数字化背景下《线性代数》课程教学改革与探究

The Teaching Reform and Exploration of the “Linear Algebra” Course in the Digital Era

摘要: 随着数字化教育技术的迅速发展，传统的线性代数教学面临着诸多挑战，尤其是如何提升学生的数学能力、培养跨学科的思维方式、以及有效地解决实际问题。本文针对线性代数课程教学中的三大“痛点”问题，即学生的理解深度不足、教学模式单一、学科之间缺乏有效关联，提出了基于数字化背景下的“三联”教学改革举措。具体包括创新教学模式、构建知识图谱、强化学科关联，优化课程考核，以达到“数学能力培养与思政文化渗透为核心、打通专业课程间关联性为连续、解决实际问题能力为拓展”的“三位一体”教学目标。通过对该改革方案的探讨与实施，结合教育心理学和跨学科教学理论，旨在为线性代数课程教学提供新的思路与方法，推动课程的内涵式发展，提升学生的综合素质。特别是在通过创新教学模式和多元化考核体系的基础上，充分激发学生的学习兴趣和跨学科思维能力，帮助学生更好地解决实际问题。

Abstract: With the rapid development of digital education technology, traditional linear algebra teaching faces numerous challenges, particularly in enhancing students’ mathematical abilities, cultivating interdisciplinary thinking, and effectively solving practical problems. This article addresses three major “pain points” in linear algebra course teaching: insufficient depth of student understanding, monotonous teaching modes, and a lack of effective interdisciplinary connections. It proposes “three-connection” teaching reform measures in the digital context. These include innovating teaching modes, constructing knowledge maps, strengthening interdisciplinary connections, and optimizing course assessments to achieve a “trinity” of teaching objectives centered on “cultivating mathematical abilities and ideological and political culture infiltration, establishing continuity among specialized courses, and expanding problem-solving abilities in practical situations.” By exploring and implementing this reform plan, combined with educational psychology and interdisciplinary teaching theories, the aim is to provide new ideas and methods for linear algebra course teaching, promote the connotative development of the course, and enhance students’ overall qualities. Especially through innovative teaching modes and a diversified assessment system, the plan fully stimulates students’ learning interest and interdisciplinary thinking abilities, helping them better solve practical problems.