人工智能在高等代数教学中的有效使用

Effective Use of AI in the Teaching of Advanced Algebra

摘要: 随着人工智能技术的迅猛发展，其在教育领域的应用日益广泛。高等代数作为大学数学专业的基础核心课程，具有高度的抽象性、严密的逻辑性和广泛的应用性，传统教学模式面临教学内容陈旧、教学方法单一、学生学习兴趣不足等挑战。本文立足当前高等代数教学实践，系统探讨了AI技术在高等代数教学中的应用路径与有效策略。文章首先分析了高等代数课程的教学现状与面临的困境，继而以APOS理论为认知分析线索，从智能辅导、自适应学习、可视化教学、自动评测等多个维度阐述了AI技术对学生概念认知建构各阶段的支持作用；在此基础上，通过教学案例展示了AI辅助教学在提升学生理解深度、激发学习兴趣和培养数学思维方面的实践效果。研究进一步讨论了AI赋能教学的优势与潜在局限，并提出了构建人机协同教学模式、优化课程内容与评价体系、提升教师数字素养等改革建议，以期为高等代数教学改革和高校数学教育数字化转型提供理论参考与实践借鉴。

Abstract: With the rapid advancement of artificial intelligence technology, its applications in the field of education have become increasingly widespread. As a fundamental core course for mathematics majors in universities, Advanced Algebra features high abstraction, rigorous logic and extensive applicability. Traditional teaching modes are confronted with challenges such as outdated teaching content, monotonous teaching methods and insufficient learning motivation among students. Based on current teaching practices of Advanced Algebra, this paper systematically explores the application approaches and effective strategies of AI technology in Advanced Algebra instruction. It first analyzes the teaching status and dilemmas of the Advanced Algebra cand then, taking the APOS (Action-Process-Object-Schema) theory as the cognitive thread, elaborates on specific application scenarios of AI technology across multiple dimensions including intelligent tutoring, adaptive learning, visual teaching and automated assessment, and how these applications support students’ cognitive construction at different stages of concept formationessment. On this basis, teaching cases are presented to demonstrate the practical effects of AI-assisted teaching in deepening students’ comprehension, stimulating their learning interest and cultivating mathematical thinking. The study further discusses the advantages and potential limitations of AI-empowered teaching, and puts forward reform proposals such as constructing a human-AI collaborative teaching model, optimizing curriculum content and evaluation systems, and improving teachers’ digital literacy. It aims to provide theoretical references and practical experience for the teaching reform of Advanced Algebra and the digital transformation of university mathematics education.