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How to Use Geometry Teaching to Train Students’ Thinking—Taking the “Circumferential Angle Theorem” as an Example
DOI: 10.12677/CES.2023.111021, PDF, HTML, XML, 下载: 23  浏览: 61

Abstract: In the current stage of mathematics teaching after the reform of curriculum standards, the teaching of logical thinking has become the top priority in the mathematics classroom. Mathematics has a certain degree of abstraction, and in the process of teaching practice, it is often difficult for students to find, understand and apply some subtle “coincidences”. But education itself is an innovative process, an endless path to find an effective teaching model that can not only improve the quality of teaching, but also promote the development of students’ thinking. This article takes the proof of the “circumferential angle theorem” as an example to describe how to use geometry teaching to train students’ thinking. In the process of teaching, the proof of geometry is found to have three common drawbacks: it does not guide students well to discover the relationships in geometry, fails to analyze how to classify and discuss well, and does not explain clearly how to add auxiliary lines. Therefore, we will give corresponding suggestions to solve the above three shortcomings one by one, and explain how to cultivate and train students’ thinking.

1. 引言

2. 培养与训练学生思维的重要性

“思维”一词，我们先将两个字拆分开进行解释，“思”即为思考、思索，“维”即为维度，常说多维度也就是多个角度。那么和在一起的“思维”，我们就可以理解成思考的维度。在学校里，教师总会夸某某的思维很活跃就可以理解成某某经常进行多维度思考问题，其思考的广度和深度在同龄人之中显得出类拔萃。

3. 几何教学中的常见的思维误区

3.1. 未能很好引导学生发现几何中的关系

3.2. 未能较好分析如何进行分类讨论

Figure 1. Three cases of the circumferential angle theorem

3.3. 未解释清楚如何添加辅助线

4. 如何培养与训练学生的思维

4.1. 引导学生发现几何中的关系

4.2. 解释分析如何进行分类讨论

Figure 2. Sequence diagram that appears in the geometry artboard

4.3. 解析如何添加辅助线

5. 结语

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