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Summer2011/253
TeachingEnglishLanguageLearners(ELLs)
MathematicsinEarlyChildhood
AccordingtotheNationalCenterforEducationStatistics(NCES),47millionpeoplelivinginthe
UnitedStatesspokealanguageotherthanEnglishathomein2000,representingapproximately18%ofthetotalU.S.popula-tion(NCES,2004).Itisexpectedthatthesedemographicswillcontinuetochange,andminoritieswillbecomethemajorityby2030(U.S.CensusBureau,2009).OfspecialinterestisthefactthatthepopulationofEnglishlanguagelearners(ELLs),especiallythosewhoarelearningEnglishinK-12schoolsettings,willcon-tinuetogrow(Chang,2008).Accordingtoan“IssueBrief”bytheAmericanYouthPolicyForum(AYPF),about20%ofstudentswereidentifiedasanELLin2007,andaquarterofthosestudentshavedifficultywithEnglish(AYPF,2009).ArecentreportfromtheCensusBureau(2009)suggeststhatoneineveryfourchildrenundertheageof5intheUnitedStatesiscurrentlybeingraisedinahomewherealanguageotherthanEnglishisbeingspoken.
ThemajorconcernofeducatorswhoworkwithELLsisthatthesechildrenfacemanydifficultieswhenenteringtheU.S.publiceducationsystem.Morespecifically,thesechil-drentendtofallbehindtheirmainstreamcounterpartsinscience,reading,andmathematics(NCES,2003;U.S.DepartmentofEducation,2001).AvastamountofresearchconductedintheareaidentifiesseveralfactorsassociatedwithELLunderachievement(Cappsetal.,2006;Chang,2008).Forinstance,sociolinguistshaveconfirmedthatELLsexperiencedif-ficultieslearninganewlanguageandanewsetofculturalnorms,resultinginpooracademicperformance(Teranishi,2004).MathematicsisoneofthecriticalareasinwhichELLshave
by Joohi Lee, Young Ah Leeand Carla Amaro-Jiménez
Joohi Lee is Associate Professor, Curriculum and Instruction, College of Education and Health Progressions, University of Texas at Arlington. Young Ah Lee is Assistant Professor, Education,
The Ohio State University, Lima. Carla Amaro-Jiménez is Assistant Professor, Bilingual/ESL Education, Department of Curriculum & Instruction, The University of Texas at Arlington.
254\ChildhoodEducation
language-associatedlearningdifficulties(Lee&Jung,2004;Veel,1999). TheNationalCouncilofTeachersofMath-ematics(NCTM)stronglyrecommendsthat“studentswhospeakafirstlanguageotherthanEnglishorhaverelatedculturaldifferencesmustnotfacespecialbarrierstolearningmathematics”(NCTM,2008,p.1).BasedonanNCESreport(2002),morethan40%ofteachershavehadELLsintheirclassrooms,butthemajorityreportedthattheywerenotpreparedtoteachELLsduetolackoftraining(Byrnes,Kiger,&Manning,1998).AnotherevenmorecriticalproblemaffectsteachingELLsmathematics:manyeducatorsbelieve,becausemathematicsisbasedonlanguageofnumbersandsymbols(Janzen,2008),thatstudentsdonotneedproficiencyinEnglishtoperformmathematicswell(Lee&Jung,2004).However,studieshaveshownastrongcorrelationbetweenchildren’sEnglishproficiencyandmath-ematicsperformance(Ron,1999;Schleppegrell,2007).TohelpELLssucceedinschoolmathe-matics,culturallyandlinguisticallyresponsivein-structionalsupportsforEnglishlanguagelearningarevital.TeachersofELLsshouldbeknowledge-ableaboutnon-Englishspeakingchildren’sreac-tionstotheirteachingpracticesinmathematicsandmakeuseofeffectiveresearch-basedstrategieswhenitcomestoteachingmathematicstothisgroupofstudents. Tomakemathematicslearningmeaningful,Co-pley(2000)andtheNCTM(2000)recommendthatteachersconnectmathematicsconceptswithchildren’sownexperiencesandcultures.Thefol-lowingepisode,experiencedbyoneoftheauthorsofthisarticle,reflectshowchildrencanbecomeenthusiasticaboutmathwhentheyareabletomakeconnectionstotheirownculture.
Haeun,a2nd-gradeELL,calledmeexcitedly.“Aunt,Ihavetoshowyousomething.”Iwaswonderingwhatshewasgoingtotellme.Fromtheexpressiononherface,itshouldbesomethingbig.Iasked,“Whatisit?”Haeunstartedtounpackherbackpackandtriedtofindsomethinginhermathematicsbook.Shewasnotsup-posedtobringthebookhome,butshehadaskedtheteacherforspecialpermission.Finally,shefoundthepageandshowedittome.“Aunt,lookatit,thisismyfavoritesnack.SeetheKoreanletterstoo?”ThepageHaeunwasshowingmefeaturedapictureofaKoreansnackwithKoreanlettersonit.Thepicturewasplacedatthebottomofthepageandcouldbarelybeseensincethesizeoftheletterswastoosmalltoread.IwasamazedthatHaeunwasabletoseethelettersandbeexcitedaboutit.
Thisanecdoteshowsthesignificantimpactonachildwhensheseesherownculturalheritagereflectedinaschooltextbook.AccordingtoJanzen(2008),goodteachersofELLsareabletoappropriatelydemonstratetochildrenthattheyvaluechildren’sfirstlanguagesandcultures.ThisiscriticallyimportantinteachingELLsmath-ematics,sincethemajorityofELLshaveshownpoorperformanceinmathematicscomparedtotheirEnglish-speakingcounterparts(Zehr,2010).Theauthors,inutilizingacross-referencingmeth-odofexaminingexistingliteratureassociatedwithELLsandlearningmathematics,identifiedthefollowingfivecomponentsascriticalelementsthatneedtobeconsideredwhenteachingmath-ematicstoELLs:
• Usingchildren’sownstoriesinteaching mathematics• Integratingconversationallanguageandlan-
guagethatisfamiliartostudentsinteachingmathematics
• Promotingchildren’snativelanguage• Allowingstudentstothinkaloudasastrategy
topromoteunderstanding• Integratingnon-linguisticmaterialstofacilitate
mathlanguage.
Using Children’s Own Stories inMathematics TeachingThebestpracticeforintegratingELLs’culturalknowledgeandexperiencesinteachingmath-ematicsistoutilizetheirownstoriestomakemathematicsproblems(LoCicero,Fuson,&Allexsaht-Snider,1999).ELLsoftenexperiencedifficultiesinunderstandingmathematicswordproblems.Robertson(2009)stronglyrecom-mendsthatteachersofELLsintegratechildren’sreal-lifeexamplessothattheycanpictureandunderstandmathematicsproblemsbetter. Childrencometoschoolwithmanystoriesacquiredfromtheirculturalcontexts.Forex-ample,Yechan,a2nd-grader,sharedhowheandhismommadekimchi,atraditionalKoreandish.Theteacher,Ms.Lee,paidcloseattentiontohisstoryandrecognizedthatYechanusedfrac-tionwordsindescribingtheprocessofcuttingacabbageintofourequalpieces.Ms.LeecreatedateachablemomentusinghisstoryandmadeafractionwordproblemtohelpYechanreachaconceptualunderstandingoffractions. Childrenoftenshareinclassstoriesfromtheirhomelives.TeachersofELLsneedtolistentochildren’sstoriescarefullyandtakeadvantageofthemtoteachmathematicsinameaningfulman-
Summer2011/255
ner.Robertson(2009)recommendsthatteachersofELLscontinuouslylookforfamiliarideasorpropsthatcanbeusedtoengagethechildrenmoreactively,suchasintegratingfamilyrecipesorusingpersonalstories.Furthermore,encour-agingELLsintheprocessofmakingtheirownmathematicswordproblemsalsobenefitsthem,inthattheycancomeupwiththemathematicswordproblemsthathavefamiliarcontextsandnaturallyreflecttheirlivesaswellastheirownculture(Coggins,Kravin,Coates,&Carroll,2007).
Integrating Familiar Language ELLscometoschoolwithvariouslevelsofEnglishproficiency.Regardlessoftheirprofi-ciencylevel,ithasbeenwellprovedthatELLsinschoolsettingsacquireconversationallanguageskillsmuchearlierthanmathematicslanguageoracademicvocabularyrelatedtomathematics(Cogginsetal.,2007).AccordingtoCummins(2005),ELLsneedabouttwoyearstoacquireconversationallanguage,butfarmoretimeto
masteracademiclanguage.Usually,thisaca-demiclanguagetakesbetweenfivetosevenyearstodevelopandacquire.TeachersofELLsshouldtakethisintoconsiderationwhenteachingthemmathematics.Forexample,ateachermayaskachildtosolvethefollowingdivisionproblem:“Thereare5childrenand20cookies.Howcanyoudivide20cookiesamong5children?”Intheprocessofsolvingthisproblem,achildmightuseconversationallanguage,suchas“theyshare,everyonegetthesame”(Cogginsetal.,2007,p.10).Althoughthechilddidnotuseformalmathematicslanguage,heorshedidshowacon-ceptualunderstandingofdivisionusingconversa-tionallanguage. Ateacheralsoneedstopromoteachild’sunderstandingofmathematicsbypresentingpromptsusingconversationallanguage.Inthefollowingexample,Daniela,a3rd-gradeELL,isattemptingtosolveastoryproblemwhilearesearcher(oneofauthorsofthisarticle)usesconversationallanguagetohelpherunderstandtheproblem(Amaro-Jiménez,2008).Mrs.
Figure1Useofcognates;beanbagswithvocabularyinEnglishandSpanish
256\ChildhoodEducation
James,Daniela’steacher,hasaskedherandherpeerstocomparethenumberofchildreninagivenfamilytothatintheirownfamiliesandthenfindthedifference.Mrs.Jamesusestheword“difference,”whichisamorefamiliartermforthechild,insteadoftheword“subtraction.”Theresearcherstressestheword“difference”topromptDanielatosolvetheproblem,andDan-ielafinallycomesupwiththeword“subtraction.”Asseenbelow,Danieladoesnotunderstandwhatsubtractionmeansuntilsheisgivenlanguagethatisfamiliartoher.
Daniela(D):Mrs.JamessaysIhavetofindthenumberofchildreninmyfamily,butIdon’tknowhow.
Researcher(R):Okay,sodoyouknowhowmanychildrenthereareinyourfamily?
D: Yes,therearetwo.R: Nowwhatelsedoyouneedtodo?D: Comparethenumberofchildreninthebig
familywithmyfamily.
R then asked D if she knew what she had to do to find that number. She nodded and showed R her piece of paper. R then asked her if she could explain
what she had done.
D: Thisisthenumberofchildreninmyfam-ily(pointingtothenumbertwo).Thisisthenumberofchildreninthelargefamily(pointedtothenumber69.Shethenhesitated,paused).Wait...no,thisisnotthenumber.Thisisalotofchildreninonefamily(laughed).
She then asked the girl sitting on her right if that was the number of children. The girl told her that that was the correct number.
D: Thetwonumbers.Okay...whatnow?R: Well(pause),ifyouneedtofindoutthedif-
ference(emphasis)inthenumberofchildren,whatdoyouneedtodo?
D: Oh(pause).Difference(pause).Ineedtodo(pause),Ineedsubtraction.
R: Yes,Daniela,youneedtosubtract.
TheresearcherusedconversationallanguagepromptsthatweremorefamiliartoDaniela.Us-ingconversationallanguagehelpsELLsgraduallyconnecttheireverydaylanguagewithmathematicslanguage(Irujo,2007;Ron,1999).
Figure2MathematicsWordBankinEnglishandSpanish
Summer2011/257
Directly Integrating the Children’sNative Language Into InstructionThebiggestdifficultythatELLsencounterwhentheysolvemathematicsproblemsisunderstandingmathematics-relatedtermsinEnglish.Teach-ersofELLsshouldallowthemtomakesenseofthesetermsandconceptsintheirnativelanguage(Olivares,1996)andencouragethemtousetheirprimarylanguageinlearningmathematicsiftheyaremoreproficientandcomfortabledoingso(Cogginsetal.,2007). Teachingmathematicsterms/vocabularyisacriticalpartofhelpingELLstolearnnewmathematicsskillsandconcepts.TeachersofELLsshouldmakeanattempttoidentifythetermstheyareusingintheirclassroomthathavecognatesinthechildren’snativelanguage(Slavit&Ernst-Slavit,2007).TheuseofcognateseffectivelyhelpsELLsmoreeasilyunderstandmathematicstermsinEnglishbyconnectingwiththeirnativelanguage(Hernandez,1999).Forinstance,someoftheshapesandcolorsthatchil-drenneedtolearnearlyonhavesimilarnamesinsuchlanguagesasSpanish(e.g.,circle–círculo,triangle–triángulo;seeFigure1). AlthoughteachersofELLsmayattempttousecognateswhenteachingchildrenmathematicsterms,teachersshouldbeawarethatitissome-timesverydifficultforELLstomemorizethesenewmathtermsinEnglish.Mostmathematicstermsaresocialknowledge,whichmeansthatchildrenshouldlearnthembymeansofasocialagentinagivensocialandculturalcontext(Co-pley,2000).Asaresult,ELLsshouldbeexposedtomathematicstermsinvariouswaysonadailybasis. OnewaytoexposeELLstomathtermsinEnglishisthroughenvironmentalmathprint.GivingELLsaccesstomathematicstermsonaneverydaybasishelpsthembecomefamiliarwiththetermsinawrittenformat.Specifically,displayingmathematicswordbankcharts(seeFigure2)thatincludetermsinEnglishandintheELL’snativelanguagecanhelphimbecomefamiliarwithEnglishmathematicsvocabulary,whilepreservingthemothertongueifthechildisabletoreadandwriteinthenativelanguage.Likewise,creatingawordbankchartthatcanbesenthomecanhelpsolidifythehome-schoolcon-nection.Parentscanbeencouragedtousethesewordbankchartstohelptheirchildrenwithhomeworkandunderstandwhattheirchildrenarelearningintheclassroom.DisplayingthesechartsintheclassroomalsowillbearesourcefornativeEnglish-speakingchildren;theywill
becomeawareoflanguagevarietyandlearntorespectotherpeople’slanguages,andmaybegintolearnsomeofthisacademicmathematicalvocabularyaswell.
Encouraging ELLs To Use Self-Talkas a Strategy To UnderstandMathematics ProblemsBuck(2000)recommendsthatELLsuse“self-talk”or“thinkaloud”strategy,ineithertheirnativelanguageorEnglish,tohelpthemclarifytheirunderstandingofmathproblemsortheirlearningprocesswhilereducingtheirlevelofanxietyaboutthecontenttheyarelearninginschool.Intheexamplethatfollows,Daniel,a3rd-grader,istryingtosolveamathstoryproblemonaweb-basedsoftwarecalledStudyIsland(Amaro-Jiménez,2008).Forthistestitem,Danielwasaskedtodeterminethemissingnumberinanumberline(i.e.,findthepattern).Theproblemfocusedonachildwhohadtogothroughacertainnumberofstepsonhiswaytoschool;Danielneededtodeterminehowmanystepsthechildhadwalkedafterthethirddayofwalkingtotheschool.Hewasgiventhenumberofstepsthechildhadwalkedonhisfirst,second,andfourthdaysofschool.Ashereadtheprob-lem,hebeganself-talking:
1. Differentnumbers(pause).2. Markcouldn’tgobycar(pause). 3. Hehadtowalkuptogotohisschool.4. Hewalkedupthesamenumberofstepseach
day(points to this sentence).5. Hewalkedupthesamenumberofstepseach
day.Hewalkedupthesamestepseachday(pause)eachday(points to these two words and holds his index finger there).
6. It’stwohundredfour,twohundredforty-four,threehundredtwenty-four...(counts with fingers).
7. Oh,(pause)sohewalkedupthesamenumberofstepseachday.
8. Twohundredforty-fourminustwo(pause)hundredfour.
9. Becauseitgoesbyfours(pause).10.Hmm,byforties(pause).11.Yeah,it’s284.
Inthiscase,Danielre-readthepassagemorethanoncetodetermineexactlywhathehadtodo.Asnotedinlines4-5andinline7,Daniel’sself-talkindicateshereadandre-readthepartaboutthechildhavingtowalkthesamenum-berofstepseachdaymultipletimes.Self-talk
258\ChildhoodEducation
allowedhimtothinkthroughtheproblem,ashewastryingtomakesenseoftheproblemhehadtosolve.Moreover,Danielwasabletouseself-talkasastrategytointerpretwhathewasbeingaskedtodointheproblemandtoclarifyproblem-solvingprocesses.AsIrujo(2007)emphasizes,aself-talkstrategyclearlyhelpsELLsinterpretthelanguagetounderstandwhattheproblemisaskingandincreasethestudents’ownunderstandingofthetaskathand.
Providing Non-LinguisticMathematics Materials To Facilitate Mathematics LanguageTeachingmathematicsusingonlyverbalcom-municationfrequentlylimitsELLs’mathematicslearning.Providingnon-linguisticmathematicsmaterialsthathavenoorlimitedlanguagecom-plexity(e.g.,manipulatives,pictures,diagrams,orgraphicorganizers)helpsELLsunderstandmath-ematicsproblemsbetteranddemonstratewhattheyknowaboutconcepts,skills,andprocesses(Lee&Jung,2004;Robertson,2009).However,Khisty(1995)claimsthatteachersofELLsoftenpresent“decontextualized”mathematicsmateri-alsthatdonotappropriatelyinvolvevisualsandconcretematerials.AskingELLstosolvemath-ematicsproblemsinEnglishwithoutprovidingappropriatevisualorconcretematerialswould
placeELLsinaquandary,becausetheycannotunderstandeithertheEnglishmathematicstermsorthemathematicsconceptsbeingtaught. Concretematerialsoftenfacilitateunderstand-ingofmathematicslanguages(Cogginsetal.,2006).Forexample,concretematerialscanhelpELLslearnthemeaningofsuchmathematicstermsas“edge,”“corner,”“arc,”“rotate,”andsoforth.Childrencanlearnthesetermsbytouchingmathematicsmaterials,suchasattributeblocksorpatternblocks.AccordingtoGarrisonandMora(2005),thebasicpremiseofteachingmathemat-icstoELLsistorelatenewmathematicstermstotangiblematerials.Thesematerials,whilemathematicallychallenging,mayrequireless-re-finedreadinglevelorlanguageskills(TeachersofEnglishtoStudentsofOtherLanguages,2006).TeachersofELLsshouldbecautiouswheninte-gratingconcretematerialstoteachmathematics,however,becausetheydonotalwaysbringaboutpositivelearningoutcomes(Clements,1999;Cle-ments&McMillen,1996).Whenateacherusesconcretematerialsinaprescribed,step-by-stepmanner,childrentendtomimictheprocessthattheteacherpresentswithoutgainingaconceptualunderstanding(Moyer,2001).Concretematerialsneedtobeusednotasagoal,butratherasave-hicletofacilitateanddevelopELLs’understand-ingofmathlanguageandmathematicscontent.
Figure3ExamplesofTrianglesandNon-Triangles(NCTM,2000,p.98)
Examples of Triangles
Examples of Non-Triangles
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ELLsneedtimetoexploremathmaterials,makemistakes,andmakesenseofmathusingtheconcretematerials.Beforeteachersprovideverbaldefinitionsofmathematicsterms,theyshouldaskELLstodefinethetermsintheirownwords(Irujo,2007;Robertson,2009),encouragingthemtousevariousrepresentations(thechild’snativelanguage,drawings,manipulatives,etc.).Forexample,tohelpELLsbuildaconceptualunderstandingofa“triangle,”insteadofprovidingthedefinitionoftriangle,teachersneedtoprovidematerialsthatdemonstratetheattributesoftrianglesandthetimetoexplorethem.Ateachermayprovidevisualfigures(seeFigure3)andhavethestudentsprovidetheirperspectives.Finally,ateachercanintroducetheterm“triangle”andhaveELLsdefinethetermintheirownwords,ineithertheirnativelanguageorinEnglish.Asthefinalstep,ateachermayintroducethedefinitionoftriangleusingmathematicslanguage(ormath-ematicsregister).
SummaryTherehasbeenamisguidedbeliefthatELLsshouldfindmathematicstobelesschallenging,sinceitismostlycomposedofsymbolsandnum-bers(Lee&Jung,2004;Veel,1999).However,astrongcorrelationexistsbetweenmathematicsperformanceandlanguageproficiency(Tera-nishi,2004).Inlearningmathematics,ELLsshouldunderstandnotonlymathematicsprob-lemsfromatextbook,butalsoorallanguage,becausemostmathematicscontentisdeliveredbyateacherinEnglish(Janzen,2008).Mostcritically,itisessentialforELLstoacquiremathematicslanguageskills(Ron,1999;Slavit&ErnstSlavit,2007). TheprimaryjobofteachersofELLsistohelpchildrenbridgetheirconversationaleverydaylanguageintomathematicslanguage(seeRon,1999,p.25,forthepathwayofacquisitionofmathematicssymboliclanguage).Thegoodnewsisthattherehasbeensomerecentim-provementinELLs’performanceinmathemat-icsintheUnitedStates.Nevertheless,thegapsbetweenELLsandnon-ELLsinbothmathandlanguageremainstatisticallysignificant(Zehr,2010).WithoutprovidingELLswithcarefulandresponsivesupporttounderstandmathematicslanguage,thisgapwillcontinueandthemajorityofELLsmayfallbehindinschoolmathematics.Therefore,itiscriticallyimportantforteachersofELLstoprovideacul-turallyandlinguisticallysupportivemathematicsenvironmentbytakingintoconsiderationwaysto
appreciateandusechildren’snativecultureandlanguageintheirmathematicsteachingaswellasbyadaptingtheirteachingmethodstoensurethattheydonotrelyonlyonEnglishwordstocommunicateconcepts.
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