Teaching Reform and Practice of Linear Algebra Based on the "Three Transformations and Six Dimensions" Progressive Model

Abstract

Linear Algebra serves as a crucial foundational course for economics and management majors in universities, where its abstract nature and complexity often pose challenges to student learning. To address the pain points of the course, we have proposed a "Three Transformations and Six Dimensions" Progressive model. This model integrates Linear Algebra with professional education and course education, using stratified and progressive teaching strategies to simplify teaching content, guide learning methods, and achieve effective teaching evaluation. Specific measures include reconstructing course content, building knowledge maps, integrating course ideology and politics, optimizing teaching models, strengthening practical innovation, and advancing a diversified evaluation system across six dimensions. Practice has demonstrated that this model effectively enhances teaching quality and markedly boosts students' mathematical literacy, logical thinking, and application capabilities. The questionnaires show that students have a relatively high level of satisfaction with the teaching methods, instructional tools and diversified assessment processes of this course. Statistical analysis of grades over the past three years indicates a significant increase in the proportion of students achieving excellent or good results in their final exams, along with a decrease in the failure rate. Students have been able to apply the knowledge of linear algebra in academic competitions and innovation and entrepreneurship practices, achieving remarkable success. Concurrently, the teaching outcomes are bountiful, with the course team's teachers winning the second prize in the provincial teaching innovation competition and the second prize in the provincial young teacher teaching competition. The MOOC and AI courses based on knowledge graphs have been adopted by over 600 universities in China, with more than 100,000 students using them. The demonstration and radiating promotion effects are quite good.