线性代数课程思政案例式教学的探索与实践——以矩阵的初等变换与线性方程组为例

Exploration and Practice of Ideological and Political Case-Based Teaching in Linear Algebra Courses—A Case Study of Matrix Elementary Transformation and Systems of Linear Equations

摘要: 线性代数是高等院校理工科及经管类专业的重要数学基础课程，具有理论抽象、应用广泛的特点。传统的教学方式偏重于理论推导与计算训练，缺乏与实际问题的联系，导致学生理解困难、学习动力不足。本文结合课程思政理念与案例教学方法，围绕“矩阵的初等变换与线性方程组”这一核心内容，设计“家庭饮食营养规划”教学案例，将知识讲解、能力培养与价值引领有机结合，旨在提升学生的学习兴趣、数学建模能力与社会责任感，实现知识传授、能力培养与立德树人的统一。

Abstract: Linear Algebra is an important foundational mathematics course for science, engineering, economics, and management majors in higher education, characterized by abstract theories and wide applications. Traditional teaching methods focus heavily on theoretical derivation and computational practice, lacking connection with real‑world problems, which results in difficulties in understanding and insufficient learning motivation among students. By integrating the ideology and politics education philosophy with the case‑based teaching approach, this paper designs a teaching case titled Household Diet and Nutrition Planning around the core content of Elementary Matrix Transformations and Systems of Linear Equations. It organically combines knowledge instruction, ability cultivation, and value guidance, aiming to improve students’ learning interest, mathematical modeling ability, and sense of social responsibility, so as to achieve the unity of knowledge imparting, competence development, and moral education.