工程化导向下土建类线性代数课程教学改革探索

Exploration on Engineering-Oriented Teaching Reform of Linear Algebra for Civil Engineering Majors

摘要: 新工科建设背景下，土建类专业对学生数学基础、工程建模能力与数字化分析能力提出了复合性要求。线性代数课程中的矩阵、向量、线性方程组、特征值与最小二乘法等核心内容，不应局限于符号演算与手算训练，而应转化为学生理解结构计算、空间定位、工程数据处理与工程决策的基础工具。针对当前土建类线性代数教学中存在的内容学科化倾向突出、工程背景弱化、计算工具应用不足以及评价方式单一等问题，文章提出工程化导向的课程教学改革框架。该框架以土建工程典型问题为牵引，以矩阵和向量为知识主线，以计算工具为技术支撑，以专业衔接为培养出口，构建“结构矩阵基础、空间几何变换、工程数据求解”三模块递进式内容体系，并设计“问题导入–数学抽象–软件赋能–工程反思”四步课堂教学法。通过桁架内力计算、构件坐标转换、沉降观测数据拟合等典型案例，实现数学知识传授、工程应用能力培养、职业责任塑造与价值引领的有机融合。同时，文章加入准实验验证方案、实施挑战与应对策略及附录化教学设计样例，明确该框架仍需通过实验班–对照班比较、学习过程数据和质性反馈持续检验，以增强改革结论的证据支撑和可复制性。

Abstract: Under the background of emerging engineering education, civil engineering majors are required to have comprehensive abilities in mathematical foundation, engineering modeling and digital analysis. The core contents of linear algebra, including matrices, vectors, systems of linear equations, eigenvalues and the least-squares method, should not be limited to symbolic manipulation and manual calculation. Instead, they should be transformed into fundamental tools for students to understand structural computation, spatial positioning, engineering data processing and decision-making. In view of the prominent problems in current teaching, such as discipline-centered content, weak engineering context, insufficient application of computational tools and single assessment method, this paper proposes an engineering-oriented teaching reform framework for linear algebra courses. Guided by typical civil engineering problems, organized by matrices and vectors, supported by computational tools and oriented toward professional connection, the framework constructs a progressive three-module content system consisting of “structural matrix foundation, spatial geometric transformation and engineering data solution”, and designs a four-step classroom teaching method of “problem introduction-mathematical abstraction-software empowerment-engineering reflection”. Through typical cases such as truss internal force calculation, component coordinate transformation and settlement observation data fitting, the organic integration of mathematical knowledge teaching, engineering application ability training, professional responsibility shaping and value guidance is realized. In addition, this paper supplements a quasi-experimental verification design, an analysis of implementation challenges and countermeasures, and an appendix-based teaching design example, emphasizing that the framework should be continuously examined through comparisons between experimental and control classes, learning-process data and qualitative feedback.