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本文试图举例说明反例在数学分析教学中的作用,很不成熟,敬请批评指正。 一、列举反例是数学概念教学的重要环节。 在数学概念的教学中,只有使学生不但知道适合概念的那些数学对象,而且了解不适合概念的一些数学对象,才能使学生对概念有真正的理解。例如在讲一致连续函数概念的时候,如果只从正面解释,学生是很难接受的,学生会错误认为在区间上连续的函数必一致连续,没有必要引入一致连续的概念,只有当学生掌握了在区间上连续而不一致连续的例子,才能使学生了解引入一致连续函数概念的必要,从而乐意探索和掌握一致连续函数概念的实质。
This article attempts to illustrate the role of counterexamples in mathematics analysis teaching. It is immature and please criticize and correct me. First, enumerating counterexamples is an important part of mathematics teaching. In the teaching of mathematical concepts, only students who know not only the mathematical objects suitable for the concept, but also some mathematical objects that are not suitable for the concepts can make students have a real understanding of the concepts. For example, when speaking about the concept of unanimous continuous function, if it is only explained from the front, the student is very difficult to accept. Students will mistakenly believe that the continuous function in the interval must be consistent and continuous, there is no need to introduce a consistent and continuous concept, only when the student masters the Consecutive and inconsistent examples on the interval can make students understand the necessity of introducing the concept of a consistent continuous function, so they are willing to explore and master the essence of the concept of a consistent continuous function.