基于课程群的数学与应用数学专业基础课程改革研究

Research on the Reform of Basic Courses of Mathematics and Applied Mathematics Based on Curriculum Group

摘要: 数学分析、高等代数、解析几何作为数学与应用数学专业的三门核心基础课程，长期存在孤岛式教学格局，导致学生认知结构碎片化、知识迁移能力薄弱、学习动机持续衰减。本文以课程群建设理论为统领，融合布鲁姆教育目标分类学、皮亚杰发生认识论与布鲁纳学科结构理论，构建三维融合课程群模型，从纵向认知深度、横向知识广度与智能技术密度三个维度系统推进教学改革。研究提出以桥接概念为支点进行跨课程内容重构，以认知发展阶段适配为原则设计差异化教学过程，以人机协同为路径实现AI赋能的精准教学。实践表明，该模式在提升学生学业成绩、知识迁移能力与数学统一观方面具有显著成效，为数学专业基础课程群建设提供了可复用的理论框架与实践方案。

Abstract: As three core foundational courses in the mathematics and applied mathematics major, mathematical analysis, advanced algebra, and analytic geometry have long been taught in isolation, resulting in fragmented cognitive structures, weak knowledge transfer abilities, and a sustained decline in students’ learning motivation. Guided by curriculum cluster theory and informed by Bloom’s taxonomy of educational objectives, Piaget’s genetic epistemology, and Bruner’s theory of the structure of disciplines, this study proposes a three-dimensional integrated curriculum cluster model. The model promotes systematic instructional reform along three dimensions: vertical cognitive depth, horizontal knowledge breadth, and intelligent technology integration. Specifically, it reconstructs cross-course content around bridging concepts, designs differentiated instructional processes according to students’ cognitive developmental stages, and implements AI-enabled precision teaching through a human-AI collaborative approach. Empirical practice demonstrates that the proposed model significantly enhances students’ academic performance, knowledge transfer abilities, and understanding of the unity of mathematics. The findings provide a reusable theoretical framework and practical implementation pathway for the development of foundational curriculum clusters in mathematics education.