反例在微积分教学中的作用

The Role of Counterexamples in Calculus Teaching

反例在微积分的教学中有着重要意义,通过列举反例可以有效加深学生对数学概念、公式、定理的正确理解和应用,构造反例是一种创造性的学习,对培养学生具有较好的数学素养和创新思维能力具有不可替代的作用,本文结合微积分学的教学实践,归纳了反例在微积分教学中的具体应用方法,探讨了构造反例的途径.

Counterexamples play an important part in teaching.Students' correct understanding and application of mathematics concepts,formulas and theorem can be deepened effectively through counterexamples.Making counterexamples is a kind of creative study and it has an irreplaceable influence for cultivating a better mathematical literacy and creative thinking ability.Combined with the teaching practice of calculus,the specific application of counterexamples in calculus teaching was induced,approaches to make a counterexample was discussed.