数学课程改革的国际比较课件.ppt

1、Development of competencies oriented mathematics curriculum in ChinaBinyan XuCollege of Teacher EducationEast China Normal UniversityDecember 10th-16th 2018,LyonpThe newest developmentpWhen and Why?pWhat？The newest developmentpThe revised version of the High School Mathematical Curriculum Standards(

2、2017 Edition)(MOE 2018)was released in January 2018(2017 Standards,hereafter).pThe version High School Mathematics Curriculum Standards(Experimental version)was published in 2003(hereafter referred to as the 2003 Standards;MOE 2003).pAt the end of the twentieth century,China decided to improve the q

3、uality of its educational system so that it would prepare its citizens with the knowledge and skills required to meet the demands of an increasingly globalized world.When and WhypAt the end of 2014,the MOE launched the work of revising curricula for all high school subjects(MOE 2014b,December 8).pOn

4、e reason related to the governments requirement;the another was based on the national survey.the governments requirementpIn response to the governments requirement for the visible development of citizens,the MOE proposed and released its Suggestions for Fully Deepening the Curriculum Reform and Prac

5、tising the Fundamental Mission of Citizen Development(MOE 2014a,April 8)to guide basic education in China.pIt was announced that the“MOE would organise studies to promote students at each school level to develop a core competency system,and to develop characteristics and core abilities that would en

6、able students to adapt to life-long learning and meet the requirements of social development”.缘起：中国学生的核心素养体系必备品格与关键能力必备品格与关键能力人文人文底蕴底蕴科学科学精神精神健康健康生活生活责任责任担当担当学会学会学习学习实践实践创新创新人人文文积积淀淀人人文文情情怀怀审审美美情情趣趣理理性性思思维维批批判判质质疑疑勇勇于于探探究究乐乐学学善善学学勤勤于于反反思思信信息息意意识识真真爱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责任任国国家家认认同同国国际际理理解解劳劳动动意意

7、识识问问题题解解决决技技术术应应用用文化基础文化基础社会参与社会参与自主发展自主发展core competency system includes:pCultural cultivationnhumanistic connotation(humane feelings,aesthetic appeal)nscientific spirit(rational thinking,critical thinking,be brave in inquiring)p Self-developmentnLearning to learn(interesting in learning,be diligen

8、t in reflection,identifying information)nLiving healthy(healthy personality,self management)p Social ParticipationnResponsibility bearing(national identify,international understanding)nPractice innovation(labor consciousness,technical application)National survey on curriculum implementationpECNU mat

9、hematics education team got this task from the MOE in China,Bao etc.developed survey framework which included the following aspects:Curriculum design:properties of the curriculum,objectives,structureCurriculum content:difficulty level,systematical structure of contentCurriculum implementation:teachi

10、ng situation,textbooks,teacherCurriculum evaluation:assessment tool,examinationpMethods:group/individual interview,questionnaire survey,content analysispParticipants:teachers,students,school leaders,teaching inspectors,textbook editors,administratorspSome results which contributed to modification of

11、 the standardThe modules and sequence of content should be modified in order to reach cohesion of content(connection between compulsory and optional modules)The important math skills(arithmetic,reasoning,spatial imagination)should be paid more attentionStudents still had heavy learning burdenTeacher

12、s focused more on training math skills than fostering competenciesThe standard played very weak role in developing university entrance examination.pThe both reasons pushed forward and guided the improvement/development of high school math curriculum.What happened mainly?pRevise curriculum objectives

13、 focused on core competenciespRevise curriculum structurepRevise curriculum evaluationcurriculum objectives in 2017 standardpTo obtain basic knowledge,basic skill,basic thought and activity experience(four basic)pTo enhance abilities of discovering and posing problems mathematically,of analyzing and

14、 solving problems(four abilities)pTo develop mathematics core competencies including mathematical abstraction,logic reasoning,mathematical modelling,intuitive imagination,mathematical operation and data analysis.pTo improve learning interesting in mathematics,self confidence in learning mathematics,

15、to develop self-learning abilities,to cultivate scientific spirits of criticizing,thinking,rigorous fact attitude.to improve practical and innovative abilitiespCompare to 2003 standard,the 2017 standard emphasized 6 core mathematics competencies explicitlypThe core mathematics competencies were defi

16、ned as“necessary thinking quality and key abilities that related to mathematics,for students to adapt to life-long development and social development”and were“based on social participation,self-development,and cultural cultivation”(government requirement).core mathematics competenciesMathematical ab

17、stractionto form mathematical concepts and rules;to form mathematical proposition and model,to form mathematical methods and thinking,to form mathematical structure and systemlogical reasoningto discover and pose proposition;to master basic reasoning forms;to explore and represent argumentation proc

18、essintuitive imaginationto describe and understand mathematics problems using graph;to explore and solve problems,to construct mathematical intuitive modelsmathematical modellingto discover and pose problems,to construct models to solve model,and to examine and modify math modelmathematical operatio

19、nto understand operational objects;to master arithmetic rules,to explore arithmetic processdata analysisto obtain data,to analyze data,construction of knowledgepthese six core competencies could help develop“mathematical perspectives to observe the world”,for which mathematical abstraction and intui

20、tive imagination play important roles;p“the ability to think mathematically about the world”,for which logical reasoning and mathematics operation are necessary;pand“mathematical language to express the world”,which needs mathematical modelling and data analysis.Revise curriculum structurep2003 stan

21、dard set up such module structurepThe survey showed that teachers were unprepared to implement the modules curriculum.pThe structure in the 2017 standard follows the principles of common basic and diversified option,it includes compulsory curriculum and optional curriculum.nCompulsory curriculum con

22、sists of 5 topics(knowledge for preparing,function,geometry and algebraic,possibility and statistics,mathematical modeling and mathematical inquiring)nOptional compulsory curriculum consist of function,geometry and algebraic,possibility and statistics,mathematical modeling and mathematical inquiring

23、nOptional curriculum provides students with free selection according their own interesting in mathematics.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

24、 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 evaluationpIn the 2003 standard,Evaluati

25、on principles were mentioned in general.It pays attention to nStudents mathematics learning processes,nStudents fundamental knowledge and basic skillsnStudents abilitiespIt also emphasized the implementation of multifarious evaluation that promotes student development.pBut based on survey results,ma

26、thematics curriculum still paid attention to the summative assessment,instead of formative assessment,the curriculum is more oriented on final examination.pAccording to 2017 version standard,the curriculum focuses on“learning achievement”,and sets up three achievement levels which concern performanc

27、es of mathematics competencies.pThe 2017 standard sets up four aspects of students performances of math competenciesnContext and problemnKnowledge and skillnThinking and representationnCommunication and reflectionpThree achievement levels have been described,focused on math competencies,using the fo

28、ur aspects,as well as based on mathematics content.Cited from Baos representationFor 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 s

29、ituations;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

30、 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 th

31、em 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 mat

32、hematical 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 math

33、ematical 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 examinationpThe 2017 Standard explains thatp nthe achievement level one should be reached by all high

34、 school graduates nthe achievement level two is the basis of developing university entrance examinationnthe achievement level three could be reference for independent recruitment of universityExample 1The distance between school dormitory and office is a m.A classmate has important materials to give

35、 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.pComment In the actual situation,the graph can be used to rev

36、eal the function properties,and reflect overall the basic characteristics of the function.pWhen answering this question,you can give most of the schematic diagrams of the speed function or the path function,then can be considered to meet the requirements of the mathematical abstract competence level

37、 one.pCan fully draw the speed function and the path function graph(the two independent variables are consistent),then can be considered to meet the requirements of mathematical abstract competence level twoExample 2The inner ring of the 400-meter standard runway is shown in Figure,where the left an

38、d right sides are half-arcs with a radius of 36 meters.（1）Find the length of each straight(The pi is 3.14,and the result is accurate to 1 meter.)（2）Establish a plane rectangular coordinate system xOy,Write the function analytic corresponding to the upper half of the runwaypComment If the calculation

39、 of(1)can be completed,it can be considered that the requirement of intuitive imagination level 1 can be achieved.The ability to basically obtain the expression required by(2)can be considered to meet the requirements of the intuitive imagination level 2.pThis question can also be examined for mathe

40、matical operations and other competencies.pThe answer to this question is as followspNowadays we meet new challenges of curriculum development.nFour basic,four abilities and six competenciesnMathematics competencies and three achievement levelsnAchievement evaluation and final examinationpTextbooks based on 2017 standard are under constructionpThe implementation of this standard will be launched earliest in next year Many thanks谢谢！