數(shù)學(xué)課程改革的國際比較課件

1、Development of competencies oriented mathematics curriculum in ChinaBinyan XuCollege of Teacher EducationEast China Normal UniversityDecember 10th-16th 2018, LyonThe newest developmentWhen and Why? What？The newest developmentThe revised version of the High School Mathematical Curriculum Standards (2

2、017 Edition) (MOE 2018) was released in January 2018 (2017 Standards, hereafter).The version High School Mathematics Curriculum Standards (Experimental version) was published in 2003 (hereafter referred to as the 2003 Standards; MOE 2003).At the end of the twentieth century, China decided to improve

3、 the quality 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 WhyAt the end of 2014, the MOE launched the work of revising curricula for all high school subjects (MOE 2014b, Decembe

4、r 8).One reason related to the governments requirement; the another was based on the national survey.the governments requirementIn response to the governments requirement for the visible development of citizens, the MOE proposed and released its Suggestions for Fully Deepening the Curriculum Reform

5、and Practising the Fundamental Mission of Citizen Development (MOE 2014a, April 8) to guide basic education in China.It 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 t

6、hat would enable students to adapt to life-long learning and meet the requirements of social development”.緣起：中國學(xué)生的核心素養(yǎng)體系必備品格與關(guān)鍵能力人文底蘊(yùn)科學(xué)精神健康生活責(zé)任擔(dān)當(dāng)學(xué)會(huì)學(xué)習(xí)實(shí)踐創(chuàng)新人文積淀人文情懷審美情趣理性思維批判質(zhì)疑勇于探究樂學(xué)善學(xué)勤于反思信息意識(shí)真愛生命健全人格自我管理社會(huì)責(zé)任國家認(rèn)同國際理解勞動(dòng)意識(shí)問題解決技術(shù)應(yīng)用文化基礎(chǔ)社會(huì)參與自主發(fā)展core competency system includes:Cultural cultivationhumanistic

7、connotation (humane feelings, aesthetic appeal)scientific spirit (rational thinking, critical thinking , be brave in inquiring)Self-developmentLearning to learn (interesting in learning, be diligent in reflection, identifying information)Living healthy (healthy personality, self management)Social Pa

8、rticipationResponsibility bearing (national identify, international understanding)Practice innovation (labor consciousness, technical application)National survey on curriculum implementationECNU mathematics education team got this task from the MOE in China, Bao etc. developed survey framework which

9、 included the following aspects:Curriculum design: properties of the curriculum, objectives, structureCurriculum content: difficulty level, systematical structure of contentCurriculum implementation: teaching situation, textbooks, teacherCurriculum evaluation: assessment tool, examinationMethods: gr

10、oup / individual interview, questionnaire survey, content analysisParticipants: teachers, students, school leaders, teaching inspectors, textbook editors, administratorsSome results which contributed to modification of the standardThe modules and sequence of content should be modified in order to re

11、ach 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 burdenTeachers focused more on training math skills than fostering competenciesThe standar

12、d played very weak role in developing university entrance examination.The both reasons pushed forward and guided the improvement / development of high school math curriculum.What happened mainly?Revise curriculum objectives focused on core competenciesRevise curriculum structureRevise curriculum eva

13、luationcurriculum objectives in 2017 standardTo obtain basic knowledge, basic skill, basic thought and activity experience (four basic )To enhance abilities of discovering and posing problems mathematically, of analyzing and solving problems (four abilities)To develop mathematics core competencies i

14、ncluding mathematical abstraction, logic reasoning, mathematical modelling, intuitive imagination, mathematical operation and data analysis. To improve learning interesting in mathematics, self confidence in learning mathematics, to develop self-learning abilities, to cultivate scientific spirits of

15、 criticizing, thinking, rigorous fact attitude.to improve practical and innovative abilitiesCompare to 2003 standard, the 2017 standard emphasized 6 core mathematics competencies explicitlyThe core mathematics competencies were defined as “necessary thinking quality and key abilities that related to

16、 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 abstractionto form mathematical concepts and rules; to form math

17、ematical 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 processintuitive imaginationto describe and understand mathem

18、atics 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 operationto understand operational objects; to master arithme

19、tic rules, to explore arithmetic processdata analysisto obtain data, to analyze data, construction of knowledgethese six core competencies could help develop “mathematical perspectives to observe the world”, for which mathematical abstraction and intuitive imagination play important roles;“the abili

20、ty to think mathematically about the world”, for which logical reasoning and mathematics operation are necessary;and “mathematical language to express the world”, which needs mathematical modelling and data analysis.Revise curriculum structure2003 standard set up such module structureThe survey show

21、ed that teachers were unprepared to implement the modules curriculum.The structure in the 2017 standard follows the principles of common basic and diversified option, it includes compulsory curriculum and optional curriculum. Compulsory curriculum consists of 5 topics (knowledge for preparing, funct

22、ion, geometry and algebraic, possibility and statistics, mathematical modeling and mathematical inquiring)Optional compulsory curriculum consist of function, geometry and algebraic, possibility and statistics, mathematical modeling and mathematical inquiringOptional curriculum provides students with

23、 free selection according their own interesting in mathematics.Curriculum A is constructed for students with interesting in math or sciencesCurriculum B is constructed for students who have interesting in economic, society oriented researchCurriculum C is designed for students who want to learn huma

24、nistic subjects (language, history)Curriculum D is designed for students who are good at sport or artsCurriculum E focuses on extending perspectives, local specific curriculum, and also AP curriculumRevise curriculum evaluationIn the 2003 standard, Evaluation principles were mentioned in general. It

25、 pays attention to Students mathematics learning processes, Students fundamental knowledge and basic skillsStudents abilitiesIt also emphasized the implementation of multifarious evaluation that promotes student development.But based on survey results, mathematics curriculum still paid attention to

26、the summative assessment, instead of formative assessment, the curriculum is more oriented on final examination.According to 2017 version standard, the curriculum focuses on “l(fā)earning achievement”, and sets up three achievement levels which concern performances of mathematics competencies.The 2017 s

27、tandard sets up four aspects of students performances of math competenciesContext and problemKnowledge and skillThinking and representationCommunication and reflectionThree achievement levels have been described, focused on math competencies, using the four aspects, as well as based on mathematics c

28、ontent. 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 situations; able to use inductive or ana

29、logical 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 t

30、he 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 problem

31、s; 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 propositionsA

32、chievement 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; a

33、ble 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 examinationThe 2017 Standard explains that the achievement level one should be reached by all high school graduates the

34、 achievement level two is the basis of developing university entrance examinationthe 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 to the teacher. From

35、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.Comment In the actual situation, the graph can be used to reveal the function

36、properties, and reflect overall the basic characteristics of the function. When 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 one.Can fully draw the speed function and the path function graph (the two independent variables are consistent), then can be