从积分上限函数的学习看工科高等数学抽象概念的教学方法

On Advanced Mathematics Teaching Based on the Experience of Accumulation Function Learning

针对高等数学中抽象概念的教学难题,以积分上限函数的学习为例,探讨并提出一种有效降低数学抽象层次的教学方法.该方法的主要思想是以具体对象替代抽象对象,以具体过程重现抽象理论和事实,以计算机辅助工具实现、验证并应用重要的理论和方法.所提出的教学方法以传统方法为主、诱导式方法为辅,促进了学生的学习主动性,增强了学生对抽象知识的理解程度.

The Abstraction of mathematics is one of the major obstacles in advanced mathematics education.The key tasks of undergraduate mathematics education focus on helping students reduce the Abstraction of important concepts,theorems,and approaches,building and improving the capabilities of thinking Abstractly,and learning how to apply mathematical knowledge in the real world.This paper presents an effective approach for reducing the Abstraction levels in advanced mathematics teaching for engineering students based on the discussion of teaching method for the accumulation function.The main idea of the approach is about substituting Abstract objects with concrete objects,designing concrete procedures that reproduce Abstract theorems and facts,and utilizing computer tools to realize,validate and apply important theorems and methods.Combining the methods of traditional teaching with inductive teaching,the proposed methodology can motivate students to learn actively and improve the understanding on Abstract knowledge.