生成式人工智能视域下高校公共数学课程优化设计及教学实践路径探索

Exploration on Optimal Design and Teaching Practice Path of College Public Mathematics Curriculum from the Perspective of AIGC

摘要: 公共数学是高校面向非数学专业开设的通识必修课程，承担着培育学生数理逻辑、定量思维以及运用数学工具解决专业实际问题的育人使命。大班化授课、学生数学基础分化、教学案例与专业场景脱节、个性化辅导资源供给有限等问题长期制约公共数学课堂教学质量的提升。生成式人工智能(AIGC)技术的兴起，为公共数学课程教学改革带来了新的契机。作为一种新型教学辅助工具，AIGC在学情诊断、案例生成、交互式答疑、分层学习资源供给等方面具备显著优势，但同时也存在生成内容推理失真、学生产生思维惰性、教师数字教学能力不足等现实风险。本文结合建构主义、维果茨基最近发展区理论、认知负荷理论等教育学心理学理论，剖析AIGC介入公共数学教学的内在作用机理，从课程目标优化、教学内容重构、课堂流程再造、多元评价革新四个维度完善AIGC融入公共数学课堂的教学设计思路，构建课前课中课后一体化的人机协同实施路径，补充单元教学案例与评价量规，提出对应的风险防控策略，以期为高校公共数学教学创新提供可参考的教研方案。

Abstract: Public mathematics is a compulsory general-education course offered by universities for non-mathematics majors. It undertakes the educational mission of fostering students’ mathematical-logical thinking, quantitative thinking, and their ability to apply mathematical tools to solve practical professional problems. For a long time, the improvement of classroom teaching quality of public mathematics has been restricted by such problems as large-class teaching, diversified students’ mathematical foundations, disconnection between teaching cases and professional scenarios, and insufficient supply of personalized tutoring resources. The rise of Artificial Intelligence Generated Content (AIGC) brings new opportunities for the teaching reform of public mathematics courses. As a new-type teaching assistant tool, AIGC shows remarkable advantages in learning-situation diagnosis, case generation, interactive Q&A, and provision of differentiated learning resources. Nevertheless, it also involves practical risks including distorted reasoning in generated outputs, students’ intellectual inertia, and teachers’ insufficient digital teaching competence. Combining pedagogical and psychological theories such as constructivism, Vygotsky’s Zone of Proximal Development, and cognitive load theory, this paper analyzes the internal mechanism of AIGC applied in public mathematics teaching. It improves the instructional design for integrating AIGC into public mathematics classrooms from four dimensions: optimizing curriculum objectives, reconstructing teaching content, redesigning classroom procedures, and innovating multi-dimensional evaluation. This study constructs an integrated human-AI collaborative implementation path covering pre-class, in-class and after-class stages, supplements unit-teaching cases and assessment rubrics, and puts forward corresponding risk-prevention and control strategies. It aims to provide referable research-based schemes for teaching innovation of public mathematics in higher education.