人工智能赋能下线性代数课堂学生学习体验的提升研究

AI-Empowered Improvement of Students’ Learning Experience in Linear Algebra Teaching

摘要: 线性代数是我国高校新工科建设背景下工科专业的核心公共基础课，是培养学生数学建模与工程应用能力的重要载体。当前国内该课程教学中，重理论轻应用、重计算轻思维、学生课堂参与度不足等问题仍普遍存在，难以适配创新人才培养需求。本研究将人工智能大语言模型融入线性代数课程教学，采用项目式学习与主动学习结合的模式，引导学生结合自身工科专业背景选取实际工程问题，运用线性代数知识建模，并借助人工智能工具完成模型求解、代码实现与结果分析。学生问卷调查结果显示，人工智能的融入显著提升了学生的学习兴趣与课堂参与度，有效培育了其跨学科应用能力和算法素养，同时助力学生建立起“数学理论–工程应用”的关联思维。本研究为人工智能赋能高等数学教学改革、适配新工科创新人才培养提供了实践参考。

Abstract: Linear algebra serves as a core foundational course for engineering majors in Emerging Engineering Education initiative, playing a vital role in cultivating students’ mathematical modeling and engineering application capabilities. Current teaching practices in this discipline still face challenges such as overemphasis on theory at the expense of practical application, prioritizing computation over critical thinking, and insufficient classroom engagement, which fail to meet the demands of innovative talent development. This study integrates large-scale AI language models into linear algebra instruction, adopting a project-based learning approach combined with active learning strategies. Students are guided to select practical engineering problems aligned with their engineering backgrounds, apply linear algebra knowledge for modeling, and utilize AI tools to solve problems, implement code, and analyze results. Survey results indicate that AI integration significantly enhances students’ learning interest and classroom participation, effectively develops their interdisciplinary application abilities and algorithmic literacy, while helping to establish their correlative thinking connecting mathematical theories with engineering practices. This research provides practical references for AI-powered reforms in advanced mathematics education and aligns with the innovative talent cultivation goals of Emerging Engineering Education.