中小学数学课程中函数内容的发展主线研究

发布时间：2018-04-04 15:36

本文选题：函数　切入点：课程发展主线　出处：《华东师范大学》2017年硕士论文

【摘要】：世界各国在进入21世纪后都加紧了课程改革的脚步,我国的全国课程标准和上海市课程标准也在修订之中.本文是上海市2015年教育科学研究重大项目:中小学数学教材的有效设计(项目编号D1508)的子课题1中小学数学课程内容发展主线的顶层设计的阶段性研究成果.由于函数在中小学尤其是中学阶段占有非常重要的地位,因此本文将研究"函数"的内容发展主线.本文总体上的研究问题是函数内容在中小学教育阶段是如何发生、发展的?具体说来有两个研究问题:(1)学校数学中函数的核心内容有哪些?(2)函数的核心内容是怎样在学校数学的课程中展开的?本文的研究方法是定性研究,包含了文本分析、比较和访谈.文本包括美国、英国、新加坡、澳大利亚、我国全国高中及义务教育课程标准和上海市中小学数学课程标准共6个课程标准.访谈对象包括11名专家,分别涵盖了大学数学系的数学教授(分析、代数、几何方向)、大学数学教育研究者、教材编写者和高中数学教研员.访谈采用半结构式,问题主要用来对函数内容的拟发展主线进行修正.本文的发展主线的构建是建立在学生认知、课程论、数学的逻辑与实证研究之上的,它还可以不断地进行改进.本研究得到的结果为:问题(1)中小学阶段函数的核心内容有:函数的概念、函数的性质、函数的应用(与建模),并由6类基本初等函数作为载体来展开.对问题(2)的回答阐述如下:综合数学中函数内容的逻辑安排与学生的认知特点,以及访谈专家的意见,得到,函数在中小学阶段是按照"函数的铺垫→函数的'变量说'概念→具体函数(1)→性质→应用→具体函数(2)→性质→应用→……→函数的'对应说'概念→抽象性质→具体函数(3)→性质→应用→具体函数(4)→性质→应用→……"展开,并以"基本初等函数→性质→应用"为单元展开.详见本文图19中小学函数内容的发展主线图,图中从左至右、从下到上的函数内容发展变化表示了随着时间的推移,函数的内容从简单到复杂的发展过程.同时本研究还探讨了学习函数内容前所需要的铺垫及函数内容所体现的数学能力和思想方法.本研究理清了函数内容在中小学阶段的发展主线,为中小学数学课程标准和教材编写提供设计思路,同时有助于教师站在较高的角度把握教材编写脉络、找准函数的重点并合理安排函数内容.
[Abstract]:After entering the 21st century, every country in the world has stepped up the pace of curriculum reform, and the national curriculum standards of our country and the curriculum standards of Shanghai are in the process of being revised.This paper is the achievement of the stage research on the top-level design of mathematics curriculum content development of primary and middle schools in Shanghai in 2015: the effective Design of Mathematics textbooks for Primary and Middle Schools (Project No. D1508).Since function plays a very important role in middle school, especially in middle school, this paper will study the main line of content development of "function".The overall research problem in this paper is how the function content occurs and develops in the primary and secondary education stage.Specifically, there are two research questions: 1) what is the core content of function in school mathematics? how does the core content of function develop in the curriculum of school mathematics?The research method of this paper is qualitative research, including text analysis, comparison and interview.The text includes six curriculum standards, including the United States, Britain, Singapore, Australia, China National High School and compulsory Education Curriculum Standard and Shanghai Primary and Middle School Mathematics Curriculum Standard.The subjects included 11 experts, including mathematics professors in the department of mathematics (analysis, algebra, geometry orientation, university mathematics education researchers, textbook writers and senior high school mathematics teachers).The interview is semi-structured, and the problem is mainly used to modify the main line of function content.The main development of this paper is based on student cognition, curriculum theory, mathematics logic and empirical research, it can also be continuously improved.The results of this study are as follows: question 1) the core contents of the function in primary and secondary schools are: the concept of function, the nature of function, the application of function (and modeling), and is carried out by six basic elementary functions as the carrier.The answer to question No. 2 is as follows: the logical arrangement of functional content and the cognitive characteristics of students in comprehensive mathematics, as well as the opinions of the experts, are obtained.In the primary and middle school stage, the function is applied according to the 'variable theory' concept of the function's bedding function and the application of the concrete function's property."Expansion, and the "basic elementary function properties of the application" as the unit expansion.In figure 19, the development of function content is shown in figure 19. The development of function content from left to right and from bottom to top shows that the content of function develops from simple to complex over time.At the same time, this study also discusses the need of learning function content and the mathematical ability and thought method of function content.This study clarifies the main line of development of function content in primary and secondary schools, provides design ideas for mathematics curriculum standards and textbook compilation in primary and secondary schools, and helps teachers to grasp the writing context of textbooks from a higher perspective.Find out the key points of the function and arrange the content of the function reasonably.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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