthinkingaspartoftheirMITeducation.

Onecouldargue(andsomefacultymembersdo)thatsincethemajorityofMITundergraduatesalreadytakeatleastoneclassincomputation,thereisnoneedto

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requireitofallstudents.However,MITeducationalrequirementsarealsoastatementtoourcommunityandtotheworldofwhatMITbelievestobeoftheutmostimportanceinitsundergraduateeducation.Theworkinggroupbelievesthatcomputationalthinkingisofsuchimportanceastomeritbeingrequired.Moreover,thereisvalueinMITstatingthatallofitsstudentslearncomputationalthinking.Insupportofthis,considerthestatementinMIT’sBulletinabouttheScience/MathGIRs:

“MITexpectsitsgraduatestohaveanunderstandingandappreciationofthebasicconceptsandmethodsofthephysicalandbiologicalsciences.…TheyareanessentialpartofthebackgroundthatMITgraduatesbringtotheirrolesandprofessionalsandasbroadlyeducatedcitizensinaworldstronglyinfluencedbyscienceandtechnology.”

Intheviewoftheworkinggroup,thisstatementappliesequallystronglytoanunderstandingandappreciationofthebasicconceptsandmethodsofcomputation.Additionalconsiderations:Thechargetotheworkinggroupraisedsomeadditionalquestions,whicharebrieflyaddressedbelow.

i) Whenintheircareerdoweexpectstudentstolearncomputationalthinking?Thereisarangeofviewsonthisquestion.However,theworkinggroupagreedthatideallystudentswouldgainexposuretocomputationalthinkingearlyintheirstudentexperience.Thisviewissharedbymanydepartments.Theworkinggroupiscognizantoftheconcernofoverloadingthefirstyearwithexpectationsofsubjectstobetaken,especiallysincesomanyfirstyearstudentsundertakemostoftheScienceGIRrequirementsinthatyear.Thegroupalsofelt,however,thatmanydepartmentswillexpecttheirstudentstohavemultipleexperienceswithcomputation–bothintroductoryanddisciplinespecific–andthusanearlyexposuretofoundationalconceptswouldenableamoredetailed,discipline-centric,explorationasanupperclassman.Theworkinggroupnotesthatoneoftheoptions(discussedbelow)mightenablethisopportunity,byencouraginga6-unitintroductorysubjectearlyinastudent’scareer,followedbyadiscipline-centricfollow-onsubjectlater.

ii) Arecomparablerequirementsinplaceatourpeerinstitutions?Theworkinggroupwasnotabletoconductanextensiveexaminationofpeerinstitutions.Wenotethefollowingobservations:a. Theonlypeerinstitutionthatweareawarehasaninstitute-wide

requirementofasubjectincomputationisHarveyMuddCollege,whichdescribesitselfasascience,engineeringandmathematicsliberalartscollege(allnineofitsmajorsareinscience,engineeringormathematics).Wearenotawareofanyotherpeerinstitutionthathas

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aninstitute-widerequirementofasubjectincomputationalthinking.Manyinstitutionshaveintroducedintroductorycomputationcoursesintendedfor“non-majors”andencouragetheirstudentstotakesuchcourses,butnoneofwhichweareawarerequiresuchparticipation.

b. SomeSchoolsofEngineeringatpeerinstitutionsdohaveacomputationrequirement,asdosomepeerinstitutionswithseparateSchoolsofComputation,orSchoolsofInformationScience(e.g.,Cornell,GeorgiaTech,CarnegieMellon).Interestingly,itappearsthatnotallengineeringdepartmentsatStanfordhaveaspecificcomputationcourserequirement,whereasallengineeringdepartmentsatUCBerkeleyandallengineeringdepartmentsatCornelldohavesuchanexplicitcourserequirement.

Ingeneral,wenotethatwhilewearenotawareofpeerinstitutionswithspecificinstitute-widecomputationrequirements,wedoobservethatmanysuchinstitutionsaremovingtowardsencouragingstudents,especiallyinscienceandengineering,toacquirecomputationalskills(forexample,currentlythemostpopularcourseatHarvardisCS50–introductiontocomputation).Giventhesetrends,thereisanopportunityforMITtoleadthewayinformalizingtheexpansionofeducationincomputationalthinkingtoincludetheentireundergraduatestudentbody.

ConcernsraisedbymembersofthecommunityMembersofthecommunityraisedmanythoughtfulcommentsandquestions.Wediscussthesebelow:

1. Totheextentthattherewasresistancetoarequiredcomputationalthinkingexperience,thiswasgenerallycenteredontheimpactofaddingarequirementontopofotherexistingrequirements,especiallythecurrentScienceGIRsubjects.TheworkinggroupagreesthatMITstudentscannotsimplyaddanothergraduationrequirementwithoutnegativelyimpactingtheirworkandlives.WebelievethatanyimplementationofachangeinrequirementsmustconsidertheimpactofpotentialchangesonotherpartsoftheMITeducationandtheintellectualbenefitsofaneducationalexperience.Thisisdiscussedinmoredetailbelow.

2. Whilemanycolleaguesfeelthatcomputationalthinkingshouldbeanintegralpartofeverystudent’sundergraduateexperienceatMIT,manyalsofeelthatadiscussionofchangesinrequirementsshouldconsiderthebroaderquestionofotherpotentialadditionsorchanges.Morespecifically,theworkinggroupheardsuggestionsthatjustascomputationhasbecomeanessentialelementinvirtuallyeveryintellectualdisciplineatMIT,sotoohasstatistics,probabilityandreasoningunderuncertainty.Whileadiscussionoftheroleofstatisticalreasoninginourcurriculumisbeyondthescopeofthisworkinggroup’scharge,thegroupacknowledgesthatthereismeritinconsideringtheroleofsuchamodeofthoughtintheMITundergraduate

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educationalexperience.Buttheworkinggroupalsobelieves,especiallysincesuchalargepercentageofourundergraduatesalreadytakeatleastonecomputationclass,theInstituteshouldmoveforwardinconsideringpossibleimplementationmechanismsforaddingaformalrequirementtothecurriculum.

3. Asnotedabove,alargeportionofrecentgraduatingclasseshavetakenacomputationclass,eitherbecauseitisadepartmentaldegreerequirement,orbecauseofapersonalinterestinthearea.Inlightofthis,somefacultyandstudentshavequestionedtheneedtoincorporateaspecificrequirementforallstudents.Whyshouldwerequirethateverystudenttakeasubjectincomputationalthinking?Whynotletindividualdepartmentsdeterminewhatisbestfortheirstudents?Inprinciple,thesameargumentcouldbeappliedtocurrentscienceGeneralInstituteRequirements.Sincemoststudentswouldpresumablytakebasiccoursesincalculus,physics,andperhapsbiologyandchemistry,whyrequirethatallstudentsdoso?ThattopichasbeendebatedattheInstituteinthepast,includingaspartoftheSilbeyreportontheGeneralInstituteRequirements.Thegenerallyacceptedrationaleforrequiringallstudentstohavecompetencyinmathematicsandsciencesisthatthemodesofthoughtassociatedwiththosedisciplinesareimportanttounderstandingtheworldandthechallengesconfrontingit.Manyofourundergraduateswillnotusethespecificelementsofanintroductorysubjectinbiologyorchemistryinanyoftheirdepartment-specificrequirements,buttheInstitutefeelsthatknowledgeofbiologicalreasoningisimportanttothebroadereducationofallofourstudents.ThequestioniswhethertheInstitutealsobelievesthatcomputationalreasoningrisestothesamelevelofimportance–thateverystudentshouldbeabletounderstandcomputationalapproachestophysical,biological,orsocialchallenges,thateverystudentshouldunderstandtheimpactofcomputationalapproachesinaddressingsuchchallenges,andthateverystudentshouldunderstandhowcomputationalagentsarechangingvirtuallyeveryaspectofmodernlife.Theworkinggroupunanimouslybelievesthistobecase–thatcomputationalthinkingisasessentialatoolforeverystudentasisscientificthinking.Whilenoteverystudentorfacultymemberagrees,theresponsetothedraftreportandthefeedbackacquiredbytheworkinggroupstronglysuggeststhatthatasubstantialmajorityofthecommunityalsosupportsthisperspective.

4. Aquestionwasraisedabouthowouralumniandalumnaeperceivetheneedfororvalueofexposuretocomputationalthinkingintheircareerpaths.Althoughunfortunatelywedonothaveexplicitdatafromrecentalumni/alumnaesurveysontheroleofcomputationintheircareers,wehaveanecdotalfeedbackthatsuggestsastrongsenseoftheneedforcomputation,acrossawiderangeofprofessions.Individualresponsestothedraftreport,aswelldiscussionswithalumni/alumnaeinothersettingsstronglysupporttheroleofunderstandingcomputationasanimportantelementintheircareers.

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5. AsimilarquestionwasraisedabouttheperspectiveofemployersontheneedforallMITundergraduatestudentstohavesignificantexposuretocomputationalmethods.Whilenoexplicitsurveyofemployershasbeenconducted,avarietyofindirectmeasuressuggestthatthereisastronginterestinsuchexposure.Theseincludethedistributionofcompaniesthatregularlyparticipateintheannualcareerfair–adistributionthatincludesnotonlyaverylargepresenceofinformationtechnologycompanies,butalsoalargearrayofothercompaniesexplicitlyseekinggraduateswithbackgroundsinotherdisciplineswhohaveexposuretocomputationalmethods.Additionally,demandfrompharmaceuticalcompanies,banks,investmentfirms,biotechnologycompanies,medicaldevicecompanies,consultingcompanies,andothers,forstudentswithbothadisciplinaryknowledgeofthesectorandabackgroundincomputationisverystrong,asevidencedbythehiringpatternsofthesecompaniesandtheirexpressedinterestinMITgraduates.

6. Althoughtheroleofcomputationalthinkinginthesciences,inmanagement,andintheengineeringdisciplinesiswellaccepted,somestudentshavequestionedtheimportanceofcomputationalthinkinginthehumanities,artsandsocialsciences.Whiletheworkinggroupbelievesthattheargumentsputforwardforwhyeverystudentshouldunderstandcomputationapplytothehumanitiesaswellastothenaturalsciences,thegroupalsonotesthattherearemanyareasofthehumanities,artsandsocialscienceswithnaturalinteractionswithcomputationalthinking:economics,finance,linguistics,andothers.Butmoregenerally,theworkinggroupstressesthatcomputationalthinkingisnotjustaboutcomputationaltoolsandtheirimpactonworkinadiscipline,itisalsoabouttheimpactthatcomputationhasintheframingofquestionswithinadiscipline.Thegroupnotesthatmanyareasofhumanities,artsandsocialsciencesarealreadybeingchangedbytheemergenceofcomputation–asameansofsocialinteraction,asafacilitatorofnewmodesofcommunication,asacurationmechanismfordigitalandothermaterial,andasaninfluenceonthecentralelementsofdisciplines.Thusknowledgeofcomputationislikelytobeofimportinallofouracademicdisciplines.

PotentialoptionsforsatisfyingacomputationrequirementAlthoughtheworkinggroupwasnotexplicitlychargedwithdevisinganimplementationplan,wewereaskedtoarticulatepossibleoptionsformeetingtheneedforacommoncomputationalexperience,includingdiscussionofthestrengthsandweaknessesofsuchoptions.Wedosobelow.However,theworkinggroupalsonotesthatanydiscussionofaddingageneralrequirementforourundergraduatestudentsmaybebestimplementedifithappenedinthecontextofalargerdiscussionoftheGeneralInstituteRequirements.Whilemanyfacultymembersviewcomputationasacriticalmodeofthought,thereareothertopicsthatmaymeritsimilarconsideration.Inparticular,membersofthe

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workinggroupandmanyfacultymembershaveproposedexaminingthestateofinstructionandimportanceofstatisticalthinkingandreasoningunderuncertainty.Thus,theworkinggroupencouragestheInstitutetoconsideranydiscussionofpossibleinclusionofacomputationrequirementwithinthebroadercontextofallInstituterequirements.Giventhatsuchabroaddiscussionmaynotoccurimmediatelyoreveninthemediumterm,theworkinggroupwilldiscussoptionsforbalancinganewcomputationalrequirementwithareductioninotherrequirements(specificallytheRESTrequirement)below.Theworkinggrouplists,butdoesnotnecessarilyendorse,eachofthefollowingpossibleoptionsforsatisfyingacomputationalthinkingrequirement,whilenotingthattheremaybeotherpossibilities(forexample,thegroupdiscussedtheoptionofintegratingcomputationasamoduleintoexistingGIRsubjects,eitherdirectlyorasanonlinemodule,butconcludedthattheseoptionswerenotcompatiblewiththeamountofmaterialtobecoveredandtheadvantagesofhavingthatmaterialtaughtbyafacultymemberwithacomputationalbackground).Thethreeoptionsthatthecommitteediscussedatlengthwere:

1. Asingle,Institute-wide,subject:a. Description:

i. TheInstitutewouldcreateasinglesubject(orreviseanexistingsubject)thatincorporatescommonlyacceptedelementsofcomputationalthinkingincludingprogrammingskills.

b. Advantages:i. Thedevelopmentofasubjectfocusedonacomputationalexperienceforallstudentswouldensurethatkeyconceptsarepresentedtoallstudentsinasimilarmanner.

ii. AswithseveraloftheotherInstitutewiderequirements,therewouldbeasharedexperienceforallstudents.

iii. Thiswouldallowafocusoncomputationasamodeofthought,separatefromembeddingofcomputationindomain-specificcontexts.

c. Challenges:i. Studentshavevastdifferencesofpriorexperienceincomputationalwork,especiallyprogramming,potentiallyleavingsomestudentsdiscouragedandoverwhelmedandsomeotherstudentsboredanddisengaged.

ii. Givingstudentstheoptionofpassingoutofthesubjectwouldaddressthelatterissue,butwouldalsoexacerbatedifferencesinthe“real”numberofrequirementstograduatethatalreadyexistinotherGIRs(forinstance,becauseofpriorCalculusexperienceorcreditsfromAPclasses).Therequirementwoulddisproportionatelyfallonstudentsfromhighschoolswith

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loweracademicstandardswhoalreadyfaceadditionaldifficulties.

iii. Asinglesubjectcouldnotcoverallthebasicandextendedtopicsdiscussedabove,andthusstudentsmightnotbeguaranteedexposuretomodesofcomputationalthinkingmostrelevanttotheirowndisciplinesandinterests.

d. Recommendationi. Giventhechallengesabove,theworkinggroupdeclinestoendorsethisoption.

2. Asubjectthatisdesignedforamajor,orsubjectsthataredesignatedassuitableforamajor:

a. Description:i. Adepartmentwouldeitherdevelopacomputationcoursespecifictotheinterestsoftheirstudentsoruseasubjectofferedbyanotherdepartment.

ii. ThisapproachwouldbesimilartothecurrentCI-Mcommunicationrequirement,whereinspecificskillsaretaughtinthecontextofamajor.

b. Advantages:i. Studentswouldhavetheopportunitytoseecomputationinacontextthatisparticularlyappealingtothem,therebyincreasingtheutilityoflearnedconceptsinfutureeducationalexperiences.

ii. Embeddingtheintroductionofcomputationwithinaspecificfieldhasthepotentialtoincreasestudentengagement,sinceitwouldappearincontextsofinteresttothestudent.

c. Challenges:i. Somecoordinationofofferingswouldberequired,toensurethatsubjectofferingsbyindividualdepartmentsweremeetingthegoalsoftherequirement.Thiswouldincludeensuringthatcorefundamentalconceptsarecoveredbyallsuchofferingsatanappropriatedepthandlevel.AstructuresuchasSOCR(SubcommitteeontheCommunicationRequirement)mightberequiredtoprovideanongoingMIT-wideperspectiveasthisisaccomplished.

ii. Departmentswishingtoofferinstructioninfocusedand/oradvancedcomputationalthinkingwouldneedtoeitherteachbasicprogrammingskills(requiringadditionalteachingresources)orrequireaprerequisitebasicprogrammingclasstherebyextendingtherealreachoftherequirement.

iii. Somedepartmentsmaynotfeelcapableof,orhavetheresourcesto,developspecificcomputationcourses.Thiscouldbeaddressedbyprovidingadditionalresources,orbyencouragingcollaborationwithdepartmentswithexperienceinteachingcomputation.

d. Recommendation

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i. Theworkinggroupbelievesthatthisoptionisworthconsideringinmoredetail.

3. Aninterdepartmentalcomputationalthinkingrequirementfollowedbyadisciplinarycomputationalthinkingclass.

a. Descriptioni. Thefirstpartoftherequirementwouldbesatisfiedbyasmallgroupof6-unit,probablyhalf-termsubjectsthatgiveanintroductiontocomputationalthinking(offeredatdifferentlevels--fromnopriorknowledgetoadvancedprogramming).Studentswouldnotbeabletowaivethisrequirement,soevenstudentswithextensivepriorprogrammingexperiencewouldtakeaclassaimedattheirlevelofbackground.

ii. Thesecondpartoftherequirementwouldbesatisfiedbyanupperlevelclass,whichcouldbepartofadepartment’srequirements,thatusescomputationalthinkingasapartofthemodesofthinkingandlearninginaspecializedfield.

iii. Thesecondrequirementcouldbeastand-alone6-unitclassoraspartofalargerunitsubjectthatofferssubstantialcomputationalthinkinginstruction.

iv. ThedivisionbetweengeneralandspecificinstructionwouldbecomparabletothedivisionbetweenCI-HandCI-Mclassesinthecommunicationrequirement,whiletheabilitytoembedsix-unitsofcomputationalthinkingwithinalargerclassfindsananalogyincertainlabcoursesthatprovidesixunitsoflabcreditwithina12unitclass.

b. Advantagesi. Byofferinganinterdisciplinarysubjectfollowedbyadisciplinespecifiedsubject,studentswouldacquireknowledgeandmodesofthinkingthatwouldbebothflexibleandnarrowlytailoredtoaspecificdomain.

ii. Skillsincomputationalthinkingintheinterdisciplinarysubjectcouldbepairedwithclasseswithdifferinglevelsofprogrammingexperiencecreatingachallengingbutrewardingrequirementforstudentsofallbackgrounds.

iii. Byrequiringoneorbothpartsoftherequirementasaprerequisite,departmentalsubjectscouldbeofferedthatcanassumeknowledgeofcomputationalalgorithmsandprogrammingskills,allowingadvancedtopicstobeofferedmoreeasilythantheycanbenow.

c. Challengesi. Althoughnodepartmentorunitwouldberequiredtocreateitsowndisciplinarysubject,somedepartmentsmaywishtodosobutmaybelimitedintheirresourcesortheirabilitytodevelopsuchaclass.Collaborationwithotherdepartmentstodevelopappropriatesubjectsorusinganexistingsubjectofferedbyanotherdepartmentarepossiblesolutionstothisissue.

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ii. Thetwo-partrequirementissufficientlycomplexthatadditionaladvisingandeducationabouttherequirementwouldbenecessary.

iii. Atleastinitially,anoversightcommitteesimilartoSOCRwouldneedtobecreatedtodeterminewhethersubjectsfulfillthegoalsandexpectationsofcomputationallyrigorousthinking.

d. Recommendationi. Theworkinggroupbelievesthatthisapproachoffersmyriadadvantagesandthechallengesareofamanageablesize.Itrecommendsthatimplementationdetailsbecarefullyexplored,includingimpactonoverallstudentload,resourcerequirements,andotherimplicationsofcreatingandofferingsuchsubjects.

MitigationofTotalRequirementsAlloftheoptionsthattheworkinggrouplistedabove,whichweretheonlychoiceswefeltgaveaworthwhileintroductiontocomputationalthinking,add12unitsofrequirementstotheexistingMITGIRs.Givenhowtightlythecurriculumalreadyconstrainsstudentchoice,thiswouldbechallenging.AnoptionstudiedinthepastwouldbetoaddanadditionalGIR,butallowstudentstoselect6of7GIR’s(whileallowingdepartmentstospecifyasubsetoftheGIR’sasrequiredforstudentschoosingtomajorinthatdepartment).ThisoptionwaspreviouslyexploredbytheSilbeycommittee,andmaymeritrevisiting.However,theworkinggroupnotesthatthiswouldruncountertothedesiretohaveallstudentsacquireacommandofcomputationalmodesofthinking.Asecondoption,thatwasmuchmoreappealingtotheworkinggroup,istouseoneofthetwocurrentRESTrequirementsasacomputationrequirement.ManyexistingCoursesalreadydesignatearequiredRESTsubjectthatteachessomeorallofthemodesofcomputationalthinkingdescribedabove.However,wenotethatmanydepartmentdegreerequirementsalready“capture”oneortwoRESTsubjectsfordifferentreasons.Thus,acarefulstudyontheimpactofallocatingaRESTsubjecttocomputationondepartmentaldegreerequirementswouldbeneededbyafutureimplementationgroup.Anassociatedissuethatwillneedcarefulconsideration,ifthedecisiontoimplementacomputationalrequirementforallstudentsismade,istheimpactofaddingadegreerequirementtoABETaccreditationofengineeringdepartments.ManyengineeringdepartmentsuseRESTsubjectsorcurrentdepartmentalsubjecttomeettheconstraintsofprofessionalaccreditationofdegreeprograms;thusanyproposedchangestoinstituterequirementswillneedtocarefullyconsidertheimpactofdifferentoptionsontheabilityofdepartmentstopreservetheiraccreditationstatus.

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SummaryTheworkinggroupunanimouslybelievesthatcomputationalthinkingisanessentialpartoftheeducationalexperienceforeveryundergraduatestudentattheInstitute.Thisisbasedontheviewthatcomputationalthinkingprovidesanewintellectualmodeofthoughtofrelevancetovirtuallyeveryintellectualdisciplineandthatcomputationalthinkingrequiresanddevelopsimportantmodesofcommunication.ThesefactorsareinadditiontothepragmaticadvantagesthatcomputationaltoolsmightgiveatMITorinprofessionallife.TheworkinggrouprecommendsthattheInstituteproceedwithaconsiderationofmechanismsbywhichacomputationrequirementcouldbeinstitutedforallundergraduatestudents,whileaddressingtheimpactaddinganadditionaldegreerequirementwouldhaveonstudentloadandtheneedtoconnectcomputationalthinkingtodomain-specificcontextsacrossdifferentintellectualdisciplines.Submittedby:

• EricGrimson,EECS,Chair• DeeptoChakrabarty,Physics• MichaelScottCuthbert,MusicandTheaterArts• PekoHosoi,MechanicalEngineering• CaitlinMueller,Architecture• JamesOrlin,Sloan• TroyVanVoorhis,Chemistry

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Appendix:Thefullchargetothecommitteefollows:

StudyGrouponAlgorithmicandComputationalThinkingforMITUndergraduates

Charge

Formanyyears,atleastsincethe2004-2006TaskforceontheUndergraduateEducationalCommonschairedbyProf.RobertSilbey,variousMITfacultymembershaveaskedwhether,andifsohow,MITshouldensurethatallitsundergraduateslearnalgorithmicreasoningandcomputationalthinking.Toanswerthisquestion,wearechargingasmallgroupoffacultytoconductanin-depthstudyofwhatthephrases“algorithmicreasoning”and“computationalthinking”meaninthecontextoftheeducationofMIT’sundergraduatesacrossallfiveschools.Inconversation,manycolleagueswhohavethoughtaboutthisissueareclearinsayingthatthesephrasesshouldmeanmorethananintroductiontoprogramminglanguages.Asaplacetobeginthisstudy,webelievethatcomputationalthinkingshouldencompassanintellectualframework,notjustaskill.PhrasesthatwereusedintheSilbeyreportinclude“computationalmodesofanalysis”,“algorithmicreasoning”,“dataabstraction”,“designingcomputationalsolutionstotheoreticalandpracticalproblems”,and“providingacomputationalparadigmforreasoningandproblemsolving.”Weareaskingyoutodoacareful,deliberativeassessmentofwhattheseandotherphrases(“abstractionandcomplexity”,“modularityandinterfaces”,“complexityofalgorithmicsolutions”,“algorithmicparadigms”)meanacrossMIT.Questionsthatwewouldaskyoutoexamineinclude:1)Howdofaculty,studentsandalumniindifferentfieldsofendeavor,acrossthefullbreadthrepresentedbyMIT’sfiveschools,usecomputationalthinking?Isitanimportantmodeofthinkingin(forexample)economics,policyformation,management,architecture,biologyandbiologicalengineering,chemistryandchemicalengineering,andotherdisciplines?2)What,ifany,isthecommonintellectualframeworkthatpeopleacrossMITemploywhentheyspeakofcomputationalthinkingandalgorithmicreasoning?Inwhatwaysisdiversityamongthemeaningsofsuchphrasesindifferentdisciplinarycontextsimportant?3)Towhatextentarealgorithmicreasoningandcomputationalthinkingalreadybeingtaught?Whatfractionofourgraduates,acrossallfiveschools,learntheminthecourseofmeetingtheexplicitrequirementsoftheirmajors?Whatfractiontakeacoursethatcoverscomputationalthinkingevenifnotanexplicitrequirementoftheirmajors?Towhatextentandinwhatwaysdowealreadyimplicitlyexpectthat

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abroadspectrumofMITundergraduatesacrossmanymajorsunderstandalgorithmicandcomputationalthinkingbythetimetheygraduatefromMIT?WhenintheircareeratMITdoweexpectstudentstolearncomputationalthinking?4)Shouldweacknowledgealgorithmicandcomputationalthinkingasanexplicitexpectationofallourgraduates?Ifyes,whatistherationale/caseforthis?5)Ifyes,whatarethekeyelementsofalgorithmicandcomputationalthinkingandwhataretheassociatedlearningobjectivesandmeasurableoutcomesforknowledge,skillsandattitudes?HowaretheycommonacrossthebroadspectrumofMITundergraduates,andhowdotheydiffer?AcrossMIT,howaretheyrelevanttosolvingproblemsandmasteringendeavors?6)Ifyes,doesitmatterwhenduringtheircareersatMITourstudentsareexposedtocomputationalthinkingandalgorithmicreasoning?Whatbenefitswouldaccruefromauniformapproachtoteachingthemandwhatmightthedownsidesbe?Whatbenefitswouldaccruefromdiscipline-specificapproachesandwhatmightthedownsidesbe?7)Whatareourpeerinstitutionsdoing?AretherepossiblemodelsoutsideMITthatmeritourconsideration?Asyoustarttoformulateyouranswerstothequestionsabove,wewouldaskthatyoudevelopalistofpossibleoptionsforaccomplishingthegoalsforthecomputationaleducationofMITundergraduatesthatyouarticulate,ifthesegoalsarenotalreadybeingmet.Pleasedescribeeachsuchoptionasconcretelyasyoucan,includingprosandcons,includingwhichgoalsamongthoseyouarticulateeachoptionaddresses,andincludingactionablenextsteps.Examplesofoptionsthatyoumightconsiderinclude:

i) Modules,withorwithoutonlinecomponents,thatcouldbeincorporatedwithinMIT’sexistingGIRsubjects.

ii) Newsubjectsormoduleswithnoprerequisites,rangingindurationfromonemonthtoonesemester,whosedevelopmentandteachingmayinvolvecollaborationamongdepartmentsandotheracademicunits.

iii) AmodelforteachingcomputationalthinkingalongthelinesofhowCI-Msubjectsteachcommunication,whereeachmajorcanmakediscipline-specificchoicesforhowtoachieveoverarchingMIT-widegoalsthatyouhavearticulated,viamoreadvancedsubjectsormodulesdesignedforstudentsinthespecificmajor.

Thefirsttwoareexamplesofoptionswherenextstepswouldincludecurriculumdevelopment.Forsuchoptions,wehopethatyouwillprovidepreliminaryexamplesofpartialsyllabi,withexplanationsofyourrationalesfortheelementsinthesesyllabi,andasenseofthe(groupsof)colleagueswhomightbeaskedtodevelopthecurricula.Thatis,theseareexamplesofoptionsthatwewouldhopeyoudevelopto

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thepointthatthenextstepcouldbeDeanFreemanpullingtogetherpeopleandresourcesforimplementation.Thethirdisanexampleofanoptionwhereyourstudymightpromptsomedepartmentstoinitiatenextsteps,perhapswithsupportfromDeanFreeman.Allareexamplesofoptionswherethenextstepswouldincludeconsiderationbyabroadergroupoffaculty,includingrelevantfacultycommittees.WeareconvincedthatadeepstudyasdescribedaboveisakeysteptowardevaluatingwhetherornotchangestoMIT’sundergraduatecurriculumandpedagogyaremerited.Dependingonyourfindings,yourstudymayprovidethefoundationforsubsequentadvancesinhowweeducateourstudents.Weareaskingyoutofocusonquestionsasaboveandonoptionswithnear-termactionablenextsteps.Wehopethattheanswersthatyourstudyprovides,togetherwithanysubsequentcurriculumdevelopmentthatitprompts,willserveasvaluableinputtoanyfuturediscussionofourGIRs.WewouldaskthatyousetasyourgoalthatbyJune30,2016youhavecompletedthemajorityofyourworkandreportedyourprogressandyouremergingconclusionstous,sothatbythatdatewehaveafullunderstandingofwhatremainsforyoutodo,andafirmlate-summerorearlySeptemberdeadlineforyourreport.Sincerely,Prof.DennisFreemanDeanforUndergraduateEducationProf.KrishnaRajagopalChairoftheMITFaculty———————————Membership:EricGrimson,Chair,EECSDeeptoChakrabarty,PhysicsMichaelCuthbert,MusicandTheaterArtsPekoHosoi,MechanicalEngineeringCaitlinMueller,ArchitectureJimOrlin,SloanTroyvanVoorhis,Chemistry