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在几何定理教学中,定理内容固然值得我们重视,但是更应引起我们重视的是定理证明中的思想方法。学生一旦掌握了某种思想方法,便可以用来解决一类问题,甚至还可能得出新的发现。初中几何中许多定理的证明都包含着重要的数学思想方法,现举几个典型的例子来说明。(所举例子均依据统编教材) 例1.三角形的中位线定理该定理的证明,课本采用的是对称变换,这是初中几何解题中的三大变换之一。在教学中,要引导学生从中提炼出这一重要的思想方法,使学生切实掌握,并会应用它来简捷处理课本上的习题。
In the teaching of geometry theorem, the theorem content certainly deserves our attention, but more should draw our attention to the theorem proving method of thinking. Once mastered a certain way of thinking, students can be used to solve a problem, and may even come up with new findings. The proofs of many theorems in junior middle school geometry all contain important mathematical thinking methods. Here are some typical examples. (The examples are based on the unified textbook) Example 1. The median line theorem of triangles Proof of this theorem, the textbook uses a symmetric transformation, which is one of the three major changes in the geometry of junior high school. In teaching, to guide students to extract from this important method of thinking, so that students can effectively grasp, and will use it to deal with simple textbook exercises.