人工智能赋能线性代数课程教学研究

AI-Empowered Teaching Research on Linear Algebra Courses

摘要: 针对线性代数传统灌输式教学模式存在的问题，如理论脱离实际、学生学习积极性不高、考核方式单一等，本文提出一种人工智能赋能的三阶融合教学模式。该模式将教学过程划分为课前、课中、课后三个阶段，分别发挥人工智能在学情诊断与个性化预习、交互探究与实时反馈、巩固内化与过程评价中的差异化辅助功能。借助超星学习通智慧教学平台的数据管理能力，大语言模型(LLM)的智能问答与代码生成能力，实现精准学情分析、课堂即时干预、作业智能批改与分层练习推送，并构建覆盖学习全周期的过程性评价体系。该模式有助于将抽象的线性代数知识转化为可视化的认知体验，提升学生的学习主动性与应用能力，为理工科数学课程的智能化改革提供了可操作的实施路径。

Abstract: In response to the problems existing in the traditional lecture-based teaching model of linear algebra, such as theory being disconnected from practice, low student motivation, and a single assessment method, this paper proposes an AI-empowered three-stage integrated teaching model. This model divides the teaching process into three stages: pre-class, in-class, and post-class, in which artificial intelligence plays differentiated supporting roles in learning diagnosis and personalized preview, interactive inquiry and real-time feedback, and consolidation and internalization and process evaluation, respectively. With the help of the data management capabilities of the Chaoxing Learning Platform smart teaching platform and the intelligent question-answering and code-generation capabilities of large language models (LLMs), it achieves precise learning analysis, immediate classroom intervention, intelligent homework grading, and tiered practice push. It also builds a process-oriented evaluation system covering the entire learning cycle. This model helps transform abstract linear algebra knowledge into visualized cognitive experiences, enhances students’ learning initiative and application ability, and provides an actionable implementation path for the intelligent reform of mathematics courses in science and engineering.