生成式人工智能背景下《MATLAB与数值计算》课程改革思考

Reflections on the Curriculum Reform of “MATLAB and Numerical Computation” in the Context of Generative Artificial Intelligence

摘要: 《MATLAB与数值计算》兼具数学理论、算法设计与程序实践属性。针对传统教学中数值方法原理、算法程序化表达和计算结果分析容易脱节，以及生成式人工智能(Artificial Intelligence, AI)可能带来的代码依赖问题，本文在保留经典数值计算知识体系和MATLAB实践主线不变的基础上，提出了相应的课程改革方案。具体而言，我们构建了数值思维、程序实现与AI协同三维课程目标，形成了“问题建模–算法分析–自主编程-AI辅助–结果验证–反思迁移”的人机协同教学闭环，并设计了基础训练、综合训练和开放探究相衔接的分层实验体系。教学中将AI定位为程序诊断、方案比较和学习反馈工具，通过实践引导学生理解算法、实现算法并验证结果，同时建立过程性评价和AI使用规范，为人工智能背景下数值计算类课程转型提供参考。

Abstract: “MATLAB and Numerical Computation” is a course that combines mathematical theory, algorithm design and programming practice. To address the common disconnection among the principles of numerical methods, the implementation of algorithmic programming and the analysis of computation in traditional teaching, along with the potential over-reliance on code generation brought by generative artificial intelligence (AI), this paper proposes a curriculum reform approach while preserving the established knowledge framework of numerical computation and the MATLAB-based practical approach. Specifically, we construct a three-dimensional course objective system encompassing numerical thinking, programming implementation, and AI collaboration, forming a human-machine collaborative teaching closed loop that follows the sequence of “problem modeling - algorithm analysis - independent programming - AI assistance - result validation - reflection and transfer” and design a tiered experimental system comprising foundational training, comprehensive training, and open-ended investigation. In teaching practice, AI is positioned as a tool for program diagnosis, solution comparison, and learning feedback, guiding students to understand algorithms, implement programs, and verify results through hands-on practice. Meanwhile, process-based evaluation and AI usage guideline are established. This reform offers a reference for the transformation of numerical computation courses in the context of AI.