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中文题名:

 反证法在中学数学的教学设计    

姓名:

 刘仁新    

保密级别:

 公开    

论文语种:

 chi    

学科代码:

 070101    

学科专业:

 数学与应用数学    

学生类型:

 学士    

学位:

 理学学士    

学位年度:

 2024    

校区:

 北京校区培养    

学院:

 数学科学学院    

研究方向:

 数学教育    

第一导师姓名:

 曹外香    

第一导师单位:

 数学科学学院    

第二导师姓名:

 王立东    

提交日期:

 2024-05-17    

答辩日期:

 2024-05-07    

外文题名:

 Reduction to Absurdity in the Teaching Design of High School Mathematics    

中文关键词:

 反证法 ; 中学数学 ; 教学设计 ; 逻辑思维基础.    

外文关键词:

 Reduction to Absurdity ; High School Mathematics ; Instruction Design ; Fundamentals of Logical Thinking.    

中文摘要:

新高考中对证明题的要求不断提高,而反证法作为一种重要的数学证明方法,其教学却在以往的中学中被严重忽视,基于这一背景,本文进行了反证法的中学教学设计。对比研究反证法教学的国内外现状,结合自身学习经历,对反证法提出了教学难点的分析以及教学建议。由于在现有的反证法教学设计中缺乏完整的教学过程的设计,对此,本文的教学设计也将侧重于对反证法的教学过程的研究,用情景模拟法设置了两个课时的内容:第一课时由生活实例引入反证法,再介绍非命题以及逻辑思维规律中的矛盾律和排中律,并由此完整推出反证法;第二课时是对反证法的四个例题讲解,中间引入了逆否命题法并与反证法进行对比教学,加深学生对反证法的理解并让学生学会如何将反证法运用到题目中去。

外文摘要:

In the context of the new high school entrance examination, the demand for proof questions continues to increase. However, reduction to absurdity, as an important mathematical method, has been severely neglected in previous high school education. Based on this background, this paper conducts a middle school teaching design for the method of contradiction. By comparing the current situation of the teaching of the method of contradiction at home and abroad, and combining with the author's own learning experience, the paper analyzes the teaching difficulties of the method of contradiction and provides teaching suggestions. Since there is a lack of a complete teaching process design in the current teaching design of the method of contradiction, this paper's teaching design will also focus on the research of the teaching process of the method of contradiction. The article uses scenario simulation to set up two class periods of content. The first class period starts with a real-life example to introduce the method of contradiction, then introduces non-propositions and logical thinking laws such as the law of contradiction and the law of excluded middle, and thus completes the introduction of the method of contradiction. The second class period is an explanation of four examples of the method of contradiction, in which the method of contrapositive is introduced and compared with the method of contradiction for teaching purposes, deepening students' understanding of the method of contradiction and teaching them how to apply the method of contradiction to problems.

参考文献总数:

 14    

作者简介:

 北京师范大学数学与应用数学专业2020级刘仁新    

插图总数:

 0    

插表总数:

 2    

馆藏号:

 本070101/24019    

开放日期:

 2025-05-19    

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