新工科背景下基于Python的《线性代数》教学模式探索与实践

Exploration and Practice of a Python-Based Teaching Model for “Linear Algebra” in the Context of Emerging Engineering Education

摘要: 针对新工科背景下线性代数教学中“重计算、轻思想”及传统教学模式与学生主体性脱节的问题，本文旨在探索一种与Python深度融合的教学模式，将Python从辅助工具重塑为认知媒介。方法：以四阶行列式和逆矩阵为核心案例，设计递推法、多行展开验证、过程演示、伴随矩阵法及高斯–约当消元法等多种算法实现；并在两个学期共297名大一学生中开展教学实践，采用混合式教学(理论28学时 + 编程实践4学时)，通过大作业、学生反思报告和课堂观察进行质性评估。结果：超过80%的学生能成功将Python方法迁移至新应用场景；学生反思表明编程显著加深了对行列式唯一性、逆矩阵代数构成等概念的理解；课堂提问从“如何笔算”转向“如何选最优算法”。结论：该模式能有效促进学生从机械计算到计算思维的转变，为Python融入线性代数教学提供了可操作的实践路径。

Abstract: To address the issues of “emphasizing computation over conceptual understanding” in linear algebra instruction and the disconnection between traditional teaching models and student-centered learning in the context of emerging engineering education, this paper aims to explore a teaching model deeply integrated with Python, repositioning Python from an auxiliary tool to a core cognitive medium. Methods: Taking fourth-order determinants and inverse matrices as typical cases, the study designs multiple algorithmic implementations, including recursive expansion, multi-row expansion verification, step-by-step process demonstration, adjugate matrix method, and Gauss-Jordan elimination. The model was implemented in two semesters involving 297 first-year students majoring in computer science and software engineering. A blended teaching approach (28 lecture hours + 4 Python practice hours) was adopted, and qualitative assessment was conducted through student projects, reflective reports, and classroom observations. Results: Over 80% of students successfully transferred the Python methods to new application scenarios. Student reflections revealed that programming significantly deepened their understanding of concepts such as the uniqueness of determinants and the algebraic structure of inverse matrices. Classroom questioning shifted from “how to compute manually” to “how to select optimal algorithms”. Conclusion: The proposed model effectively facilitates students’ transition from mechanical computation to computational thinking and from “tool usage” to “thinking construction”, providing a practical pathway for integrating Python into linear algebra teaching.