类比在高中数学教学中的应用

发布时间：2018-04-27 13:04

本文选题：类比 + 高中数学　；参考：《河南大学》2015年硕士论文

【摘要】：类比是在两个或两类事物间进行对比,找出若干相同或相似点后,猜测在其他方面也存在相同或相似之处,并作出某种判断的推理方法,类比也叫类比推理。它是一种重要的科学方法,在数学史上,很多重要的定理和发现都与类比有关,波利亚曾说过:“类比是一个伟大的引路人”,可以说,类比是探索问题、解决问题与发现新结果的一种卓有成效的思维方法;它是发现新概念、方法、定理和公式的一种重要手段,同时也是开拓新领域和创造数学新分支的重要途径。在数学学习中,我们不仅要让学生掌握数学知识,更重要的是让学生领会其中的数学思想方法,领悟数学的真谛,懂得数学的价值。随着教育改革的深入开展,学生素质教育和创新能力的培养越来越受到教育界的关注,类比作为一种重要的思想方法正受到数学研究者的青睐。在2003年出版的《普通高中数学课程标准》中明确提到了合情推理,而类比作为合情推理的一种方法也引起了教师和学生的高度重视,所以在数学教学过程中,教师可以有意识地引导学生进行类比,培养学生的类比能力。本文是从以下五个方面来研究的:第一部分主要介绍了类比教学提出的原因,国内外关于类比的研究现状以及类比的教育理论基础和研究意义;第二部分主要介绍了类比的概念、分类以及类比和归纳、演绎的区别;第三部分介绍了类比在高中教材各个模块中的应用,在每个模块中主要围绕教材中知识点的类比和怎样用类比来解题两个方面展开分析;第四部分以具体的教学案例来分析类比的课堂教学,通过实践来说明类比教学的优点以及在教学中存在的问题;最后对本文的研究内容作了总结,发现使用类比作为一个切入点时,可以使课堂效果达到事半功倍,然后分析了研究中的不足之处,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]:Analogy is a kind of reasoning method of making some judgment after comparing two or two kinds of things and finding out some similarities or similarities in other aspects. It is an important scientific method. In the history of mathematics, many of the important theorems and discoveries are related to analogy. Polia once said, "analogy is a great guide." analogy is a question of exploration. It is an important means of discovering new concepts, methods, theorems and formulas, as well as an important way to open up new fields and create new branches of mathematics. In mathematics study, we should not only let the students master the mathematics knowledge, but also let the students understand the mathematics thought method, understand the true meaning of mathematics and understand the value of mathematics. With the development of educational reform, the cultivation of students' quality-oriented education and innovative ability has been paid more and more attention by the educational circles. Analogy, as an important ideological method, is being favored by mathematics researchers. In the course Standard of Mathematics in General Senior Middle School published in 2003, reasonable reasoning is explicitly mentioned, and analogy as a method of reasonable reasoning has also aroused great attention of teachers and students, so in the process of mathematics teaching, Teachers can consciously guide students to carry out analogies and cultivate their abilities of analogy. This article is from the following five aspects to study: the first part mainly introduces the reason of analogy teaching, the domestic and foreign research status of analogy, the theoretical basis and significance of analogy education; The second part mainly introduces the concept of analogy, classification and the difference between analogy, induction and deduction. The third part introduces the application of analogy in various modules of senior high school textbooks. In each module, it mainly focuses on the analogy of the knowledge point in the textbook and how to solve the problem by analogy. The fourth part analyzes the classroom teaching of analogy with specific teaching cases. Through practice to explain the advantages of analogical teaching and the problems existing in teaching. Finally, the research content of this paper is summarized, and it is found that the use of analogy as a breakthrough point can make the classroom effect twice the result with half the effort. Then it analyzes the shortcomings of the research and expects that these conclusions can provide some references for teachers in the process of analogical teaching.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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