线性代数课堂渗透人文关怀的教学探究——以“逆矩阵”为例

Teaching Exploration of Infusing Humanistic Care into Linear Algebra Classroom—A Case Study of the “Inverse Matrix”

摘要: 当前，线性代数课堂在知识传授过程中普遍缺少人文关怀。由此，学生对本课程的理解仅局限于抽象公式与复杂计算方法层面。为弥补这一短板，本文深入剖析线性代数教学中逆矩阵相关人文渗透的核心切入点，并构建融合人文关怀的案例教学模式。依据矩阵元素排布规律以及线性方程组系数设定规则，将计算结果与特定情感表达相关联。把密码破译、路径探寻的全过程置于“解锁浪漫密码”教学情境之中，巧妙融合数学知识与浪漫美学。这一创新教学模式既能有效激发学生的学习主动性，又能引导学生在审美体验中深化对知识点的理解。该模式可显著提升线性代数课程的人文关怀效果，为本学科人文教学的长效发展与持续优化筑牢根基。

Abstract: Currently, linear algebra classrooms generally lack humanistic care in the process of knowledge delivery. As a result, students’ understanding of this course is often confined to the level of abstract formulas and complex computational methods. To remedy this deficiency, this paper deeply analyzes the core entry points for humanistic penetration related to inverse matrices in linear algebra teaching, and constructs a case-based teaching model that integrates humanistic care. By following the arrangement rules of matrix elements and the coefficient-setting rules of linear systems, the computed results are associated with specific emotional expressions. The entire process of code decryption and path exploration is placed within the teaching context of “unlocking romantic ciphers,” skillfully blending mathematical knowledge with romantic aesthetics. This innovative teaching model not only effectively stimulates students’ learning initiative but also guides them to deepen their understanding of knowledge points through aesthetic experience. The model can significantly enhance the humanistic care effect of the linear algebra course, thereby laying a solid foundation for the long-term development and continuous optimization of humanistic teaching in this discipline.