ContentslistsavailableatScienceDirect
Thinking Skills and Creativity
jo u r n al h om epa ge : h t tp : / / w w w . e l s e v i e r . c o m / l o c a t e / t s c
Playful fostering of 6- to 8-year-old students’ inductive reasoning 夽
Gyöngyvér Molnár
∗InstituteofEducation,UniversityofSzeged,30-34.PetofiSsgt,SzegedH-6723,Hungary
a rt i c l e i n f o
Articlehistory:
Received9November2010
Receivedinrevisedform25April2011 Accepted4May2011
Available online 12 May 2011
Keywords:
Inductivereasoning Thinking Training Earlyintervention
a b s t r a c t
Thispaperfocusesonatrainingprogramininductivereasoningforfirst-gradestudents andpresentsthedirectresultsaswellasthelongitudinaleffectsoftheevaluationstudy.
ThetrainingisbasedonKlauer’stheoryofinductivereasoningandonhis“Cognitivetrain- ingforchildren”concept(Klauer,1989a).Thetrainingprogramconsistsof120problems whichcanbesolvedthroughinductivereasoning.Thetoolsforthetrainingexerciseswere selectedtocorrespondwiththeageofthetargetedcohort.Theexperimentalgroupinthe studyconsistedof90students,whereasthecontrolgroupwasmadeupof162.Aninductive reasoningtestwasusedinthepre-andposttestaswellasinthefollow-upstudy(oneyear later).Thetestcomprised33figural,non-verbalitems(Cronbach˛=.86).Ontheposttest, theexperimentalgroupsignificantlyoutperformedthecontrolgroupbymorethanone standarddeviation.Theexperimentalgroupscoredsignificantlyhigherineachskillarea targetedbythetraining.Themostnoticeabledevelopmentwasfoundinsystemformation.
Nogenderdifferencesweredetectedonthepre-ortheposttest.Theeffectsizeofthetrain- ingprogramwasd=1.12.Inthefollow-upstudy,theexperimentalgroupstillsignificantly outperformedthecontrolgroup;however,theirrespectivelevelsofdevelopmenthadnot changedinthisone-yearperiod.Thus,thetrainingeffectprovedtobestableovertime independentofindividualstudents’originallevelofinductivereasoning.Thisstudypro- videdevidencethatinductivereasoningcouldbedevelopedveryeffectivelyatthisearly age.
© 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Findingsfrompriorresearchhavehighlightedtheprimaryimportanceofdevelopinginductivereasoningin knowl- edgeacquisitionandapplication(Bisanz,Bisanz,&Korpan,1994;Hamers,DeKoning,&Sijtsma,2000;Klauer,1990,1996;
Pellegrino&Glaser,1982),inproblemsolving(Chi,Glaser,&Rees,1982;Egan&Greeno,1974;Johnson-Laird,1983;Klauer, 1989b,1996;Polya,1954)andinthedevelopmentofexpertise(Cheng&Holyoak,1985;Chietal.,1982);therefore,itplays acentralroleingainingadeeperunderstandingofthesubjectmatterinaclassroom.Thiscertainlysuggeststhatthese thinkingskillsshouldbecomeanintegralpartoftheschoolcurriculum(deKonig,2000;Resnick,1987)andshouldplaya roleinabroadrangeoflearningactivitiesinschool.
Nevertheless,thestimulationofthinkingskillsisnotpursuedexplicitlyinschools.Educationfocusesonreading,writing, andmath,whichareconsideredtobethemainrequirementsforparticipationinwesternsociety(deKoning,Hamers,Sijtsma,
夽 ThepresentstudywasconductedwiththefinancialsupportoftheK75274OTKAresearchprogram,theSzegedCenterforResearchonLearningand InstructionandtheSZTEMTAResearchGroupontheDevelopmentofCompetencies.TheauthorwasonaBolyaiJánosResearchFellowshipatthetimethe presentstudywaswritten.
∗ Tel.:+36207756478.
E-mailaddress:gymolnar@edpsy.u-szeged.hu
1871-1871/$–seefrontmatter© 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tsc.2011.05.002
s n o i t a l e R s
e t u b i r t t A
Item class Ite m-type Ite m-clas s Ite m type Similarities Generalizati on
-Class formatio n
Recognizin g relation s
-Ord er serie s n o i t e l p m o c s e i r e S - n
o i s n a p x e s s a l C -
-Fin din g comm on attributes
-Simple analogies Difference s Discri mination -Cl ass exc lusio ns Discr imination
relation s
-Disrupte d ser ies Similarities and
difference s
Cross- class ificati on
-4,6,9 fold schemes, matrix figure s
Syste m for matio n
-Mat rix-figures with complex analogies
Fig.1.Klauer’staxonomyoftheclassesofinductivereasoningtasks.
&Vermeer,2002).Itiscommonlyassumedthatreasoningskillsdevelopspontaneouslyasa“by-product”ofteachingordinary schoolmaterial(deKonig,2000).Thatiswhyinductivereasoningskillswereinthefocusoftheexperimentpresentedhere.
Twodirectionscanbedistinguishedinthedevelopmentofthinkingskills.Researchersbelongingtothefirstbelievethat thinkingskillscanonlybetaughtexplicitly(seee.g.Feuerstein,Rand,Hoffman,&Miller,1980;Klauer,1989a,1991,1993;
Lipman,1985).Researchersthatidentifywiththesecondbelievethatitshouldbeembeddedinschoolsubjects(e.g.the CASEproject,seeDienes,1963,1973;Shayer&Adey,1981).Inthepresentstudy,inductivereasoningstrategiesweretrained explicitly.
Intheprocessofselectingthetargetpopulation,Piaget’sdevelopmentaltheories(conservationanddevelopmentalstages) andthecurrentunderstandingofskilldevelopmentineducation(Csapó,1997,2003;Molnár&Csapó,2003)wereconsidered, alongwiththeresultsofprecedingtrainingprogrammes(seee.g.Józsa&Zentai,2007;Nagy&Gubán,1987;Pap-Szigeti, 2007)thatinvestigatedtheeffectivenessofinterventioninrelationtothetargetpopulationandthesuccessoftraining.All inall,thesepreliminaryfindingssuggestedthattheearlierdevelopmentstarts,themoreeffectiveitcanbe.
ThetrainingpresentedisbasedonKlauer’stheoryofinductivereasoningandtheGerman“Cognitivetrainingforchildren”
program(Klauer,1989a;Klauer&Phye,2008).Klauerdefinedinductivereasoningasthediscoveryofregularitiesthrough thedetectionofsimilarities,dissimilarities,oracombinationofboth,withrespecttoattributesorrelationstoorbetween objects(Klauer,1993).Thistotalssixclasses(generalization,discrimination,cross-classification,recognizingrelations,dis- criminatingbetweenrelations,andsystemformation).Klauerprobablyconstructedthemostelaboratesystemforinductive reasoning,definingitselementsandtheirrelationships.Ataxonomyoftypesofinductivereasoningtasksanditemtypes usedareshowninFig.1.
2. Methods 2.1. Participants
Existingclassesoffirst-gradestudentswereinvolvedinthestudy.Fiveclasses(n=90)constitutedtheexperimental group.Thecontrolgroupconsistedofsimilarchildreninrespectofbackgroundvariables(n=162).
2.2. Instruments
SimilarlytoKlauer’soriginalprogram,thistrainingconsistsof120problems,i.e.20problemsineachclassofinductive reasoning,whichcanbesolvedthroughtheapplicationofappropriateinductivereasoningprocesses.Additionally,thescope andquantityoftoolsappliedinmanipulativetaskswereexpanded,thesub-structureoftheprogramwaschanged,andthe images,objectsandproblemswerefitintotheprogramaccordingtotheinterestsofchildrentodayandthestoriestheyare familiarwith.Theprogramusesobjectsandpicturesthatcorrespondtotheageofthetargetedcohort,andonequarterof thetasksaremanipulative(performede.g.withcolorfulbuildingblocks,Dienes’slogicalset,matches,etc.).Thecontexts changeinasimilarwayineachclassofinductivereasoningthroughouttheprogram,frommanipulationofobjectstouse inreal-lifesituations.
Halfofthetrainingtasksconcentrateonthecharacteristicfeaturesoftheobjectsandimagesoccurringinthesetasks andtherelationsbetweentheseobjectsandimages,suchastheirsimilarities,differencesandco-occurringsimilaritiesand differences.
Inthetasksthataimattraininginthe(1)operationofgeneralization,thestudentswereexpectedtogroupobjectsby(a) creatingclasses,(b)completingalreadyexistinggroupsor(c)findingcommonattributes.Inthefollowingsection,sample itemsareprovidedforeachtype:
(a)Classformation.StudentsweregivenpiecesofDienes’slogicalsetandaskedtoclassifythesepiecesintofourseparate groups(seeFig.2).
Fig.2.Examplesoftasksintheprogram.
(b)Classexpansion.Studentswereshownimagesof4+3objects,e.g.(1)alemon,anapple,apear,andacherry,and(2)a flower,abug,andabanana.Theythenhadtofindtheonlyobjectinthesecondgroupthatischaracterizedbythefeature thatalltheitemsinthefirstgrouphadincommon.
(c)Findingcommonattributes.Studentsweresuppliedwiththreeimages:abird,anairplane,andabutterfly.Theywerealso instructedtodescribewhattheimageshadincommon.
Theproblemsofthetaskstargetingthe(2)operationofdiscriminationfocusedonthedifferencesintheattributesofthe objectsthatoccurinthetasks.Studentsweretoldtofindtheoneobjectthatdifferedonlyinasinglefeaturefromallthe otherobjectswithsimilarandidenticalfeatures.Forinstance,sevenimagesofdifferentballswereprovided(seeFig.2).The questionwastoascertainwhichoftheseelementsaredifferentfromtheothersandwhy.
Thetasksthataimedatfostering(3)cross-classificationincludedboththeoperationsofgeneralizationanddiscrimination.
Here,studentswereinstructednotonlytoconsiderthesimilaritiesordifferencesintheattributesofindividualobjects,but alsotogrouptheobjectsbasedonasetofsimilaritiesordifferencestobetakenintoaccount.Forinstance,flowersofdifferent colorscouldbeseeninthevariouswindowsofacertainhouse.Intheupperleft-handwindowtherewereonlyredflowers, intheupperright-handwindowflowersofvariouscolors,inthelowerleft-handwindowonlyredgeraniums,andcolorful geraniumsinthelowerright-handwindow.Studentshadtodecidewheretheownerofthehousewouldplaceanewly boughtyellowtulip(seeFig.2).
Fig.3. Examplesoftasksintheinductivereasoningtestwiththemeasuredclassesofinductivereasoning.
Theotherhalfofthetrainingtaskswasbasedontherelationstoorbetweenobjects,theirsimilarities,theirdifferences andtheco-occurringsimilaritiesanddifferences.Inthetaskstargeting(4)recognitionofrelations,studentswereinstructed to(a)organizeitemsintoseries,(b)completeseriesor(c)findsimpleanalogiesbetweenobjectsorpictures.Inthefollowing section,sampleitemsareprovidedforeachtype:
(a)Orderingtasksrequiredstudentstoorderobjects,imagesorevents.Inonesuchtask,theywereexpectedtoorganize picturesfromabedsidestoryintoameaningfulsequence(seeFig.2).
(b) Inthecompletiontasks,studentswereaskedtocontinueaserieswhilekeepingtheoriginalrelationshipsoftheitems intheseries.Forinstance,WinniethePoohkeepseatinghoneyfromapotthatisnaturallybecomingevermoreempty.
Followingthepaceofhoneyconsumption,studentsweretoselecttheappropriatepicturesfromamongthosedepicting potsofvariouslevelsoffullness.
(c)Inthetasksthataimatfosteringsimpleanalogies,studentsweremeanttorecognizetherelationshipsbetweenpairsof objectsandapplythissamerelationshiptoanotherpairofobjects.Forexample,honeyistoabearas...(cheese)istoa mouse.
Twokindsof“biased”seriescouldbefoundinthetaskscontaining(5)operationsofdiscriminatingrelations.Inthefirst case,studentswereinstructedtorecognizewhichtwoelementsofthesequencehadbeenexchanged,whileinthesecond typetheyhadtofindtheextraelementthatdoesnotfollowtherulesofthesequence.Forexample,threeboysandtwogirls arestandingnexttoeachother.Exchangeaboywithagirlintherowsothatagirlisalwaysstandingnexttoaboy(Fig.2).
Inthetasksfor(6)systemformationthatrequirematrixfigureswithcomplexanalogy,studentshadtoconsiderboththe factthatrelationsshouldbeidenticalandthatnotonlyone(horizontallyorverticallyappearing)relationisimportant,but acomplexoftwo(horizontalandvertical)oreventhreerelations.Forinstance,thereisabigpuppyintheupperleft-hand cellofafour-cellbox.Thereisasmallpuppyunderthiscell,andnexttothisfirstcelltherearetwobigpuppies.Thequestion is:whatgoesinthelowerright-handcell?Asmallpuppy,twosmallpuppies,asmallandabigpuppy,oronebigpuppy(see Fig.2)?
Itwasintendedthatthetasksforthetrainingprogrambeconstructedsuchthatstudentswouldperceivetheworkof developmentasplayinggames,notaslearning,hencesuitingstudents’developmentandotherage-specificconsiderations.
Thebasicstructureoftheprogramstartswithmanipulativetasksinwhichstudentscanplayanddrawusingcolorfulbuilding blocks,elementsofthelogicalset,colorpencils,matchesandcards.Thesemanipulativetasksgraduallygivewaytoplayful taskswithimagesofvariousobjects,toysorstorycharacterswhich,bytheendoftheprogram,arereplacedbysymbolsand real-lifesituations.Carryingoutthetasksrequiresnoreading,sinceitwouldbeunfairtoexpectstudentstoreadatsuchan earlyage.
Theeffectivenessofthetrainingwasmeasuredwitha33itempaper-and-penciltestofinductivereasoning,developed specificallyforyounglearners.Duetotheyoungageofthetargetpopulation,specialcarewastakentoensurethenon-verbal characterofthetest;i.e.ithadtocontainnumerouspictures,figuresandimagesandaslittlereadingtextaspossible.This istoavoidmeasuringstudents’readingskillsinsteadoftheirinductivereasoningskills.Thestructureofthetestisbasedon thedefinitionofinductivereasoning,citedabove;i.e.theitemsbelongedtothesixsub-classesofinductivereasoning(see Fig.3).ThereliabilityindexforthewholetestwasCronbach␣=.87.Validityofthetestwasensuredbyconstructionanda precisealignmentbetweentheframeworkandthetest.
2.3. Procedures
Intermsofthemethodsandworkformsofthetraining,thestudentsweregiventhetrainingindividuallyorinpairor groupwork.Themainbenefitofindividualworkisitsintensity,whilethedrawbacksincludehightimeconsumptionand
fasterstudentexhaustion.Onlychildrenwitharoundthesamelevelofskillswereputintopairsandgroups(3–4children) suchthateachstudentwasindividuallysuppliedwiththetaskandtheassistanceneededtocarryitoutandthen,after thetaskwascarriedout,eachwasexpectedtoprovideherorhissolutionone-by-one.Wedonothavedataaboutwhat proportionofthesamplewastrainedindividually,inpairsorinsmallgroups.
Theworkingmethodsmightfurtherincludedirecteddiscovery,thinkingaloudandfollowingtheteacher’sdemonstration ofthesolutions.Forfurtherdetails,seeMolnár(2006).Thetimerequiredfortheworkofdevelopmentdependedonthe individualstudents.Itisrecommendedthateachsessionshouldlastfor20minandcontain12tasksatmost.Thismeant thatthe120tasksweredividedinto10sessionsonaverage,dependingonthestudents’skilllevel,abilitytoconcentrate, motivationandlevelofexhaustion.Thetrainingwasperformedafterthelessons,duringdaycare,whentheremainingpart oftheclasscouldgoouttotheschoolyardandplay.
Therewasateamofimplementers,namelytheclassteachers,whointroducedtheactivitiestothechildren.Twoweeks beforethetrainingtheimplementersreceivedashort(2–3-hlong)on-spotgrouptrainingfromtheresearchersabout(1) howskillsandabilities,especiallythinkingskillsandabilitiesdevelopduringtheage-rangeofschooling(e.g.development islogisticand notlinear)and whatquestionscouldberaisedfromthesefeaturesofskillsandabilities (e.g.questions ofearlyselectionanditseffects).TopresentthetheoreticalframeworkIprimarilydrewonnationalsourcese.g.Csapó (1997)andMolnárand Csapó(2003)(2)theroleofcontextandissuesregardingtransferinconnectionwithdifferent developmentprogrammes(3)thedefinitionandcharacteristicsofinductivereasoningandabilitiestargetedinthetraining, (4)thestructureofthetraining,workingmethodsandtimerequiredfortheworkofdevelopment,(5)theprocessingof thetrainingtaskswithexamples,(6)resultsandexperiencesofthefirstpilotstudy,wherethetrainingwasperformed.
Theworkingmethodofthefirstpartofthetrainingwasfrontal,whiletheremainingpartofthetrainingwascommon groupwork,whereconcreteexampleswerestudied.Atthebeginningofthetrainingtheimplementersweregivenprinted materialstofollowaswell,inwhichalloftheabovementionedtopicsweredescribedinamoredetailedformwithseveral examplesgivenfromtheactualtraining.Besidestheprintedmaterial,everytaskincludedmethodologicalsuggestionsfor theimplementersthatcouldberaisedandappliedintheactualtrainingsituations:e.g.inconnectionwithtask7:“Aspart ofagamelet’sfindtherightshapestogetherwiththestudentsandlet’splacethemontothepicture!Let’sputonemorered triangularprism,ayellowsquare,agreenprismandaredsquare.Thenaskthestudentstocontinuethesequence.Drawtheir attentiontothedependentandindependentvariables!Ifwedonotsucceed,let’shelpthemtofindouttheruleswithclues anditsapplication.Ifthestudentmanagestodothetask,askthemwhattheruleis!”[Ajátékkedvéértadiákokkalegyütt keressükmegamegfelel ˝oalakzatokatéstegyükazokatráaképre.Adiákelétegyünklemégegy-egypirosháromszögalapú hasábot,sárgakockát,zöldhasábotéspiroskockát.Kérjükmeg ˝oket,hogyfolytassákasorozatot.Tudatosítsukbennüka függetlenésfügg ˝ováltozókat.Hanemmegy,vezessükrá ˝oketaszabályraésannakalkalmazására,hamegy,kérdezzükmeg, miaszabály.]andsamplequestions(inconnectionwithtask7theoriginalquestionwas:“Pleasecontinuethetaskwith onebuildingblock”[Folytasdasortegyépít ˝okockával]andthealternativequestionswere:“AccordingtowhatrulecouldI haveput/placethebuildingblocks?”[Milyenszabályszerinttehettemleazépít ˝okockákat?]“Andbasedonthatrulewhich buildingblockcouldcomenext?”[Ésazalapjánmelyiképít ˝okockakövetkezikasorban?]).
Thestudydesignmadeitpossibletomeasurenotonlythedirecteffectofthetraining,butalsoitslongitudinaleffect.
Threestagesofdatacollectionwererequiredtoassessboththedirectandthelongitudinaleffect.Thefirsttwodatacollection stagestookplacebeforeandimmediatelyafterthetrainingprocess.Theintervalbetweenthepretestandtheposttestwas8 weeks,theperiodinwhichthetrainingwasperformed.Thethirddatacollectionstage,thefollow-upstudy,wasconducted oneyearaftertheendofthetraining.Allgroupstookthesamepre-andposttestbeforeandafterthedevelopmentprocess andthesamefollow-uptestoneyearlater.
Studentswerenotallowedtouseanykindofaidsindoingthetest,but,duetotheiryoungage,theteacherswerepermitted toreadouttheinstructionsforthetasks,thuscompensatingforthedifferencesinstudents’readingskilldevelopment.One schoolsessionwasprovidedtodothetest.
Beforetheresearchquestionswereanswered,therawscoresweretransformedintopercentagescores.Tocompareboth students’performanceintheexperimentalandcontrolgroupsandthesub-groupsofthesample(e.g.genderdifferences), meanandstandarddeviationwerecomputedandanindependentsamplet-testwasused.Toanswertheresearchquestions ofwhetherthetrainingresultedinasimilareffectonstudentswithadifferentoriginallevelofinductivereasoningand whetherthetrainingeffectwasstableovertime,thedistributioncurvesforthesub-sampleswerecompared.Toplacethe programintoaninternationalcontextbyeffectsize,Cohen’s(1988)categorizationwasused.
3. Results
Nosignificantdifferenceswerefoundbetweentheperformanceoftheexperimentalandthecontrolgroup(t=1.2,p=.22) priortotheexperiment.Ontheposttest,theexperimentalgroupsignificantlyoutperformedthecontrolgroupbymorethan onestandarddeviation(seeTable1).Someofthestudentsmanagedtoachievesignificantdevelopmentintheexperiment period(8weeks)evenwithoutparticipatinginthetrainingprogram,whileothers’skillsstagnatedorevendecreased.Onthe whole,thereisasignificantchangeinperformanceinboththeexperimentalandcontrolgroups.Ayearaftertheendofour trainingprogram,thefollow-upstudystillindicatedasignificant(p<.001)advantagefortheexperimentalgroupcompared tothecontrolgroupinlevelofinductivereasoningskills.
Table1
Meansandstandarddeviationsofthetestforinductivereasoning(%).
Pretest Posttest Follow-uptest
M SD M SD M SD
Exp.group(n=90) 37.1 15.8 61.0 16.3 60.4 15.0
Contr.group(n=162) 39.3 16.2 47.0 16.7 54.5 15.1
Fig.4. Distributioncurvesofexperimentandcontrolgroupinthepre-,post-andfollow-uptest.
Inthecaseofthecontrolgroup,thedistributioncurveforthepretest(seeFig.4)isinclinedtotheleft,whileforthe posttestitleansslightlytotheleft.Thedelayedposttestshowedadistributioncurveskewedslightlytotheright,reflecting theeffectofspontaneousschooldevelopment.Furthermore,eachmemberoftheexperimentalgroupattainedsignificant improvementinperformanceasaresultofthetraining.Theoriginalcurveskewedtotheleftturnedintooneskewedtothe rightbytheendofthetrainingprogramandretainedthisshapeinthefollowingyear.
TheresultsabovearesupportedbythetwodiagramsinFig.5thatshowthechangesinexperimentalandcontrolgroup performanceonthestudentlevel,thecurvesforperformanceduringthefirstandseconddatacollectionstagesareprojected ontoeachother.Theabscissashowscomparativeperformancefromthefirstdatacollectionstageandtheordinatedisplays thisfromthesecond.Thesymbolsforthosestudentswhoperformedidenticallyinthetwocasesfallontheline.Ifapointis positionedabovetheline,itmeansthatthegivenstudentshoweddevelopmentfromonedatacollectionstagetotheother, whileifitisbelowtheline,itrepresentsworseperformanceontheposttestthanonthepretest.Thebrokenlinesindicateone standarddeviation.Inthecaseofthecontrolgroup(graphontheleft),thesymbolsaredistributedhomogeneouslyaround themeanline;i.e.themajorityofthesestudentsperformedquitesimilarlyinthetwodatacollectionphases.Theincreased standarddeviationmentionedabovewasaresultofsomestudentsoutdoingtheirpretestperformancebymorethan50%
intheposttest,andsomeunderachievingbyalmost30%.Awhollydifferenttendencyisdisplayedontheright-handgraph,
Fig.5. Changesoftheachievementofthecontrolandtheexperimentalgroupfrompretesttoposttest.
Cross-classification Discrimination
Generalization
Discriminating relations
Recognizing relations System formation
0 20 40 60 80
Follow- Posttest Pretest
up study
(%) n.s.
p<.05
n.s.
0 20 40 60 80
Follow- Posttest Pretest
up study
(%)
n.s.
p<.01 p<.01
0 20 40 60 80
Follow- Posttest Pretest
up study
(%)
n.s. p<.01
p<.05
0 20 40 60 80
Follow- Posttest Pretest
up study
(%)
n.s.
0 20 40 60 80
Follow- Posttest Pretest
up study
(%)
n.s.
p<.01
0 20 40 60 80
Follow- Posttest Pretest
up study
(%)
Control group Experimental group n.s.
p<.01 p<.05 p<.01
n.s.
n.s.
Fig.6.Themeanachievementofthecontrolandexperimentalgroupinthepre-andposttestandthefollow-upstudyintermsofthesixbasicstructures.
showingtheperformanceoftheexperimentalgroup.Asignificantnumberofsymbolsarelocatedonorabovethemeanline.
Therewerenostudentsinthisgroupwhoseperformancedroppedsignificantlyfrompretesttoposttest;moreover,several studentsimprovedbymorethanonestandarddeviation.Inaddition,therewasoneparticipantwhoreflectedadevelopment of67%.
Thetrainingresultedinasignificant(p<.001)improvementfortheexperimentalgroupinallsixclassesofinductive reasoning.Fig.6displaysthechangesinskilllevelsforeachclassofinductivereasoningimmediatelyafterthetrainingand ayearlater.
Posttestsrevealednosignificantdifferenceinperformancebetweentheexperimentalandthecontrolgroupsinitems thatmeasuregeneralizationskills,sincetherehadbeenasignificantdifferenceonthepretestwhichhadbeenoffsetbythe training.Hence,theexperimentalandcontrolgroupsreflectnodifferenceintheirspontaneousdevelopmentbetweenthe twoposttestsinthisdomain.
Theperformanceofthetwosub-samples,however,hadnotbeenstatisticallydifferentintheitemsthatmeasuredis- criminationpriortotheexperiment.Yettheyindicatedamorethan10%(p<.001)meandifferenceontheposttest.This advantagefortheexperimentalgroupwasevenincreasedbythetimeofthefollow-upstudy.
Experimentalgroupperformanceimprovedbymorethan15%inthecross-classificationitemsaswell.Here,thecomplete lackofchangeinperformanceamongthecontrolgroupstudentsaswellastheslightdeteriorationoftheexperimental groupintheyearfollowingthetraining suggestthatschooldoesnotmanagetoenhancetheseskillsinthisagegroup atall.
Wefindadifferentpictureintheitemsforrecognitionrelations.Accordingtothefirstposttest,thetrainingresultedinan extra20%improvementintheperformanceoftheexperimentalgroupbeyondthespontaneousdevelopmentofthecontrol group.Theexperimentalgroupreachedthesamelevelofdevelopmentinthiseight-weekperiodthatthecontrolgroupdid onlyayearlater.Thatis,lackingadditionalstimulationinschool,membersoftheexperimentalgroupdidnotdisplayany moreimprovement;instead,theywaitedfortheirschoolmates.
Thefindingsaresimilarinthedomainofdiscriminatingrelations.Theadvantageoftheexperimentalgroupreached20%
bytheendofthetraining;however,itincreasednofurtherinthefollowingyear.Moreover,membersoftheexperimental groupscoredloweronthesecondposttestthanonthefirstone,demonstratingthesamelevelofdevelopmentasthestudents inthecontrolgroup.
Themostconsiderabledevelopmentaleffectwasfoundinsystemformation.Thedevelopmentmeasuredinthisdomain wasalmost35%atthetimeofthefirstposttest.However,experimentalgroupstudentsdidnotdevelopfurtherinthefollow- ingyear,whilethecontrolgroupmanifestedsignificantimprovementinthisdomainaswell.Inspiteofthisphenomenon, theexperimentalgroupmaintainedsomeoftheadvantageithadgainedinthetraining,sincethefollow-upstudystill detectedasignificantdifferencebetweenthesub-samples.
Table2
Meansandstandarddeviationsofthetestforinductivereasoninginrelationtogender(%).
M SD t M SD t M SD t
Exp. Male 33.7 15.7 ns 61.0 14.7 ns 57.5 13.2 ns
Exp. Female 39.6 15.6 60.9 17.6. 62.4 16.0
Contr. Male 38.0 15.6 ns 45.1 16.0 ns 54.9 15.5 ns
Contr. Female 41.0 17.0 49.4 17.2 54.1 14.7
Table2showsthemeanperformanceoftheexperimentalandcontrolgroupsingenderdivision.Nosub-samplesdisplayed significantdifferencesintherelativeperformanceofboysandgirls,i.e.thedevelopmentisnotgender-specific.Similarly, thespontaneousimprovementmeasuredinthisperiodisindependentofgender.
Theeffectsizeofthetrainingprogramwasd=1.12(p<.01).UsingCohen’s(1988)conventionfordescribingthemagnitude effectsize,itisclearlyalargeeffect.Placingtheprogramintoaninternationalcontextaccordingtoitseffectsizeallowsfor favorableconclusions.Similarlytomanyotherresearchersinthe1980s,deKonig(2000)attainedaneffectsizeof.79with third-gradestudentsusingKlauer’soriginalprogram.
4. Discussion
ThispaperaddressesatrainingprogramofinductivereasoningforGrade1studentsandpresentsthedirectresultand thelongitudinaleffectoftheevaluationstudy.Accordingtotheresults,thedevelopmentalleveloftheexperimentaland controlgroupstudentsdidnotdifferpriortotheexperiment,meaningthatthecontrolgroupmeetstherequirementfor acontrolgroupinthestudy.Asaresultofthetraining,theinductivereasoningskillsoftheexperimentalgroupshowed greaterimprovementthanthatofthecontrolgroup.Theoperationsofinductivereasoningskillsdevelopedmoreinthe eightweeksoftheexperimentthantheywouldnormallyhaveinayearofconventionalschooling.
Comparingthedistributioncurvesmadeitpossibletoconsiderthechangesinexperimentalandcontrolgroupperfor- mancewithregardtostudents’originallevelofinductivereasoningskills.Theshapeofthedistributioncurvesshoweda significantdifferenceintherelativeperformanceoftheexperimentalandcontrolgroups.Inthecaseofthecontrolgroup, thechangeofthedistributioncurvescorrespondedtotheexpecteddevelopment,whileeachstudentintheexperimental groupattainedsignificantimprovementintheirperformanceasaresultofthedevelopment.Thetraininghadasimilarly strongeffectonstudentswithhighlydiverselevelsofskills.Thismeansthattheskillsofallthe6-to8-year-oldstudents whoparticipatedintheexperimentwereenhancedtoasimilardegree.Inthecaseoftheexperimentalgroup,theshape ofthedistributioncurvedidnotchangebythetimeofthefollow-upstudy.Thisfindingsuggestedalong-termeffecton developmentindependentofindividualstudents’originallevelofinductivereasoning.Theeffectivenessoftheprogram provedtobestableovertime.
Theeffectivenessofthetrainingprogramineachdimensionofbasicstructuresresembledsignificantlythatofthewhole program.Themanipulative,playfultrainingresultedinasignificantimprovementinallsixbasicstructuresofinductive reasoningskills. Themostconsiderableadvance,more than30%,tookplace inthedomains ofsystemformation, dif- ferentiatingrelationsandrecognizingrelations.Thelowest,butstillconsiderablysignificantdevelopmenttookplacein cross-classification.Ineachdimensionofinductivereasoning,membersoftheexperimentalgroupdevelopedthesameor moreintheeightweeksofthetrainingthantheywouldnormallyhaveinayearofconventionalschooling.
Theeffectofthetrainingprovedtobestableineachdimensionofinductivereasoning,thoughfurtherimprovementwas notattainedduetothelackofconscioustraining.Probably,studentsdonotdevelopanyfurtheruntilmateswhodidnot participateintheexperimentreachtheirlevel.Thentheymightdeveloptogetherspontaneously.Expandingthetraining programcouldeffectivelyincreasetheadvantageoftheexperimentalgroupfurther.Ontheotherhand,theapplicationof theexistingprogramcouldencouragethoselaggingbehindtocatchupwiththeirschoolmateswithanaverageoreven aboveaveragelevelofskillsinthiscruciallyimportantdomain.
Theeffectivenessoftheprogramprovedtobeunrelatedtogender;i.e.ithadasimilareffectonboysandgirls.No gender-baseddifferenceswerefoundinanyofthedomainsformostofthemeasurementpoints.Theeffectsizeachievedis outstandingnotonlyintheHungariancontextbutinternationallyaswell.
Theresultssuggestthattheelaborationofthisdomain-general developmentprogramcanbeconsideredsuccessful, which,whenappliedinpairandgroupwork,developsstudents’inductivereasoninginaplayfulway.Itwasnotanaimof thestudytoexplorehowtheimprovementininductivereasoningtransferstootherareasofcognition.However,anumber ofotherstudiesreportedstrongcorrelationsbetweeninductivereasoningandsuccessfullearningofseveralschoolsubjects, forexample,secondlanguages(Csapó&Nikolov,2009).
Thefindingsofthetrainingprogramsuggestthatinductivereasoningskillscansignificantlyandeffectivelydevelop betweentheagesof6and8.Anon-verbal,figuraltestofinductivereasoningwasalsoconstructedaspartofthepro- grampackagewhich–accordingtoitsreliabilityandvalidity–canbeeffectivelyappliedtomeasurethedevelopmentof elementarystudents’inductivereasoningevenindependentlyoftherestofthetrainingprogram.
Futureplansincludedigitizationoftheentiredevelopmentalprogramandreleaseintheformofcomputersoftware.This stepmightimproveapplicabilityandfostertheavailabilityoftheprogram.
References
Bisanz,J.,Bisanz,G.,&Korpan,C.A.(1994).Inductivereasoning.InR.Sternberg(Ed.),Thinkingandproblemsolving.SanDiego:AcademicPress.
Cheng,P.W.,&Holyoak,K.J.(1985).Pragmaticversussyntacticapproachestotrainingdeductivereasoning.CognitivePsychology,17,391–416.
Chi,M.T.H.,Glaser,R.,&Rees,E.(1982).Expertiseinproblemsolving.InR.S.Sternberg(Ed.),Advancesinthepsychologyofhumanintelligence(pp.1–75).
Hillsdale,NJ:Erlbaum.
Cohen,J.(1988).Statisticalpoweranalysisforthebehavioralsciences.Hillsdale,NJ:Erlbaum.
Csapó,B.(1997).Developmentofinductivereasoning:Cross-sectionalmeasurementsinaneducationalcontext.InternationalJournalofBehavioural Development,20(4),609–626.
Csapó,B.(2003).(Thedevelopmentofcompetenciesandtheirimprovementinaschoolcontext)Aképességekfejl ˝odéseésiskolaifejlesztése.Budapest:Akadémiai Kiadó.
Csapó,B.,&Nikolov,M.(2009).Thecognitivecontributiontothedevelopmentofproficiencyinaforeignlanguage.LearningandIndividualDifferences, 19(2),209–218.
deKonig,E.(2000).InductiveReasoninginPrimaryEducation:Measurement,Teaching,Transfer.Zeist,Kerckebosch.
deKoning,E.,Hamers,Jo,H.M.,Sijtsma,K.,&Vermeer,A.(2002).Teachinginductivereasoninginprimaryeducation.DevelopmentalReview,22,211–241.
Dienes,Z.(1973).(Buildingupmathematics)Építsükfelamatematikát.Budapest:GondolatKiadó.
Dienes,Z.P.(1963).Anexperimentalstudyofmathematicslearning.London:Hutchinson.
Egan,D.E.,&Greeno,J.G.(1974).Theoriesofruleinduction:Knowledgeacquiredinconceptlearning,serialpatternlearning,andproblemsolving.InL.
W.Gregg(Ed.),Knowledgeandcognition.Hillsdale,NJ:LawrenceErlbaumAssociates.
Feuerstein,R.,Rand,Y.,Hoffman,M.B.,&Miller,R.(1980).Instrumentalenrichment:Aninterventionprogrammeforcognitivemodifiability.Baltimore,MD:
UniversityParkPress.
Hamers,J.H.M.,DeKoning,E.,&Sijtsma,K.(2000).Inductivereasoninginthethirdgrade:Interventionpromisesandconstraints.ContemporaryEducational Psychology,23,132–148.
Johnson-Laird,P.N.(1983).Mentalmodels:Towardacognitivescienceoflanguage,inferenceandconsciousness.Cambridge,MA:HarvardUniversityPress.
Józsa,K.,&Zentai,G.(2007).Hátrányoshelyzet ˝uóvodásokjátékosfejlesztéseaDIFERProgramcsomagalapján[PlayfulfosteringofSES-kindergarden childrenbasedontheDIFERprogrampackage].ÚjPedagógiaiSzemle,5,3–17.
Klauer,K.J.(1989a).DenktrainingfürKinderI.Göttingen:Hogrefe.
Klauer,K.J.(1989b).Teachingforanalogicaltransferasameansofimprovingproblem-solving,thinkingandlearning.InstructionalScience,18,179–192.
Klauer,K.J.(1990).Paradigmaticteachingofinductivethinking.InH.Mandl,E.DeCorte,S.N.Bennett,&H.F.Friedrich(Eds.),Learningandinstruction.
EuropeanResearchinanInternationalcontext.Analysisofcomplexskillsandcomplexknowledgedomains(pp.23–45).Oxford:PergamonPress.
Klauer,K.J.(1991).DenktrainingfürKinderII.Göttingen:Hogrefe.
Klauer,K.J.(1993).DenktrainingfürJugendliche.Göttingen:Hogrefe.
Klauer,K.J.(1996).BegünstigtinduktivesDenkendasLösenkomplexerProbleme?ExperimentellenStudienzuLeutnerssahel-Problem[Doesinductive thinkinghaveapositiveeffectoncomplexproblemsolving?].ZeitschriftfürExperimentellePsychologie,43(Heft1),361–366.
Klauer,K.J.,&Phye,G.D.(2008).Inductivereasoning.Atrainingapproach.ReviewofEducationalResearch,78,85–123.
Lipman,M.(1985).ThinkingskillsfosteredbyPhilosophyforChildren.InJ.W.Segal,S.F.Chipman,&R.Glaser(Eds.),Thinkingandlearningskills(pp.
83–108).Hillsdale,NJ:LawrenceErlbaumAssociates.
Molnár,G.(2006).Azinduktívgondolkodásfejlesztésekisiskoláskorban[Fosteringinductivethinkinginelementaryschoolpupils].MagyarPedagógia,1, 63–80.
Molnár,G.,&Csapó,B.(2003).Aképességekfejl ˝odéséneklogisztikusmodellezése[Logisticalmodelofskillsdevelopment].Iskolakultúra,13(2),57–69.
Nagy,J.,&Gubán,G.(1987).Arendszerezésiképességkialakulásaésfejlesztése[Thedevelopmentandimprovementofsystemizingability].Pedagógiai Szemle,11,1108–1118.
Pap-Szigeti,R.(2007).KritériumorientáltfejlesztésSZÖVEGFERprogramcsomaggal:eredmények.InJ.Nagy(Ed.),Kompetenciaalapúéskritériumorientált pedagógia(Competence-basedandCriterion-referencedEducation)(pp.334–346).Szeged:MozaikKiadóKft.
Pellegrino,J.W.,&Glaser,R.(1982).Analyzingaptitudesforlearning:Inductivereasoning.InR.Glaser(Ed.),AdvancesinInstructionalPsychology(pp.
269–345).Hillsdale,NJ:LawrenceErlbaumAssociates.
Polya,G.(1954).Mathematicsandplausiblereasoning.Princeton,NJ:PrincetonUniversityPress.
Resnick,L.(1987).Educationandlearningtothink.Washington,DC:NationalAcademyPress.
Shayer,M.,&Adey,P.(1981).Towardsascienceofscienceteaching:Cognitivedevelopmentandcurriculumdemand.London:HeinemannEducationalBooks.
