The common curriculum framework for K-9 mathematics : Western and Northern Canadian Protocol

2006·8.6 MB·English

by  Alberta. Alberta Education

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The Common Curriculum Frame
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MATHEMATICS
K-9
Ex Libris
Universitatis
Albertensis
Copyright©2006,theCrowninRightoftheGovernmentsofAlberta,BritishColumbia,Manitoba,Northwest
Territories,NunavutTerritory,SaskatchewanandYukonTerritoryasrepresentedbytheMinisterofEducation,
Alberta;theMinisterofEducation,BritishColumbia;theMinisterofEducation,CitizenshipandYouth,Manitoba;
theMinisterofEducation,CultureandEmployment,NorthwestTerritories;theMinisterofEducation,Nunavut;the
MinisterofSaskatchewanLearning,Saskatchewan;andtheMinisterofEducation,YukonTerritory.
Permissionisgivenbythecopyrightownerstoreproducethisdocumentforeducationalpurposesandonanonprofit
basis.
WNCPCCFforK-9Mathematics /ii
©AlbertaEducation,Alberta,Canada May2006
ACKNOWLEDGEMENTS
TheCommonCurriculumFrameworkforK-9Mathematicswasdevelopedthroughthecooperativeeffortsofthefourwesternprovincesandthree
territories. Thesejurisdictionswouldliketoacknowledgethefollowingmathematicsconsultants.
Alberta
VivianAbboud AlbertaEducation,FrenchLanguageServicesBranch
RichardDeMerchant AlbertaEducation,CurriculumBranch
JenniferDolecki AlbertaEducation,CurriculumBranch
DebbieDuvall AlbertaEducation,LearningandTeachingResourcesBranch
PaulLamoureux AlbertaEducation,FrenchLanguageServicesBranch
LomeLindenberg AlbertaEducation,CurriculumBranch
BritishColumbia
WaelAffifi BritishColumbiaMinistryofEducation,ContentandAchievementUnit
Marie-ChristineBamhardt BritishColumbiaMinistryofEducation,ContentandAchievementUnit
RichardDeMerchant BritishColumbiaMinistryofEducation,ContentandAchievementUnit
PierreGilbert BritishColumbiaMinistryofEducation,ContentandAchievementUnit
PamelaHagen BritishColumbiaMinistryofEducation
WemerLiedtke BritishColumbiaMinistryofEducation
Manitoba
CaroleBilyk ManitobaEducation,CitizenshipandYouth,Instruction,CurriculumandAssessmentBranch
PauleBuors ManitobaEducation,CitizenshipandYouth,Bureaudel’educationfranfaise
MarcelDruwe ManitobaEducation,CitizenshipandYouth,Bureaudel’educationfran9aise
GilbertLeNeal ManitobaEducation,CitizenshipandYouth,BureaudeVeducationfranfaise
GrethaPallen ManitobaEducation,CitizenshipandYouth,Instruction,CurriculumandAssessmentBranch
NorthwestTerritories
StevenDaniel NorthwestTerritories,DepartmentofEducation,CultureandEmployment
Nunavut
BrianYamamura Nunavut,DepartmentofEducation
Saskatchewan
GerryCraswell SaskatchewanLearning,CurriculumandInstructionBranch
LilianeGauthier SaskatchewanLearning,Bureaudelaminoritedelangueofficielle
GaleRussell SaskatchewanLearning,CurriculumandInstructionBranch
YukonTerritory
LeeKubica YukonDepartmentofEducation
PaulaThompson YukonDepartmentofEducation
WNCPCCFforK-9Mathematics Acknowledgements/iii
©AlbertaEducation,Alberta,Canada May2006
WNCPCCFforK-9Mathematics /iv
©AlbertaEducation,Alberta,Canada UNIVERSITYLIBRARY May2006
UNIVERSITYOFALBERTA
8
TABLE OF CONTENTS
BACKGROUND
1
INTRODUCTION 2
PurposeoftheDocument 2
BeliefsaboutStudentsandMathematicsLearning 2
AboriginalPerspectives 3
AffectiveDomain 3
EarlyChildhood 4
GoalsforStudents 4
CONCEPTUALFRAMEWORKFORK-9MATHEMATICS 5
MathematicalProcesses 6
NatureofMathematics 10
Strands 13
OutcomesandAchievementIndicators 13
Summary 14
INSTRUCTIONALFOCUS 15
GENERALANDSPECIFICOUTCOMES 17
GeneralandSpecificOutcomesbyStrand 18
Number
1
PatternsandRelations 32
ShapeandSpace 38
StatisticsandProbability 46
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GeneralandSpecificOutcomesWithAchievementIndicators 52
Kindergarten 52
Grade 1 56
Grade2 63
Grade3 73
Grade4 86
Grade5 97
Grade6 110
Grade7 122
Grade8 134
Grade9 147
APPENDIX: REFERENCES 160
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©AlbertaEducation,Alberta,Canada May2006
BACKGROUND
Partnerjurisdictions: The WesternCanadianProtocolforCollaborationinBasicEducation
KindergartentoGrade12wassignedDecember 1993bytheMinistersof
Alberta EducationfromAlberta,BritishColumbia,Manitoba,NorthwestTerritories,
BritishColumbia SaskatchewanandYukonTerritory. InFebruary2000,followingtheadditionof
Manitoba Nunavut,theprotocolwasrenamedtheWesternandNorthernCanadianProtocol
NorthwestTerritories (WNCP)forBasicEducation.
Nunavut
Saskatchewan In2005,theMinistersofEducationfromalltheWNCPjurisdictionsunanimously
YukonTerritory concurredwiththerationaleoftheoriginalpartnershipbecauseoftheimportance
placedon:
• commoneducationalgoals
• theabilitytocollaboratetoachievecommongoals
• highstandardsineducation
• planninganarrayofeducationalopportunities
• removingobstaclestoaccessibilityforindividuallearners
• optimumuseoflimitededucationalresources.
TheCommonCurriculumFrameworkforK-9Mathematicswasdevelopedbythe
sevenministriesofeducationincollaborationwithteachers,administrators,
parents,businessrepresentatives,post-secondaryeducatorsandothers.
Theframeworkidentifiesbeliefsaboutmathematics,generalandspecificstudent
outcomes,andachievementindicatorsagreeduponbythesevenjurisdictions.
Eachoftheprovincesandterritorieswilldeterminewhenandhowtheframework
willbeimplementedwithinitsownjurisdiction.
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INTRODUCTION
PURPOSEOFTHEDOCUMENT enhancetheformationofsound,transferable,
mathematicalconcepts. Atalllevels,students
Thisdocumentprovidesacommonbaseforthe benefitfromworkingwithavarietyofmaterials,
curriculumexpectationsmandatedbyeach toolsandcontextswhenconstructingmeaning
Theframework provinceandterritory,whichwillresultin aboutnewmathematicalideas. Meaningful
communicates consistentstudentoutcomesinmathematicsacross studentdiscussionscanprovideessentiallinks
high jurisdictionsandenableeasiertransferforstudents amongconcrete,pictorialandsymbolic
expectations movingfromonejurisdictiontoanother. Itsintent representationsofmathematics.
forstudents. istoclearlycommunicatehighexpectationsfor
studentsinmathematicseducationtoalleducation Thelearningenvironmentshouldvalueandrespect
partnersacrossthejurisdictionsandfacilitatethe allstudents’experiencesandwaysofthinking,so
developmentofcommonlearningresources. thatlearnersarecomfortabletakingintellectual
risks,askingquestionsandposingconjectures.
Studentsneedtoexploreproblem-solving
BELIEFSABOUTSTUDENTS situationsinordertodeveloppersonalstrategies
ANDMATHEMATICSLEARNING andbecomemathematicallyliterate. Learners
mustrealizethatitisacceptabletosolveproblems
Studentsarecurious,activelearnerswith indifferentwaysandthatsolutionsmayvary.
individualinterests,abilitiesandneeds. They
cometoclassroomswithvaryingknowledge,life
Mathematical experiencesandbackgrounds.Akeycomponentin
understanding successfullydevelopingnumeracyismaking
isfostered connectionstothesebackgroundsandexperiences.
whenstudents
buildontheir Studentslearnbyattachingmeaningtowhatthey
ownexperiences doandneedtoconstructtheirownmeaningof
andprior mathematics. Thismeaningisbestdeveloped
knowledge. whenlearnersencountermathematicalexperiences
thatproceedfromthesimpletothecomplexand
fromtheconcretetotheabstract. Theuseof
manipulativesandavarietyofpedagogical
approachescanaddressthediversityoflearning
stylesanddevelopmentalstagesofstudents,and
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ABORIGINALPERSPECTIVES orregion,andstrivetoachievehigherlevelsof
multiculturaleducation(BanksandBanks, 1993).
Aboriginalstudentsinnorthernandwestern
Canadacomefromdiversegeographicareaswith
variedculturalandlinguisticbackgrounds. AFFECTIVEDOMAIN
Studentsattendschoolsinavarietyofsettings
includingurban,ruralandisolatedcommunities. Apositiveattitudeisanimportantaspectofthe
Teachersneed Teachersneedtounderstandthediversityof affectivedomainthathasaprofoundeffecton
tounderstand culturesandexperiencesofstudents. learning.Environmentsthatcreateasenseof Toexperience
thediversity belonging,encouragerisktakingandprovide success,students
ofcultures Aboriginalstudentsoftenhaveawhole-worldview opportunitiesforsuccess,helpdevelopand mustbetaught
andexperiences oftheenvironmentinwhichtheyliveandlearn maintainpositiveattitudesandself-confidence. tosetachievable
ofstudents. bestinaholisticway.Thismeansthatstudents Studentswithpositiveattitudestowardlearning goalsandassess
lookforconnectionsinlearningandlearnbest mathematicsarelikelytobemotivatedand themselves
whenmathematicsiscontextualizedandnottaught preparedtolearn,participatewillinglyin astheywork
asdiscretecomponents. classroomactivities,persistinchallenging towardthese
situationsandengageinreflectivepractices. goals.
Aboriginalstudentscomefromcultureswhere
learningtakesplacethroughactiveparticipation. Teachers,studentsandparentsneedtorecognize
Traditionally,littleemphasiswasplaceduponthe therelationshipbetweentheaffectiveand
writtenword. Oralcommunicationalongwith cognitivedomains,andattempttonurturethose
practicalapplicationsandexperiencesare aspectsoftheaffectivedomainthatcontributeto
importanttostudentlearningandunderstanding. positiveattitudes. Toexperiencesuccess,students
Itisalsovitalthatteachersunderstandandrespond mustbetaughttosetachievablegoalsandassess
tonon-verbalcuessothatstudentlearningand themselvesastheyworktowardthesegoals.
mathematicalunderstandingareoptimized.
Strivingtowardsuccess,andbecoming
Avarietyofteachingandassessmentstrategiesis autonomousandresponsiblelearnersareongoing,
requiredtobuilduponthediverseknowledge, reflectiveprocessesthatinvolverevisitingthe
cultures,communicationstyles,skills,attitudes, settingandassessingofpersonalgoals.
experiencesandlearningstylesofstudents.
Thestrategiesusedmustgobeyondtheincidental
inclusionoftopicsandobjectsuniquetoaculture
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EARLYCHILDHOOD GOALSFORSTUDENTS
Youngchildrenarenaturallycuriousanddevelopa Themaingoalsofmathematicseducationareto Mathematics
varietyofmathematicalideasbeforetheyenter preparestudentsto: educationmust
kindergarten. Childrenmakesenseoftheir • usemathematicsconfidentlytosolveproblems preparestudents
environmentthroughobservationsandinteractions • communicateandreasonmathematically touse
athome,indaycares,preschoolsandinthe • appreciateandvaluemathematics mathematics
Curiosityabout community. Mathematicslearningisembeddedin • makeconnectionsbetweenmathematicsandits confidently
mathematics everydayactivities,suchasplaying,reading, applications tosolve
isfostered storytellingandhelpingaroundthehome. • committhemselvestolifelonglearning problems.
whenchildren • becomemathematicallyliterateadults,using
areactively Activitiescancontributetothedevelopmentof mathematicstocontributetosociety.
engagedintheir numberandspatialsenseinchildren. Curiosity
environment. aboutmathematicsisfosteredwhenchildrenare Studentswhohavemetthesegoalswill:
engagedinactivitiessuchascomparingquantities, • gainunderstandingandappreciationofthe
searchingforpatterns,sortingobjects,ordering contributionsofmathematicsasascience,
objects,creatingdesigns,buildingwithblocksand philosophyandart
talkingabouttheseactivities. • exhibitapositiveattitudetowardmathematics
Positiveearlyexperiencesinmathematicsareas • engageandpersevereinmathematicaltasksand
projects
criticaltochilddevelopmentasareearlyliteracy
experiences. • contributetomathematicaldiscussions
• takerisksinperformingmathematicaltasks
• exhibitcuriosity.
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