Mathematics teaching and learning strategies in PISA [electronic resource]

2010·7.7 MB·English

by  Programme for International Student Assessment

Mathematics Teaching
and Learning Strategies
in PISA
m
OECD
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Mathematics Teaching
and Learning Strategies
in PISA
ProgrammeforIntermnationalStudentAssessment
OECD
ORGANISATIONFORECONOMICCO-OPERATION
ANDDEVELOPMENT
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ISBN978-92-64-03951-3(print)
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Thisthematicreportexploresresultsofthe2003cvcleoftheProgrammeforInternational
StudentAssessment(PISA)inordertoidentifyteachingandlearningstrategiesthatcontribute
toincreasedachievement,particularlyinmathematics.Theanalysishelpstoclarifyanunder-
standingofthefollowing:(i)thedifferencesbetweenteachingandlearningpracticesacross
countriesthatcanallowcountriestobenchmarkpractices;(ii)theextenttowhichteaching
andlearningpracticesvaryamongschoolsineachcountry;and(Hi)theextenttowhichindi-
vidualaspectsofteachingandlearningstrategiesareassociatedwithbetterperformancein
mathematics.
Teachingstrategiesrangefromthewavsinwhichclassroomsandresourcesareorganised
andusedtothewavsinwhichteachersandstudentsengageindav-to-dayactivitiesinorder
tofacilitatelearning.Studentlearningstrategiesincludethecognitiveandmeta-cognitive
processesemployedbvstudentsattemptingtolearnsomethingnew.PISAmeasuresthese
strategiesusingavarietyofquestionnaireitems,whichcanbecombinedandscaledtoyield
anumberofcompositeorindexvariablesrepresentingbroadconstructs.Examplesofthe
constructsexaminedherearedisciplinaryclimate,teacher-studentrelations,memorisation
strategiesandtimespentonvariouslearningactivities.
Afterpresentingthetheoreticalframework,thereportfollowsatwo-stageanalytical
approach.Itfirstoffersananalyticaldescriptionofmathematicsteachingandlearningindif-
ferentcountriesandidentifiessimilaritiesanddifferencesbetweencountries.Inthesecond
stage,thereportpresentsfindingsgeneratedfromamultilevel,predictionmodelofthefactors
influencingmathematicalachievement.Aftercontrollingforotherfactors,thismodelshows
the“unique”effectsofaparticularfactoronachievement.Theresultspresentedinthisreport
areniainlvbasedonseparateanalysesforeachcountry.Thewithin-countrvresultsarethen
combinedtoallowforcomparisonsacrossarangeofcountries.
Thereportoffersusefulinformationandanalysestoeducationpolicymakersandacademic
researchersconcernedwithmathematicsteachingandlearningstrategies.Furtheranalysis
oftheeffectsofthesestrategiesonstudentlearning,particularlyinreadingandscience,are
usedandwillbepossibletouseinlaterPISAsurveys.Thisreportalsoofferssuggestionson
howtoimprovedatacollectionandmeasurementofteachingandlearningstrategiesinlarge
internationalcross-sectionalsurveyssuchasPISA.
Thisreportistheproductofacollaborativeeffortbetweenthecountriesparticipatingin
PISA,theexpertsandinstitutionsworkingwithintheframeworkofthePISAConsortium,
theOECD,andEdudataCanadaattheUniversityofBritishColumbia.RobertCrocker,
professoremeritusatMemorialUniversityofNewfoundland,theprincipalauthor,drafted
M^them^ticsTeachingandLearningStrategi PISA©OECD2010 3
I
thereportwiththecollaborationofChristianMonseur,UniversityofLiege,VictorGlickman,
UniversityofBritishColumbia,BenLevin,UniversityofToronto,LindaSchachter,L.L.Schachter
FohewoM Research,JohnAnderson,UniversityofVictoria,CharlesUngerleider,UniversityofBritish
Columbia,andAndreasSchleicher,ClaireShewbridgeandPabloZoidofromtheOECD.
JuliaTompsonproposededitorialcomments,JulietEvansprovidedadministrativeguidance,
ElisabethVilloutreix,NiccolinaClementsandSimoneBloemofferededitorialinput,andPeter
Vogelpoelpreparedthetypesettingofthereport.
LornaBertrand BarbaraIschinger
ChairofthePISAGoverningBoard DirectorforEducation,OECD
4 MathematicsTeachingandLearningStrategi PISA©OECD2010
T^ble ofContents
Contents
of
EXECUTIVESUMMARY 9 Table
Mainmessages 9
Overviewofthereport’sapproach 10
Organisationofthisreport 11
References 12
REAPER'SG171DE H
Abbreviationsusedinthisreport 13
Technicaldefinitions 14
Svmbolsformissingdata 14
Furtherdocumentation 14
COHVAEPRTVEIREW1ANPRATIONALEFORTHESTVPY 15
OverviewofPISA 16
Aimandaudienceofthisreport 17
Backgroundofthisreport 17
Definitionandrelevanceofteachingandlearningstrategies 20
Earlyresearchonteachingandlearningstrategies 22
TheCarrollmodelasatheoreticalframework 24
Keyteachingandlearningvariables 26
Controlvariables 27
Othervariables 28
Overviewoftheanalyticalapproach 28
References 29
CHAPTER2
FEATl/RESOFTEACHINGANPLEARNING 31
Introduction 32
Factorsdescribingteachingandlearning 32
Allocationanduseoftime 34
Studentlearningstrategiesandpreferences 40
Teachingstrategiesandclimate 51
Studentperceptionsofthelearningenvironment:overview 58
Summary:aprofileofmathematicsteachingandlearning 64
References 67
M^them^ticsTeachingandLearningStrategi PISA©oecDzolo 5
CHAPTER3
Contents ARRELEASTTEiPyPTEONTMS'ATPHEERCMEAPTTIICOSNSPOEFRFTOHREMIRANMCAETSHEMATICSTEACHINGANPLEARNING 69
of Introduction 70
Reportingtheresults 71
Table Howmuchperformancevariationisduetoschooldifferencesandhowdoarangeoffactorscontributetothis
variation? 73
Themeasuredeffectsofantecedentstolearningincludedintheanalvticalmodel 76
Themeasuredeffectsofteachingandlearningintheanalvticalmodel 93
Teachingstrategies 106
Highlightsoftheanalyticalresults 113
References 118
CHAPTER4
SUMMARYANPIMPLICATIONSFORFURTHERRESEARCH 119
Introduction 120
Backgroundfactorsthatprovidethecontextforteachingandlearning 121
Studentlearningstrategies 124
Teachingstrategies 128
Wliatdoestheevidencesav? 130
References 137
CHAPTER5
CONCLUSIONSANPIMPLICATIONSFORPOLICYANPPRACTICE 139
Overview 140
Overarchingissues 141
Studentlearningstrategies 143
Teachingstrategies 144
Conclusion 145
ANNEXA
PESCRIPTIVESTATISTICS 147
ANNEXB
CORRELATIONS 161
ANNEXC
BIVARIATEANPMULTILEVELMOPEL5 165
Boxes
Box1.1 TheOECDTeachingandLearningInternationalSurvey 19
Box3.1 Interpretingtheeffectsofregressioncoefficients 72
6 MathematicsTeachingandLearningStrategiesinPISA©OECD2010
Figures
Figure1.1 AmapofPISAcountriesandeconomies 14 Contents
Figure1.2 SummaryoftheassessmentareascoveredinPISA2003 16
Figure1.3 Multiplecomparisonsofmeanperformanceonthemathematicsscale 17 of
FFiigguurree22..12 FFlloouurrssppeerrwweeeekkssppeennttoonnhtuotmoeriwnograknfdoroumta-tohf-esmcahtoioclsclaansdseosthersubjects 3379 Table
Figure2.3 Hoursperweekofhomeworkorotherstudysetbyteachersintotal 41
Figure2.4 Students’useofmemorisation/rehearsalstrategiestolearnmathematics 45
Figure2.5 Students’useofelaborationstrategiestolearnmathematics 47
Figure2.6 Students’useofcontrolstrategiestolearnmathematics 48
Figure2.7 Students’preferenceforcompetitivelearningsituations 50
Figure2.8 Students’preferenceforco-operativelearningsituations 52
Figure2.9 Students’viewsonteachersupportintheirmathematicslessons 60
Figure2.10 Students’viewsonthedisciplinaryclimateintheirmathematicslessons 62
Figure2.11 Students’viewsonstudent-teacherrelations 63
Figure3.1 Totalstudentandschoolvarianceaccountedforbvthemodel 74
Figure3.2 Averageproportionsofstudentandschoolvarianceaccountedforbythemodel 76
Figure3.3 Parents’highestoccupationalstatus(FlISEI)andmathematicsperformance 77
Figure3.4 Parents’highesteducationallevel(HISCED)andmathematicsperformance 78
Figure3.5 Numberofbooksinthehomeandmathematicsperformance 79
Figure3.6 Students’attitudestowardsschoolandmathematicsperformance 80
Figure3.7 Students’senseofbelongingatschoolandmathematicsperformance 82
Figure3.8 Students’interestinandenjoymentofmathematicsandmathematicsperformance 83
Figure3.9 Students’instrumentalmotivationinmathematicsandmathematicsperformance 84
Figure3.10 Anxietyinmathematicsandmathematicsperformance 86
Figure3.11 Self-efficacvinmathematicsandmathematicsperformance 87
Figure3.12 Self-conceptinmathematicsandmathematicsperformance 88
Figure3,13 Schoolsize 89
Figure3.14 Schoolsizeandmathematicsperformance 90
Figure3.15 Schoolaveragehighestparents’occupationalstatus 91
Figure3.16 Schoolaverageofthehighestinternationalsocio-economicindexofoccupationalstatus(HISEI)
ofbothparentsandmathematicsperformance 92
Figure3.17 Hoursperweekoftotalhomeworkandmathematicsperformance 94
Figure3.18 Hoursperweekofmathematicshomeworkandmathematicsperformance 95
Figure3.19 Studentsbeingtutoredinmathematicsandmathematicsperformance 96
Figure3.20 Out-of-schoolclassesandmathematicsperformance 97
Figure3.21 Memorisation/rehearsalstrategiesandmathematicsperformance 100
Figure3.22 Elaborationstrategiesandmathematicsperformance 101
Figure3.23 Controlstrategiesandmathematicsperformance 103
Figure3.24 Preferenceforco-operativelearningsituationsandmathematicsperformance 104
Figure3.25 Preferenceforcompetitivelearningsituationsandmathematicsperformance 105
Figure3.26 Disciplinaryclimateandmathematicsperformance 108
Figure3.27 Schoolaveragedisciplinaryclimateandmathematicsperformance 109
M^them^ticsTeachingandLearningStrategiesinPISA©OECD2010 7
Figure3.28 Student-teacherrelationsandmathematicsperformance 110
Contents Figure3.29 Teachersupportandmathematicsperformance Ill
of Tables
T^ble Table1.1 Keyteachingandlearningvariables 25
Table1.2 Controlvariables 26
Table2.1 Distributionoflearningtimeandrelationshipwithperformance 35
Table2.2 Distributionoftheuseoflearningstrategies/preferencesandrelationshipwithperformancein
mathematics 42
Table2.3 Distributionofstudents’experienceofclassroomclimateandteacher-studentrelations,
andtherelationshipofthesefactorswithperformance 58
Table4.1 Summarvofteachingandlearningeffectsandpolicyimplications 132
TableA.l Instructionalweeksperyear:mean,standarddeviationandpercentiledistributionamong
schools 148
TableA.2 Instructionalhoursinschoolweek:mean,standarddeviationandpercentiledistributionamong
schools 149
TableA.3 Indexoftotalinstructionalhourspervear:mean,standarddeviationandpercentiledistribution
amongschools 150
TableA.4 Hoursperweekofmathematicsinstruction:mean,standarddeviationandpercentiledistribution
amongschools 151
TableA.5 Hoursperweekofhomeworkorotherstudysetbyteachersintotal;mean,standarddeviation
andpercentiledistributionamongschools 152
TableA.6 Hoursperweekofhomeworkorotherstudysetbymathematicsteachers:mean,standard
deviationandpercentiledistributionamongschools 153
TableA.7 Schoolprincipals’viewsonmathematicsteachers’supportforinnovativeteachingpractices....154
TableA.8 Schoolprincipals’perceptionsofmathematicsteachers’expectations 155
TableA.9 Schoolprincipals’perceptionsofmathematicsteachers’supportofteachinggoals 156
TableA.10 Streamingofstudentsinsomeorallmathematicsclasses 157
TableA.il Abilitygroupingwithinmathematicsclasses 158
TableA.12 Methodsofassessment 159
TableA.13 Useofassessmentresults 160
TableB.1 Latentcorrelationsamongselectedmeasuresusedintheteachingandlearninganalyticalmodel..162
TableC.l Multivariateregressioncoefficientsandstandarderrors 166
TableC.l Bivariateregressioncoefficientsandstandarderrors 169
TableC.3 Varianceexplainedbythemultivariatemultilevelmodelonteachingandlearningstrategies...172
TableC.4 Varianceexplainedbymodelchanges 173
TableC.5 Effectofmathematicsachievementoflearningstrategiescontrollingforself-efficacy 176
8 MathematicsTeachingandLearningStrategiesinPISA©OECD2010