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高中数学可类比内容教学的研究

【作者】 宋兰英

【导师】 李延林;

【作者基本信息】 首都师范大学, 学科教学, 2017, 硕士

【摘要】 《普通高中数学课程标准》中的理念部分第四条明确提出“注重提高学生的数学思维能力”。类比思维是数学思维能力的有机组成部分。类比推理是极其重要的思维方法,在数学学习中有着广泛的应用。据笔者统计,在《标准》中,“类比”一词在理念、内容及教学建议中,共计出现11次。本文对《标准》中的“类比”做了详细分析,论述了类比在高中数学教学中的地位和作用,并对高中数学内容中可以类比的内容进行了研究。能力的培养要以具体的学习内容为载体。数学思维能力建立在数学基础知识、基本技能、基本活动经验的基础之上,因此,高中生的类比思维能力在数学教学中的培养必须建立在具体的数学内容之上。高中数学可类比内容承载着高中生类比思维能力的培养。高中数学可类比内容的教学目标是双重的,一是知识层而的目标,二是能力层面的目标。如何实施高中数学可类比内容的教学才能达到在保证知识目标的前提下培养高中生的数学类比思维能力呢?本文提出了高中数学可类比内容教学实施的四项基本原则,即循序渐进原则、学生自主原则、结构化原则、知识与能力并重原则。结合案例,本文讨论了高中数学可类比内容的基于学生自主的类比教学。在高中数学教学中,注重提高高中生的类比思维能力,正是领会了《标准》中的科学理念,并付诸在教学实践。本文主要解决以下三个问题:1,类比思维能力的培养在高中数学教学中的地位与必要性?2,高中数学可类比内容有哪些?3,如何实施高中数学可类比内容的教学?

【Abstract】 The fourth item of the concept of the 《High school mathematics curriculum standards》 clearly stated to focus on improving students’ mathematical thinking ability. The analogy is the organic component of mathematical thinking ability. Analogical reasoning is an extremely important way of thinking,and it has been widely applied in mathematics learning. In the "standard", the word "analogy" in concept, content and teaching suggestions, a total of11times. This paper analyzes the "analogy" in the "standard", discusses the status and role of analogies in high school mathematics teaching, and sort out analog content in high school math.Ability training need to be specific learning content as a carrier. Mathematical thinking is built on the basic knowledge of mathematics, basic skills, basic activities of the basis of experience, therefore, the cultivation of high school students to analogical thinking capability in teaching mathematics must be built on top of a specific mathematical content. Analog content in high school math carries the ability training of high school students analogical thinking. The two teaching objectives of Analog content in high school math are knowledge level and ability level. How to implement the analog content of the teaching of high school mathematics in order to culture analogical thinking ability of high school students under the premise to ensure the knowledge target? This paper presents four cardinal principles which run through the teaching of analog content in high school mat, the principle of gradual and orderly progress, the principle of student autonomy, the principle of structured and the principle of knowledge and ability to equality. This paper discusses the teaching of the high school math analog content based on students’ own analogy, according to two cases. In high school mathematics teaching, focus on improving high school analogical thinking is to understand the scientific concept of "standard", and put into practice in teaching.This article is mainly to solve the following three questions:1, What is the status and necessity of analogical thinking abilities in high school mathematics teaching?2, What are the analog content in high school mathematics?3, How to implement the teaching of analogous content high school math?

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  • 【网络出版投稿人】 首都师范大学
  • 【分类号】G633.6
  • 【下载频次】48
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