基于数学史的高中导数教学设计研究

发布时间：2018-10-10 15:43

【摘要】：微积分的诞生是数学发展史上一个划时代的成就,为研究函数和变量提供了重要的方法和手段。二十一世纪以来,微积分教学进入一个新的时期,世界各国纷纷将微积分引入高中数学课程。2003年,我国教育部颁发了《普通高中数学课程标准(实验)》,将微积分列为高中数学的选修课程。但是,新发行的教科书中并没有按照“极限——导数——积分”的传统方式编写,淡化了极限知识的学习,将导数作为一种特殊的极限(增量比的极限)来处理,直接通过反映导数思想和本质的具体实例(如瞬时速度)引导学生认识和理解导数的概念。HPM主要研究如何运用数学史促进数学教育,是数学教育研究的重要组成部分。目前数学教育专家都已经意识到数学史在数学教育中的重要性,不仅能促进学生课堂学习效率,还可以增加学生的数学史与数学文化方面的知识,是新课程改革的有效实践。本文中,笔者将基于HPM的相关研究探讨在高中导数教学中融入数学史的教学设计。首先,由于导数是微积分的重要组成部分,要从历史的角度提高导数概念教学的效率,将导数概念的产生和发展过程有效地渗透于导数教学实践,必须对微积分的发展历史进行系统地了解,全面认识从近半个世纪的酝酿到牛顿、莱布尼茨创立微积分,直到十八世纪柯西等人将微积分严格化的过程。其次,调查研究高三学生导数学习的现状及理工类大一学生微积分学习的现状,了解高中导数的学习对于大学微积分的学习是否有影响。对高中数学教师和高校高等数学教师进行访谈,了解教师们关于这部分知识教学所持有的观点。最后,根据调查研究,给出融入数学史的导数概念的教学设计,并在课堂上实施检验其效果,其目的在于为中学教师在数学教学中融入数学史提供参考与借鉴。
[Abstract]:The birth of calculus is an epoch-making achievement in the history of mathematical development, which provides an important method and means for the study of functions and variables. Since the 21 century, the teaching of calculus has entered a new period, and many countries in the world have introduced calculus into the mathematics curriculum of senior high school. The Ministry of Education of our country issued the ordinary Senior High School Mathematics Curriculum Standard (experiment), which included calculus as the elective course of senior high school mathematics. However, the newly published textbook is not written in the traditional way of "limit derivative integral," which weakens the learning of limit knowledge and treats derivative as a special limit (the limit of incremental ratio). Through concrete examples (such as instantaneous speed) which reflect the thought and essence of derivative, students are guided to know and understand the concept of derivative. HPM mainly studies how to use the history of mathematics to promote mathematics education, which is an important part of mathematics education research. At present, mathematics education experts have realized the importance of mathematics history in mathematics education, which can not only promote students' classroom learning efficiency, but also increase students' knowledge of mathematics history and mathematics culture, which is an effective practice of the new curriculum reform. In this paper, the author will discuss the teaching design of mathematics history in derivative teaching based on HPM. First of all, since derivative is an important part of calculus, it is necessary to improve the efficiency of derivative concept teaching from the historical point of view, and effectively infiltrate the process of producing and developing derivative concept into derivative teaching practice. It is necessary to systematically understand the history of the development of calculus, from the brewing of nearly half a century to Newton, Leibniz's creation of calculus, until Cauchy et al. Secondly, we investigate the current situation of derivative learning for senior three students and the present situation of calculus learning for freshmen in science and engineering, and understand whether the derivative learning in senior high school has an influence on the learning of college calculus. This paper interviews high school mathematics teachers and higher mathematics teachers in colleges and universities to find out the teachers' views on this part of knowledge teaching. Finally, according to the investigation and research, this paper gives the teaching design of the concept of derivative into the history of mathematics, and tests its effect in the classroom. The purpose of the design is to provide reference and reference for the middle school teachers to integrate the history of mathematics into the teaching of mathematics.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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