新加坡小学数学大纲

MathematicsSyllabusPrimaryMinistryofEducationSINGAPORE©Copyright2006CurriculumPlanningandDevelopmentDivision.Thispublicationisnotforsale.Allrightsreserved.NopartofthispublicationmaybereproducedwithoutthepriorpermissionoftheMinistryofEducation,Singapore.Yearofimplementation:from20071FOREWORDThe2007PrimaryMathematicssyllabusreflectstherecentdevelopmentsandtrendsinmathematicseducation.Therevisedsyllabuscontinuestoemphasiseconceptualunderstanding,skillproficienciesandthinkingskillsintheteachingandlearningofmathematics.Thesecomponentsareintegraltothedevelopmentofmathematicalproblemsolvingability.Emphasisisalsogiventoreasoning,applications,anduseoftechnology.Advancesintechnologyhavechangedthewayweteachandlearnmathematics.Thecomputerandhand-heldcalculator,forexample,offergreatpotentialtoenhancetheteachingandlearningofmathematics.Studentswillhaveopportunitiestodiscover,reasonandcommunicatemathematics.Theywillengageinstimulatingdiscussionsandactivitieswheretheycanexplorepossibilitiesandmakeconnections.Thesequalitativechangesrequireachangeintheteachingandlearningapproaches;incorporatingactivity-basedandlearner-centredmethodologies.Thesyllabusesareconceptualisedafterextensiveconsultationwithteachers.Wehopethatteacherswillfindthedocumentusefulandcontinuetoprovideuswithvaluablefeedbackonsyllabusmatters.Wewishyouanenjoyableandsuccessfulteachingexperience.MathematicsUnitCurriculumPlanningandDevelopmentDivisionMarch20062CONTENTSPreface4PARTAINTRODUCTION1Rationale52AimsofMathematicsEducationinSchools53MathematicsFramework63.1Concepts3.2Skills3.3Processes3.4Attitudes3.5MetacognitionPARTBPRIMARYMATHEMATICSCURRICULUM4ObjectivesofthePrimaryMathematicsCurriculum105UseofCalculatorandTechnology116SyllabusContents6.1Primary1126.2Primary2156.3Primary3186.4Primary4216.5Primary5266.6Primary6306.7Primary5(FoundationMathematics)336.8Primary6(FoundationMathematics)383PREFACEThisdocumentconsistsoftwoparts.PartAexplainsthephilosophyofthesyllabusandthespiritinwhichitshouldbeimplemented.Italsospellsouttheaimsofthemathematicscurriculum.Theframeworkofthemathematicscurriculumsummarisestheessenceofmathematicsteachingandlearninginschools.Thelearningofmathematicsatalllevelsinvolvesmorethanthebasicacquisitionofconceptsandskills.Italsocruciallyinvolvesanunderstandingoftheunderlyingmathematicalthinking,thegeneralstrategiesofproblemsolvingandpositiveattitudestoandappreciationofmathematicsasanimportantandpowerfultoolineverydaylife.Theframeworkservesasaguideformathematicsteachingandlearninginschools.PartBspellsouttheobjectivesofthemathematicscurriculumandprovidesthesyllabuscontentforeachlevel.AcomparisonofthespecifictopicscoveredintheMathematicsandFoundationMathematicsisalsoprovidedtoassistteachersinplanningtheirlessonsaccordingtostudents’proficiencyandaptitudeinthesubjects.Carehasbeentakentoensurethatthereiscontinuityfromtheprimarytothesecondarylevels.Usingaspiraldesignofthecurriculum,eachtopicisrevisitedandintroducedinincreasingdepthfromoneleveltothenext.Thisenablesstudentstoconsolidatetheconceptsandskillslearnedandthenfurtherdevelopthem.Theconcrete-pictorial-abstractdevelopmentofconceptsisadvocatedandthisisevidentintheteachingandlearningapproachesinthesyllabus.ThecontentforMathematicsincludesallthetopicscoveredfromP1toP6.ThecontentforFoundationMathematicsrepeatssomeoftheimportanttopicscoveredfromP1toP4.ThisistoensurethatstudentsdoingFoundationMathematicshaveagoodunderstandingofbasicmathematicalconceptscoveredinP1toP4.ThepaceoftheFoundationMathematicscurriculumisalsoslower,givingmoretimeandemphasisonhands-onactivitiestoprovidetheconcreteexperienceintheconcrete-pictorial-abstractlearningsequence.Thissyllabusisaguideforteacherstoplantheirmathematicsprogrammes.Teachersneednotbeboundbythesequenceoftopicspresentedbutshouldensurethatthehierarchyandlinkagearemaintained.Schemesofworkshouldbedevelopedwiththeinterestsandabilitiesofthestudentsuppermostinmind.Teachersshouldexerciseflexibilityandcreativitywhenusingthesyllabus.Theyareencouragedtouseawidevarietyofstrategiesandresourcestomeetstudents’diverserangeofabilitiesandneeds,andtoenhancethelearningofmathematics.45PARTAINTRODUCTION1RATIONALEMathematicsisanexcellentvehicleforthedevelopmentandimprovementofaperson’sintellectualcompetenceinlogicalreasoning,spatialvisualisation,analysisandabstractthought.Studentsdevelopnumeracy,reasoning,thinkingskills,andproblemsolvingskillsthroughthelearningandapplicationofmathematics.Thesearevaluednotonlyinscienceandtechnology,butalsoineverydaylivingandintheworkplace.Thedevelopmentofahighlyskilledscientifically-andtechnologically-basedmanpowerrequiresastronggroundinginmathematics.Anemphasisonmathematicseducationwillensurethatwehaveanincreasinglycompetitiveworkforcetomeetthechallengesofthe21stcentury.Mathematicsisalsoasubjectofenjoymentandexcitement,whichoffersstudentsopportunitiesforcreativeworkandmomentsofenlightenmentandjoy.Whenideasarediscoveredandinsightsgained,studentsarespurredtopursuemathematicsbeyondtheclassroomwalls.2AIMSOFMATHEMATICSEDUCATIONINSCHOOLSMathematicseducatio