“三聚焦三重塑”驱动下线性代数教学与MWORKS软件融合的探索

Exploration on the Integration of Linear Algebra Teaching and MWORKS Software Driven by the “Three Focuses and Three Reshapings”

摘要: 线性代数是高等学校工科类本科教育的公共基础课，其抽象性与工具性的双重属性既支撑着后续专业课程的知识体系，也对学生逻辑思维、建模能力提出了高要求。当前线性代数教学普遍存在“重理论轻应用、重计算轻思维、重统一轻分层”的痛点，与新工科背景下“强基础、跨学科、能实践”的人才培养需求脱节。本文以“三聚焦三重塑”理念为核心，聚焦能力目标、内容体系、教学路径，重塑认知逻辑、教学方法、评价体系，引入国产科学计算软件MWORKS作为理论与应用的衔接工具，构建“理论阐释–软件实践–专业赋能”的线性代数教学新模式。本文的探索既为线性代数课程改革提供了有益的参考，也为数学基础课与国产工业软件的融合教学提供了实践范式。

Abstract: Linear algebra is a compulsory fundamental course for engineering undergraduate education in universities. Its dual attributes of abstraction and instrumentality not only support the knowledge system of subsequent professional courses, but also place high demands on students’ logical thinking and modeling abilities. Current linear algebra teaching generally suffers from such problems as “emphasizing theory over application, calculation over thinking, and uniformity over stratification”, which is disconnected with the demand for cultivating talents with “solid foundation, interdisciplinary competence and practical ability” under the background of Emerging Engineering Education. Centered on the concept of “Three Focuses and Three Reshapings”, this paper focuses on competency objectives, content system and teaching path, reshapes cognitive logic, teaching methods and evaluation system. By introducing MWORKS, a domestic scientific computing software, as a bridge between theory and application, a new teaching mode of linear algebra is constructed, which integrates “theoretical interpretation, software practice and professional empowerment”. The exploration in this paper not only provides a useful reference for the reform of linear algebra courses, but also offers a practical paradigm for the integrated teaching of basic mathematics courses and domestic industrial software.