分类教学视域下的高等数学教学改革探索——基于“方向导数与梯度”教学案例的实践分析

Exploration of Advanced Mathematics Teaching Reform from the Perspective of Classified Teaching—A Practical Analysis Based on the Teaching Case of “Directional Derivatives and Gradient”

摘要: 当前高等数学教学存在教学内容与专业需求错位、重知识传授轻实践能力培养的突出问题。为此，本文提出“以分类教学为途径、以能力培养为目标”的教学改革框架。该框架从专业分类与目标差异、模块重构与知能融合、任务驱动与学用贯通三个维度展开设计。研究以计算机类专业为对象，以“方向导数与梯度”章节为教学案例，设计了“情景导入–新知讲解–实践应用–总结提升”四环节教学过程，并构建了“过程性评价 + 终结性评价”相结合的多元评价体系。在此基础上，进一步讨论了电子信息类与自动化类等不同专业背景下的实施差异。实践表明，该改革方案能够有效提升学生的学习积极性、数学应用能力与专业实践能力，为高等数学课程分类教学改革提供了具有可操作性的实践路径。

Abstract: Higher mathematics instruction currently faces prominent problems, namely the misalignment between teaching content and professional needs and the overemphasis on knowledge transmission at the expense of practical ability cultivation. To address these issues, this paper proposes a teaching reform framework characterized by “classified teaching as the approach and competency cultivation as the goal.” This framework is designed along the following three dimensions: professional classification and objective differentiation, module restructuring and knowledge-competency integration, and task-driven learning-application articulation. Taking computer science majors as the research subject and the “Directional Derivative and Gradient” section as the teaching case, this study designs a four-stage instructional process, i.e. “scenario introduction, new knowledge instruction, practical application and summary and enhancement” and constructs a diversified evaluation system that combines process-oriented assessment with summative assessment. On this basis, the study further discusses the implementation differences across different professional backgrounds, such as electronic information engineering and automation. Practical results demonstrate that the proposed reform scheme can effectively enhance students’ learning motivation, mathematical application ability and professional practical competence, thereby providing an actionable pathway for the classified teaching reform of higher mathematics courses.