高等数学中微积分教学优化与实践研究

Optimization and Practical Research on Calculus Teaching in Higher Mathematics

摘要: 微积分作为高等数学的核心内容，是理工科学生后续专业学习的重要基础。然而，传统微积分教学存在概念抽象化、理论与应用脱节、学生学习主动性不足等问题，导致教学效果不佳。本文结合教学实践，从教学内容重构、教学方法创新、实践教学强化三个维度提出优化策略：通过“问题驱动”重构知识体系，弱化抽象概念的理解难度；引入“案例教学”和“多媒体互动”提升课堂参与度；设计分层实践任务实现理论与应用的衔接。最后，通过教学实验验证优化策略的有效性，结果表明，该策略能显著提高学生的微积分成绩及问题解决能力，为高等数学教学改革提供参考。

Abstract: As the core content of Higher Mathematics, Calculus serves as a crucial foundation for science and engineering students in their subsequent professional studies. However, traditional Calculus teaching has problems such as abstract concepts, disconnection between theory and application, and insufficient learning initiative of students, which lead to poor teaching effects. Combining teaching practice, this paper proposes optimization strategies from three dimensions: reconstruction of teaching content, innovation of teaching methods, and strengthening of practical teaching. Specifically, it reconstructs the knowledge system through “problem-driven” approach to reduce the difficulty of understanding abstract concepts; introduces “case teaching” and “multimedia interaction” to improve classroom participation; and designs hierarchical practical tasks to connect theory with application. Finally, the effectiveness of the optimization strategies is verified through teaching experiments. The results show that these strategies can significantly improve students’ Calculus scores and problem-solving abilities, providing a reference for the teaching reform of Higher Mathematics.