线性代数课程教学的探索与实践——以数学证明教育价值实现的课堂教学为例

Research and Practice on Teaching Linear Algebra Course——the Educational Value of Mathematical Proof to Realize in Classroom as Model

要教好线性代数课程,其核心问题就是要通过课堂教学,使学生理解相关的数学知识;训练和培养学生的思维能力以及数学交流能力;帮助学生寻找新旧知识之间的内在联系,使知识系统化;在巩固已有知识的基础上,让学生自己去发现新知识.要实现这一教学目标,训练学生掌握＂数学证明＂的概念和在实践中的应用至关重要.传统的做法往往是通过＂定义一引理一证明一定理一证明一推论＂这种复杂的、程序化方法来进行训练的.由于在初等代数课程中,学生很少接受严格数学证明的训练,所以这种俗套的做法成效甚微.相反,如果把线性代数的主题和概念用一种完全合理的探究式方法来引入,那么数学证明的概念和架构将牢固植根于学生的头脑,并且这种思维习惯将对他们后续课程的学习和掌握公理化推理方法都会有很大帮助.

For teaching the ＂Linear Algebra＂ courses successfully,by the classroom teaching,we should let students to understand the related mathematical knowledge;to train and develop students the ability of thinking and mathematics exchange;to help students find the internal link between the new and old knowledge,enable knowledge systematization;to consolidate existing knowledge and let students discover new knowledge.The goal for this teaching,training students to grasp ＂mathematical proof concepts and applications in practice is important.This is done badly with a sophisticated Definition-LemmaProof -Theorem-Proof-Corollary approach;badly since students in Linear Algebra courses have very little experience with proofs and mathematical rigor.Instead,the subjects and concepts of Linear Algebra can be introduced in an exploratory and fundamentally reasoned way,the concept and construct of a ＂math proof becomes firmly embedded in the students＇ minds and helps with future math courses and general scientific reasoning.