智能体技术赋能数学分析教学改革的实践探索——以WorkBuddy智能体平台为例

The Practical Exploration of Empowering the Teaching Reform of Mathematical Analysis with Agent Technology—A Case Study of the WorkBuddy Agent Platform

摘要: 数学分析是数学类专业最重要的基础课程之一，其理论抽象、逻辑严密，历来是教与学的难点。本文在系统梳理人工智能在数学教育中应用脉络的基础上，以WorkBuddy智能体平台为例，探讨智能体技术赋能数学分析教学改革的实践路径。文章首先给出该平台在数学符号处理与逻辑推理方面的能力分层：它能稳定完成公式排版、定义复述、常规证明套路与逐句解说，而在量词次序、构造性证明与一致性全局估计上则易出错；继而以“一致连续性”教学为例，呈现未经修饰的人机对话实录、智能体生成的分层习题与反馈原文，并逐项作出专业评析；再以一个含参变量反常积分的反面案例，完整展示智能体的出错过程，剖析其成因并提出教学警示。实践表明，智能体能够在保持教师主导地位的前提下承担资源整合、分层辅导、评价辅助等程序性工作，是推动数学分析课程数字化转型的一条可行路径，但其输出必须经教师专业审核方可进入课堂。

Abstract: Mathematical Analysis is one of the most essential foundational courses for mathematics majors. Featuring abstract theories and rigorous logic, it has long posed challenges for both teaching and learning. On the basis of systematically sorting out the development of artificial intelligence applications in mathematics education, this paper takes the WorkBuddy agent platform as an example to explore practical approaches for empowering the teaching reform of Mathematical Analysis with agent technology. First, this paper establishes a capability hierarchy of the platform concerning mathematical symbol processing and logical reasoning: the platform can reliably perform formula typesetting, restate definitions, follow standard proof templates, and provide sentence-by-sentence explanations. Nevertheless, it is prone to errors when dealing with quantifier order, constructive proofs, and uniform global estimates. Taking the teaching of “uniform continuity” as a case, we present unedited human-agent conversation transcripts, tiered exercises generated by the agent, and original feedback texts, together with item-by-item professional evaluations. A counterexample involving improper integrals with parameters is then used to fully demonstrate the agent’s error-making process, analyze its root causes, and raise corresponding pedagogical caveats. Practice shows that, while preserving the leading role of instructors, agents can undertake procedural tasks such as resource integration, differentiated tutoring, and assessment assistance, offering a viable pathway to advance the digital transformation of the Mathematical Analysis course. Still, all outputs generated by the agent must undergo professional review by teachers before being used in classroom instruction.