微分概念的历史发展及教学启示

Historical Development of Differentiation and Its Teaching Enlightenment

微分的形式化定义是学生学习微分概念的主要困难.微分概念的历史发展表明,形式化的微分定义是微积分严格化的产物,朴素的微分定义更能体现微积分思想,而非标准分析给微分概念带来重生.在微积分学中应用非形式化的方法构建微分概念,以微分为主线(传统教材一般以导数为主线)进行微积分教学可以促进学生学习效果.

The formal definition of differentiation is the main difficulty for students to learn its concept. The historical development of the concept of differentiation shows that the formal definition of differentiation is a product of the strict Calculus, and the naive definition of differentiation can better embody the idea of Calculus. Non--standard analysis brings the differentiation to a new state. Using the informal differentiation concept as the main line in Calculus can promote students＇ learning effectiveness.