论文：数学中的类比法

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毕业论文论文题目浅论数学中的类比法

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目录

摘要 (3)

英文摘要 (4)

第一章类比分类 (5)

1.1 数学思想的类比 (5)

1.2 结构形式的类比 (5)

1.3 概念类比 (5)

1.4 方法类比 (6)

1.5 升降维类比 (6)

1.6 特殊与一般的类比 (7)

第二章类比的运用 (7)

第三章类比的作用 (9)

3.1创设类比情景,激发学习兴趣 (9)

3.2类比思想方法,温故知新 (9)

3.3通过类比联想,启发解题思路 (10)

3.4利用类比方法,发展创新思维 (10)

第四章运用类比推理应注意的几个问题 (10)

第五章总结与展望 (11)

参考文献 (12)

致谢 (13)

浅论数学中的类比法

摘要

波利亚说:“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.在数学中,类比是发现概念、方法、定理和公式的重要手段,也是开拓新领域和创造数学新分支的重要途径.

类比法是在两个或两类事物间进行对比，找出一些相同或相似点后,猜测在其他方面也可能存在相同或相似之处，并做出某种判断的推理方法，类比法（Method of analogy）也叫“比较类推法”。随着课程改革的深入展开,培养学生的综合解题能力越来越重要,数学学习更应重视数学思想方法的渗透和培养。类比思想是一种重要的数学思想方法。类比可以使学生经历探究的学习过程,改变学生的学习方式;类比能培养学生直觉思维能力,是一种很重要的思维方法;类比可以增强学生的数学应用意识,提高解决问题的能力。类比法的一般模式为：类事物具有性质类事物具有性质所以，类事物可能具有性质在教学中，适当对学生进行类比法的训练，这也是培养学生创造性思维的一种方法。不过，对类比法得到的结论，要提醒学生养成想想是否正确的习惯，学会用实例进行检验，以提高学生判断问题的能力。

关键词：推理；解题法；类比法；思维；创造性；检验

Shallow the analogy method teaching of mathematics

Abstract

BoLiYa said: "analogy is a great guide." say that analogy is to explore the problems and solutions to the problems and discover new results of a fruitful thinking methods. In mathematics, analogy is found concept, methods, theorem and the important method, also is formula explore new fields and creating new mathematics branch of important ways.

Anology is in two or two things, find some comparison between the same or similar points, guess in other respects may also exists identical or similar, and make a judgment reasoning Method, the Method of analogy (of analogy) also called "of comparative analogy". With the deepening of the reform of course on problem solving, to cultivate students the comprehensive ability more and more important, learning mathematics mathematical way of thinking more should attach importance to the penetration and develop. Analogical thought is an important mathematical thinking methods. Analogy so that students can experience exploring learning process, change student's study way; Analogy can train students' intuition thinking ability, is a kind of very important thinking methods; Analogy can enhance student's mathematics application consciousness and improve the ability to solve problems. The general mode of analogy method for: things with properties with properties things such things might have, therefore, in the teaching, proper nature of the training students' analogy method, this also is to cultivate students creative thinking of a kind of method. But, for the analogy method, the conclusions to remind students form the habit of right think whether, learn to use the example for inspection, to improve the students' judgment question ability.

Keywords: reasoning; Problem-solving method; The analogy method; Thinking; Creative; inspection