75Scientific Thinking in Young Children
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75Scientific Thinking in Young Children
ScientificThinkinginYoun；Science337,);；DOI:10.1126/science.1223；Thiscopyisforyourpersona；Permissiontorepublishorr；Thefollowingresourcesrel；www.sciencemag.org(thisi；Updated
　Scientific Thinking in Young Children: Theoretical Advances,Empirical Research, and Policy ImplicationsAlison GopnikScience 337, );DOI: 10.1126/science.1223416This copy is for your personal, non-commercial use only.Permission to republish or repurpose articles or portions of articles can be obtained byfollowing the guidelines here.The following resources related to this article are available online atwww.sciencemag.org (this information is current as of October 6, 2012 ):Updated information and services, including high-resolution figures, can be found in the onlineversion of this article at:http://www.sciencemag.org/content/337/.full.htmlSupporting Online Material can be found at:http://www.sciencemag.org/content/suppl//337..DC1.htmlA list of selected additional articles on the Science Web sites related to this article can befound at:http://www.sciencemag.org/content/337/.full.html#related This article cites 29 articles, 8 of which can be accessed free:http://www.sciencemag.org/content/337/.full.html#ref-list-1 This article appears in the following subject collections:Psychologyhttp://www.sciencemag.org/cgi/collection/psychologyScience (print ISSN ; online ISSN ) is published weekly, except the last week in December, by theAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. 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The title Science is aregistered trademark of AAAS.Downloaded from www.sciencemag.org on October 6, 2012If you wish to distribute this article to others, you can order high-quality copies for yourcolleagues, clients, or customers by clicking here.ScientificThinkinginYoungChildren:TheoreticalAdvances,EmpiricalResearch,andPolicyImplicationsAlisonGopnikNewtheoreticalideasandempiricalresearchshowthatveryyoungchildren’slearningandthinkingarestrikinglysimilartomuchlearningandthinkinginscience.Preschoolerstesthypothesesagainstdataandtheylearnfromstatisticsandinformalexperimentation,andfromwatchingandlisteningtoothers.ThemathematicalframeworkofprobabilisticmodelsandBayesianinferencecandescribethislearninginpreciseways.Thesediscoverieshaveimplicationsforearlychildhoodeducationandpolicy.Inparticular,theysuggestboththatearlychildhoodexperienceisextremelyimportantandthatthetrendtowardmorestructuredandacademicearlychildhoodprogramsismisguided.hirtyyearsago,theideathat2-year-oldsthinklikescientistswouldhaveseemedabsurd.JeanPiaget,thegreatpioneerofcognitivedevelopment,claimedthatpreschoolers’thinkingwasjusttheoppositeofscientificthink-ing.Preschoolerswereirrational,illogical,“pre-causal,”andlimitedtothehereandnow(1).Theseideasinformedbotheducationandpolicy.Theseclaimshaveturnedouttobewrong.Severalwavesofempiricalworkhaveshownthateveninfantsandveryyoungchildrenhaveintuitivetheoriesoftheworldaroundthem.Morerecently,mathematicalmodelsoflearninghavebeendeveloped.Empiricalresearchin-formedbythosemodelsshowsthatearlylearningisalsoremarkablysimilartoscientificinduction(Fig.1).Duringthe1980sand1990s,researchersdis-coveredthatveryyoungchildrenhaveabstract,structured,coherent,causalrepresentationsoftheworldaroundthem―representationsthataresim-ilartoscientifictheories.Theyusethoserepre-sentationstomakewide-rangingnewpredictions.Theserepresentationsappeartobeinplaceevenininfancy,butitisparticularlyclearthatpre-schoolershaveintuitivetheoriesofthephysical,biological,psychological,andsocialworld(2C4).Newmethodsledtothisfirstrevolutioninourunderstandingofdevelopment.Theadventofvideorecording,andstrikingexperimentalingenuity,ledtoafloodofresultsthatshowedsophisticatedknowledgeineventheyoungestinfants.Bystudyingwhatbabieslookedat,reachedfor,orimitated,researcherscouldshowthateveninfantsunderstandbothphysicalob-jectsandotherpeople[e.g.,(3,5)].Piagettriedtoassesspreschoolchildren’sknowledgebyask-ingthemopen-endedquestionsabouthypotheticalscenarios.Butpreschoolersshowmuchmoretweenstimuli.Associativelearningappearstobeverydifferentfromthehypothesistestingandex-perimentationofscience.Inthepast10years,however,theoreticalandempiricalresearchhasbeguntoshowthatchil-dren’slearningmechanismsdoindeedresem-blethebasicinductiveprocessesofscience.Wenowhaveamorepreciseandformaltheoryofchildren’slearningmechanisms,derivedfromideasaboutprobabilisticmodelsandBayesianlearningmethodsthatoriginatedincomputersci-ence,statistics,andphilosophyofscience.ProbabilisticModelsPhilosophyofscience,artificialintelligence,anddevelopmentalpsychologyallfacethesamefundamentaldilemma.Asadults,weseemtohavehighlystructured,abstract,coherentknowl-edgeoftheworldaroundus.Thisknowledgeallowsustomakewide-rangingpredictionsandinferences.Butwealsoseemtolearnthathighlystructuredknowledgefromthecontingent,con-crete,probabilisticevidenceofoursenses.Howcanthisbe?Traditionally,philosophersandpsy-chologistshaverespondedtothisdilemmaintwoways.“Nativists”havearguedthatthisab-stractstructuremustbeinplaceinnatelybe-causeitcouldnotpossiblybelearned.“Empiricists”havearguedthatthisabstractstructureisillu-inrealitythereareonlyspecificlearnedas-sociationsbetweenparticularpiecesofevidence.Theprobabilisticmodelsapproach[e.g.,(6C9)]addressesthisdilemmainanewway.Imaginethatthereissomerealstructureintheworld―aspatialconfiguration,agrammar,oranetworkofcausalrelationships.ThatstructuregivesriseTsophisticatedknowledgewhentheyrespondtofocusedquestionsaboutreal-lifeexamples(2C4).Thisresearchshowedthatyoungchildren’sknowledgeisstructurallysimilartoscientificthe-ories,butnotnecessarilythatchildrenlearnlikescientists.Itcouldbethatmuchofthisknowl-edgeisinnateratherthanlearned―evolutionarilydeterminedratherthaninferredfromexperience.Moreover,untilquiterecently,therewerefewthe-oreticalaccountsthatcouldencompasslearningmechanismsinbothchildhoodandscience,orempiricalresultsthatshowedthosemechanismsweresimilar.Infact,thepredominanttheoriesoflearningemphasizedcomplexassociationsbe-DepartmentofPsychology,UniversityofCalifornia,Berkeley,CA94720,USA.E-mail:gopnik@socrates.berkeley.eduFig.1.Child’splayisscience.[“PlayingDoctors”byFrederickDanielHardy();image:StapletonCollection/Corbis]SCIENCEVOL33728SEPTEMBER2012www.sciencemag.org1623Downloaded from www.sciencemag.org on October 6, 2012REVIEWtosomepatternsofevidenceratherthanothers―edgethatweseeinscientificandintuitivethe-higher-ordercausalstructure―forexample,theaparticularsetofvisualimages,orspokensen-ories.Inparticular,causalknowledgeiscentraltogeneralframeworkprinciplesthatprevailinatences,orstatisticalcontingenciesbetweenevents.bothkindsoftheories.Causalgraphicalmodelsscientificparadigmandthatshapeparticularcaus-Thatspatialorgrammaticalorcausalstructureor“Bayesnets,”developedinthephilosophyofalhypotheses(14).Therehasalsobeenworkoncanberepresentedmathematicallybyagenera-scienceandcomputerscience,provideapartic-anevenmoregeneral“probabilisticlogic”thattivemodel,suchasamaportreestructureoraularlypowerfulandsuccessfulaccountofcausalcanencodeamuchwiderrangeofrelationships,graphicalnetwork.Therepresentationisahypoth-knowledgeandlearning(6,12,13).Algorithmsincludingspatialandlogicalaswellascausalesisaboutwhattheactualstructureislike.ThisthatuseBayesnetsallowcomputerstoactuallyones.Atleastinprinciple,thislogicallowsahypothesiscanbepreciselydescribedinformaldosomekindsofscience,suchasdiscoveringthewiderangeofgenerativemodelstobelearnedways.Therepresentationisgenerative,whichcausalstructureofweathersystems,geneexpres-fromprobabilisticdata(15).meansthatitwillallowyoutomathematicallysion,orbrainfunctionfromdata.Unliketraditionalnativism,theprobabilisticcomputethepatternsofevidencethatfollowfromMostrecently,thisworkhasbeenexpandedmodelsapproachgivesusawaytoactuallyinferthatstructureandthenmakenewinferencesac-toallowforformalrepresentationsofmoreabstractabstracthierarchicalstructurefromdata,atleastcordingly:Aparticularmapwillletyoupredicthowtoreachapar-ticulargrammaticaltreewillletyoupredictwheth-eranewsentaparticularcausalgraphwillletyoupredictwhetheraneweventwillbefollowedbyotherevents.Ifthehypothesisiscorrect,thenthesepredictionswillturnouttoberight.Thesegenerativemodels,then,candescriberepresentationsoftheworldandexplainhowthoserepresentationsallowustomakeawiderangeofnewinferences.Critically,thesystematiclinkbetweenstructureandevidenceinthesemod-elsalsoallowsyoutoreversetheprocessandtomakeinferencesaboutthenatureofthestructurefromtheevidenceitgenerates.Itletsyoudecidewhichmaportreeorcausalgraphbestaccountsfortheevidence,andsoleadsyoutoadoptthemostlikelyhypothesis.Theideathatmentalmodelsofthestructureoftheworldgeneratepredictions,andthatwecaninvertthatprocesstolearnthestructurefromevidence,isnotitselfnew.Thebigadvancehasbeenintegratingideasaboutprobabilityintothatbasicframework.Typically,agreatmanyhypothe-sesare,inprinciple,compatiblewithanypatternofevidence,sohowcanwedecideonthebestone?Integratingprobabilitytheorymakesthislearningproblemmoretractable.Althoughmanyhypothesesmaybecompatiblewiththeevidence,somehypotheseswillbemoreorlesslikelytohavegeneratedtheevidencethanothers.OneofthemostpowerfulandgeneralwaystosolvethelearningproblemistouseBayesianinference.Ifweknowthepriorprobabilityofahypothesis,andagenerativemodeltellsusthelikelihoodoftheevidencegiventhehypothesis,thenwhenweobserveanewpatternofevidence,wecanuseBayes’ruletodeterminetheprob-abilitythatthehypothesisistruegiventhatevi-dence.Ratherthansimplygeneratingayes-or-nodecisionaboutwhetheraparticularhypothesisistrue,theprobabilisticBayesianlearningalgo-rithmsconsidermultiplehypothesesandassignprobabilitiestothosehypotheses.Bayesianmeth-odsletyoudeterminetheprobabilityofpossibilities.BayesianideashavebeensuccessfullyappliedFig.2.Schematicrepresentationoftheping-pongballexperiment.Theexperimentershowedtheinfantstoawiderangeofproblems,includingvisionandaboxfullofwhiteandredballs.Thensheclosedhereyesandrandomlytooksomeballsfromtheboxandmotorcontrol(10,11).Thiskindofperceptualputtheminanothersmallbin.Ifthesamplewastrulyrandom,thenthedistributionofballsinthebinandmotorlearningmaynotappeartoresembleshouldmatchthedistributionoftheballsinthebox.Infantssawasamplethateithermatchedordidnotmatchthedistribution,andtheylookedlongeratthenonmatchingsample.Inacontrolcondition,infantsscientificlearning.Butprobabilisticmodelshavesawjustthesamesequenceofevents,buttheexperimentertooktheballsoutofherpocketratherthanalsobeenappliedtopreciselythekindsofknowl-takingthemfromthebox,andthelooking-timedifferencedisappeared.162428SEPTEMBER2012VOL337SCIENCEwww.sciencemag.orgDownloaded from www.sciencemag.org on October 6, 2012REVIEWinprinciple.Ifchildrenlearnedinthisway,theycoulddrasticallyrevisetheirrepresentationsoftheworldonthebasisoftheirexperience,asscientistsdo.Theywouldnotbelimitedtomakingsmalladjustmentstoinnatelydeterminedrepre-sentations.Unliketraditionalempiricism,theap-proachproposesthatchildren,alsolikescientists,neverstartfromacompletelyblankslateorwithcompletelypuredata.Instead,fromtheverybe-ginning,theywouldbetestinghypothesesandassessingthedatainthelightofthosehypotheses.ChildrenasScientificLearnersDochildrenactuallylearnabouttheworldinthisway?Overthepast10years,researchershavesystematicallygivenyoungchildrenpatternsofevidenceabouttheworldandthenobservedtheconclusionsthattheydraw[e.g.,(7)andarticlesin(16,17);foranextensivereviewandtutorial,see(18)].Toastrikingextent,childrenusedatatoformulateandtesthypothesesandtheoriesinmuchthesamewaythatscientistsdo.Scientistslearnabouttheworldinthreeways:Theyanalyzestatisticalpatternsinthedata,theydoexperi-ments,andtheylearnfromthedataandideasofotherscientists.TherecentstudiesshowthatchildrenalsolearninthesewaysandthattheyoftenresembleidealBayesianlearners.Proba-bilisticmodelsmakeaccurateanddetailedpre-dictionsaboutchildren’slearning.Statistics.Anyonewhohasevertaughtameth-odscourseknowsthatadultshaveahardtimeexplicitlyunderstandingstatistics.Itmaybesur-prising,then,thatevenveryyounginfantscanimplicitlyreasonstatistically.Thefirstwaveoftheseexperimentsshowedthatevenyoungin-fantsaresensitivetostatisticalpatterns[e.g.,(19)].Morerecently,researchershaveshownthatin-fantsandyoungchildrennotonlydetectstatis-ticalpatterns,theyusethosepatternstotestcausalhypothesesaboutpeopleandthings.Forexample,XuandGarcia(20)demon-stratedthat8-month-oldsweresensitivetostatis-ticalsamplingpatterns.Theyuseda“looking-time”techniquethathasbeenextensivelyusedtostudyinfantcognition.Itdependsonthefactthatin-fantslooklongeratunexpectedevents.Whentheexperimentertookasampleofmostlyredping-pongballsfromaboxofmostlywhiteballs,in-fantslookedlongerthanwhenshetookasampleofmostlyredballsfromaboxofmostlyredballs(Fig.2).Notethattheunlikelyeventsinthisexperi-myoucould,afterall,pullmostlyredballsfromaboxofmostlywhiteballs.Theeventsweremerelyimprobableifyourcausalmodeloftheeventassumedthattheballsinthebinwerearandomsample.It’sasiftheinfantssaidtothemselves,“Aha!Lessthan0.05probabilitythatthisoccurredbychance!”Butwouldthesurprisingevidencedrivethechildrentoanewcausalmodel?Kushniretal.(21)foundthatitwould.Infact,childrenasyoungas20monthsinterpretednon-randomsamplingpsychologically.Anexperi-mentertookfrogsfromaboxofallfrogsorshetookfrogsfromaboxofalmostallducks.Thenshelefttheroomandanotherexperimentergavethechildasmallbowloffrogsandaseparatebowlofducks.Whentheoriginalexperimenterreturned,sheextendedherhandambiguouslybetweenthebowls.Thechildrencouldgivehereitherafrogoraduck.Whenshehadtakenfrogsfromaboxofallfrogs,childrenwereequallylikelytogiveherafrogoraduck.Whenshehadtakenfrogsoutoftheboxthatwasalmostallducks,childrengaveherafrog.Inthefirstcase,thechildrenconcludedthatshehadmerelydrawnarandomsamplefromthebox,butinthesecondcasetheyconcludedthatshehaddisplayedapreferenceforfrogs.Thus,childrenlessthan2yearsoldhadinferredanunderlyingmentalstate―apreference―fromastatisticalpattern.Inanotherlineofresearch,mycolleaguesandIdesignedasimpletesttoseewhetheryoungchildrenwouldappropriatelyinferphysicalcaus-alrelationshipsfromstatisticalevidenceaboutcovariation(7,22).Weshowedchildrena“blicketdetector”―aboxthatplaysmusicwhenyouputsomeobjectsonitbutnotothers―andthenshowedthemvariouspatternsofstatisticalde-pendencebetweentheobjectsandtheeffect.Thenweaskedchildrentomakethemachinegoorturnitoff.Figure3showsonesuchexperi-ment.Basedonthechild’spriorknowledgeaboutthemachine,itcouldhaveanyofthecausalstructuresrepresentedinFig.3.Wefoundthat2-,3-,and4-year-oldscouldusethepatternofco-variationbetweentheblocksandthemachine’sactivationtoinferwhichofthesecausalstruc-tureswascorrect,andsotomakethemachinegoorstop.Otherstudiesshowthattoddlersasyoungas24monthscanmaketheseinferencesevenwhenthestatisticalpatternismorecompli-cated(23).Onerecentstudyshowsthateven16-month-oldscanusecovariationtoinfercausationinthisway(24).Schulzetal.(25)showedthat4-year-oldchil-drencouldalsousestatisticaldependenciestoinfermorecomplexcausalstructures.Childrensawasimplemachinewithaswitchononesideandtwodisksthatspunontop.Eventhissimplemachinecouldworkinmanydifferentways(theswitchcouldmakethebluediskgo,whichcoultheswitchetc.).Preschoolersusedevidencecorrectlytodistinguishbetweencausalchainstruc-tures(theswitchmakesthebluediskgo,whichmakestheyellowdiskgo),commoncausestruc-tures(theswitchmakesbothdisksgo),andcon-junctivecausestructures(theswitchandthebluediskarebothnecessarytomaketheyellowdiskgo).Bayesianinferenceconsidersbothnewevi-denceandthepriorprobabilityofhypotheses.ThisgivesBayesianlearningacharacteristiccombi-nationofstabilityandflexibility.Inscience,weholdontowell-confirmedhypotheses,butenoughnewevidencecaneventuallyoverturneventheABABObject A activatesthe detector by itselfObject B does not activatethe detector by itselfBoth objects activatethe detectorCausal interpretationsFig.3.Theblicketdetectorexperiment.ChildrensawthatthemachinedidnotactivatewhenBalonewasplacedonit,butdidactivatewhenAwasplacedonitandcontinuedtodosowhenBwasaddedtoA.Thentheywereaskedtomakethemachinestop.Giventhisevidence,thecorrectcausalinterpretationisthatAaloneactivatesthemachine,andthechildrenshouldactonAandnotB.www.sciencemag.orgSCIENCEVOL33728SEPTEMBERDownloaded from www.sciencemag.org on October 6, 2012REVIEWmostcherishedidea.Severalrecentstudiesshowtesteachbeadbyitself.The“allbeads”conditiontubes,eachofwhichdidsomethingdifferentthatchildrenintegratepriorknchildrencanassumethatbothbeads(onelitup,onemadeasqueakingsound,etc.).Inevidence,too.Forexample,4-year-oldsbeginbywillmakethemachinego.Sureenough,childrenonecondition,childrensawtheexperimenterac-thinkingthatpsychologicalcauses(e.g.,beingspontaneouslypulledthebeadsapartandtestedcidentallybumpagainstthetoy,settingoffoneofanxious)areunlikelytocausephysicaleffectsthemseparatelyintheirplayinthe“somebeads”thesqueakytubes.Thenshesimplyleftthechild(e.g.,havingastomachache)andrejectevidenceconditionbutnotintheotherwiseidentical“allalonetoplaywiththetoy.Thechildrenimitatedtothecontrary.Butifyougivethemaccumulat-beads”condition.thesqueakbutalsodiscoveredalltheotherthingsingevidenceinfavorofthis“psychosomatic”Similarly,Legare(34)showed4-year-oldsthatthetoycoulddo.Inanothercondition,thehypothesis,theygraduallybecomemoreandmorethatredblocksmadea“blicketdetector”machineexperimenterintroducedthetoybysaying“Herelikelytoacceptthatinitiallyunlikelyidea(26),goandthenshowedthemananomaly―aredismytoy”andthenmadeitsqueak.LiketheandaBayesianmodelcanpredictthischangeblockthatfailed.Sheaskedthem“Whydidthatchildrenintheimitationexperiment,childreninquiteprecisely.happen?”andletthemplaywiththemachine.thisconditionsimplyrepeatedwhattheexperi-Childrenalsousestatisticstoinfertheexis-Childrensystematicallyplayedwiththemachinementerdid,anddidn’texplorethemachine’stenceofunobservedcauses―hidden“theoreticalinwaysthattestedthehypothesesthattheyex-otherpossibilities.entities.”Gopniketal.(7)foundthatwhenthepressedintheirexplanations.AnotherrecentstudyThesenewstudies,andmanysimilarones,observedvariablescouldn’texplaintheevidence,showsthatpretendplayisalsocloselyrelatedtosuggestthatchildrenaswellasscientistslearnchildrenwouldlookforunobservedvariablesin-counterfactualreasoning―aparticularlysophis-inwaysthatarewelldescribedbyprobabilisticstead,inawaythatcouldbepredictedbyBayesticatedtypeofcausalinference(35).models.Thisresearchalsoraisesmyriadnewnets.SchulzandSommerville(27)foundthatTheseresultsindicatethatwhenyoungchil-problemsandexcitingdirectionsforfurtherwork.whenchildrensawa“blicketdetector”thatwentdrenfaceacausalpuzzle,theytrytosolvethatHowaretheseabstractcomputationsactuallyim-offonly2of6times,theyinferredthatsomepuzzleintheirspontaneousplay.Children’sac-plementedindetailbylimitedhumanmindsand,hiddenvariablewasresponsibleforthefailures.tionsensurethattheyreceivecausallyrelevantultimately,howaretheyinstantiatedinhumanFinally,wecanaskwhetherchildrenarere-andinformativeevidence.Oncethatevidencebrains?Childrenandscientistsoftenseemtode-strictedtomakingspecificinferencesaboutisgeneratedthroughplay,childrencanuseittovelopradicallynewhypotheses.Wheredotheseparticularcausalrelationshipsorwhether,likemakethecorrectcausalinferences.hypothesescomefrom?Arechildrensimplylearn-scientists,theycanalsomakeinferencesabouterswithlessexperience―inBayesianterms,dobroader“frameworkprinciples”―generaltheoret-LearningfromOtherstheysimplyhaveadifferentprior?Ordotheyicalideasor“paradigms.”Anexcitingdevelop-Thepictureofthechildasa“littlescientist”haslearninwaysthatareBayesianbutarequalita-mentinthecomputationalworldhasbeenthesometimesbeentakentoimplythatchildrenaretivelydifferentfromadultlearning?Forexample,discoverythatmoreabstracttheoreticallawscansolitarylearners.Ofcourse,realscienceisahigh-dotheysearchawiderspaceofhypothesesthanactuallysometimesbelearnedmorequicklythanlysocialendeavor,andscientistsmustconstantlyadultsdo(29)?Howisthislearninginfluencedthespecificcausalhypothesestheysubsume(28).interpretthedemonstrationsandreportsofotherbythedevelopmentofexplicitsymbolsystems,Tworecentstudiesalsosuggestthatpreschoolerspeople.Childrencanalsolearnaboutcausalrela-fromlanguageitselftothecomplexmathematicalcanmakethesebroadergeneralizationsswiftlytionshipsbywatchingwhatotherpeopledoandnotationofphysics?Whatistheidealbalanceandappropriately(29,30).whathappensasaresult.Inourlab(36),4-year-betweenindividualdiscoveryandlearningfromoldssawanexperimenterperformfivedifferentothers,anddoesthisbalanceshiftindifferentdrenExperiments.hasseenhowAnyonetheywhoceaselesslywatchesfiddleyoungwithchil-sequencesofthreeactionsonatoy,whichac-educationalandscientificcontexts?Thenewthe-thingsandobservetheresults.Children’splaytivatedordidnotactivateoneachtrial.Asta-oreticalideasandexperimentalmethodsgivecanlooklikeexperimentation.RecentresearchtisticalanalysisofthedatawouldsuggestthatusaframeworkforaskingandansweringthesebySchulzandcolleaguesshowsthatchildren’sonlythelasttwoactionswerenecessarytoactivatequestions.exploratoryplaydoesindeedinvolveakindofthetoy.Whenchildrengotthetoy,theyoftenintuitiveexperimentation.Children’splayisnotproducedjustthetworelevantactions,ratherthanImplicationsforPolicyasstructuredastheidealexperimentsofinstitu-imitatingeverythingthattheexperimenterdid.Sonewtheoreticalworkletsusdescribebothsci-evenadultscanhaveahardtimeMoreover,veryyoungchildrenandevenin-entificlearningandchildren’slearninginanewlydesigningideallycontrolledexperiments[e.g.,(31)].fantsaresensitivetotheintentionsofothers,par-systematicandrigorousway.NewempiricalworkHowever,recentformalworkinthephilosophyticularlytheirintentiontoteach,andmaydrawshowsthatyoungchildrenlearnfromstatistics,ofsciencehasshownthatmuchlesssystematicdifferentconclusionsfromtheevidencethatteach-experiments(i.e.,play)andfromtheactionsofexperimentationcanyieldaremarkableamountersgivethemthanfromtheevidencetheygatherothersinmuchthesamewaythatscientistsdo.ofcausalknowledge(32).Theempiricalresearchthemselves.Bayesianmodelscanincorporateped-Whatdoesallthismeanforeducationandpolicy?showsthatplayissufficientlysystematictohelpagogicalinformationbyassumingthatteachersFirst,thisworkprovidesanexplanatoryfoun-childrendiscovercausalrelationships.provideadifferentandmoreinformativesampledationforthedemonstrableimpactofhigh-qualityForexample,Cooketal.(33)performedaofevidencethanonewouldgetfromarandompreschoolandcareforchildrenonlaterlife(39).variantofthe“blicketdetector”experimentsusingsample(37).Veryyoungchildrenarespontaneouslyandper-“We(36)didexactlythesamestatisticalimi-vasivelylearningfromexperience.Moreover,thehookedpop-beads,together”smalltomakeplasticlargerbeadsunits.thatcouldFirst,thebetationexperimentbutnowincludedpedagogicalBayesianpictureprovidesabettermodelfortheseexperimenterputindividualbeadsonthema-information:Theexperimentersaid“Here’smyeffectsthanthinkingaboutearlychildhoodasanchine.Onegroupof4-year-oldssawthatsomeoftoy,I’mgoingtoshowyouhowitworks.”Inthisirreversible“criticalperiod.”Withouttherightse-thebeadsmadethemachinegoandsomedidn’t.condition,childrenweremuchmorelikelytoas-quenceofevidence,theoreticaladvanceswillbeAsecondgroupsawthatallthebeadsmadethesumethateverythingtheadultdidwascausallydelayedormayneveremergeatall.Conversely,machinego.Then,theexperimentersimplygaveeffectiveandtoimitateallheractions.ABayesianwhenparticularhypothesesareespeciallywellthechildrenthemachineandtwonewbeadsthatmodelmadequiteprecisequantitativepredictionsconfirmedearlyinlife(hypotheses,forexam-werehookedtogetherandletthemplay.aboutwhatthechildrenwoulddointhepeda-ple,thatexpressingdistresscausescaregiverstoThe“somebeads”conditionsetsupacausalgogicalandnonpedagogicalcontext.turnaway,orthatthreatleadstoviolence),itmayproblemforthechildren:WhichbeadsmaketheSimilarly,Bonawitzetal.(38)gavechildrenbemuchmoredifficultforthemtoberevisedmachinego?Tosolvethatproblem,youneedtoacomplicatedtoytoexplore.Thetoyhadfourlateron.Eventhemostentrencheddysfunctional162628SEPTEMBER2012VOL337SCIENCEwww.sciencemag.orgDownloaded 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