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摘要反证法是数学命题证明方法中十分重要而且常用的一种证明方法，也是一种重要的数学思想。本文将探究学生在反证法的理解和运用上存在的问题，为引导学生正确理解反证法、有效运用反证法解题提供一定的教学参考。本文首先从反证法的概念及其理论依据来简要分析其理论基础，为方便学生理解反证法做好铺垫。再者笔者将针对反证法教学与练习中出现的典型问题和理解难点，对学生进行访谈来收集相关数据和信息，进一步了解学生在反证法理解与运用中的问题，找出学生认知与理解上出错的原因。根据学生存在的几点问题，笔者将从“新知引入-理解新知-拓展新知”这三个教学过程制定一个关于反证法的教学设计，为反证法教学提供一个案例。最后简要概括一下在研究中，笔者关于反证法的几点思考。一个教师只有不断钻研学生的问题，才能更好地提高教学水平，促进学生更好地发展。48253
ABSTRACT A reduction to absurdity is extremely important and commonly used in mathematical proof process, which is also a kind of important mathematical ideas.
The article explores the students’ problems in the understanding and applications of reduction to absurdity. This can guide students to correctly understand the reduction to absurdity , effectively solve problems, and provide some reference for the teaching. Firstly, we briefly analyze its theory based on the concept of reduction to absurdity, which can help students to received it easily. Secondly, for the typical problem and understanding difficulties in the teaching and students’ practice, we collect the relevant data and information by interviewing our students. So that we can find out the reasons that the students often make mistakes in the understanding and applications. According to the above questions, we put forward a teaching design from "new knowledge introduction - understanding new knowledge - to expand new knowledge", which provides a case for teaching of reduction to absurdity. Finally, this article summarize some ideas about the reduction to absurdity. Only when a teacher constantly work on the problems of students, can he improve his teaching level and promote students to develop better.
毕业论文关键词：反证法: 教学； 逻辑思维
Key words：reduction to absurdity; teaching; logical thinking
目 录
一、 绪论 6
二、 反证法的概念及其理论依据 6
（一）反证法的由来 6
（二）反证法的定义 7
（三）反证法的逻辑依据 7
（四）反证法的证明模式 7
三、 中学生对反证法的理解与应用 8
（一）学生在理解反证法中出现的几个误区 8
（二）学生在应用反证法中出现一些问题 9
四、教学实际中的案例 10
（一）熟悉情境，引入新知 10
（二）辨析反证，理解新知 11
（三）拓展提高，应用新知 11
五、关于反证法的几点思考 13
（一）为什么要用反证法？ 13
（二）学生为什么不习惯用反证法？ 14
（三）什么情况下可以考虑用反证法？