工程案例、可视化技术与人工智能融合的高等数学教学实践

Integrating Engineering Cases, Visualization Technology, and Artificial Intelligence into Higher Mathematics Teaching Practice

摘要: 为解决高等数学传统教学中概念抽象、学用脱节所导致的学生认知难度大与学习动力不足的痛点，本文以定积分几何应用中的核心内容“旋转曲面的面积”为载体，进行教学模式的改革创新。在情境导入、方法构建环节，借助真实工程场景及参数、GeoGebra软件动图演示，有效解决学生工程建模弱、空间想象困难的问题，从而使学生深度内化微元法思想。在问题解决环节，通过对比分析人工智能工具与数学软件的计算结果，发现前者可以提供解决问题的方法，然而计算结果却未必可靠，据此引导学生合理使用人工智能、避免对人工智能产生盲从心理。

Abstract: To address the pain points of students’ high cognitive difficulty and insufficient learning motivation caused by abstract concepts and the disconnect between learning and application in traditional higher mathematics teaching, this paper takes the area of surfaces of revolution, a core topic in the geometric applications of definite integrals, as a vehicle for reforming and innovating the teaching model. In the stages of contextual introduction and method construction, real engineering scenarios with parameters and GeoGebra animation demonstrations are employed to effectively address students’ weaknesses in engineering modeling and difficulties in spatial imagination, thereby enabling students to deeply internalize the idea of the infinitesimal method. In the problem-solving stage, by comparatively analyzing the computational results of artificial intelligence tools and mathematical software, it is found that while the former can provide methods for solving problems, their computational results are not necessarily reliable. Accordingly, students are guided to use artificial intelligence rationally and avoid blind conformity to it.