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Summer 2011 / 253 Teaching English Language Learners (ELLs) Mathematics in Early Childhood A ccording to the National Center for Education Statistics (NCES), 47 million people living in the United States spoke a language other than English at home in 2000, representing approximately 18% of the total U.S. popula- tion (NCES, 2004). It is expected that these demographics will continue to change, and minorities will become the majority by 2030 (U.S. Census Bureau, 2009). Of special interest is the fact that the population of English language learners (ELLs), especially those who are learning English in K-12 school settings, will con- tinue to grow (Chang, 2008). According to an “Issue Brief” by the American Youth Policy Forum (AYPF), about 20% of students were identified as an ELL in 2007, and a quarter of those students have difficulty with English (AYPF, 2009). A recent report from the Census Bureau (2009) suggests that one in every four children under the age of 5 in the United States is currently being raised in a home where a language other than English is being spoken. e major concern of educators who work with ELLs is that these children face many difficulties when entering the U.S. public education system. More specifically, these chil- dren tend to fall behind their mainstream counterparts in science, reading, and mathematics (NCES, 2003; U.S. Department of Education, 2001). A vast amount of research conducted in the area identifies several factors associated with ELL underachievement (Capps et al., 2006; Chang, 2008). For instance, sociolinguists have confirmed that ELLs experience dif- ficulties learning a new language and a new set of cultural norms, resulting in poor academic performance (Teranishi, 2004). Mathematics is one of the critical areas in which ELLs have by Joohi Lee, Young Ah Lee and 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, e Ohio State University, Lima. Carla Amaro-Jiménez is Assistant Professor, Bilingual/ESL Education, Department of Curriculum & Instruction, e University of Texas at Arlington.

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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.

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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-

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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

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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

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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

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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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