泛函分析中定理教学的改革尝试

Reform Tries at Teaching and Learning of Theorems in Functional Analysis

泛函分析中的定理可分为3类:内容和证法都重要的定理,重要定理的引理、推论及过渡性质、例题性质的定理,重要定理的明显的等价性定理和枝叶性定理.泛函分析的教学过程应包含6个环节:指导预习,复习引入,形成假说,校正推证,反思回顾,复习巩固.

By the example of the teaching and learning of Hahn-Banach theorems, combining teaching reality and the research achievement concerned modern education theory, this paper introduced the reform tries at teaching method of theorems in functional analysis, put forward three categories of the theorems and six links in the course of the theorems teaching in this curriculum, guiding preparing lessons before class, review and introduction, forming hypotheses, rectifying and reasoning, retrospect, review and consolidation.