AI赋能项目化学习重构高中数学高效课堂——以“二项式展开的几何证明”为例

Reconstructing Efficient Senior High School Mathematics Classrooms via AI-Enabled Project-Based Learning—Taking the “Geometric Proof of Binomial Expansion” as an Example

摘要: 本文基于项目化学习理念，以二项式展开的几何证明为例，探讨重构数学高效课堂的实施路径。聚焦于${\left(a-b\right)}^n$ 展开式的几何探究，融合技术动态演示三维立方体的分割过程与容斥原理应用，帮助学生直观理解${\left(a-b\right)}^3$ 的展开本质，并引导其将三维空间的分割逻辑推广至n维情形，突破高维符号变化的想象瓶颈。项目化学习的融入有效激发了学生的学习动机，推动其从被动接受转向主动建构，促进了深度学习和核心素养的全面发展。

Abstract: This paper explores ways to build efficient math classrooms via project-based learning, using geometric proofs of binomial expansion as an example. Focusing on the geometric inquiry of the expansion of ${\left(a-b\right)}^n$ , it integrates AI technology to dynamically demonstrate the segmentation process of three-dimensional cubes and the application of the inclusion-exclusion principle, helping students intuitively understand the essential nature of the expansion of ${\left(a-b\right)}^3$ . It guides students to extend 3D segmentation logic to n-dimensional cases, overcoming high-dimensional imagination bottlenecks. Project-based learning integration boosts learning motivation, drives the shift from passive reception to active construction, and advances deep learning and core competency development.