专业导向下的线性代数分类教学实践

Profession-Oriented Classified Teaching Practice of Linear Algebra

摘要: 线性代数是理工科专业的重要公共基础课，但统一的教学内容、案例和节奏往往难以兼顾不同专业的应用需求与学生基础。本文以认知负荷理论为指导，面向电气自动化专业118名学生和高分子材料与工程专业120名学生，构建“基础统一、应用分化”的分类教学模式，分别融入电路与控制、实验数据处理与材料表征案例，并依托学习通采集预习、互动和作业等过程数据，将本届期末成绩与近三届同专业传统教学均值进行比较。结果显示，两专业作业完成率均超过90%；高分子专业平均分、及格率和应用题得分率分别提高5.7分、12.1个百分点和15.1个百分点，电气专业分别提高5.6分、11.4个百分点和17.7个百分点，纯计算题得分率基本稳定。研究表明，专业熟悉案例与差异化教学节奏有助于降低外在认知负荷，提升学习参与度和知识应用能力，可为公共数学基础课的差异化改革提供参考。

Abstract: Linear algebra is an important public basic course for science and engineering majors. However, unified teaching contents, cases and teaching rhythms can hardly satisfy the practical application demands of different majors as well as students’ varied academic foundations. Guided by cognitive load theory, this paper constructs a classified teaching mode featuring “unified fundamentals and differentiated applications” for 118 students majoring in electrical automation and 120 students majoring in polymer materials and engineering. Subject‑specific cases concerning circuit and control, experimental data processing and material characterization are integrated into teaching respectively. Process‑oriented data including preview performance, classroom interaction and homework completion are collected via the Xuexitong teaching platform. The final exam scores of students under this teaching practice are compared with the average scores obtained from traditional teaching over the previous three academic years for the same majors. The results show that the homework completion rates of both majors exceed 90%. For polymer materials and engineering major, the average score, pass rate and score rate of application questions rise by 5.7 points, 12.1 percentage points and 15.1 percentage points respectively. For electrical automation major, these indicators increase by 5.6 points, 11.4 percentage points and 17.7 percentage points correspondingly, while the score rate of pure computational questions remains generally stable. The research indicates that subject-familiar cases and differentiated teaching rhythms help reduce extraneous cognitive load, improve students’ learning engagement and their ability to apply knowledge, which can provide references for the differentiated reform of public basic mathematics courses.