从学术形态走向教育形态:线面积分教学之分析

From Academic Form to Educational Form: A Teaching Analysis of the Curved Line Integration and the Curved Surface Integration

从宏观层面对教育形态的高等数学提出了四点认识;以此为逻辑起点,就学生学习线面积分时所产生的问题根源做了分析;从微观角度对线面积分中包含的教育形态的内容进行了挖掘;对线面积分的具体教学提出了五条建议:统一各种积分的历史背景,区别各类积分的符号标记,建立各类积分的一般算法,探讨各类积分的特殊算法,展示各种积分的实际应用.

This article puts forward four points of macroscopically higher mathematics of educational form.Based on this logical starting point,it analyzes the root causes of the problems caused by students’learning the curved line integration and the curved surface integration.Then,it explores the content of educational form included in the curved line integration and the curved surface integration from the microscopic point of view.Five suggestions are put forward for its specific teaching:concerning all kinds of integrations,to unify the historical background,distinguish the symbolic marks,establish and explore the general and particular algorithms,and show their practical application.