关键词: 高数教学创新, 大模型, 知识图谱, 学生小讲堂, 教学实践, 师生共创

Abstract: This article proposes an innovative teaching model of“AI + knowledge graph”to address the long-standing problems of knowledge fragmentation, passive learning of students, and disconnection between theory and practice in the teaching of advanced mathematics courses in science and engineering in universities. Build a cross chapter AI knowledge network based on a large model, and use the generated mind maps and knowledge graphs to strengthen the relationships between various knowledge points; Through the dormitory group system of student lecture halls, effectively stimulate students'initiative in classroom and collaborative exploration; Integrate high-quality real-life exercises to enhance students'ability to apply abstract theories to solve practical engineering problems. The practical results show that the winning rate of math competitions in teaching classes has increased from 26% to 40%, and the proportion of high scoring students in final grades has increased from 13% to 31.3%. This model not only solves the structural dilemma of higher mathematics teaching, but also provides a replicable technical path and organizational paradigm for the reform of basic courses in science and engineering, and has broad promotion value.

Key words: Innovation in high mathematics teaching, Large model, Knowledge graph, Student lecture hall, Teaching practice, Co creation between teachers and students