高校名师慕课获奖作品解构与线下教学融合的数学建模教学实践研究

Research on Practical Teaching of Mathematical Modeling Integrating Deconstruction of Award-Winning Works in Famous Teachers’ MOOCs with Offline Teaching

摘要: 数学建模竞赛的获奖作品，通常能直观反映出学生的综合应用能力、逻辑思维水平与创新意识。但在目前高校的数学建模教学里，慕课资源大多停留在知识讲解、步骤演示和公式推导上，线下课堂又常常把重点放在模型教学、算法套用和结果计算上，很少真正去拆解获奖作品背后的思考过程、决策逻辑和试错经验。这就导致很多学生出现“看得懂答案，自己不会做”的尴尬情况。针对这一普遍存在的教学痛点，本文提出一种线上线下深度融合的数学建模教学方式，把名师慕课中对全国大学生数学建模竞赛一等奖作品的详细解构作为核心学习材料，再与线下课堂的过程性指导、错误分析、实时干预相结合，实现线上资源与线下教学在认知层面的互补与联动。文章构建了“拆解–重构–干预”三段式教学模型，希望打通学生从“看懂别人怎么做”到“自己会建模、能解题”之间的壁垒，为数学建模课程改革提供更实用、更接地气、更容易落地的思路。

Abstract: Award-winning works in mathematical modeling competitions can usually directly reflect students’ comprehensive application ability, logical thinking level and innovative awareness. However, in current college mathematical modeling teaching, MOOC resources mostly focus on knowledge explanation, step demonstration and formula derivation, while offline classrooms often emphasize model teaching, algorithm application and result calculation, rarely deconstructing the thinking process, decision-making logic and trial-and-error experience behind award-winning works. This leads to the common problem that students can understand the answers but cannot solve problems independently. Aiming at this widespread teaching pain point, this paper proposes an online-offline deeply integrated teaching method for mathematical modeling. Taking the detailed deconstruction of first-prize works in the National College Students’ Mathematical Modeling Competition in famous teachers’ MOOCs as the core learning material, combined with procedural guidance, error analysis and real-time intervention in offline classrooms, it realizes cognitive complementarity and linkage between online resources and offline teaching. This paper constructs a three-stage teaching model of “deconstruction-reconstruction-intervention”, hoping to break the barrier for students from “understanding how others do it” to “modeling and solving problems independently”, and provide more practical, down-to-earth and feasible ideas for the reform of mathematical modeling courses.