THE JOURNAL OF TEACHER ACTION RESEARCH 24 · Keywords: elementary math, word problems, reading comprehension, English learners Introduction This article describes an action research

THEJOURNALOFTEACHERACTIONRESEARCH 24

JournalofTeacherActionResearch- Volume3,Issue3,2017,<practicalteacherresearch.com>,ISSN#2332-2233©JTAR.AllRights

MORETHANWORDS:STRUGGLINGREADERS’COMPREHENSIONOFWORDPROBLEMSLeannaR.MacDonaldandLeslieC.Banes

UniversityofCalifornia-Davis

AbstractBeforetheyareabletosolvemathematicalwordproblems,studentsmustbeabletoreadandcomprehendtheproblems.Althoughchallengingforallstudents,strugglingreadersfaceadditionalcognitivedemandswhensolvingwordproblemsthatproficientreadersdonot.Inthisactionresearchstudy,fourfocalstudents,includingtwoEnglishlearnersandtwonativeEnglishspeakers,weregivenamultiplicativecomparisonproblemandpromptedtoretellitintheirownwords,solvetheproblemusingaselectedstrategy,andthenretelltheproblemagain.Aretellrubricwasusedtoanalyzestudents’comprehensionbymeasuringthecompletenessoftheretell,whileadrawingandwritingrubricmeasuredstudents’visualrepresentationsandmetacognitivestrategiesinvolvedincomprehension.ResultssuggestdiscussionprovidedopportunitiesforstudentstolearnfromoneanotheranddrawingsespeciallyhelpedEnglishLearners’whocommunicatedtheirunderstandingthroughsymbolsandvisuals.Writingsupportedstudents’metacognitiveskillsleadingtogreatercomprehension,butmaybeproblematicforstudentsatthebeginningstagesofEnglishacquisition.Itisimperativeforteacherstoprovideopportunitiesforstrugglingreaderstodiscuss,draw,andwriteaboutwordproblemstosupporttheircomprehensionandtoextendtheseskillstomathintherealworld.

Keywords:elementarymath,wordproblems,readingcomprehension,Englishlearners

Introduction

Thisarticledescribesanactionresearchprojectconductedbyafirst-yearteacherwiththegoalofincreasingherunderstandingofhowstrugglingreaderscomprehendmathematicalwordproblems.Suggestionsandimplicationsforinstructionarediscussed.

LiteratureReview

Substantialresearchinthefieldofmathematicshasbeenconductedontheuseofdiscussionsandthinks-aloudstocomprehendmathematics.Researchershavefoundthatwhenstudentsareprovidedwithopportunitiestoengageinmeaningfulmathematicaldialogue,students’comprehensionofamathematicalsituationincreasesassodoestheirmathematicaljustifications(Bargh&Schul,1980;Chi,2000;Frankeet



al.,2009;King,1992;Rogoff,1991).Therefore,discussioncanprovideanotherwayforstudentstointeractwithtext,hopefullyleadingtomoreunderstandingofapresentedmathematicalsituationinagivenwordproblem.Otherresearchershavefoundthattheuseofpicturesanddrawingssupportsstudents’comprehensionandconceptualunderstandingofmathematics(Marinoetal.,2010;O’Connelletal.,2005).Drawingapicturemighthelpstudentsconnectwhattheythinkorsayinaretelltoatangiblerepresentationintheirsolutionprocess.Italsoallowsstudentstocommunicatetheircomprehensionofawordprobleminmultipleways.Givingstudentsopportunitiestoprovideamentalmodeltoamathproblemallowsthemtointernalizeandcontemplateamathematicalsituation(Dexter&Hughes,2011).EdensandPotter(2008)foundthatdrawingscanreducethelinguisticdemandcommonlyfoundinwordproblems—animportantfindingwhencontemplatingstrategiesforELswhoarestrugglingreaderstouse.Therefore,usingdrawingsasastrategytosupportstudents’comprehensionofwordproblemsisimportanttoexplore.Writinghasalsobeenfoundtobeausefulstrategyasitsupportsstudents’metacognition(Artz&Armour-Thomas,1992;Carr&Biddlecomb,1998;Powell,1997;Pugalee,2001),animportantthoughtprocessforstudents’comprehension.Althoughthetestsubjectsfromtheseresearchprojectsaremucholderinage(whichseemsquestionabletousewritingforfourthgraders)JulietBaxterandhercolleagues(2005)foundthat7thgraderswithwritingandreadingdisabilities,operatingatleasttwoyearsbelowgradelevel,showedmultipleinstancesofstudents’comprehensionandconceptualunderstandingofproblemswhengivingopportunitiestojournaltheirmathematicalthinking.Accordingly,studentswhofacedadditionalacademicchallenges,whichaffectedtheirabilitytowrite,stillbenefitedfromwritingabouttheirmathematicalthinking.Forthisreason,providingopportunitiesforstudentstowriteabouttheirthinkingisimportanttoinvestigateaswritingcouldfostertheircomprehension.

Methodology

Context.ThisinquiryprojectwasconductedinafourthgradeclassroomatapublicTitle1schoollocatedinasuburbanneighborhoodknownforgunandgangviolence.About86%ofstudentsatApplegateElementary(pseudonym)receivefreeandreducedlunch,anindicatorofhighlevelsofpoverty.Forty–twopercentofstudentsareELs(EnglishLearners)andApplegateisaprogramimprovementschoolthathasastrongfocusonliteracy.

Theclassroomconsistedof29students,ofwhich14wereELs.AccordingtotheCaliforniaEnglishLanguageDevelopmentTest(CELDT)thatmeasuresstudents’Englishproficiencyonascaleof1-5,theaverageELlevelintheclasswas3,representinganintermediatelevelEnglishproficiency.OftheELstudentsintheclassroom,13students’nativelanguagewasSpanishandonestudents’nativelanguagewasHmong.Fifteen



studentswereHispanic,sixwhite,fiveAfricanAmerican,andtheremainingthreewerePacificIslander,AlaskaNative,orHmong.Twenty-twostudentswerereadingbelowgradelevel,with13studentsreadingoneormoreyearsbehindgrade-levelnorms.

Forthisinquiryproject,fourfocalstudentswereselectedforindepthdataanalysis.Thesefocalstudentswereeitherreadingatafirstorsecondgradelevel,andwerechosenbecausetheyrepresentthereadinglevelsofalargeportionoftheclass.TwoofthefocalstudentswereELswithCELDTlevels1and2(beginningandearlyintermediate)andtwostudentswereEOs(studentswhospeakEnglishonly).AcombinationofELandEOstudentswerechoseninordertoexplorehowparticularinstructionalstrategiesmaysupportstudentswithdifferentlinguisticneeds.Thefourfocalstudentsareusuallypassiveandtheirvoicesgounheardingroupdiscussion.Theyareusuallyhesitantwhensolvingwordproblemsindependentlyandwaitforotherstoprovidesuggestionsoranswers.Aprimarygoalofthisprojectistoprovidestudentswithmoreopportunitiestosharetheirideasandgaintheconfidenceneededtoattemptwordproblems.Priortothisstudy,theteacherprimarilyhadstudentsattemptwordproblemsasawholeclasswithguidingquestionstoscaffoldstudentsthinking.However,theteacherdesiredamorestudent-centeredapproachbyprovidingherstudentswithstrategiestheycouldusetoengageinmathematicalthinking.

Purpose.Inthefieldofmathematics,comprehensioniscrucialforstudents’successinwordproblemsandinrealworldapplications.Notonlymuststudentsunderstandwhatawordproblemisaskinginreal-lifecontexts,theymustalsobeabletointeractwiththetextofwordproblemstosolvethem.Inamathematicaltext,readingbecomesevenmoredifficultastextisnotalwaysreadfromlefttoright(dependingifstudentsneedtoalsointerpretandreferencegraphs/tables)anditisusuallyvisuallycomplexastherearecallouts,sidebarsofgraphs,historicalfacts,and/orpracticeproblems(Bartonetal.2002).Thesetasksbecomeespeciallydifficultforstrugglingreadersastheyfaceadditionalcognitivedemandsthatproficientreadersdonot.Whenreadingwordproblems,strugglingreadersareaskedtosimultaneouslydecodetext,alreadyanareaofdifficulty,whilecomprehendingandrelatingthesewordstomathematics.Readingcomprehensionisstronglycorrelatedwithstudents’successonmathematicalwordproblems(Vilenius-Tuohimaa,Aunola,&Nurmi,2008).Therefore,findingstrategiesthatstudentscanusetohelplessenthecognitivedemandofwordproblemsisimportanttoprovideeducationalequityforourstrugglingreadersinorderforthemtoreachstandardsandusetheseskillsintherealworld.

Hegartyandcolleagues(1995)definecomprehensioninmathematicsonatieredscalewhichinvolves(1)understandingtheproblem,(2)formingaplantosolvetheproblemand(3)carryingouttheplanbysolvingit.Forthepurposesofthisproject,comprehensionisdefinedasunderstandingthemathematicalsituationdescribedinawordproblemandbeingabletoformaplantosolveit.

MultiplicativeComparisonProblemsaredefinedas“involvingacomparisonoftwoquantitiesinwhichoneisdescribedasamultipleoftheother”(Carpenter,Fennema,



Franke,Levi,&Empson,2015,p.66).Theseproblemswereemphasizedinthisinquiryprojectbecausetheyincludelanguagethatcanbeparticularlydifficultforstudents(Stern,1993),suchasunderstandingthemeaningof“twiceasmany,”andtheyareprevalentin4thgrademathcurriculaandassessments.

Asdocumentedbystateanddistrictreadingassessments,thecurrentfourthgradeclassatApplegatestruggleswithreadingandcomprehendingtext.Moreover,atthebeginningoftheyear,studentscompletedathirdgrademathtestcontainingwordproblems,manyofthemmultiplicativecomparisonproblems.Theclassaverageonthistestwasonly51%,indicatinganeedforadditionalsupportwiththiskindofproblem.Multiplicativewordproblemshavetheaddedadvantagesofofferingawindowintostudents’understandingoftheproblem,becauseitisdifficulttogetacorrectanswersimplyby“numbergrabbing”(Littlefield&Rieser,1993)—wherestudentspickthenumbersseeninawordproblemandrandomlychoseanoperationwithoutfullyunderstandingthemathematicalsituationdescribed.

Thefollowingresearchquestionsguidedthedesignofthisinquiryproject:

1.)Whatstrategiescanstrugglingreadersusetobettercomprehendmultiplicativecomparisonwordproblems?

2.)DoELsandEOscomprehendwordproblemsdifferently,andifso,how?

3.)Whatpartsofwordproblemsarestudentsstrugglingwith?

DataCollectionandAnalysis.Theeffectivenessofretellstomonitorandaidcomprehensioniswellknownthroughouttheliteracyresearchcommunity(Brown&Cambourne,1987;Hoyt,1999;Mowbray,2010).Therefore,foreachofthethreeroundsofdatacollection,studentswerepromptedto(1)retellapresentedwordproblemintheirownwords,(2)solvetheproblemusingoneofthethreestrategies,and(3)retelltheproblemagain.Theteacherconductedallthreerounds.Students’retellswereevaluatedwithaRetellRubric(Ambrose&Molina,2014),whichunpackswordproblemsintotheircomponentelements,indicatingthepartsoftheproblemstudentsunderstoodorattendedto,andthepartstheydidnot.Theelementsofeachwordproblemthatwereanalyzedarethenumbers,theunits,themathematicalrelationship,andthequestion.Foreachelement,studentswhocorrectlyretoldthatpartoftheproblemreceivedascoreof2,studentswhoretoldanelementdifferentlyfromhowitwasstatedintheproblemreceivedascoreof1,andstudentswhoomittedanelementcompletelyreceivedascoreof0(AppendixA).

ForRound1,studentsweregivenahandoutofthefollowingproblem:Thomasbuiltafencethatwas12timesaslongasTerry’s.Terrybuiltafencethatwas4feetlong.HowlongwasThomas’sfence?Theywerepromptedtoretelltheproblemintheirownwordsafterrereadingtheproblemasmanytimesastheyneeded.Foreachretell,studentsworkedwithmeone-on-onesothattheirpeersdidnotinfluencetheirresponses.Then,



inpartners(ELsandEOswerepartneredtogether),studentswerepromptedtodiscussthewordproblemtooneanother,notingsimilaritiesordifferencesinthinkingabouttheproblem(aclassroomnorm).Here,students’conversationswereaudio-recordedandtranscribed.Independently,studentssolvedtheproblemontheirhandout.Theteachertookfieldnotesofstudents’explanationstotheirsolutions.Lastly,studentswereagainpromptedtoretellthewordproblemintheirownwords,rereadingtheproblemasmanytimesastheyneeded.Theteacherrereadthetranscribeddiscussionandcomparedwhatstudentssaidintheirexplanationstothewrittenworkonthehandout.Thisallowedthemestoemergeaboutthematchandmismatchbetweenstudents’oraldiscourseandtheirwrittensolutionstrategies.

ForRound2,studentsweregivenahandoutofthefollowingproblemandpromptedtoretellitintheirownwordsafterrereading:Thegiraffeinthezoois3timesastallasthekangaroo.Thekangaroois6feettall.Howtallisthegiraffe?Theteacherthenaskedstudentstosolvetheproblembydrawingapictureofit.Oncetheyreachedasolution,theteachertookfieldnotesofstudents’explanationsfortheiranswers.Studentswerethenpromptedtoretelltheproblemintheirwordsagain.Toanalyzestudents’drawings,aniterativeprocessofcreatingcodeswasusedbyresearchingthenecessarycomponentsinadrawingneededtocomprehendawordproblem(Dexter&Hughes,2011;Edens&Potter,2008)(AppendixB).VandeWalle’s(2012)four-pointrubricwasmodifiedbyaddinganothercategorytitled“Outstanding,”indicatingnoerrorsinthedrawing.Thisrubric,(AppendixC),allowedstudents’worktobeanalyzedagainstasetofdesiredlearnerresponsesandtoplacetheirunderstandingsonadevelopmentalcontinuum.Studentswerenotexpectedtoreceiveaperfectscoreonthedrawingrubricasstudents’drawingswereintendedforthemtomakesenseoftheproblem—nottopresenttoanaudience.

Forround3,studentsretoldthefollowingwordproblemintheirownwords:Jilllived5timesasmanymilesasLeodidfromtheocean.Leolived20milesfromtheocean.HowmanymilesdidJilllivefromtheocean?Theteacherthenaskedstudentstosolvetheproblembyjournaling,orwritingtheirthoughts,aboutit.Theteacheremphasizedthattheirgrammarandspellingwasnotimportant.Afterstudentsjournaledontheirhandoutandarrivedatasolution,studentsretoldtheproblemagain.Students’writingwasanalyzedintwodifferentways.First,usingAmbroseandMolina’s(2014)retellrubricwasusedtoassessstudents’writing.Thiswasanalyzedtodetermineifstudents’retellsweredifferentwhentheywerewrittenfromwhentheywerespoken.

Second,students’writingwasanalyzedbygoingthroughadeductiveprocessofcreatingaMetacognitiveStrategiesRubric(AppendixD).Metacognitivestrategieswereanalyzedbecauseresearchindicatesastrongcorrelationbetweenmetacognitiveskillsandstudents’comprehension(Lippmann&Linder,2007).DrawingontheworkofTanner(2012),whosuggeststeacherssupportthedevelopmentofmetacognitionbyaskingself-reflectivequestionsforplanning,monitoring,andevaluating,theteachercreatedarubrictoassessstudents’metacognitionwithintheirmathematicalwriting.Studentsreceivedofscoreof1for“yes”andascoreof0for“no.”Atotalpossiblescore



was3,althoughitwasnotexpectedstudentswouldreceiveamaximumscoreastheywereaskedtojournalabouttheproblemonlyforthemselvesandwerenottoldtheirwritingwouldbereadbyadistantaudience.

ResultsandDiscussion

FindingsfromRound1suggestthefocalstudents’comprehensionofwordproblemsimprovedwhentheyweregivenopportunitiestodiscussaproblemwiththeirpeers.Firstgradelevelreadersimprovedthemostsignificantly,asseeninthefiguresbelow.Forexample,Sharron’sabilitytoincludeelementsoftheoriginalwordproblemduringthesecondretellingincreasedby50%,andDominick’ssecondretellingincreasedby38%.YusufandSharronwereabletoidentifytherelationshipoftheproblemaftertheirpeerdescribeditinthestudentdiscussion.Thesestudentswhoinitiallystruggledwiththeconceptlearnedfromtheirpeeroncegivenopportunitiestodiscuss.Thisfindingissupportedbyotherresearchstudiesasstudentslearnfromoneanotherwhenengaginginstudent-talk(Frankeetal.,2009).

AlthoughMarywasabletocorrectlyrestatetheprobleminherownwordswith100%accuracyduringthepreandpost-discussionretellings,therewasamisalignmentbetweenwhatshesaidandhowshesolvedtheproblem.Theotherthreestudents’retellmatchedhowtheysolvedtheproblem.Thisfindingmayindicatethelimitationsofusingretellsasawaytogaugewhetherstudentsunderstandwordproblems.Perhapsasacompensationstrategyforlowreadingability,somestudentsareabletomemorizeandrestateaproblemwithoutreallyunderstandingthepresentedmathematicalsituation.

Figure1:GraphofPre-andPost-DiscussionRetellScores.

AsimilarphenomenonoccurredinRound2whenstudents’retellsappeartoworsenaftertheuseofthedrawingstrategy,seeninFigure2.However,threestudentssolvedtheproblemcorrectlyandwereabletoexplaintheirsolutions,demonstratingtheircomprehension.TheaveragescoreontheDrawingRubricwas3.5outof5.Nostudentincludedarepresentationoftheunknown,whichismirroredbytheirretells.However,thedrawingwasintendedtosupportstudents’comprehension,nottopresentafullpicturetoanaudience.Drawingsprovidedfocalstudentswithanalternativemeanstocommunicatetheircomprehensionofthewordproblem.Thiswasespeciallybeneficial

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PrePost PrePost PrePost PrePost

Mary Dominick Yusuf Sharron

Rubricscores

DiscussionRetells

Question

Relationship

Units

Numbers



fortheELstudents(DominickandYusuf),perhapsduetoareductioninlinguisticdemandthroughdrawing.Dominickrepresentedtherelationshipbetweentheanimals’heightswithanarrowandYusufdrewabarindicatingdifferencesinheight.ThesesamplesarefoundinAppendixE.Studentsoftenpointedtotheirdrawingstocontextualizewhattheywereexplainingtotheteacherintheirplanningprocesstosolvetheproblem,afindingwhichisaffirmedbypriorstudiesofcommunicationviadrawinginmathematics(Dexter&Hughes,2011;Edens&Potter,2008).Althoughtheirretellswereincomplete,students’comprehensionofthewordproblemwasrepresentedthroughtheirdrawingsandexplanations.

Figure2:GraphofPre-andPost-DrawingRetellScores.

FindingsfromRound3suggeststudentsbenefitedfromwritingaboutthemathproblem,displayedinFigure3.Comparingthepre-andpost-retells,weseethatYusufandSharronhadsimilardifficultiesretellingtherelationshipinvolvedinthisproblem.ThissuggeststhatinterpretingrelationshipsincomparisonwordproblemsareequallydifficultforEOandELstudents.BothELstudents,YusufandDominick,alsosharesimilarimprovementsintheirpost-retellasbothstudentswereabletocorrectlyidentifyingthenumbersintheproblem.Thissuggeststhattheirwritingmighthavehelpedtheminternalizetheproblemandassociatednumbersatdeeperlevelthanverballyspeaking.ThisissupportedbyBaxterandcolleagues’(2005)whofoundthatstudents’comprehensionofwordproblemswasmoreevidentintheirwritingthanintheiroraldiscourse.Sharron’sandYusuf’swritingincludedmoreelementsofthewordproblemthantheirpreviousretell,suggestingthatwritinggavestudentsanopportunitytothinkabouttheproblemmoredeeply.However,thispatternisreversedforDominick,whoincludedonlytherelationshipintheprobleminhiswritingandnootherelementsoftheproblem,asseeninFigure4.ThissuggeststhatforCELDTlevel1students,writingmaynotbeaseffectiveastrategytosupportstudents’thinkingandcomprehensionofaproblem.ThisfindingisaffirmedbyresearchersEdens&Potter(2008)whofoundthatlinguisticdemandsaredecreasedforELstudentswhenpicturesareutilizedbutareincreasedwhenwritingtasksarerequired.Itappearsthatwritingmayhaveencouragedstudentstoformulateaplantosolve(AppendixF).However,whenverballyprompted,studentsillustratedevenmoremetacognitiveskills.For

0

2

4

6

8



Rubricscores

DrawingRetells

Question

Relationship

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example,Yusufwrote,“youcandoaddup”butwhenaskedbytheteacherwhywouldweaddhestated,“Uh!No!You’resupposetotimes!Causeitsays5times.Somultiply!”Thissuggeststhatespeciallywhenpairedwithteacherquestioning,writingcanhelpstudentsthinkabouttheirjustificationforsolvingaprobleminaparticularway.

Figure3:GraphofPre-andPost-WritingRetellScores.

Figure4:GraphofElementsIncludedinStudents’Writing.

ConclusionandImplications

Thisactionresearchprojectinvestigatedstrugglingreaders’comprehensionofwordproblemsutilizingthreedifferentstrategies:discussingwithapartner,drawing,andwriting.Studentswiththelowestreadingscoresshowedthemostimprovementafterdiscussingthewordproblemwithapartner.Thissuggeststeachersshouldpartnerstudentsofdifferentreadinglevelstogetherbecausestrugglingreadersseemtobenefitwhenpartneredwithhigher-leveledreadingpartners.Drawingandwritingaboutwordproblemscanalsobeeffectivestrategiesforstrugglingreaders,especiallythosewhoareEnglishlearners.DrawingwasespeciallyhelpfulforELstudentsperhapsbecauseit

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Rubricscores

RetellScoresBeforeandAfterWriting

Question

Relationship

Units

Numbers

0

2

4

6

8


ElementsinStudents'Writing

Writing-RetellQuestion

Writing-RetellRelationship

Writing-RetellUnits

Writing-RetellNumbers



offersanopportunitytocommunicatemathematicalunderstandingthroughsymbolsandvisualrepresentations.Writingalsoseemedtosupportstudents’comprehensionofwordproblems,althoughitcreatedadditionalchallengesforDominick,anELwithbeginninglevelEnglishproficiency.Thus,teachersmaywanttobecautiouswhenusingwriting-to-learnstrategieswithstudentswhoareatthebeginningstagesofEnglishdevelopment.BeginningELsmaybebetterabletocommunicatetheirunderstandingthroughothermodes,suchasdrawing,discussion,orusingmanipulatives.

Multipleandvariedmeasuresofassessmentmayhelpteachersgainadeeperunderstandingoftheirstudents’comprehensionofwordproblems.Althoughtheyprovidevaluableinformationaboutstudents’understandingofaproblem,usingretellsalonemaybemisleading.Forexample,Maryretoldtheproblemwith100%accuracybuttherewasamisalignmentbetweenwhatshesaidandhowshesolvedtheproblem.Furthermore,acrossallthreeroundsMary’spreandpostretellscoresremainedunchanged,althoughshedidnotalwayssolvetheproblemscorrectly.Thissuggestsretellsalonearenotenoughtodeterminewhetherastudentunderstoodtheproblem.Multipleassessments,suchausingacombinationofretells,drawings,writing,andoraldiscussion,canofferabroader,perhapsmoreaccurateviewofstudents’comprehensionofmathematicalwordproblems.Futureresearchcanexplorehowdifferentkindsofpromptsforwritingcanelicitdifferencesinstudents’mathematicalwriting,andwhetheritismorebeneficialforstudentstodrawapictureofthemathematicalsituationbeforeorafterdiscussingtheproblemwithpeers.

AbouttheAuthors

LeannaR.MacDonaldteachesfourthgradeinaTitleIpublicschool.ShereceivedhercredentialsandmasterdegreeineducationfromUC,Davisandisinterestedinresearchandinstructionthathelpshergainadeeperunderstandingofherstudents'mathematicalthinking.Email:[email protected]

LeslieC.Banesisaformerbilingualelementaryschoolteacher.SheisaninstructorfortheMAEducationprogramatUC,DavisinCaliforniaandcollaborateswithteacherstoexploretherelationshipbetweenmathematicsandlanguagelearning. Email:[email protected]



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Lippmann,R.K.,&Linder,C.(2007).Metacognitiveactivityinthephysicsstudentlaboratory: Isincreasedmetacognitionnecessarilybetter?MetacognitionandLearning,2(1),41-56.Littlefield,J.,&Rieser,J.J.(1993).Semanticfeaturesofsimilarityandchildren'sstrategiesfor identificationofrelevantinformationinmathematicalstoryproblems.Cognition&Instruction,11, 133-188.Marino,M.,Black,A.,Hayes,M.,Beecher,C.(2010).Ananalysisoffactorsthataffect strugglingreaders’achievementduringatechnology-enhancedSTEMastronomycurriculum. JournalofSpecialEducationTechnology,25(3),35-47.Mowbray,T.(2010).Thepowerofreadandretell.PracticallyPrimary15(2),10-12.O'Connell,S.R.,Beamon,C,Beyea,J.M.,Denvir,S.S.,Dowdall,L.A.,Friedland,N.G.,etal. (2005).Aimingforunderstanding:Lessonslearnedaboutwritinginmathematics.Teaching ChildrenMathematics,12,192-199.Osman,M.E.,&Hannafin,M.J.(1992).Metacognitionresearchandtheory:Analysisand implicationsforinstructionaldesign.EducationalTechnologyResearchandDevelopment,40(2), 83-99.Powell,A.B.(1997)Capturing,examiningandrespondingtomathematicalthinking throughwriting.TheClearingHouse71(1),21–25.Pugalee,D.K.(2001).Writing,mathematicsandmetacognition:Lookingforconnections throughstudents’workinmathematicalproblemsolving.SchoolScienceand Mathematics101(5),236–245.Rogoff,B.(1991).Guidanceandparticipationinspatialplanning.InL.Resnick,J.Levine,&S. Teasley(Eds.),Perspectivesonsociallysharedcognition(pp.349-383).Washington, DC:AmericanPsychologicalAssociation.Stern,E.(1993).Whatmakescertainarithmeticwordproblemsinvolvingthecomparisonofsets sodifficultforchildren?JournalofEducationalPsychology,85(1),7-23.Tanner,K.B.(2012).PromotingStudentMetacognition.CBE-LifeSciencesEducation,11(2), 113-120.VandeWalle,J.A.;Karp.K.S.;Bay-Williams,J.M.(2012).ElementaryandMiddleSchool Mathematics:TeachingDevelopmentally(8thed.).USA:Pearson.Vilenius-Tuohimaa,PM;Aunola,K.;Nurmi,JE.(2008).Theassociationbetweenmathematical wordproblemsandreadingcomprehension.EducationalPsychology,28(4),40.



AppendixA:RetellRubric

Element Same

(2)

Different

(1)

Missing

(0)

Numbers Containsbothnumbersfromoriginalproblem.

Containstwonumbers.Atleastonenumberisdifferentthanoriginal.

Atleastonenumberintheproblemismissing.

Units Unitisidentifiedinproblem. Unitisdifferentfromoriginalproblem.

Unitismissing.

Relationship Relationshipisconsistentwithwordproblem.

Relationshipdiffersfromwhatwasdescribedinwordproblem.

Relationshipismissing.

Question Containsaquestionconsistentwithwordproblems.

Containsaquestionwithmeaningdifferentfromoriginal.

Questionismissing.



AppendixB:ElementsWithinDrawing

Student Kangaroo Giraffe Kangaroo’s height

Giraffe’s relationship

Unknown

Rubric Score

X X X X X X X



AppendixC:DrawingRubric

NoAttempt

0

Unsatisfactory

1

Marginal

2

Proficient

3

Excellent

4

Outstanding

5

Thetaskisnotcompleted.Noelementsindrawingarecorrectlyindicated.

Fragmentsofaccomplishment,butlittletonosuccess.Onlyoneelementindrawingiscorrectlyindicated.

Partoftaskisaccomplished,butlackofevidenceofunderstanding.Twoelementsindrawingarecorrectlyindicated.

Couldworktofullaccomplishmentwithminimalfeedback.Threeelementsarecorrectlyindicated.

Drawingmeetsdemandsoftask.Mayhaveminorerrors.Fourelementsarecorrectlyindicated.

Drawingmeetsdemandsoftaskwithnoerrorsandallfiveelementsarecorrectlyindicated.



AppendixD:MetacognitiveRubric

Student Planning

Doesthestudentwriteaboutakindofplantosolvetheproblem?

Monitoring

Doesthestudentwriteaboutanycontemplationtheyarehavingabouttheproblem?

Evaluating

Doesthestudentchecktomakesureananswermakessense,ordoublechecktheirthinking?

X X X X



AppendixE:Drawings

Yusuf’sDrawing Dominick’sDrawing

Documents

THE JOURNAL OF TEACHER ACTION RESEARCH 24 · Keywords: elementary math, word problems, reading comprehension, English learners Introduction This article describes an action research