类比思想在高中数学教学引入的应用

发布时间：2018-02-09 17:46

本文关键词： 类比思想高中数学数学教学引入　出处：《华中师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：类比思想是高中数学一种重要的思维方法,在整个高中数学的教学与学习过程起着非常重要的作用。在数学史上,很多重要定理的发现和相关概念得到的性质结论都与类比有关,波利亚曾说过:“类比是一个伟大的引路人”。学生熟练掌握类比思想,可以帮助他们对不同的数学概念、性质结论和定理有一个清晰地认识和理解,这样有助于学生对数学知识进行整合归纳,对于数学学习具有非常重要的意义。本文旨在对整个高中数学教学中涉及类比关系的知识点按照类比形式进行总结,并根据实际课堂教学引入如何应用类比思想展开具体说明,在此针对数学课堂上三种类型的课,分别是概念课、定理讲解课、单元小结课,对这三种类型的课举例说明如何在教学引入上恰当地利用类比思想,并给出教案分析和设计。本文从以下4个方面进行研究:第一部分主要介绍类比思想在高中数学教学中的研究背景,国内外关于类比的研究现状和研究意义;第二部分主要介绍类比的概念和在数学教学的几种形式,将人教A版高中数学课本中涉及到相似的知识点对应总结归纳到不同形式下,并把类比思想用于高中数学课堂上三种不同类型的课上,分别是概念课的引入、定理讲解课的引入、单元小结课的引入,同时分别进行举例说明在高中数学课堂引入如何采用类比思想,介绍具体实施步骤:类比教学的准备,类比教学的实施,验证类比结论;第三部分将类比思想运用于课堂教学引入中,分别举例说明上述三种不同类型课的教学设计,并针对教学设计提出教学反思;最后对本文的研究内容进行总结,发现使用类比思想作为一个切入点时,可以使课堂效果达到事半功倍,然后分析研究中的不足之处,期望这些总结可以为教师在进行类比教学的时候提供一定的参考。
[Abstract]:The thought of analogy is an important method of thinking in high school mathematics, which plays a very important role in the teaching and learning process of mathematics in senior high school. Many of the discoveries of important theorems and the nature of the related concepts are related to analogy. Polia once said, "analogy is a great guide." students are proficient in the idea of analogy, which can help them understand different mathematical concepts. The nature of the conclusion and theorem has a clear understanding and understanding, which is helpful for students to integrate mathematical knowledge, The purpose of this paper is to summarize the knowledge about analogy relation in the whole senior high school mathematics teaching according to the form of analogy, and to explain how to apply the analogy thought to the actual classroom teaching. In view of the three kinds of classes in mathematics classroom, they are concept class, theorem explaining class, unit summary lesson. Examples are given to illustrate how to introduce the analogy thought into the teaching. The first part mainly introduces the research background of analogy thought in mathematics teaching in senior high school, the research status and significance of analogy at home and abroad; The second part mainly introduces the concept of analogy and several forms of mathematics teaching. And the analogy thought is applied to three different kinds of high school mathematics classes, namely, the introduction of concept class, the introduction of theorem explaining class, the introduction of unit summary class, the introduction of the introduction of the concept class, the introduction of the theorem explanation class, the introduction of the unit summary class. At the same time, examples are given to illustrate how to adopt analogy in high school mathematics classroom, and the concrete steps are introduced: preparation of analogy teaching, implementation of analogy teaching, verification of analogical conclusion; The third part applies the analogy thought to the classroom teaching, explains the teaching design of the three kinds of courses mentioned above with examples, and puts forward the teaching reflection on the teaching design. Finally, it summarizes the research contents of this paper. It is found that the use of analogy thought as an entry point can make the classroom effect double the result with half the effort, and then analyze the shortcomings of the research, and hope that these conclusions can provide some reference for teachers in the process of analogical teaching.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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