数学分析课程与人工智能技术深度融合的教学

Mathematics Analysis Instruction with Deep Integration of Artificial Intelligence Technologies

摘要: 数学分析作为数学学科的核心基础课程，其抽象性、逻辑严密性及计算复杂性对教与学均构成持续挑战。本文旨在探索人工智能技术在数学分析教学中的融合应用，提出一个包含“知识图谱重构认知路径、智能交互辅助教学过程、数据驱动优化评价方式”的整合框架。通过构建学科知识图谱、开发智能教学助手、设计自适应学习系统以及尝试人机协同评价机制等路径，本研究尝试推动教学模式由传统“传授–接受”向更具交互性的“探究–建构–协同”方向探索。本工作提供了一套初步的融合路径与实践案例，旨在探讨其对学生数学抽象思维、逻辑推理与问题解决能力可能产生的积极影响，并为数学基础课程在教学智能化方向的转型提供一种理论参考与实践尝试。

Abstract: As the core foundational course in mathematics, Mathematical Analysis presents persistent challenges to both teaching and learning due to its abstract nature, rigorous logic, and computational complexity. This paper aims to explore the integrated application of artificial intelligence technologies in the teaching of Mathematical Analysis and proposes a framework that encompasses “restructuring cognitive pathways through knowledge graphs, assisting the teaching process via intelligent interaction, and optimizing evaluation methods through data-driven approaches”. By constructing subject-specific knowledge graphs, developing intelligent teaching assistants, designing adaptive learning systems, and experimenting with human-machine collaborative evaluation mechanisms, this study seeks to promote a shift in teaching models from the traditional “transmission-acceptance” approach toward a more interactive “exploration-construction-collaboration” direction. This work provides a preliminary set of integration pathways and practical case studies, aiming to examine the potential positive impacts on students’ mathematical abstract thinking, logical reasoning, and problem-solving abilities, while offering theoretical reference and practical attempts for the intelligent transformation of foundational mathematics courses.