第一型线面积分的研究型教学方案探析

Case Analysis of Research Teaching about Line Integral and Surface Integral of Type One

高等数学研究型教学的本质就是在教学过程中创设一种类似于科学研究的情境和途径,指导学生自主发现问题、探究问题和获得结论的一种教学模式,而目前大量有关研究型教学的论文缺少具体的案例分析,本文以第一型的线面积分为例,以问题教学为原则,将教学过程分为课前预习,课堂教学,课后提升三个阶段,在每个阶段都以问题为主线,从新知识引入,例题讲解,计算技巧,课堂小结,课后提升各方面详细阐述了研究型教学的实施过程.

The essence of research teaching of higher mathematics is to create a situation similar to scientific research,namely,the students can question,explore and discuss the problem freely.So far,most of of relevant research teaching papers seldom focus on specific case analysis.In this paper,we give a specific case analysis about line integral with respect to arc length and surface integral of a scalar field.The teaching process is divided into preparation before class,classroom teaching,after class promotion three stages,in each stage,from the introduction of new knowledge to examples,from calculation skills to brief summary,we elaborated the research teaching implementation process in detail.