基于《数学分析》课程的人机协同混合教学模式的探索与实践

Exploration and Practice of a Human-Computer Collaborative Blended Teaching Model Based on the “Mathematical Analysis” Course

摘要: 《数学分析》作为数学类专业的核心基础课程，长期面临教学方法单一、“上课听懂、下课不会做”的困境，而生成式AI技术的快速发展为人机协同教学提供了新的可能。本文在“师–机–生”三元教学模式基础上，构建了“教师主导设计–AI智能体多维辅助–学生个体深度建构–小老师反转教学”的协同课堂生态。并结合导数概念的课程教学内容，设计了“课前智能诊断–课中协同建构–课后精准巩固”的三阶段教学闭环，阐述了AI智能体的创设与使用、动态几何演示、实时测试干预、小组探究展示等教学环节的具体实施方法。同时，本文探讨了该模式对师范生的工具应用能力、协同设计能力以及创新引领能力的提升作用，并对过度依赖、算法偏见和公平性三大潜在风险提出了针对性的规避策略。该模式为人机协同在高等数学教育中的深度融合提供了可操作的实践范式，也为培养具备AI素养的未来数学教师创造了“做中学”的真实场域。

Abstract: Mathematical Analysis, as a core foundational course for mathematics majors, has long faced the problems of monotonous teaching methods and the common dilemma of “understanding in class but being unable to solve problems after class”. The rapid development of generative AI technology offers new possibilities for human-computer collaborative teaching. Based on the “teacher-AI-student” triadic teaching model, this paper constructs a collaborative classroom ecosystem characterized by “teacher-led design, multi-dimensional AI agent assistance, students’ individual deep construction, and ‘little teacher’ flipped teaching”. Taking the teaching of the derivative concept as an example, we design a three-stage teaching loop of “pre-class intelligent diagnosis, in-class collaborative construction, and post-class precise consolidation”. The paper elaborates on the specific implementation methods of AI agent creation and use, dynamic geometric demonstration, real-time test intervention, and group inquiry presentation. Furthermore, this paper discusses the model’s role in enhancing normal university students’ abilities in tool application, collaborative design, and innovative leadership. It also proposes targeted strategies to mitigate three potential risks: over-reliance, algorithmic bias, and fairness. This model provides an actionable practical paradigm for the deep integration of human-computer collaboration in higher mathematics education and creates an authentic “learning by doing” environment for cultivating future mathematics teachers equipped with AI literacy.