思维导图在高等数学课程教学中的作用探究——以微分中值定理为例

Exploration of the Role of Mind Maps in Advanced Mathematics Curriculum Teaching—Taking the Differential Mean Value Theorem as an Example

摘要: 高等数学是理工科专业的一门基础必修课，微分中值定理是其核心内容之一。微分中值定理涉及罗尔定理、拉格朗日中值定理、柯西中值定理等多个定理，各定理之间既有联系又有区别，逻辑结构复杂。本文分析了微分中值定理的教学现状，探究和构建了微分中值定理思维导图，强调了思维导图的构建不仅能够增强知识的直观性，也能够引导学生主动思考。

Abstract: Advanced mathematics is a fundamental and compulsory course for science and engineering majors. The differential mean value theorem is one of its core contents, which involves multiple theorems such as Rolle’s theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem, etc. There are both connections and differences between the theorems, and the logical structure is complex. In this paper, we analyze the current teaching status of the differential mean value theorem, explore and construct a mind map of the differential mean value theorem. Also, we emphasize that the construction of a mind map can not only enhance the intuitiveness of knowledge, but also guide students to think actively.