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InßuenceofsituationalandconceptualrewordingonwordproblemsolvingSantiagoVicente,JoseOrrantia*andLievenVerschaffelUniversityofSalamanca,SpainCatholicUniversityofLeuven,BelgiumBackground.Studiesonrewordingwordproblemscanbegroupedintotwomaingroups:situationalrewording,inwhichthesituationdenotedbythetextisdescribedmorerichly,andconceptualrewording,inwhichtheunderlyingsemanticrelationsareOuraimsaretodeÞneanddistinguishthesetwokindsofrewordingandtotestempiricallytheirrelativeeffectivenessintwodifferentstudies.Sample.IntheÞrststudy,79thirdgraders,64fourthgradersand65Þfthgraderstookpart;thesampleforStudy2wassimilar.InStudy1,childrenwereaskedtosolvebotheasyanddifÞculttwo-stepchangeproblemsinthreedifferentversions:standard,situationalandconceptualrewording.InStudy2,threedifferentversionsofthesituationalversionwerecompared:onewithonlytemporalelaborations,onewithonlycausalelaborationsandaÔcompleteÕversioncombiningbothelaborations.InStudy1,conceptuallyrewordedproblemselicitedthebestresults,especiallyamongyoungerchildrenandfordifÞculttwo-stepproblems.NeitherinStudy1norinStudy2didthesituationallyrewordedproblemsyieldbetterperformancethanstandarditems.OnlyconceptualrewordinghasprovedtobeusefulforimprovingchildrenÕsperformance,especiallyamongyoungerchildrenandfordifÞcultproblems.Thelackofimpactofsituationalrewordingcannotbeexplainedintermsofthelengthoftheresultingtext. *CorrespondenceshouldbeaddressedtoJoseOrrantia,UniversidaddeSalamanca,FacultaddeEducacion,Pso.Canalejas169,37008,Salamanca,Spain(e-mail:orrantia@usal.es). TheBritish subsequentresearch,distinguishingthreeclassesofproblemsituationsmodelledbyadditionandsubtraction.ThesearesituationsinvolvingachangefromaninitialtoaÞnalstatethroughtheapplicationofatransformation(changeproblems),thecombinationoftwodiscretesetsorsplittingofonesetintotwodiscretesets(combineproblems)andthequantiÞedcomparisonoftwodiscretesetsofobjects(compareproblems).Withineachofthesethreemajorsemanticcategories,furtherdistinctionsweremaderesultingin18differenttypesofone-stepadditionandsubtractionproblems(Riley,Greeno,&Heller,1983;seealsoFuson,1992;Reed,1999;Riley&Greeno,1988;Verschaffel&DeCorte,1993,1997).Numerousempiricalstudiescarriedoutduringthisperiodwithchildrenbetweentheagesof5and8yearsdemonstratedthepsychologicalandeducationalsigniÞcanceofthisclassiÞcationscheme,especiallythatwordproblemsthatcanbesolvedbythesamearithmeticoperation(i.e.adirectadditionorasubtractionwiththetwogivennumbersintheproblem)butthatbelongtodifferentsemanticproblemtypesyielddifferentdegreesofdifÞculty,differentwaysofrepresentingandsolvingtheseproblems,anddifferenterrorcategories(forreviewsofthisresearch,seeFuson,1992;Reed,1999;Verschaffel&DeCorte,1997).Computersimulationsweredevelopedconcurrentlywiththeempiricalresearch(Briars&Larkin,1984;Rileyetal.,1983).Underlyingthesecomputermodelswasthegeneralassumptionthataskilfulsolutionprocessofawordproblemstartsfromanetworkrepresentationofthebasicsemanticrelationshipsbetweenthemainquantitiesintheproblem,intermsofoneofthethreeabove-mentionedbasicsemanticstructures.Thisnetworkisconsideredtheresultofacomplexinteractionbetweenbottom-upandtop-downanalysis;thatis,theprocessingoftheverbalinput,aswellastheactivityofsemanticschemata,contributestotheconstructionofthisnetworkrepresentation.MoredifÞcultproblemtypesrequirere-representationsintermsofotherschematabeforeaproperarithmeticactionoroperationcanbeselectedandperformed.Forinstance,accordingtotheRileyetal.model,changeproblemswithanunknowninitialsetorcompareproblemswithanunknowncomparedorreferencesetcanonlybesolvedaftertheoriginalproblemrepresentationintermsof,respectively,achangeoracompareschemahasbeenre-representedintermsofapart-wholestructure.Themorecompetenttheproblemsolveris,themoreable(s)heistoprocessthetextinatop-downwaybyrelyingonhis(her)well-developedschemata.Anumberofstudiescomparedtheperformance,strategyanderrordataofstudentswiththebehaviourofthesecomputermodels(forreviewsoftheseempiricalstudies,seeFuson,1992;Reed,1999;Verschaffel&DeCorte,1997).Forexample,empiricalsupportfortheassumedcentralroleofpart-wholeknowledgeinchildrenÕsadditionandsubtractionwordproblemsolvingcomesfromtheworkbySophian(Sophian&McCorgray,1994;Sophian&Vong,1995).However,itwasclearfromanearlystagethattherewerestillseveralproblematicissuesandquestionsremaining.BynomeansallempiricalÞndingswereconsistentwiththe(computer)models(forsystematiccomparisonsoftheseempiricaldatawiththepredictionsofthecomputermodels,seeCarpenter&Moser,1984;DeCorte&Verschaffel,1988;Fuson,1992).ManyoftheseinconsistencieshadtodowiththefactthatÐbecauseoftherelativelyweakelaborationoftheinitialtext-processingstageofthewordproblemsolvingprocessandbecauseoftheneglectofthebroader(instructional)environmentwhereinthisproblem-solvingprocessoccursÐthese(computer)modelswereunabletoaccountfortheinßuenceoftextualandcontextualvariablesonSantiagoVicenteetal. childrenÕsproblemrepresentationsandsolutions(Cummins,Kintsch,Reusser,&Weimer,1988;Kintsch&Greeno,1985;Reusser,1990).Indeed,anumberofempiricalstudieshaveshownhowsmallchangesinthewordingoftheproblemtextsmayhaveadramatic(positive)impactonchildrenÕssolutionprocessesandskills(Cummins,1991;Cumminsetal.,1988;Davis-Dorsey,Ross,&Morrison,1991;DeCorte,Verschaffel,&DeWin,1985;Hudson,1983;Staub&Reusser,1992;Stern&Lehrndorfer,1992).Underlyingallthesestudiesistheideathatmodifyingthetextoftheproblem,withoutchangingitssemanticstructure,willleadtoahighersuccessrate.ApioneeringstudyontherewordingeffectwascarriedoutbyHudson.Hepresentednurseryschool,kindergartenandÞrst-gradechildren,eightpicturesofcompare1situations(showing,e.g.Þvebirdsandtwoworms).Eachtimetwoquestionswereasked:Þrst,theusualquestionincompareproblems:ÔHerearesomebirdsandherearesomeworms.Howmanymorebirdsthanwormsarethere?Õandsecond,analternativequestionÔHerearesomebirdsandherearesomeworms.Supposethebirdsallraceoverandeachonetriestogetaworm.HowmanybirdswonÕtgetaworm?ÕHudsonfoundthat,asexpected,theproblemwassigniÞcantlyeasierwhenthesecondquestionwasasked.LaterinvestigationsreplicatedHudsonÕsstudyandappliedhismethodtoothertypesofwordproblemsaswell.Thesestudiesontheimpactofrewordingwordproblemscanbedividedintotwomaingroups.First,studieswhereinthesemanticrelationsbetweenthesetsimpliedintheproblemarestatedmoreexplicitlyandmademoretransparently(conceptualrewording),asinthestudiesbyCummins(1991),Davis-Dorseyetal.(1991)andDeCorteetal.(1985).Second,investigationswhereinthe(real-world)situationtowhichtheproblemstatementisreferringtoispresentedinamoreenrichedandelaboratedway(situationalrewording);illustrativeofthissecondapproacharethestudiesbyCumminsetal.(1988),StaubandReusser(1992)andSternandLehrndorfer(1992).Instudiesonconceptualrewording,rewordedproblemswereformulatedinsuchawaythattheunderlyingsemanticrelationsbetweenthegivenandunknownsetsweremademoreexplicitthaninthestandardversion,withoutaffectingtheunderlyingsemantic/mathematicalstructure.DeCorteetal.(1985)investigatedtheeffectofconceptualrewordingofchange5,combine5andcompare1problemsonÞrstandsecondgraders.Cummins(1991)testedtheeffectofconceptualrewordingonÞrstgradersÕsolutionsofcombine5problems.Davis-Dorseyetal.(1991)rewordedchange5,combine5andcompare1problemsinthesamewayasDeCorteetal.,butmanipulatedconceptualrewordingincombinationwithproblempersonalization(seeTable2).TheresultsofDeCorteetal.ÕsstudyshowedthatrewordinghadapositiveeffectforÞrstand,toalesserextent,forsecondgraders.CumminsfoundasigniÞcantrewordingeffect.Davis-Dorseyetal.observedimprovedperformancetoo,butintheirstudyonlythesecondgradestudentsbeneÞtedfromconceptualrewordingandonlywhenitwascombinedwithpersonalization.Problempersonalization,asimplementedbyDavis-Dorseyetal.(1991),comescloselytothesecondkindofrewordingmentionedabove,namelysituationalrewording.Studiesthatbelongtothissecondcategorysharetheideaofmakingthesituationalcontextinwhichtheproblemisembeddedmoreexplicitly,ratherthanbyclarifyingtheunderlyingsemanticrelationsbetweensets.However,therearesomedifferencesbetweenthissecondtypeofstudies.Cumminsetal.(1988)comparedsecondandthirdgradersÕcomprehensionsandsolutionsofcombine5,change5,SantiagoVicenteetal. change6andcompare6standardwordproblems(intheauthorsÕterminology:ÔempoverishedproblemsÕ)withenrichedproblemsembeddedintolittlestories(seeTable2)Ôshowingplausible,realisticsituationsandsettingupamotivationfortheÞnalarithmeticquestionthatcompletedthestoryÕ(p.427).SternandLehrndorfer(1992)presentedÞrstgraderswith(allsixtypesof)standardcompareproblemsandversionsoftheseproblemsthatwereembeddedinaconcrete,enrichedandfamiliarstorycontext,whereacompetitivecontextdealingwithqualitativecomparisonbeforepresentingthearithmeticwordproblemwasdescribed.ChildrenÕsperformanceontheseÔenrichedÕproblemswascomparedtotheachievementonthestandardproblemsinwhichthestoryhadnoqualitativecomparisonbetweenthetwopeopleinvolvedinthecomparison.Finally,StaubandReusser(1992)generateddifferentversionsofchange1and2,aswellasofchange5and6,problemsandaskedÞrstandthirdgraderstosolvethem.Theirrewordingconsistedofmodifyingthesequenceoftheeventsinthetext,sothatthissequencedidnolongerÞtwiththeÔordonaturalisÕoftheeventsastheyoccurintherealworld(e.g.resultingstate/transfer/initialstateforchange5andchange6problems,seeTable2),whichmakesitmoredifÞcultforchildrentorecovertheintendedsituationalstructure.Thesestudiesonsituationalrewordingyieldeddifferentresults.SternandLehrndorfer(1992)andStaubandReusser(1992)foundresultsconsistentwiththeirpredictions,namely,theformerfoundthatcompareproblemsbecameeasierwhentheywereembeddedinanÔenrichedÕsituationalcontext,whereasStaubandReusserfoundthattheirrewordedproblemswereindeedmoredifÞcultforchildren.However,Cumminsetal.(1988)didnotÞndanyfacilitationeffectfromanenrichedstorycontext.Thesetofabove-mentionedstudiesonrewordingshowssomelimitations.Probably,themainlimitationisthateachstudy(exceptDavis-Dorseyetal.Õs,1991)hasfocusedononlyonekindofrewording,makingmutualcomparisonsverydifÞcult,ifnotimpossible(seeTable2).Moreover,adetailedandformaldescriptionandaccountofthemodiÞedtextsandtheirrelationwiththeoriginalstandardversionsaremissing.STUDY1Startingfromanoverviewofthepreviousinvestigations,wesetuptwonewempiricalstudies.Study1assessedthefacilitatingeffectofthetwotypesofrewordingdistinguishedaboveandcomparedtheirrelativeeffectiveness:Þrst,arewordingaimedatfacilitatingthegenerationofasituationmodel(situationalrewording)andsecond,arewordingwherebycluesareaddedaimedatmakingmoreexplicitthesemanticrelationsbetweenthegivenandunknownsets(conceptualrewording).BesidesacomparisonoftheoveralleffectofbothtypesofrewordingonstudentsÕperformance,wealsowantedtoinvestigatetheimpactofproblemdifÞcultyandchildrenÕsageonthe(relative)effectivenessofbothkindsofrewording.Inpreviousstudies,impactofrewordingwastestedwithÞrst-,second-andthird-gradechildren(exceptinDavis-Dorseyetal.Õs,1991,study,whichalsoincludedÞfthgraders).ResultsofthislatterstudyshowedthatconceptualrewordingwasnoteffectiveforÞfthgraders,becausethesemoreexperiencedlearnersÕabilitytoconstructanaccurateproblemrepresentationevenwhenconfrontedtraditional,impoverishedtexts,asDavis-Dorseyargue.Liketheseauthors,wewereinterestedinanalysingtheimpactofrewordingonolderelementarystudentstoo.InordertoSantiagoVicenteetal. SubjectsTheexperimentaltaskwasadministeredtoasampleof208grades3Ð5children(79thirdgraders,64fourthgradersand65Þfthgraders)fromtwoschoolsofthecityofSalamanca,Spain.Ninety-fourofthemweremalesand114females,andagesvariedbetween9and11years.Themeanagewas8years10monthsforthirdgraders,9years5monthsforfourthgradersand10years11monthsforÞfthgraders.TasksTheexperimentaltaskincludedeightwordproblems:sixexperimentalproblemsandtwobufferitems.Thesixexperimentalitemsweretwo-stepchangeproblemsandinvolvedtwostandardproblems,twoconceptuallyrewordedproblems(CRP)andtwosituationallyrewordedproblems(SRP).Wecounterbalancedtheorderoftheproblems,sothatthesameproblemdidnotappearinthesamepositionacrossthedifferentversionsofthetask.Moreover,wepreventedthattwoproblemswiththesamelevelofdifÞcultyorwiththesamekindofrewordingsucceededeachother.Thetwobufferitemswereincludedtoavoidstereotypedapproachesand/oranswers.Thesebufferitemswerealsotwo-stepproblems,buttheywerecompareinsteadofchangeproblems,withthereferencesetunknown.Therewasnotimelimit,sothateverystudentcouldspendthetimeheneededtosolvethem.Thestandardproblemtextwasasfollows.Peterhad37metresofcable.HeboughtAmetresofcablemore.HeusedBmetresofcableandheendedupwith11metresofcable.Howmanymetresofcabledidhebuy/use?Figure1showsthestructureoftheabovetwo-stepchangeproblem.ItrepresentsboththetemporalstructureoftheproblemandtheactionsandtransformationsspeciÞcofchangeproblems.Forthistwo-stepproblem,theÞrstchangesituationbeginswithaninitialstate(ÔPeterhad37metresofcableÕ),onwhichanactionisexecuted(ÔheboughtAmetresofcableÕ),generatingaresultingstaterepresentedinFigure1bythesign(?).Thislattersetis,atthesametime,theinitialsetofthesecondchangesituation,onwhichanewactionisexecuted(ÔheusedBmetresofcableÕ)generatingaÞnalresultset(Ôheendedupwith11metresofcableÕ).ProblemswereconsideredtobemoreorlessdifÞcultdependingonthesetreferredtointhequestionÐthenumberofmetresofcablebeingbought(setA,seeFigure1)orthenumberofmetresofcablebeingused(setB)Ðbecausethisdetermines,Þrst,the Figure1.Problemstructureofthetwo-stepchangeproblemsusedinthestudy.Squaresrepresentstaticsets,thatisstartand/orresultsets.Circlesrepresentchangesets.Thenormalarrowsindicatethedirectionofthechange:atransfer-inactionisdenotedbyanarrowpointingtoastartsetandatransfer-outactionbyanarrowpointingtoachangeset.Dottedarrowsindicatethetemporalsequenceoftheproblem.SantiagoVicenteetal. statementnodesand11newarcs.Finally,thepropositionalanalysisrevealedthat,atthepropositionallevel,therewerenodifferencesbetweentheeasyandthedifÞcultproblems.Theinternal-consistencyreliabilityofthetaskwascomputedbymeansofCronbachÕsalphaformula.Thereliabilityofthetaskwas0.78.Thetaskwasadministeredduringthenormalschoolhours.Theadministrationtookplaceduringtwodifferentmomentsofthesamemathematicslesson,separatedfromeachotherbyabreakof15minutes.Taskinstructionsstressedthatinordertosolvetheproblemscomprehensivereadingwasrequired.Therewasnotimelimitation.AllproblemsweredistributedsothattwoproblemswiththesamedifÞcultylevelorthesameinformationdidnotappearconsecutively.DatacodingChildrenÕsresponseswerecodedascorrect(1point)orincorrect(0points).Weconsideredascorrectallsolutionswhereinthecorrectarithmeticoperationswiththeappropriatenumberswerechosen,withouttakingintoaccountthecomputationalexactnessoftheÞnalresult.WedecidedtocodethedatainthiswaybecausewewantedtoassesschildrenÕsproblemcomprehensionratherthantheircalculationability.ResultsanddiscussionTheresultsareshowninTable3.Themeansuccessrateswereanalysedina3(grade:3,4or5)2(difÞculty:easyordifÞcult)3(wording:standard,conceptualorsituational)ANOVAwithrepeatedmeasuresonthelasttwofactors.Effectsizevalueisalsoincluded.AllmaineffectsprovedsigniÞcant.First,olderchildrensuccessfullysolvedmoreproblems,03;successrateswere.51,.59and.64forgrades3,4and5,respectively.ComparisonsbetweenmeansusingtheTukeyHSDprocedurewith05indicatedthatthedifferencesweresigniÞcantbetweengrades3and4,andbetweengrades3and5.Second,themeansuccessratesforeasyproblems(.81)weresigniÞcantlyhigherthanfordifÞcultproblems(.35),53.Third,regardingwordingtype,themeansuccessrateswere.55,.52and.66forstandard,SRPandCRP,respectively,15.ThedifferencesweresigniÞcantbetweenstandardandCRP[0001,13],andbetweenSRPandCRP Table3.Study1,meansuccessratepergrade,difÞcultylevel,andkindofrewordingEasyDifÞcultTotal(grade)GradeStandarSituationalConceptualStandarSituationalConceptualMean79).74.72.73.22.17.50.5164).84.70.85.31.35.51.5965).87.89.92.33.33.44.64Mean.82.76.83.29.28.49.58Total(difÞculty).81.35SantiagoVicenteetal. Ontheotherhand,ourresultsalsopointedoutthataddingmarkersforthetemporal,intentionalandfunctionalstructureoftheproblemdidnotresultinanyimprovementinchildrenÕsproblem-solvingperformance.Inretrospect,aplausibleexplanationfortheseoutcomesisthatthesituationalmodiÞcationsinevitablyledtoproblemsthatweremuchlongerthantheoriginalstandardones,increasingthenumberofnodesandarcs,whichmighthavemadetheproblemtext,maybe,moreaccessibleandcomprehensiblefor(some)children,but,atthesametime,inevitablyresultedinaproblemstatementthatwasmuchlongerandlinguisticallymorecomplex,intermsofrelationsbetweennodesandoftheresultingstructure,thantheoriginalone.ThisexplanationwastestedinStudy2,whereinwetriedtokeeptheextratextofthesituationallyrewordedproblemssimple(whencomparedwiththestandardones),byincludingonlytwokindsofsituationaladditions,namelycausalandtemporalinformation,insteadoftheÞveinformationtypesusedinourÞrststudy.STUDY2BasedontheunexpectedresultsofStudy1forthesituationallyrewordedproblems,wedecidedtoexploretheseresultsandtheirposthocinterpretationinasecondstudythatfocusedonsituationalrewording.KeepinginmindthatincludingallÞvetypesofsituationalinformationthatwederivedfromReusserÕstheoryinevitablyresultsinaproblematicallyextensiveandlinguisticallycomplexproblemtext,wedecidedtodroptheÞrstthreekindsofsituationalinformationthatwederivedfromReusserÕstheory(namelyactions,descriptive,intentionalinformation),andtokeeponlythelasttwotypes,namely,temporalandcausalinformation.Inotherwords,whereasinStudy1wetriedtodevelopafullyelaboratedversionofsituationalrewordingstrictlyinlinewithReusserÕsSPStheory,inStudy2wetookamorepragmaticpositionbyrestrictingthesituationalenrichmenttowhatweconsideredasabsolutelycrucialforprovidingasituationallyenrichedversionandbyerasinglessimportantextrasituationalinformation.WedecidednottoincludeconceptualreformulationsinStudy2,Þrstbecausewewereonlyinterestedinunravellingthepuzzlingnegativeimpactofsituationalreformulationsandincludingalsoconceptuallyreformulatedproblemswouldhavemadetheexperimentaltaskmorepronetolearningand/orfatigueeffects,andsecond,becausethecriticalcomparisonwasbetweenthesenewtypesofsituationalreformulationsofthewordproblemsandthestandardproblems,andnotwiththeconceptuallyreformulatedones,fromStudy1.AsinStudy1,wepredictedthatchildrenÕsperformancewouldbehigherforthesituationallyrewordedproblemsthanforthestandardproblems.Theserewordedproblemswouldallowchildrentocreateamoreelaboratedepisodicsituationmodel(withoutleadingtoproblemtextsthatwereproblematicallylongandlinguisticallycomplex),andthuswouldresultinbetterperformancethanthestandardproblems.SubjectsThetaskswereappliedto192students(81malesand111females)fromtwodifferentschoolsinthecityofSalamanca,Spain.Outofthese,61werethirdgraders,61fourthgradersand70Þfthgraders(meanagewas8years6monthsforthirdgraders,9years4monthsforfourthgradersand9years6monthsforÞfthgraders).SantiagoVicenteetal. Copyright © The British Psychological SocietyReproduction in any form (including the internet) is prohibited without prior permission from the Society Table4.Study2,meansuccessratepergrade,difÞcultylevel,andkindofrewordingEasyproblemsDifÞcultproblemsStandardCausalTemporalCompleteStandardCausalTemporalCompleteMean(Grade)Grade3.60.49.55.52.14.18.110.33Grade4.61.48.74.66.26.31.23.16.43Grade5.72.71.79.75.40.35.35.34.55Mean(rewording).64.56.70.64.27.28.23.17.44Mean(DifÞculty).63.24SantiagoVicenteetal. thantheversionswithonlyonetypeofaddedsituationalinformation.Therefore,eventhoughthecompleteversioninStudy2containedalreadyconsiderablyfewerpropositionsthaninStudy1,thiscompleteversionstilldidnotyieldthebestresultsandevenresultedinslightlyworseperformancethanversionswithfewersituationaladditions.GENERALDISCUSSIONInthe1980sand1990s,severalstudiesonrewordingarithmeticwordproblemshavebeenrealized.Generallyspeaking,inthesestudies,theproblemswererewordedinoneofthefollowingtwoways.First,inasituationalway,byenrichingtheproblemstatementwithsomeextrapiecesofinformation(suchasmotives,settings,timemarkers)withaviewtoallowchildrentogenerateasituationalmodelcontainingthefunctionaland/orthetemporalstructureoftheproblem.Second,inaconceptualway,bymakingmoreexplicittheunderlyingsemantic/mathematicalrelationsbetweenthegivenandtheunknownsetsthaninthestandardversion,withoutaffectingtheunderlyingsemantic/mathematicalstructure,and,indoingso,byhelpingtheproblemsolvertobuilduptheproperconceptualrepresentationoftheproblemintermsofpart-wholerelationships.Inpreviousempiricalstudiesandtheoreticalanalyses,thesetwokindsofrewordingswerenotexplicitlydistinguishedandsometimesevenconfounded.Startingfromthiscategorizationofdifferenttypesofrewording,wesetuptwonewempiricalstudies.InStudy1,wedirectlycomparedchildrenÕssolutionsoftwodifferentrewordingsofasimpleandadifÞculttwo-stepchangeproblem:asituationalreformulation,inwhichmarkersofthetemporal,causalandintentionalstructurewereaddedtotheproblemtext,andaconceptualreformulation,inwhichthecommonwholesetofthetwosimplewordproblemsthatconstitutethetwo-stepproblemwasexplicitlymarked.Resultsshowedafacilitatingeffectofconceptualrewording,probablybecauseitallowedmappingtheproblemtexteasilyontotacitknowledgeconcerningpart-wholerelations,whilethesituationalreformulationdidnotresultinanyimprovementinchildrenÕsproblem-solvingperformance.InourdiscussionoftheresultsofStudy1,wepointedoutthatoneexplanationfortheseresultsmightbethatbyhavingÔtranslatedÕReusserÕsdeÞnitionsofepisodicsituationmodeltoostrictlyandtooexhaustively,andbythereforehavingincludedanabundantamountofextrasituationalinformation,wemayhaveturnedtheproblemtextintoaproblematicallylongandcomplexone.Inthisway,thecognitiveloadputonthe(young)problemsolversmayhavebecomeconsiderablybiggerthanforthestandardandconceptuallyrewordedversionsoftheproblems.However,theresultsofStudy2didnotsupportthisexplanation.Inthisstudy,problemswererewordedinsuchawaythatonlyonekindofextrasituationalinformation(temporalorcausal)orthecombinationofonlythesetwosituationaladditionswasprovidedinthedistinctconditions.Thisledtoanimportantdecreaseinthenumberofnodesandlinkingarcs,andaccordinglytolinguisticallyconsiderablymuchshorterandlesscomplexproblemtexts.However,resultsshowedthatthiskindofÔtextualeconomizationÕstilldidnotresultinasigniÞcantimprovementofchildrenÕsperformance(exceptanisolatedandrestrictedfacilitativeeffectoftemporalinformationoneasyproblemsforfourthgraders.)Afteranalysingtheresultsofbothstudies,itisnecessarytoquestionwhyaddedsituationalinformation(asoperationalizedinbothstudies)didnothelpchildrentosolvewordproblemsmoreaccurately.And,whysomeotherstudiesdidshowpositiveresultsonsituationallyrewordedproblems.ApossibleexplanationforwhyaddedsituationalSantiagoVicenteetal. informationdidnotresultinbetterperformance,neitherinthefullversion(Study1)norintheshorter,causaland/ortemporalversions(Study2).UsingSwellerÕscognitiveloadtheory,wehaveinterpretedhislatterfailureasduetotheirrelevanceofthisaddedsituationalinformationinrelationtothespeciÞcdifÞcultiesandgoalsofthetaskandtothespeciÞckindofgoal-orientedprocessingrequired.DoesthismeanthatReusserÕsmodel(Reusser,1985;Staub&Reusser,1992)andthe(theoreticalandeducational)implicationsthatwehavederivedfromit,arewrong?Theanswerisno.Rather,weclaimthatthenegativeresultsofourstudieswithrespecttothefacilitativeeffectofsituationalrewordingwereduetothefactthatthechildrenÕsmajordifÞcultywiththesetwo-stepproblemswasnottounderstandthesituationinwhichthearithmeticproblemwasembedded;therefore,fortheseproblems,gettingadditionalsituationalinformationwasnottheirmajorneedandactedÐinSwellerÕs(Paasetal.,2003;Sweller,1999)terminologyÐevenasanextracognitiveburden.Thatis,thedifÞcultyoftheseproblemswasconceptual,notsituational,andbecauseofthis,theonlyrewordedproblemsthatimprovedchildrenÕsachievementweretheconceptualversions,andnotsituationalversions.However,forotherwordproblems,wheretheconstructionofaproperepisodicsituationalmodelbecomesamajorchallenge,effortstoelaboratetheproblemtextwithsituationalenrichmentsmayyieldtheexpectedpositiveimpact.However,thepresentstudieshaverevealedthatsuchattemptstoprovidesituationallyricherproblemsnecessarilyresultintextsthatarelinguisticallymoreextensiveandmorecomplex(whichmightworkagainstthepositiveeffectsofthesituationalenrichment),especiallyinyoungerchildrenwithpoorer(technical)readingabilities.Providingthissituationalenrichmentthroughnon-textualmeanslikepictures,animations,etc.mightbeaÐboththeoreticallyandeducationallyÐpromisingalternative.Theinvestigationofthislattersuggestionisthetopicofourcurrentresearch.AcknowledgementsThisresearchwassupportedbyGrantBSO2003-05075toJ.OrrantiafromtheMinisteriodeCienciayTecnologõainSpainandbyGrantGOA2006/01fromtheResearchFundK.U.Leuven,Belgium.S.VicentealsogratefullyacknowledgesthesupportprovidedbytheJuntadeCastillayninSpain.ReferencesBriars,D.J.,&Larkin,J.H.(1984).AnintegratedmodelofskillinsolvingelementarywordCognitionandInstruction,245Ð296.Carpenter,T.P.,&Moser,J.M.(1984).Theacquisitionofadditionandsubtractionconceptsingradesonethroughthree.JournalforResearchinMathematicsEducation,179Ð202.Cummins,D.D.(1991).ChildrenÕsinterpretationsofarithmeticword-problems.Cognitionand,261Ð289.Cummins,D.D.,Kintsch,W.,Reusser,K.,&Weimer,R.(1988).Theroleofunderstandinginsolvingwordproblems.CognitivePsychology,405Ð438.Davis-Dorsey,J.,Ross,S.M.,&Morrison,G.R.(1991).Theroleofrewordingandcontextpersonalizationinthesolvingofmathematicalword-problems.JournalofEducationalPsychology,61Ð68.DeCorte,E.,&Verschaffel,L.(1988).Computersimulationasatoolinresearchonproblemsolvinginsubject-matterdomains.InternationalJournalofEducationalResearchSantiagoVicenteetal. Sweller,J.(1999).Instructionaldesignintechnicalareas.Camberwell,Victoria,Australia:AustralianCouncilforEducationalResearch.Verschaffel,L.,&DeCorte,E.(1993).Adecadeofresearchonword-problemsolvinginLeuven:Theoretical,methodologicalandpracticaloutcomes.EducationalPsychologyReviewVerschaffel,L.,&DeCorte,E.(1997).Worldproblems:Avehicleforpromotingauthenticmathematicalunderstandingandproblemsolvingintheprimaryschool.InT.Nunes&P.Bryant(Eds.),Learningandteachingmathematics.Aninternationalperspective(pp.69Ð97).Hove:PsychologyPress.Received28October2005;revisedversionreceived12December2006SantiagoVicenteetal.