Development of competencies oriented mathematics curriculum in ChinaBinyanXuCollegeofTeacherEducationEastChinaNormalUniversityDecember10th-16th2018,LyonpThenewestdevelopmentpWhenandWhy?pWhat？The newest developmentpTherevisedversionoftheHigh School Mathematical Curriculum Standards (2017 Edition)(MOE2018)wasreleasedinJanuary2018(2017Standards,hereafter).pTheversionHigh School Mathematics Curriculum Standards (Experimental version)waspublishedin2003(hereafterreferredtoasthe2003Standards;MOE2003).pAttheendofthetwentiethcentury,Chinadecidedtoimprovethequalityofitseducationalsystemsothatitwouldprepareitscitizenswiththeknowledgeandskillsrequiredtomeetthedemandsofanincreasinglyglobalizedworld.When and WhypAttheendof2014,theMOElaunchedtheworkofrevisingcurriculaforallhighschoolsubjects(MOE2014b,December8).pOnereasonrelatedtothegovernmentsrequirement;theanotherwasbasedonthenationalsurvey.the governments requirementpInresponsetothegovernmentsrequirementforthevisibledevelopmentofcitizens,theMOEproposedandreleaseditsSuggestions for Fully Deepening the Curriculum Reform and Practising the Fundamental Mission of Citizen Development(MOE2014a,April8)toguidebasiceducationinChina.pItwasannouncedthatthe“MOEwouldorganisestudiestopromotestudentsateachschoolleveltodevelopacore competency system,andtodevelopcharacteristicsandcoreabilitiesthatwouldenablestudentstoadapttolife-longlearningandmeettherequirementsofsocialdevelopment”.缘起：中国学生的核心素养体系必必备品格与关品格与关键能力能力人文人文底底蕴科学科学精神精神健康健康生活生活责任任担当担当学会学会学学习实践践创新新人人文文积淀淀人人文文情情怀审美美情情趣趣理理性性思思维批批判判质疑疑勇勇于于探探究究乐学学善善学学勤勤于于反反思思信信息息意意识真真爱生生命命健健全全人人格格自自我我管管理理社社会会责任任国国家家认同同国国际理理解解劳动意意识问题解解决决技技术应用用文化基文化基础社会参与社会参与自主自主发展展core competency system includes:pCultural cultivationnhumanisticconnotation(humanefeelings,aestheticappeal)nscientificspirit(rationalthinking,criticalthinking,bebraveininquiring)pSelf-developmentnLearningtolearn(interestinginlearning,bediligentinreflection,identifyinginformation)nLivinghealthy(healthypersonality,selfmanagement)pSocial ParticipationnResponsibilitybearing(nationalidentify,internationalunderstanding)nPracticeinnovation(laborconsciousness,technicalapplication)National survey on curriculum implementationpECNUmathematicseducationteamgotthistaskfromtheMOEinChina,Bao etc.developedsurveyframeworkwhichincludedthefollowingaspects:Curriculum design:propertiesofthecurriculum,objectives,structureCurriculum content:difficultylevel,systematicalstructureofcontentCurriculum implementation:teachingsituation,textbooks,teacherCurriculum evaluation:assessmenttool,examinationpMethods:group/individualinterview,questionnairesurvey,contentanalysispParticipants:teachers,students,schoolleaders,teachinginspectors,textbookeditors,administratorspSome results which contributed to modification of the standardThemodulesandsequenceofcontentshouldbemodifiedinordertoreachcohesionofcontent(connectionbetweencompulsoryandoptionalmodules)Theimportantmathskills(arithmetic,reasoning,spatialimagination)shouldbepaidmoreattentionStudentsstillhadheavylearningburdenTeachersfocusedmoreontrainingmathskillsthanfosteringcompetenciesThestandardplayedveryweakroleindevelopinguniversityentranceexamination.pThebothreasonspushedforwardandguidedtheimprovement/developmentofhighschoolmathcurriculum.What happened mainly?pRevisecurriculumobjectivesfocusedoncorecompetenciespRevisecurriculumstructurepRevisecurriculumevaluationcurriculum objectives in 2017 standardpToobtainbasicknowledge,basicskill,basicthoughtandactivityexperience(fourbasic)pToenhanceabilitiesofdiscoveringandposingproblemsmathematically,ofanalyzingandsolvingproblems(fourabilities)pTodevelopmathematicscorecompetenciesincludingmathematical abstraction, logic reasoning, mathematical modelling, intuitive imagination, mathematical operation and data analysis. pToimprovelearninginterestinginmathematics,selfconfidenceinlearningmathematics,todevelopself-learningabilities,tocultivatescientificspiritsofcriticizing,thinking,rigorousfactattitude.toimprovepracticalandinnovativeabilitiespCompareto2003standard,the2017standardemphasized6coremathematicscompetenciesexplicitlypThecoremathematicscompetenciesweredefinedas“necessarythinkingqualityandkeyabilitiesthatrelatedtomathematics,forstudentstoadapttolife-longdevelopmentandsocialdevelopment”andwere“basedonsocialparticipation,self-development,andculturalcultivation”(governmentrequirement).core mathematics competenciesMathematical abstractiontoformmathematicalconceptsandrules;toformmathematicalpropositionandmodel,toformmathematicalmethodsandthinking,toformmathematicalstructureandsystemlogical reasoningtodiscoverandposeproposition;tomasterbasicreasoningforms;toexploreandrepresentargumentationprocessintuitive imaginationtodescribeandunderstandmathematicsproblemsusinggraph;toexploreandsolveproblems,toconstructmathematicalintuitivemodelsmathematical modellingtodiscoverandposeproblems,toconstructmodelstosolvemodel,andtoexamineandmodifymathmodelmathematical operationtounderstandoperationalobjects;tomasterarithmeticrules,toexplorearithmeticprocessdata analysistoobtaindata,toanalyzedata,constructionofknowledgepthesesixcorecompetenciescouldhelpdevelop“mathematicalperspectivestoobservetheworld”,forwhichmathematicalabstractionandintuitiveimaginationplayimportantroles;p“theabilitytothinkmathematicallyabouttheworld”,forwhichlogicalreasoningandmathematicsoperationarenecessary;pand“mathematicallanguagetoexpresstheworld”,whichneedsmathematicalmodellinganddataanalysis.Revise curriculum structurep2003standardsetupsuchmodulestructurepThesurveyshowedthatteacherswereunpreparedtoimplementthemodulescurriculum.pThestructureinthe2017standardfollowstheprinciplesofcommonbasicanddiversifiedoption,itincludescompulsory curriculum and optional curriculum. nCompulsorycurriculumconsistsof5topics(knowledgeforpreparing,function,geometryandalgebraic,possibilityandstatistics,mathematicalmodelingandmathematicalinquiring)nOptionalcompulsorycurriculumconsistoffunction,geometryandalgebraic,possibilityandstatistics,mathematicalmodelingandmathematicalinquiringnOptionalcurriculumprovidesstudentswithfreeselectionaccordingtheirowninterestinginmathematics.pCurriculum A is constructed for students with interesting in math or sciencespCurriculum B is constructed for students who have interesting in economic, society oriented researchpCurriculum C is designed for students who want to learn humanistic subjects (language, history)pCurriculum D is designed for students who are good at sport or artspCurriculum E focuses on extending perspectives, local specific curriculum, and also AP curriculumRevise curriculum evaluationpInthe2003standard,Evaluationprincipleswerementionedingeneral.ItpaysattentiontonStudentsmathematicslearningprocesses,nStudentsfundamentalknowledgeandbasicskillsnStudentsabilitiespIt also emphasized the implementation of multifarious evaluation that promotes student development.pButbasedonsurveyresults,mathematicscurriculumstillpaidattentiontothesummativeassessment,insteadofformativeassessment,thecurriculumismoreorientedonfinalexamination.pAccordingto2017versionstandard,thecurriculumfocuseson“learningachievement”,andsetsupthree achievement levels whichconcernperformancesofmathematicscompetencies.pThe2017standardsetsupfouraspectsofstudentsperformancesofmathcompetenciesnContextandproblemnKnowledgeandskillnThinkingandrepresentationnCommunicationandreflectionpThreeachievementlevelshavebeendescribed,focusedonmathcompetencies,usingthefouraspects,aswellasbasedonmathematicscontent.CitedfromBaosrepresentationFor example, focused on mathematical abstraction and using aspect “context and problem”, the achievement level could be described: Achievement level oneable to abstract mathematical concepts and rules directly in familiar situations; able to use inductive or analogical methods to discover the properties of graph and quantity, quantitative relationships, or graphical relationships, to form simple mathematical propositions; able to describe the geometrical graph of the object, establish the connection between the simple graph and the object, and experience the relationship between the graph and the graph, the graph and the quantity;Achievement level twoIn the related context, able to abstract general mathematical concepts and rules, determine operational objects and random phenomena, find problems and propose or translate them into mathematical problems; Able to imagine and construct the corresponding geometric graph, find the relationship between graphics and graphics, graphics and quantity, and explore the motion law of graphics; able to understand that induction and analogy is an important way to discover and propose mathematical propositionsAchievement level threeable to discover mathematical relationships in contexts in a comprehensive context, find appropriate research objects with mathematical perspectives, express them in appropriate mathematical language, and use mathematical thinking to analyze and propose mathematical problems; able to explore the ideas of solving problems by means of graphics; able to form new propositions based on the obtained mathematical conclusions.Relationship between achievement and examinationpThe2017StandardexplainsthatpntheachievementleveloneshouldbereachedbyallhighschoolgraduatesntheachievementleveltwoisthebasisofdevelopinguniversityentranceexaminationntheachievementlevelthreecouldbereferenceforindependentrecruitmentofuniversityExample 1The distance between school dormitory and office is a m. A classmate has important materials to give to the teacher. From the dormitory, he ran 3 minutes to the office at a constant speed, stayed for 2 minutes, then walked 10 minutes to the dormitory at a constant speed. Draw a schematic diagram of the velocity function and the path function.pCommentIntheactualsituation,thegraphcanbeusedtorevealthefunctionproperties,andreflectoverallthebasiccharacteristicsofthefunction.pWhenansweringthisquestion,youcangivemostoftheschematicdiagramsofthespeedfunctionorthepathfunction,thencanbeconsideredtomeettherequirementsofthemathematical abstract competence level one.pCanfullydrawthespeedfunctionandthepathfunctiongraph(thetwoindependentvariablesareconsistent),thencanbeconsideredtomeettherequirementsofmathematicalabstractcompetencelevel twoExample 2Theinnerringofthe400-meterstandardrunwayisshowninFigure,wheretheleftandrightsidesarehalf-arcswitharadiusof36meters.（1）Findthelengthofeachstraight(Thepiis3.14,andtheresultisaccurateto1meter.)（2）EstablishaplanerectangularcoordinatesystemxOy,WritethefunctionanalyticcorrespondingtotheupperhalfoftherunwaypCommentIfthecalculationof(1)canbecompleted,itcanbeconsideredthattherequirementof intuitive imagination level 1 canbeachieved.Theabilitytobasicallyobtaintheexpressionrequiredby(2)canbeconsideredtomeettherequirementsoftheintuitiveimaginationlevel2.pThisquestioncanalsobeexaminedformathematicaloperationsandothercompetencies.pTheanswertothisquestionisasfollowspNowadayswemeetnewchallengesofcurriculumdevelopment.nFourbasic,fourabilitiesandsixcompetenciesnMathematicscompetenciesandthreeachievementlevelsnAchievementevaluationandfinalexaminationpTextbooksbasedon2017standardareunderconstructionpTheimplementationofthisstandardwillbelaunchedearliestinnextyearManythanks谢谢！