Moyer etalAERA09Paper.docx

Moyer etalAERA09Paper.docx

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MoyeretalAERA09Paper

LearningfromInstruction:

ProfilesofClassroomExperiencesUsingStandards-BasedandTraditionalCurricula

JohnC.Moyer

MarquetteUniversity

JinfaCai

UniversityofDelaware

BikaiNie

UniversityofDelaware

NingWang

WidenerUniversity

PaperPresentedatthe2009annualmeetingoftheAmericanEducationalResearchAssociation.SanDiego,CA,April13-17,2009.

Theresearchreportedinthispaperispartofalargeproject,LongitudinalInvestigationoftheEffectofCurriculumonAlgebraLearning（LieCalProject）.LieCalProjectissupportedbyagrantfromtheNationalScienceFoundation（ESI-0454739）.AnyopinionsexpressedhereinarethoseoftheauthorsanddonotnecessarilyrepresenttheviewsoftheNationalScienceFoundation.

JinfaCai,523EwingHall,UniversityofDelaware,Newark,DE19716.jcai@udel.edu

LEARNINGFROMINSTRUCTION:

PROFILESOFCLASSROOMEXPERIENCESUSINGSTANDARDS-BASEDANDTRADITIONALCURRICULA

Purpose

Theultimategoalofeducationalresearch,curriculumdevelopment,andinstructionalimprovementistoenhancestudentlearning.Historically,curriculahavebeenusednotonlytocommunicatewhatstudentsshouldlearn（NCTM,1989）,butalsotoguideinstruction（Ball&Cohen,1996）.Accordingly,manyadvocatesofmathematicseducationreformbelievethatchangingthecurriculumisaneffectivewaytoimproveclassroompracticeandenhancestudentlearning（NCTM,1989,2000;Howson,Keitel,&Kilpatrick,1981;Senk&Thompson,2003）.However,itisbynomeanscertainthatthecurriculumassignedtoateachersignificantlyinfluencesthatteacher’sclassroominstruction,letaloneinfluenceitinwaysthattheauthorsintended（Ball&Cohen,1996;Fullan&Pomfret,1977）.Therefore,importantquestionswithregardtocurriculaarewhether,how,andtowhatextenttheyinfluencetheinstructionoftheteacherswhousethem.Thepurposeofthisstudyistoshedlightonthosequestionsbyconstructinginstructionalprofilesofteacherswhouseoneortheotheroftwotypesofmiddleschoolmathematicscurricula:

Standards-basedortraditional.

BackgroundandTheoreticalConsiderations

Standards-BasedMathematicsCurricula

Inthelate1980sandearly1990s,theNationalCouncilofTeachersofMathematics（NCTM）publisheditsfirstroundofStandardsdocuments（e.g.NCTM,1989,1991,1995）,whichprovidedrecommendationsforreformingandimprovingK-12schoolmathematics.IntheStandardsandrelateddocumentsthatappeared,thediscussionsofgoalsformathematicseducationemphasizetheimportanceofthinking,understanding,reasoning,andproblemsolving,withanemphasisonrepresentations,connections,applications,andcommunication.Thisviewstandsincontrasttoamoreconventionalviewofthegoalsformathematicseducation,whichemphasizesthememorizationandrecitationofdecontextualizedfacts,rules,andprocedures,withthesubsequentapplicationofwell-rehearsedprocedurestosolveroutineproblems.

Inthe1990s,theNationalScienceFoundationprovidedextensivefundingtodevelopandimplementanumberofStandards-basedschoolmathematicscurriculathatalignwiththerecommendationsintheStandards（Senk&Thompson,2003;NationalResearchCouncil,2004）.TheresultingNSFcurriculausetheexplorationofreal-lifeproblemsasawaytostrengthenstudents’understandingofimportantmathematics.TheimplementationoftheseStandards-basedcurricularequiresthatteacherschangethewaytheyhavetraditionallytaughtmathematicsandthatstudentschangetheirviewsofwhatlearningmathematicsentails.Unfortunatelyforthereformmovement,teachersfacechallengeswhentryingtoimplementtheseinnovativecurricula.EveninclassroomswhereteachersattempttoteachforunderstandingasspecifiedbytheNCTMStandards,teachersoftenmaintainmanyexistingmathematicspracticesinconsistentwiththerecommendationsspecifiedintheNCTMStandards（Hiebert&Stigler,2000;Spillane&Zeuli,1999;Rand,2002;Gross&Merchlinsky,2002）.

Ontheonehand,NSF-fundedcurriculaarereferredtoasStandards-basedbecausetheywerefundedspecificallytosupportStandards-basedinstructionandbecausetheytypicallybuildstudents’understandingofimportantmathematicsthroughexplorationsofreal-worldsituationsandproblems.Ontheotherhand,mostpublishersofso-calledtraditionalcurriculaalsoclaimthattheircurricularmaterialsareStandards-based.Infact,theirteachers’guidestypicallydescribehowthechapters,ifnotthelessonsineachchapter,correspondtotheNCTMcontentandprocessstandards（e.g.,Baileyetal.,2006a,2006b,2006c）.Nonetheless,unliketheNSF-fundedcurricula,thesecurriculaarecommonlyreferredtoas“traditional”ratherthan“Standards-based”（Nie,Cai,Moyer,inpress）.Inkeepingwiththiscommonpractice,werefertotheNSF-fundedandtheothercurriculadiscussedinthispaperas“Standards-based”and“traditional,”respectively.

Standards-BasedCurriculumResearch

Giventhedisparitybetweenthebeliefsofreformadvocatesandreformopponents,researchontheeffectivenessofstandards-basedcurriculahasbeenongoingsincethe1990s（e.g.,Carroll,1997;McCaffreyetal.,2001;Riordan&Noyce,2001;Ridwayetal.,2003;Schoenetal.,2003;Tarr,etal.,2008）.Classroominstructionisconsideredacentralcomponentinthedevelopmentandtheorganizationofstudents'thinkingandlearning（Detterman,1993;Rogoff&Chavajay,1995;Wozniak&Fischer,1993）.However,muchoftheresearchthathasstudiedtheeffectivenessofreformcurriculaonstudentachievementdidnotinvestigatethetypeofinstructionalexperiencesthatteachersprovidewhenimplementingStandards-basedcurricula.

Ridgwayetal.（2003）conductedthreestudiesoftheeffectivenessoftheConnectedMathematicsProgram（CMP）,oneoftheStandards-basedmiddleschoolcurricula.Ofallthevariablesinthelarge-scalestudydatabase（includingteacher,class,school,site,gender,andfalltestachievementlevels）,theonlyoneassociatedwithgainsinattainmentwascurriculum.Howevernoneofthethreestudiesincludedin-depthinformationabouthowCMPwasactuallyusedintheschools.Ridgway,etal.concludedthatthereisaneedtodocumentthenatureofinstructionoccurringintheclassroomswherereformcurriculaarebeingimplemented.

AstudybySchoenetal.（2003）didjustthat.Theyexaminedtherelatednessofstudentachievementtotheinstructionalpracticesof40highschoolteacherswhowereusingaStandards-basedcurriculum（Coxfordetal.,2003）.Schoen,etal.conductedclassroomobservationsofeachteacherduringthecourseofaschoolyear;theyalsoadministeredtwoinstruction-relatedself-reportsurveystotheteachers.Resultsshowedthattheimplementationofcognitivelydemandingtasksforstudentsandadherencetoreformprinciplesduringinstructionweresignificantlyandpositivelyassociatedwithstudentachievement.Incontrast,resultsalsoshowedthatthepercentagesofclasstimespentonbothteacherpresentationsandwholeclassdiscussionswerenegativelyassociatedwithstudentachievement.Inamorerecentstudy,Tarretal.（2008）showedthattheinteractionofcurriculumwithastandards-basedlearningenvironmentinthemiddlegradeswasassociatedwithasignificantimpactonstudentachievement.

BecauseNSF-fundedcurriculalikeCMPclaimtohavedifferentlearninggoalsthantraditionalcurricula,andbecausethelayoutandorganizationofreformtextsistypicallyquitedifferentthantraditionalmathematicstexts,naturalquestionstoaskare:

DoesinstructionusingaStandards-basedcurriculumreallydifferfrominstructionusingatraditionalcurriculum?

Ifso,whataretheimportantfeaturesofinstructionusinganNSF-fundedStandards-basedcurriculumthatdistinguishitfrominstructionusingso-calledtraditionalcurricula?

InwhatwaysdoesaStandards-basedcurriculumlikeCMPinfluenceinstructionthataredifferentfromthewaysthatmoretraditionalmiddleschoolcurriculainfluenceinstruction?

Toanswerquestionslikethese,researchersneedtoinvestigatethewayteachersteachStandards-basedandtraditionalcurricula（Kilpatrick,2003,NRC,2004,Wilson&Floden,2001）.Indoingso,researchersmustattendtothoseaspectsofteachingthathavepotentialtoinfluencestudents’learningopportunities.ThepurposeofthispaperistoidentifyandcomparetheinfluentialdistinguishingfeaturesofinstructionusinganNSF-fundedcurriculumwiththeinfluentialdistinguishingfeaturesofinstructionusingatraditionallybasedcurriculum.

Inthisstudy,wefocusontwoimportantaspectsofinstructiontoexaminethekindoflearningopportunitiesstudentsmayhaveusingtwodifferenttypesofcurricula:

（1） thestructureofthelessonanduseofmaterials,

（2） thenatureandqualityoftheinstruction.Thesetwoaspectshavebeenidentifiedascriticalforstudents’learning（Grouws,1992;Hiebertetal.,2003）.

Method

TheresearchreportedherewasconductedaspartofalargeNSF-fundedprojecttitledLongitudinalInvestigationoftheEffectofCurriculumonAlgebraLearning（LieCalProject）.TheLieCalProjectisdesignedtolongitudinallycomparetheeffectsoftheConnectedMathematicsProgram（CMP）totheeffectsofmoretraditionalmiddleschoolcurricula（hereaftercallednon-CMPcurricula）onstudents’learningofalgebra.TheLieCalProjectisbeingconductedin16middleschoolsand10highschoolsofanurbanschooldistrictservingadiversestudentpopulation.Atthestartoftheproject,27ofthe51middleschoolsintheschooldistricthadadoptedtheCMPcurriculumwhiletheremaining24middleschoolswereusingothercurricula

EightCMPschoolswererandomlyselectedfromthe27schoolsthathadadopte