高中数学教材中数学建模内容的分析及再设计

发布时间：2017-12-26 22:32

本文关键词：高中数学教材中数学建模内容的分析及再设计　出处：《华东师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：我国的《普通高中数学课程标准(实验)》(以下简称《高中标准》)要求在高中学段开展数学建模活动,《高中标准》所提及的数学建模是面向所有学生的数学建模。相较于传统的数学建模课程,面向普通高中学生的数学建模有其自己的特点,而数学教材作为建模内容的载体,应尽可能将其体现。另一方面,《高中标准》希望学生通过相关内容的学习,能够逐步培养应用数学解决实际问题的能力,而这正是数学建模内容所应反馈出来的。本研究将基于其他研究的经验对中学数学建模本质及特点进行讨论,并对高中教材中数学建模内容进行分析,为其设计提供建议。本研究的研究问题是：什么是高中数学教材中的数学建模内容?教材中数学建模的内容具体有怎样的特点?现行高中教材中数学建模内容是如何呈现的?又应如何更好地设计?本文由以下部分组成：第一部分绪论,主要讨论研究的背景、意义、研究的问题和方法。第二部分文献综述,对国内外学者对中学数学建模相关研究进行综述。第三部分通过文献内容的分析对中学数学建模的内容进行界定,并讨论了数学建模内容设计应具备的要素。研究得到如下结论,高中教材中数学建模内容的定义应满足如下三条：1)经历完整的数学建模过程；2)问题从某一情境出发；3)数学模型在解题过程中被使用。同时,教材中数学建模活动的内容构成包括了六个要素。第四部分基于前文对数学建模内容特点的讨论,对我国部分高中教材中数学建模的内容进行了整理,编码和比较,并选取部分内容进行再次编写设计。第五部分结论,对高中数学建模活动开展提出建议,总结整个研究并进行展望。
[Abstract]:China's "high school mathematics curriculum standard" (hereinafter referred to as "high school standard") requires that we carry out mathematical modeling activities in senior high school. The mathematical modeling mentioned in high school standard is a mathematical modeling for all students. Compared with the traditional mathematical modeling course, mathematical modeling for senior high school students has its own characteristics. As a carrier of modeling content, mathematics teaching should reflect it as much as possible. On the other hand, "high school standard" hopes that students can gradually train practical mathematics to solve practical problems through the learning of related contents, which is the feedback from mathematical modeling contents. Based on other research experience, this study will discuss the essence and characteristics of mathematical modeling in middle school, and analyze the contents of mathematical modeling in high school textbooks, so as to provide suggestions for its design. The research questions are: what are the contents of mathematical modeling in high school mathematics teaching of mathematical modeling in? What are the features of the specific contents of the contents of the current high school textbooks of mathematical modeling? How is presented? And how to better design? This paper consists of the following parts: the first part is the introduction, problems and research methods the background and significance of the research, the main discussion. The second part of the literature review, the domestic and foreign scholars on middle school mathematical modeling related research. The third part defines the content of mathematical modeling in middle school through the analysis of the contents of the literature, and discusses the elements that should be possessed in the design of mathematical modeling content. The following conclusions are drawn from the research. The definition of mathematical modeling content in high school textbooks should meet the following three points: 1) experience the complete mathematical modeling process; 2) the problem starts from a certain situation; 3) the mathematical model is used in solving problems. At the same time, the content of mathematical modeling activities in the textbook consists of six elements. The fourth part, based on the discussion of the content characteristics of mathematical modeling, collated, encoded and compared the contents of mathematical modeling in some high school textbooks in China, and selected some of the contents to be re designed. The fifth part of the conclusion, the high school mathematical modeling activities to carry out suggestions, sum up the whole research and prospect.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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