如何运用几何教学训练学生的思维——以“圆周角定理”为例
How to Use Geometry Teaching to Train Students’ Thinking—Taking the “Circumferential Angle Theorem” as an Example

在现阶段课程标准改革后的数学教学中，逻辑思维教学成为数学课堂上的重中之重。数学具有一定的抽象性，在教学实践过程中，学生往往难以发现、理解及应用一些微妙的“碰巧”。但教育本身就是一个创新的过程，是一条寻找既能提升教学质量，又能促进学生思维发展的有效教学模式的无尽道路。而本文以“圆周角定理”的证明为例，讲述如何运用几何教学训练学生的思维。在教学过程中，发现几何的证明有常见的三点弊病：未能很好引导学生发现几何中的关系、未能较好分析如何进行分类讨论、未解释清楚如何添加辅助线。因此，我们将给出相应的建议来逐一解决以上三点弊病，并阐述如何培养与训练学生的思维。
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.