培育直观想象素养的高中方程教学——基于GeoGebra的数形结合实践

High School Equation Teaching for Cultivating Intuitive Imagination Literacy—A Practice Based on GeoGebra for Integrating Numerical and Geometric Concepts

摘要: 数形结合思想是数学方法论的重要组成部分，在高中方程教学中具有突出的认知价值。本文立足当前课堂教学实际，系统梳理数形结合思想的发展脉络与教育意义，分析学生在方程学习中存在的思维障碍及其成因，阐释几何直观与代数运算在方程问题中的相互联系与转化规律，并构建“直观感知–量化分析–融合创新”的三阶递进教学框架。同时，从教材开发、课堂实施、技术融合、评价改革等方面提出可操作的教学建议，为培养学生数学抽象与直观想象核心素养提供实践参考，推动高中方程教学从技能训练向满足未来社会发展需求的人才培养转变。

Abstract: Combining numbers and graphs is an important mathematical method that helps students understand equations better in senior high school. Based on real classroom teaching, this paper studies the background and educational value of the method. It discusses the difficulties students meet in learning equations and how to connect geometric intuition with algebraic calculation. We also build a three-level teaching model: intuitive perception, quantitative analysis, and creative integration. Moreover, we put forward practical suggestions on teaching materials, classroom teaching, technology use and teaching evaluation to improve students’ core literacy in mathematical abstraction and intuitive imagination. This research is expected to change equation teaching from mechanical practice to thinking development.