AI赋能高等数学课程创新教学模式的探索与实践

Exploration and Practice of Innovative Teaching Modes for Advanced Mathematics Courses Empowered by AI

摘要: 高等数学作为高等院校理工科与经管类专业的核心基础课程，具有理论抽象、逻辑严密、应用范围广等特点，既是培养学生理性思维、数学素养的关键载体，也是学生学习后续专业课程的重要支撑。传统教学模式以教师讲授为主，存在着学情把握不准、因材施教不足、抽象概念理解困难、答疑反馈滞后、理论与专业应用脱节等问题。人工智能(AI)技术凭借大数据分析、智能诊断、自适应学习、动态可视化、智能交互与智能批改等优势，为高等数学教学改革提供了重要支撑。本文在现代信息技术及AI技术条件下，充分利用我校泛雅网络教学平台，针对我校工科学生开展高等数学教学改革试验，旨在探索并构建高等数学教育的新模式，构建了“AI + 翻转课堂 + 探究式 + 分层教学 + 案例建模 + 混合式”六位一体创新教学模式，围绕课前、课中、课后形成智能化教学闭环，并以重积分、曲线曲面积分、无穷级数三大难点内容为载体开展教学实践设计，提出实施路径与保障措施，为提升高等数学教学质量、激发学生学习主动性、培养学生数学核心素养与创新能力提供参考。

Abstract: As a core foundational course for science, engineering, economics and management majors in institutions of higher education, Advanced Mathematics is characterized by abstract theories, rigorous logic and extensive applications. It serves not only as a crucial vehicle for cultivating students’ rational thinking and mathematical literacy, but also as an essential prerequisite for students to learn subsequent specialized courses. The conventional teaching model, which centers on teacher lecturing, is plagued by drawbacks including inadequate understanding of students’ learning status, insufficient individualized instruction, difficulties in comprehending abstract concepts, delayed Q&A feed-back, and disconnection between theoretical knowledge and professional applications. Leveraging strengths such as big data analytics, intelligent diagnosis, adaptive learning, dynamic visualization, intelligent interaction and automated grading, artificial intelligence (AI) technology provides vital support for the pedagogical reform of Advanced Mathematics. Against the backdrop of modern information technology and AI, this paper makes full use of the Fan-ya online teaching platform of our university to carry out a pedagogical reform experiment of Advanced Mathematics targeting engineering students at our institution. It aims to explore and establish an innovative educational model for Advanced Mathematics. A six-in-one innovative teaching model integrating “AI + Flipped Classroom + Inquiry-Based Learning + Layered Teaching + Case Modeling + Blended Learning” is constructed, forming an intelligent closed-loop teaching system covering pre-class, in-class and post-class stages. Taking three difficult topics—multiple integrals, line and surface integrals, and infinite series—as the carriers, this paper designs relevant teaching practices, and proposes implementation approaches and supporting measures. It can serve as a reference for improving the teaching quality of Advanced Mathematics, stimulating students’ learning initiative, and fostering students’ core mathematical literacy and innovative capabilities.