反例在数学教学中的作用与构造分析

The Application of Counterexamples in Mathematics and Its Structural Analysis

举反例是数学中一种重要思维方式,反例在数学中有很多作用,一个数学真命题的确定往往需要严密的证明,而对假命题的判定如用反例来说明则显得容易理解。文章通过具体的例子阐述了反例在数学教学中作用的体现,构造分析简单例子,总结归纳出反例构造的方法,为数学解题以及实际数学教学提供参考价值。

Giving counter-examples in mathematics is an important way of thinking,counter-examples have many roles in mathematics,as a mathematical proposition true determination often requires strict proof of the proposition,and false counter-examples cited to illustrate it are easier to understand.This paper,through specific examples of counter-examples on the role of mathematics teaching in the embodiment of a simple example of structural analysis,summarized the structure of counter-examples approach,problem-solving in mathematics and mathematics teaching in the course of the actual reference value.