高等数学“学思用”思维进阶的教学创新设计——以微分方程的概念及可分离变量方程为例

Innovative Teaching Design for Advanced Thinking of “Learning, Thinking, and Applying” in Higher Mathematics—Taking the Concept of Differential Equations and Separable Variable Equations as an Example

摘要: 以高等数学课程中的“微分方程的概念及可分离变量方程”内容为例，深入探究了以“学思用”数学思维进阶为主线的教学创新设计。对教学内容进行重构，融入思政元素，采用案例式教学，通过线上至线下、自学至互学、低阶至高阶、理论至应用的有机转化，有效提升学生高阶数学思维的培养。

Abstract: Taking “the concept of differential equations and separable variable equations” in advanced mathematics courses as an example, this study explores in depth the innovative design of teaching that focuses on the advancement of mathematical thinking through “learning, thinking, and application”. Refactoring the teaching content, incorporating ideological and political elements, adopting case-based teaching, and effectively enhancing the cultivation of students’ higher-order mathematical thinking through the organic transformation from online to offline, self-learning to mutual learning, low-level to high-level, and theory to application.