从定理的简单证明中启发学生的创新思维

To Inspire Students' Innovative Thinking from Simple Proofs of Theorems

这篇文章从目前线性代数教学改革和教学实际出发,对课堂教学进行研究,力求提高课堂教学效率,培养学生的创新思维.为此,提供了三个定理的新的简单证明方法.用启发式教学达到了三个主要目的:1.培养学生的创新思维;2.调动学生的学习积极性;3.提高课堂教学效率.

This article attempts to study how to develop the university students the ability of innovation and how to improve the teaching effectiveness in classrooms via the practice of our current teaching reforms in the course of linear algebra. It is illustrated by showing new simple proofs of three typical theorems. The main objectives are： 1. To develop students the ability of innovation; 2. To mobilize students the learning interests ; 3. To improve the teaching effectiveness in classrooms.