颜色方程类比下的空间向量基本定理教学探索

Teaching Exploration of the Fundamental Theorem of Spatial Vectors Based on the Analogy of Color Equations

摘要: 空间向量基本定理是高中立体几何的教学难点，传统的纯数学推导教学过于抽象，学生理解困难。本文基于跨学科融合思想，引入格拉斯曼光混合定律与颜色方程通过类比推理，将直观的颜色混合与抽象的向量概念关联，帮助学生从直观感知过渡到抽象理解深刻理解定理本质。同时设计了从实验到类比迁移最终进行数学建模的教学设计这贴合高中课堂的实操方案，体现了数学与科学的内在关联，培养学生核心素养与跨学科思维，为一线教学提供新思路。

Abstract: The Fundamental Theorem of Space Vectors is a difficult point in teaching solid geometry in high schools. The traditional pure mathematical derivation teaching is too abstract and difficult for students to understand. Based on the idea of interdisciplinary integration, this article introduces Grassmann’s light mixing law and color equation through analogy reasoning, associates intuitive color mixing with abstract vector concepts, and helps students transition from intuitive perception to abstract understanding to deeply understand the essence of the theorem. At the same time, we designed a teaching design that transfers from experiments to analogies and finally to mathematical modeling. This practical plan is suitable for high school classrooms. It reflects the inherent connection between mathematics and science, cultivates students’ core literacy and interdisciplinary thinking, and provides new ideas for front-line teaching.