AI时代下基于OBE理念的线性代数教学改革与实践

Teaching Reform and Practice of Linear Algebra Based on OBE Philosophy in the AI Era

摘要: 线性代数作为机械、自动化、电子等理工类以及财经、管理等经管类专业新生的核心基础课程，是后续专业课程学习的关键支撑。当前教学中存在教学内容碎片化、教学手段未适配数字时代、教学与科研脱节等问题，导致学生学习动力不足、应用能力薄弱。本文以OBE (成果导向教育)理念为指导，围绕“反向设计、正向实施”原则，从教学内容重构、AI融合、教研相长三个维度展开教学改革探索。基于同济大学版教材，对其教学内容进行重新组织，以矩阵为核心，构建“矩阵的基本运算–矩阵的初等变换–矩阵的特征分解”三大模块体系；整合雨课堂、超星学习通智能教学平台，构建AI赋能的全流程教学新模式；将科研成果(稀疏对应分析、基于Gram-Schmidt正交化的变量选择方法)融入教学，实现教研相长。

Abstract: As a core foundational course for freshmen majoring in science, engineering, economics and management disciplines including mechanical engineering, automation, electronic engineering, finance and business administration, linear algebra provides essential theoretical support for the subsequent learning of professional courses. However, the current teaching of linear algebra still suffers from fragmented teaching content, outdated teaching methods that fail to adapt to the digital era, and disconnection between teaching and scientific research, which consequently leads to students’ insufficient learning motivation and weak practical application abilities. Guided by the Outcomes-Based Education (OBE) philosophy and following the principle of “backward design and forward implementation”, this paper explores linear algebra teaching reform from three dimensions of teaching content restructuring, artificial intelligence (AI) integration, and the integration of teaching and research. Based on the textbook published by Tongji University, the teaching content is reorganized with matrices as the core, constructing a systematic teaching framework consisting of three major modules: basic matrix operations, elementary matrix transformations, and matrix eigen decomposition. By integrating intelligent teaching tools including Rain Classroom and Chaoxing Learning Platform, an AI-empowered full-process teaching model is established. Furthermore, scientific research achievements such as sparse correspondence analysis and Gram-Schmidt orthogonalization-based variable selection are introduced into classroom teaching, to realize the mutual promotion and coordinated development of teaching and scientific research.