General and specific thinking skills and

ContentslistsavailableatScienceDirect

Thinking

Skills

and

Creativity

jo u r n al hom e p ag e : htt p : / / w w w . e l s e v i e r . c o m / l o c a t e / t s c

General

and

specific

thinking

skills

and

schooling:

Preparing

the

mind

to

new

learning

Mari-Pauliina

Vainikainen

∗

,

Jarkko

Hautamäki,

Risto

Hotulainen,

Sirkku

Kupiainen

UniversityofHelsinki,DepartmentofTeacherEducation,CentreforEducationalAssessment,Finland

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received3October2014

Receivedinrevisedform17April2015 Accepted23April2015

Availableonlinexxx

Keywords:

Thinkingskills Cognitivedevelopment Formalthinking

Class-effectonthinkingskills Nestedmultilevelfactorialmodels

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b

s

t

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t

Enhancingthinkingskillsisanimportantgoalofformaleducation.Itisoftenembedded innationalcurricula,which,however,areseldombasedontheoreticalunderstandingof thestructureoftheskillsorhowtheyshouldbetaught.Accordingly,thereisonlylimited informationavailableaboutschools’successinthisimportanttask.Thepresentstudyhas twogoals:firstly,tofindsupportforthetheoreticalassumptionofthenestedstructureof thinkingskillswithacorefactorofformalthinkingandspecialisedstructuresforverbaland quantitativereasoning;andsecondly,totestthedifferentiateddevelopmentoftheseskills inschool.Thiswasdonebystudyingclass-levelvariationofsixthgraders’thinkingskillsin amultilevelfactoranalysiswheninitialbetween-classdifferencesatgradethreehadbeen takenintoaccount.Thedata(N≈1543)weredrawnfromalearningtolearnpanelstudyin oneofthemajorcitiesofFinland.Theresultsshowedthatthecorefactorforformalthinking couldbeidentifiedatboththeindividualandtheclasslevel,andthatattheindividuallevel therewerestatisticallysignificantresidualfactorsforverbalandquantitativereasoning. Initialbetween-classdifferencesexplainedonlyathirdofthevarianceofclass-levelformal thinking.Thiswasinterpretedtoindicatetheeffectofschooling.

©2015PublishedbyElsevierLtd.

1. Generalandspecificthinkingskillsandschooling

Discussionsofcurrentworkingenvironmentsandoftheskillsnecessaryforworkcallfora newapproach towards learning.Inthecontinuouslychangingworkenvironmentspeopleneedtomakecoherentdecisionswithaccessto unlim-itedinformationinalimitedtime,tothinkcreatively,toadjusttheiractionsandattitudesaccordingtopossiblerisksand problems,tolearnquickly,and totrusttheirproblemsolvingskills(Halpern,2008).Hence,educationalpolicymakers world-widehavelatelybecomeinterestedinconcepts,suchaslearningtolearn,thinkingskills,and21stcenturyskills (Recommendation2006/962/ECoftheEuropeanParliamentandoftheCouncil,2006;Rocardetal.,2007;Organisationfor EconomicCo-operationandDevelopment(OECD),2013a).

Thecommoncoreforthenewornewlyintroducedconceptsisthattheyalltapunderlyingcognitivecompetencesand non-curriculardomain-generalskillsthatregardanindividual’soveralllearningpreparedness.Dependingontheframework, theseskillsarereferred toascross-curricular, learningtolearn(LTL), transversal,or21stcenturyskills(DeakinCrick, Stringer,&Ren,2014).Regardlessoftheterm,thesedefinitionsemphasisetheimportanceofdevelopingthinkingskillsas

∗ _{Correspondingauthorat:CentreforEducationalAssessment,UniversityofHelsinki,P.O.Box9,00014Helsinki,Finland.Tel.:+358503465050.}

E-mailaddress:mari-pauliina.vainikainen@helsinki.fi(M.-P.Vainikainen). http://dx.doi.org/10.1016/j.tsc.2015.04.006

abasisforfuturelearningfromcoreprocessesandspecialisedstructuralsystemstocriticalthinking(Demetriou,2014). Enhancingthinkingskillshavebeenconsideredasacentralgoalofeducationalreadyfordecades(Resnick,1987),butit isstillquiterarethateducationalsystemspromotesuchdevelopmentdeliberately(aninterestingexceptionisHungary, wherenewframeworksinreading,mathematicsandscienceareallbasedonideasofgeneralandspecificthinkingasan explicitpart,seeCsapó&Szapo,2014).Eventhoughthinkingskillsareexpectedtoimprovewhenpupilsproceedthrough theirformalschooling,strategiesforevaluatingeducationaloutcomesandeffectivenessofschoolingmainlycentreonthe measurementofsubject-specificknowledgeandskillsoratbesttheirapplication.InFinland,theassessmentofgeneral cognitivecompetencesandtheaffectivefactorswhichsupporttheireffectiveuse,togetherlabelledLTL,weredefinedasone ofthemeasurableoutcomesofeducationalreadyinthe1990s(Hautamäkietal.,2002;NationalBoardofEducation,1999). Sincethen,theyhavebeenusedasoneindicatorformonitoringtheeffectivenessofeducation.

LTLisdefinedasthecognitivecompetenceandwillingnesstoadopttonoveltasksandnewlearning(Hautamäkietal., 2002;Hautamäki,Hautamäki,&Kupiainen,2010).InempiricalassessmentofLTL,theassessmenttasksareseentoactivate acomplexofinterrelatedcompetencesandbeliefs,leadingtoanattempttosolvethetasks.Competencereferstothe applicationofgeneralcognitiveschemasandthealreadyacquiredknowledgeorscholasticachievementtonewsituations. Beliefsrefertoanticipatedemotionswhich,onceactivated,leadtocommitmentorrefusal.Definedthisway,LTLcompetences arerelatedtointelligence,understoodinaPiagetianframeworkastheactiveuseofformaloperationalschemas.Fromthis followsthehypothesisthatthecognitiveLTLtasksmeasuregeneralthinkingskills(seeAdey&Csapó,2014).LTLasan educationalgoalisanexplicitpartoftheEUdefinitionofkeycompetencesandofthe21stcenturyskillsintheglobalcontext. However,neitherofthetwopresentsanempiricallytestedmodeltomeasurethecompetences.TheFinnishLTLFramework andscalesareoneoffewattemptstoofferatooltoassessboththecognitiveandthewillingness-orcommitment-related componentsofLTL(DeakinCricketal.,2014).

Theaimofthepresentstudyisontheonehandtotestthetheoreticalassumptionthatthethinkingskillsmeasuredwith theFinnishLTLconstructhaveanestedstructure(cf.,Härnqvist,Gustafsson,Muthén,&Nelson,1994)withformaloperational thinking(seeShayer,1979)atitscoreandwithspecialisedresidualfactorsforverbalproportionalandquantitativereasoning (seeDemetriou,Spanoudis,&Mouyi,2011).Ontheotherhand,theaimistoevaluatewhetherschoolinghasaneffecton theseskillsintheFinnishcontext,wherethinkingskillsaredefinedasagoalembeddedinallschoolsubjectsinthenational corecurriculum(NationalBoardofEducation,2004)butdetailsregardingtheirteachingaremissing.

1.1. Developmentofthinking

Developmentalpsychologistshavelongstudiedthedevelopmentofthinking.Thetheoryofcognitivedevelopment pro-posedbyDemetriouetal.(2011)andDemetriou(2014)involvesbothcentralandgeneralmechanisms,andspecialised capacitysystemsfordifferentdomainsofknowledgeorrelations.Thespatial,verbal,quantitative,categorical,causal,and socialreasoningsystemshavebeenidentifiedbymethodsfromdifferenttheoreticalorigins,andtheyareconsideredas autonomousdomainsofunderstanding,thinking,andproblemsolving.Acriticalfeatureofthistheoryisthatthe develop-mentofthespecialisedsystemsisbothlimitedbyandistherouteintothedevelopmentofthegeneralintellectualprocessor anditsexecutivecontrol(self-regulation).Thatis,thegeneralfactorisalsoamenabletoeducationalinfluence.Thereis evi-dencefromothertheoreticalbackgroundsthathighperformanceonagenerallevelfacilitatestheacquisitionofnewdomain specificskillsespeciallyontheearlyphasesofthelearningprocess(Francis,Fletcher,Maxwell,&Satz,1989;Gustafsson, 2008).Butwhenlearningisbasedonalreadyacquiredskills,thegainsaremorelikelytodependonearlierdomain-specific knowledge.Accordingly,theimprovementsarelikelytobedomain-specific.Allthismeansthatgoodsubject-specific teach-ingmakestheconnectionbetweenspecificknowledge,e.g.theuseofspecificconcepts,withthegeneraluseofconcepts, rulesandtheirapplication.Thisgraduallyleadstogainsalsointhefunctioningofthegeneralmechanisms(Demetriouetal., 2011;Gustafsson,2008).

Oneofthemoststudiedconstructsinthedevelopmentofgeneralthinkingskillsandthefunctioningofthegeneral mechanisms(cf.,Demetriouetal.,2011)isthecontrolofvariablesstrategy(CV),whichisalsooftenreferredtoasthe vary-one-thing-at-a-time(VOTAT) strategy.ItwasfirstintroducedbyInhelderandPiaget(1958)aspartoftheformal operationalthinkingconstruct(seeShayer,1979).RegardlessofcriticismsconcerningexplicitnessofInhelderandPiaget’s workitstillprovidesoverarchingillustrationhowadolescents’cognitivecompetencesdevelopduringtheseconddecadeof theirlife(Kuhn,2008).Theemergenceofformaloperationsataroundage12–15involvesreasoningbasedonhypotheses, independentofconcreteobjects,whichmeans“therealissubordinatedtotherealmofthepossible”(Piaget,2006).Age variationisseentobeingrainedinthedifferingintellectualstimuliinchildren’senvironmentsandtodependonpersonal interestsandexperiences.However,formalthinkingisnotnecessarilyappliedallthetimeoracrossalldomains(Piaget,1972, 2006).Evenifindividualdifferencesinformaloperationalthinkingarerelatedtointelligence,verbalabilityandexecutive functions,theseareconsideredtobepartlyculturallybound(Emick&Welsh,2005).Ithasbeenshownthatthatthecontrol ofvariablesstrategyiscentraltoscienceandanessentialskillattainableandtrainablebythetimechildrenarecognitively advancingfromaconcretetowardaformaloperationallevel(Neimark,1975;Shayer,2008).

Fernandes,2007;Rohde&Thomson,2007;Sternberg,1999).Generalcognitionisexpressedorinvestedinvariousways indifferentlearningsituationsandschoolachievements(Gustafsson&Carlstedt,2006).Butthedevelopmentallyoriented interpretationofgeneralcognitionasanexpressionofgrowthoflogicalthinkingopensupanoptionforintervention(Adey, Csapó,Demetriou,Hautamäki,&Shayer,2007;Shayer,2008).Thisintegratedunderstanding,educatingthedevelopingmind, iswellrepresentedintheworkofDemetriou(2014)andDemetriouetal.(2011).

AccordingtoDemetriou’stheory,weexpectthethinkingskillsmeasuredwithintheFinnishLTLcontexttobestructured inawaythatinadditiontothecoreofformalthinking,residualfactorsofallthespecialisedreasoningsystemsaretobe found.Inpractice,onlytheverbalandquantitativefactorscanbeidentifiedhereasthesixthgradeversionoftheFinnishLTL scaleusedinthepresentstudydoesnothavesufficientnumberofitemsontheareasofspatial,causalorsocialreasoning. Eventhoughninthgradedatawithalargerscopeofcognitivetaskswouldhavebeenavailable,12-year-oldswereselected asthetargetgroupofthepresentstudyduetothesensitivenessofthisagegroupinregardtoboththedevelopmentof formalthinking(Piaget,2006),andtotheenhancementofthinkingskillsingeneral(Csapó,1997).

1.2. Enhancingthedevelopmentofthinkingskills

Manyresearchersseethatinductionprocesses,suchasperformingmentalcomparisonsformabasisfor knowledge-building.This,inturn,hasbeenshowntohaveatransfereffectonlearninginschoolsubjects(Adey&Shayer,1994;Adhami &Yates2008;Bloom,Engelhart,Furst,Hill,&Krathwohl,1956; Klauer&Phye,2008;Tomic&Klauer,1996).Thus, by promotingthedevelopmentofthinkingskills,e.g.howtoputthingsinorder,classifyorperformmentalrotations,we simultaneouslyenhancefundamentallearningskills,whichhavetransfereffectsacrosstheschoolcurriculum.Thisalso facilitatestheattainmentofhigherorderthinkingskills(Anderson&Krathwohl,2001;Shayer,2008).

Itcouldbearguedthattherearetwomainwaystopromotethinkingskillsinschool.Thefirstapproachcanbecalled explicitwithspecificeducationalprogrammes,whichareexpectedtopromotethinkingskillsiftheprogrammeguidelines areappropriatelyfollowed.Theseprogrammescanbefurtherdividedintotwocategoriesaccordingtohowthetraining ofthinkingskillsisarranged(McGuinness&Nisbett,1991).Thefirstcategory,thecontent-basedmethod,consistsof pro-grammeswhichensurethatthinkingskillsaretaughtwithinconventionalcurriculumareas(e.g.mathematicsorscience). Awell-studiedprogrammerepresentingthismethodistheCognitiveAcceleration(CA)Programme(Adey&Shayer,1994) basedonPiagetiancognitivestages.Programmesbelongingtothesecondcategorysharetheideathatthinkingskillscan betaughtassuch(e.g.Feuerstein,Rand,Hoffman,&Miller,1980;Klauer,1989;Klauer,1991).Thepromotionofgeneric skillshasbeencriticisedfordevelopingthinkingskillsa-contextuallyandinhibitingthetransferofthedevelopedskillsto newcontexts.Yet,programmesbasedonKlauer’stheoryhaverecentlyshownstrongevidencefortransfereffectonboth fluidintelligenceandvariousacademicsubjects(Klauer&Phye,2008;Molnár,2011;Molnár,Greiff,&Csapó,2013). Regard-lessofstrongevidencebynowthatspecificprogramscanpromote21stcenturyskills,theirlarge-scaleusehasnotbeen widelyspreadtotheeducationalfieldduetobothshort-sightededucationalpolicy-decisionmakingandlimitedresources ofstakeholders(Pellegrino&Hilton,2012).

Thesecondapproachcanbedescribedasanimplicitone.Inthisapproach,curriculadonotperseemphasisesystematic cultivationofthinkingskillsbutsuchdevelopmentisexpectedtoresultasaside-effect(Kuhn,2005;Molnár,2011).Especially intheNordiccountries,approaches,practices,andinitiativestowardsenhancingthinkingskillsareverylimited.Forexample, intheFinnishnationalcorecurriculum,thinkingskillsareregardedtobelongintoeachconventionalcurriculumarea.Thus, itisexpectedthattheimplementedcurriculumwithannuallymoredemandingcontentcomplexity(spiralcurriculum; cf.Bruner,1960)raisesimplicitlythelevelofthinkingskills,aswell.However,researchhasshownthatthepromotion ofthinkingskillsneedstobeeitherintegratedpurposefullyinthecurriculumortheyhavetobeexplicitlytaughttogain effectiveresults(Adey&Shayer,1994;Kuhn,2005;Nisbett,1993).

AsinFinlandexplicitmethodsforteachinggeneralthinkingskillsarenotpointedoutinthecorecurriculumandthesame classteachertypicallyteachestheirclassfromthirdtosixthgrade,theFinnishschoolsystemallowsustostudyteacher-and class-relatedvariationinthedevelopmentofgeneralthinkingskills.Theexpectedclass-levelvariationinthedevelopment ofthinkingskillscouldprovideevidenceforthatevenimplicitteachingofthinkingskillscanbebeneficial.Itcanalsogive estimatesabouthowmuchoralternativelyhowlittleteacherscaninfluencethedevelopinggeneralthinkingskills.

1.3. Educationalassessmentandthinkingskills

foundbetween-classdifferencescallforfurtherresearchtogainamorecomprehensivepictureregardingthedevelopment of21stcenturyskillsinrelationtosubject-specificlearningandtore-evaluatetheequityoftheFinnisheducationsystem (cf.,Sahlberg,2007).Inthepresentstudy,afirststeptowardsthisdirectionistakenbyanalysingclass-levelvariationinthe thinkingskillsmeasuredbytheFinnishLTLscale.Thelongitudinaldataofthepresentstudyallowscontrollingforinitial differencesbetweenclasses,revealingsomeofthepossibleeffectsschoolinghasproducedascomparedtocross-sectional studies,whichmightjustindicatethenon-randomallocationofpupilsinclasses(cf.,Vainikainen,2014).

1.4. Researchquestionsandhypotheses

Asdescribedabove,thestructureofthinkingskills,theirdevelopmentineducationalsettings,andeducationalequity haveallbeenextensivelystudiedindependentfromeachother.However,thereisverylittleresearch,whichcombinesthese perspectivesandevaluatestowhatextentthinkingskillsreallydevelopasaresultofformalschoolingiftheyarenottaught explicitly.Therefore,theresearchquestionsandthehypothesesofthepresentstudyare

Q1:DothethinkingskillsmeasuredbytheFinnishLTLscaleshaveanestedhigher-orderstructureasthetheoriesabove suggest?

H1:Thereisanestedhigher-orderstructure:thehigher-ordergeneralthinkingskillsfactorisdeterminedbyformal thinkingbutthereareseparablefactorsforverbalandquantitativereasoningskills(Demetriouetal.,2011;Gustafsson, 2008;Piaget,2006;Shayer,1979).

Q2:Istherebetween-classvariationinformalthinkingandtheresidualfactorsofverbalandquantitativereasoning? H2:Thereisbetween-classvariationinallthesefactors,anditexplainsbetween10%and20%ofthevariance(Hautamäki etal.,2013;YangHansenetal.,2014).

Q3:Isthebetween-classvariationexplainedbyinitialdifferencesbetweenclasses,whichhasinearlierstudiesbeen showntoexplainabout5%ofthevariancealreadyatthestartingpoint(Vainikainen,2014),ordoesittellaboutdifferent trajectoriesofdevelopmentindifferentclasses?Thatis,havethedifferencesattheendofsixthgradebeenpartiallycaused byschoolingasthinkingskillscanbeemphasiseddifferentlyinteachingwhenexplicitmethodsarenotspecifiedinthe Finnishcurriculum?

H3:Theclass-levelvariationinthinkingskillsdoesnotonlyreflectinitialdifferencesbetweenclasses:ithasbeenshown earlierthattowardstheendofprimaryschool,between-classdifferencesexplain10–20%ofthevarianceofperformanceon differentdomains,whichismuchmorethaninitialdifferencesbetweenclasses(Vainikainen,2014YangHansenetal.,2014). Toourknowledge,therearenopriormultilevellongitudinalstudiesexplainingthepossibleschoolingeffectsonthinking skills.

2. Methods

ThedataweredrawnfromtheVantaapanelstudy,inwhichfourfullagecohorts(thefirst,third,sixthandninthgraders) ofthemunicipalitywerefollowedfrom2010to2013.Thepresentstudyutilisesthesixthgradedatafrom2013which, regardingthemeasuresusedherewerefirstreportedbyKrkovic,Greiff,Kupiainen,Vainikainen,andHautamäki(2014) andVainikainen(2014).Noneofthesestudieswasaboutthenestedstructureofthinkingskills.Morerecently,weused thenestedmodelinanotherarticleacceptedforpublicationinaFinnishspecialeducationjournal(Vainikainen,Hienonen, HautamäkiandHotulainen,inpress).Inthearticle,weappliedonlyindividual-levelmodellingandshowedthatclasssize didnotexplainthedevelopmentofformalthinkingofpupilswithspecialeducationneeds.Regardingthenestedmodel,we referredtothecurrentstudyastheoriginalpublicationanddidnotrepeatanyoftheresultspresentedhere.

2.1. Participants

Thestudiedcohortoriginallyconsistedof2113sixthgradersin118classesin37schools.Duetothepre-definedexclusion criteria,8smallspecialeducationclassesdidnotparticipate,andabout5%ofpupilswereabsentduetosicknessorother reasons.20%ofthepupilswererandomlyassignedtoapaper-basedassessmentgroupwhereas80%completedthe computer-basedversion(CBA)oftheLTLtest.OnlythedataoftheCBAgroup(N=1543,49.2%girls)wereusedinthepresentstudy, andthefinalnumberofclasseswithsufficientdataformultilevelmodellingwas102.TheageofthepupilswasM=12.67, SD=.43.Longitudinaldatacomprisingalsopupils’thirdgraderesultsinanalogicalreasoning,whichwasutilisedfortesting thelasthypothesis,wereavailablefor1303pupils.ParentswereinformedthroughtheCityEducationDepartment,and77% oftheparentsalsofilledoutabackgroundquestionnaire,whichisnotreportedhere.

2.2. Measures

Table1

Reliabilitiesofthecognitivetasksandtheattitudescales.

Scale Number of items ˛

Verbalproportionalreasoning 10 .55

Quantitativereasoning 15 .75

Formalthinking 4 .62

Analogicalreasoningthirdgrade 8 .78

sometimesfoundgoldandsilvertogether,sometimeshehasfoundsilverbyitself,everyothertimehehasfoundneither silvernorgold.Whichofthefollowingruleshasbeentruefortheprospector?Goldandsilverarefoundtogether,never apart.;ifhefoundsilverthenhefoundgoldwithit.;ifhefoundgoldthenhefoundsilverwithit.;ifhefoundgoldthenhe didnotfindsilver;seeBond,2010formoredetails).Inthelatter,thepupilsweregivenonepremiseandtheconclusion(e.g. Conclusion:LakeSaimaaistoocoldforswimming.Firstfact:thetemperatureofLakeSaimaais5centigrades),andtheyhad tochoosefromamongstfivealternativesthesecondpremisewhichwouldmaketheconclusionvalid(e.g.Mostlakesaretoo coldforswimming.;itiswintertime.;fivedegreewateristoocoldforswimming.;LakeSaimaaisalwayscold.;swimming incoldwaterisnofun.).Theitemswerescoreddichotomouslyascorrectorincorrect.

QuantitativereasoningwasassessedbysevenitemsadaptedfromtheHiddenArithmeticalOperatorstaskbyDemetriou, Platsidou,Efklides,Metallidou,andShayer(1991)andeightitemsbasedontheInventedMathematicalConceptstaskof Sternberg,Castejon,Prieto,Hautamäki,&Grigorenko(2001).Inthefirstsevenitemstherewereonetofourhiddenoperators (e.g.Whichoperatordotheaandbstandforin(5a3)b4=6?).Inthelatteritems,twoinventedarithmeticaloperatorswere conditionallydefined(e.g.ifa>b,lagstandsforsubtraction,butifa≤b,itstandsformultiplication).Afterthedefinition,the pupilshadtoselectthecorrectanswerfromamongstfourmultiplechoicealternativestoeightitems(e.g.Howmuchis7 lag5?).Theitemswerecodeddichotomouslyforthewholeequation.

FormalthinkingwasmeasuredbytheControlofVariablestask,whichisamodifiedversion(Hautamäki,1984seealso Hotulainen,Thuneberg,Hautamäki,&Vainikainen,2014,foradetaileddescriptionofthetask)ofShayer’sScienceReasoning Task‘Pendulum’(1979).ItisbasedononeoftheformalschemataidentifiedbyInhelderandPiaget(1958).Thepupilswere presentedwithfouritemsintheformofcomparisonssetintheworldofFormula1raceswithfourvariables:driver,car, tires,andtrack,withtwoalternativesforeach.Thepupilshadtojudgewhetherthesingleeffectofthedriver,car,tires,and trackcouldbeconcludedfromthecomparison(e.g.Round1:driverRäikkönen,carFerrari,tiresMichelin,trackHockenheim; Round2:driverHamilton,carFerrari,tiresMichelin,trackMonaco;canyouconcludetheeffectsofdriver/car/tires/track ontheresult?)Thereweretwocomparisonswith3or4Yes/No-choicesforthevariablesandtwocomparison-setstobe complemented.Thefouritemswerecodeddichotomouslyforacorrectanswertoallofthevariablesintheitem.

Fortestingthelasthypothesis,pupils’analogicalreasoningscoresfromthreeyearsearlierweremergedintheotherwise cross-sectionaldata.ThetaskwasadaptedfromthegeometricanalogiestestofHosenfeld,vandenBoom,andResing(1997). Thepupilswerepresentedapairofgeometricfigures,thatis,asmallsquareontheleftandabigsquareontheright.The taskwastoapplythesamerulewhenchoosingapairfromfiveoptionsforanotherfigure,thatis,asmallcircle,between5 answeroptions.Thetransformationsincludedaddinganelement,changingsizesandpositions,halvinganddoubling.The maximumnumberofsimultaneoustransformationswasfive.Theeightitemswerecodeddichotomously,andthenumber ofcorrectitemswasconvertedtopercentage.

ThereliabilitiesofthemeasuresarepresentedinTable1.Eventhoughsomeofthereliabilitiesweresomewhatlowdue tothesmallnumberofitems,thereliabilitieswereconcludedacceptableforpopulation-levelstudies.

2.3. Statisticalanalyses

DescriptivestatisticswerecalculatedwithSPSS22.Single-andmulti-levelnestedfactorialmodelsweretestedinMplus 7.2(Muthén&Muthén,2012)usingtheMLRestimatorwithoutimputationofmissingvalues.Toreducethenumberof parameterstobeestimated,theitemsofthesubtestswereparcelledintofourverbalreasoning,fourquantitativereasoning, andtwoformalthinkingparcels,whichweretreatedascontinuousvariables.AccordingtotherecommendationofMarsh, Lüdtke,Nagenkast,Morin,andVonDavier(2013),weusedahomogeneousparcellingstrategy,inwhichitemsfromdifferent theoreticaloriginswerenotmixedinthesameparcelsandtheitemsinoneparcelwereassimilaraspossible.Before parcelling,wecalculatedIRTitemdiscriminationestimatesforthethreescales,ensuringthesufficientunidimensionality ofthescales(seeMarshetal.,2013).ThemodelswereconsideredashavingagoodfitwithCFI&TLI>.95andRMSEA<.05, andanacceptablefitwithCFI&TLI>.90andRMSEA<.08.Alsoreportedare2values,butduetothelargesamplesizeand thenumberofparameterstobeestimatedsignificantp-valuesweretobeexpected.Accordingly,modelswithsignificant p-valueswerenotdiscardedifalltheotherindiceswereacceptable.

3. Results

3.1. Descriptivestatistics

Table2

Descriptivestatisticsofthevariablesusedinmodelling.

Variable

Parcel N Min Max M SD ICC

Verbal proportional 1 1522 .00 1.00 .53 .30 .07

Verbalproportional2 1512 .00 1.00 .54 .39 .07

Verbalproportional3 1506 .00 1.00 .51 .30 .05

Verbalproportional4 1504 .00 1.00 .23 .32 .02

Quantitative1 1501 .00 1.00 .52 .28 .10

Quantitative2 1401 .00 1.00 .10 .22 .03

Quantitative3 1475 .00 1.00 .57 .29 .08

Quantitative4 1471 .00 1.00 .35 .28 .07

Formal1 1495 .00 1.00 .59 .45 .07

Formal2 1480 .00 1.00 .37 .44 .07

Analogical reasoning 1303 0.00 100.00 40.19 29.88

N = Number of responses, Min = minimum value, Max = maximum value, M= Mean, SD = Standard deviation, ICC = Intraclass correlation.

Fig.1.Theexpectednestedstructureofthinkingskills.Theerrortermsofthefactorindicatorsarenotpresentedinthefigure.

3.2. Hypothesis1

Inthefirsthypothesisweexpectedthatthemeasuredthinkingskillswouldhaveanestedfactorialstructure.Thatis,the higher-ordergeneralthinkingskillsfactorwouldbedeterminedbyPiagetianformalthinkingbuttherewouldnevertheless beseparablefactorsforverbalproportionalandquantitativereasoningskills.Totestthishypothesis,themodelpresented inFig.1wasfirsttestedonindividual-leveldatawithoutmodellingbetween-levelvariance.

Thenested modelofFig.1fittedthedatawell(CFI=.978,TLI=.962,RMSEA=.034,2=73.411,df=26,p<.001)and showedabetterfitthananalternativemodelwiththreenon-nestedcorrelatedfactors(CFI=.954,TLI=.935,RMSEA=.045, 2=131.972,df=32,p<.001)oramodelwithoutcorrelationsbetweenthesecondaryfactorsofverbalproportionaland quantitativereasoning.ThestandardisedfactorloadingsforthenestedmodelarepresentedinTable3.

Table3

Standardisedfactorloadingsintheindividual-levelmodel.

Parcel Formal Verbal proportional Quantitative

Verbalproportional1 .48*** _.12*

Verbalproportional2 .46*** _.39***

Verbalproportional3 .36*** _.33***

Verbalproportional4 .24*** _.27***

Quantitative1 .45*** _.21***

Quantitative2 .31*** _.17***

Quantitative3 .35*** _.54***

Quantitative4 .42*** _.57***

Formal1 .59***

Formal2 .73***

*_p<.05. ***_p<.001.

slightlyhigherfactorloadingsandstatisticallysignificantownvariance(s2=0.004,p<.010).Theseresultstogetherindicate thatquantitativereasoningskillswereclearlyseparablefromthemoregeneralformalthinkingskills,whereasthesame wasnottrueforthemeasuredverbalthinkingskills.Thus,theresultsgaveonlypartialsupporttothefirsthypothesis.

3.3. Hypothesis2

Inthenexthypothesisweassumedthattherewouldbebetween-classeffectsthatwouldexplain15–20%ofthevariance bothinformalthinkingandinthemorespecificverbalproportionalandquantitativereasoningskills.Thebetween-level factorswerespecifiedforformalthinkingcontainingallparcelsandforquantitativereasoning.Abetween-levelverbal proportionalreasoningfactorcausedproblemswiththefitindicesandhadtoberemoved.Themodelfitthedatawell (CFI=.968,TLI=.949,RMSEA=.030,2=135.548,df=57,p<.001).Unlikeinthesingle-levelmodelofH1,thequantitative reasoningfactorwasnotstatisticallysignificantattheclasslevelandinthismodelitdidnothavestatisticallysignificant ownvarianceatanylevelregardlessofitsstatisticallysignificantfactorloadingsattheindividuallevel.Thus,theformal thinkingfactorcapturedallpupil-levelandclass-levelvariation(ICC=.18)inthismodel.

Addingtheclasslevelinthemodelchangedslightlythefactorloadingsattheindividuallevelcomparedtothesingle-level model.Thewithinandbetween-levelfactorloadingswithoutanyconstraintsacrossthetwolevelsarereportedinTable4. Table4showsthatattheclasslevel,alltheparcelsexceptthelastparcelforverbalproportionalreasoninghadstrong loadingsontheformalthinkingfactor.ItwasconcludedthatH2waspartiallysupportedregardingtheclass-leveleffectson formalthinking.

3.4. Hypothesis3

Inthelasthypothesisitwasassumedthattheclass-levelvariationinthinkingskillswouldnotonlyreflectinitial dif-ferencesbetweenclassesbutwouldbepartiallycausedbyschooling.Totestthishypothesis,longitudinaldataintheform ofanalogicalreasoningtestscoresfromthethirdgradewereused,whichwereavailableforabout85%ofthepupils.Third gradeanalogicalreasoningskillswereaddedinthetwo-levelmodelspecifiedinH2asbothwithin-leveland between-levelpredictorsofformalthinking.Themodelfitwasacceptablealsoforthismodel(CFI=.958,TLI=.939,RMSEA=.034,

Table4

Standardisedfactorloadingsinthetwo-levelmodel.

Within-level Between-level

Parcel Formal Verbalproportional Quantitative Formal Quantitative

Verbal proportional 1 .45*** _.11* _.84***

Verbalproportional2 .42*** _.39*** _.98***

Verbalproportional3 .32*** _.33*** _.92***

Verbalproportional4 .27*** _.30*** _.58(ns.)

Quantitative1 .40*** _.17** _.86*** _.56*

Quantitative2 .30*** _.16** _.71*** _.41(ns.)

Quantitative3 .32*** _.52*** _.70*** _.48(ns.)

Quantitative4 .40*** _.60*** _.79*** _.42(ns.)

Formal1 .55*** _.97***

Formal2 .71*** _.94***

Fig.2.Thefinaltwo-levelmodel.Theparcelnamesandtheerrortermsarenotpresentedinthefigure.***p<.001,ns.=non-significant.

2=185.772,df=75,p<.001).Asexpected,thirdgradeanalogicalreasoningskillspredictedsixthgradeformalthinkingat theindividuallevel(ˇ=.57,SE=.03,p<.001)andattheclass-level(ˇ=.58,SE=.14,p<.001),explaining32%and34%ofits variance,respectively.Astheverbalproportionalandquantitativefactorsturnedouttobenon-significantinthetwo-level model,itwasalsotestedwhethertheycouldbecompletelyomittedfromthemodel.However,thisdecreasedthepredictive powerofthirdgradeanalogicalreasoningskills,indicatingthatthesenon-significantfactorsneverthelessremovedsome irrelevantvariancefromtheformalthinkingfactor.Thefinaltwo-levelmodelispresentedinFig.2.

Asonlyathirdofthebetween-levelvarianceofformalthinkingdemonstratedinthesixthgradecouldbeexplainedby initialdifferencesbetweentheclasseswhenmeasuredbytheanalogicalreasoningtest,itwasconcludedthattherewastrue varianceleftaftercontrollingforinitialdifferencesandthatschoolingduringtheinterimyearscanhaveproducedaneffect onformalthinking.Thus,H3wassupported.

4. Discussion

Enhancingthinkingskillscanbeseenasoneofthemanytasksofschooling(Olson,2003),anditcanbearguedthatin the21stcenturythistaskhasbecomeincreasinglyimportantduetothechangesinworkinglife(DeakinCricketal.,2014). InFinland,thinkingskillsareembeddedinthecore-curriculumforbasiceducationbutthereisonlylimitedinformation availableabouthowschoolssucceedinthistask.Moreover,ithasnotbeenstudiedinanylargerscale,whethertheteaching ofthinkingskillsislimitedtosubject-specificareasorifschoolingmanagestotargetthemoregeneralthinkingskillsaswell. Therefore,thepresentstudyhadtwogoals:ontheonehand,theaimwastofindsupportforthetheoreticalassumption derivingfromPiaget(2001)andShayer(2008),andmorerecentlyfromDemetriouetal.(2011),aboutthinkingskillshaving anestedstructurewithitscoreinlogicalorformalthinkingbutwithadditionalspecialisedstructures.Ontheotherhand, theeducabilityoftheseskillsinacontextwherethinkingskillsareembeddedinthecurriculumwastestedbystudying class-levelvariationinformalthinkingatgradesixwheninitialdifferencesbetweenclasseshadbeentakenintoaccount. ThedataweredrawnfromalearningtolearnpanelstudyinoneofthemajorcitiesinFinland,whereafullcohort(N≈2000) ofpupilswereassessedatgradethreeandsixbytheFinnishLTLscale(Hautamäkietal.,2002).Thecognitivesubtasksof thescalecoveredformalthinking,verbalproportionalreasoning,andquantitativereasoning,whichcanallbeconsidered critical21stcenturyskills(Adey&Csapó,2014).

Shayer(1979,2008)andDemetriou(2014),whoclaimthattherearethecoreoperators,whichareneededineverytask.The resultsalsofittogetherwiththefindingsofHärnqvistetal.(1994),eventhoughtheirterminologydifferssomewhatfrom theconceptsusedinthisstudy.Also,theresidualverbalfactorwasintheirstudyofagreaterimportance,mostlikelydue tothenatureofthetasksused.

Asthefirstresultssupportedthehigher-orderstructureofthemeasuredskills,weproceededtotesttheclass-level variationofboththegeneralformalandthequantitativethinkingskills.Somewhatunexpectedly,inthetwo-levelmodel, thevarianceofthequantitativefactorwasnolongerstatisticallysignificantattheindividuallevel,inadditiontonothaving muchrelevanceattheclasslevel.However,asitclearlyremovedsomeoftheirrelevantvarianceintheformalthinking factor,itwaskeptinthemodel.TheresultsshowedthatjustasinthestudyofHärnqvistetal.(1994),therewasclass-level variationthataccountedfor18%ofthevarianceinthegeneralfactorofformalthinking.Thetestingofthethirdhypothesis showedthatthisvariationwasonlypartiallyexplainedbyinitialbetween-classdifferencesasmeasuredbyananalogical reasoningtestatgradethree.Asearlieranalogicalreasoningskillsareindicatorsofthefunctioningofthesamegeneral mechanismsthatatthelaterstageofdevelopmentcanbemeasuredbyformalthinkingtasks(Demetriouetal.,2011),itwas concludedthatpupils’formalthinkingskillshadclearlydevelopeddifferentlyindifferentclasses.Eventhoughtheremaybe otherfactorsexplainingthedevelopment,whichaccountedforapproximately12%ofthetotalvariance,forinstance socio-economicbackgroundandselectiveclasses(Härnqvistetal.,1994),theresultssupportthepossibilitythatformalthinking skillscanhavebeenenhanceddifferentlybydifferentteachers.Here,itisimportanttorememberthatanyspecifictraining programmesforthinkingskillswerenotapplied.Thus,themaincontributionofthisstudyisnotthatthehigher-orderfactor structurewasfound,butthatthegeneralfactor–hereformalthinking–couldbegivenaninterpretation,whichcanbetied toeducationalinterventions,evenifjustembeddedineverydayteaching.Alsotheresidualfactors,eveniftheirindependent variancesweredifferentatindividualandclass-levels,openwindowsforteaching-relatedinterventions.

4.1. Limitationsofthestudy

Thedatasetsomelimitstothepossibleresearchquestionsandtheanalysestobeperformed.Themultilevelanalyses couldbeconductedonlyattheclass-leveleventhoughitwouldhavebeeninterestingtolookatbetween-schooleffectsas well–especiallywhenthedifferencesbetweenschoolshavetraditionallybeenverysmallinFinlandalsointhelearning tolearnassessments(seeHautamäkietal.,2013).This,however,wasnotpossiblewiththepresentdataduetothesmall numberofschools.Therefore,itwouldbeimportanttoreplicatethisstudywithasampleconsistingofsufficientnumberof schoolsforschool-levelMFA.

Therearealsolimitationsregardingthemeasures:Theverbaltasksmeasuredproportionallogicalthinkinganddeductive reasoningbutdidnotcoverthefullscopeofverbalreasoningskills.Thismaybethereasonforthenon-significantvariance oftheverbalproportionalfactor.Regardingthelongitudinaldata,theinitialthirdgradeinitialdifferencesweremeasured onlybytheanalogicalreasoningtask,whichonlyaccountsforsomeofthepossiblesourcesofinitialvariationbetweenthe classes.Ifothermeasureshadbeenusedinadditiontoanalogicalreasoning,theshareofunexplainedvarianceofsixthgrade formalthinkingmighthavebeensomewhatsmaller.However,astheunexplainedsharewasashighastwothirdsofthe variance,theresultspointstronglytothedirectionthatthereistruevariationproducedbyclasses.Theremainingclass-level variancewasnotrelatedtopupils’initialcognitivecompetencethatoftenexplainsaboutathirdofthevariance(cf.,Duncan etal.,2007),justasinthepresentstudy,ortheveryusualnon-randomallocationofpupilsinclassesinFinnishschools(see Vainikainen,2014).

4.2. Conclusionsandpracticalimplications

reasoning,andseparationandcontrolofvariables.Accordingly,theLTLframeworkcanbeusedtoguidetheadvancementof thinkingskills,beitthroughinterventionortheirconsciousimbeddinginthecurriculum,andthesuccessofthisadvancement canbeassessedusingtheLTLscale,describedinthispaper.Bycombiningthistotheassessmentofsubject-specificoutcomes willallowfurtheranalysingtheactualorpotentialroleofthevarioussubjectsinitsadvancement(seeAdey&Shayer,2002; Titcombe,2015).

Pupilsneedtobepreparedtoseenewoptionsinsteadofobstacles,butasChristinaHowe(Howe,McWilliam,&Cross, 2005)expresses:“Chancefavoursonlythepreparedmind.”Thewell-preparedmindis,atleast,a personwitha good commandofformal,logicalandscientificthinking,andawillingnesstoapplythatskillforsolvingopenproblems.However, asKuhnandHolman(2011,p.65)remark:“...mostoftheempiricalevidencerelatedtoadolescentcognitiveskillsdoes notpresentapictureofstrongandsecurecompetence,makingthequestionofhowtosupportcognitivedevelopment inadolescenceapressingone”.Theyalsoexpresstheneedtoextendresearchoncognitivedevelopmentfrom control-of-variablesstrategystudiestostudiesregardingmultiplecausalityandevidence-basedpredictionstoreachthelevelof measuringstudents’readinesstoentertheworldofintellectualdiscoursetoparticipateincommunitiesofintellectual discourseAlsotheFinnishLTLassessmentislackinginthisrespect.YetthefindingsofthestudyshowthatLTLcanbeused tomeasurethedevelopmentofprimaryschoolpupils’thinkingskillstoasufficientdegreetoevaluatethesuccessoftheir fosteringatschool

AppendixA.

Descriptivesoftheoriginaldichotomousvariables.

N Min Max M SD

Verbal1 1515 0 1 0.69 0.46

Verbal2 1507 0 1 0.35 0.48

Verbal3 1504 0 1 0.55 0.5

Verbal4 1485 0 1 0.43 0.5

Verbal5 1500 0 1 0.64 0.48

Verbal6 1495 0 1 0.6 0.5

Verbal7 1487 0 1 0.69 0.46

Verbal8 1472 0 1 0.24 0.43

Verbal9 1467 0 1 0.27 0.44

Verbal10 1496 0 1 0.19 0.39

Quantitative1 1500 0 1 0.86 0.34

Quantitative2 1438 0 1 0.64 0.48

Quantitative3 1401 0 1 0.38 0.46

Quantitative4 1398 0 1 0.12 0.32

Quantitative5 1376 0 1 0.18 0.38

Quantitative6 1287 0 1 0.08 0.27

Quantitative7 1278 0 1 0.03 0.17

Quantitative8 1468 0 1 0.72 0.45

Quantitative9 1453 0 1 0.66 0.47

Quantitative10 1426 0 1 0.51 0.5

Quantitative11 1449 0 1 0.38 0.49

Quantitative12 1440 0 1 0.31 0.46

Quantitative13 1454 0 1 0.28 0.45

Quantitative14 1401 0 1 0.19 0.4

Quantitative15 1452 0 1 0.62 0.49

Formal1 1491 0 1 0.58 0.49

Formal2 1474 0 1 0.61 0.49

Formal3 1467 0 1 0.39 0.49

Formal4 1379 0 1 0.37 0.48

N=Numberofresponses,Min=minimumvalue,Max=maximumvalue,M=Mean,SD=Standarddeviation.

AppendixB.

Correlationmatrix.

Variable B C D E F G H I J K

A)Verbalproportional1 .308** .284** .273** .225** .240** .180** .101** .243** .312** .230** B)Verbalproportional2 .172** .228** .147** .143** .140** .097** .176** .203** .191**

C)Verbalproportional3 .460** .126** .177** .195** .119** .219** .273** .254**

D)Verbalproportional4 .220** .266** .218** .169** .230** .316** .338**

E)Quantitative1 .276** .213** .146** .294** .335** .255**

F)Quantitative2 .296** .223** .261** .337** .305**

G)Quantitative3 .164** .203** .261** .251**

H)Quantitative4 .126** .184** .177**

I)Formal1 .430** .287**

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