GeoGebra在高中三角函数图像变换教学中的应用探究

Research on the Application of GeoGebra in the Teaching of Trigonometric Function Image Transformation in Senior High School

摘要: 为破解高中三角函数图像变换教学中“抽象难懂、直观性不足、学生难以建立数形结合”的痛点，本文以GeoGebra动态数学软件为核心工具，结合高中数学新课标要求与学生认知规律，探究其在三角函数图像变换教学中的应用路径。通过梳理正弦、余弦、正切函数图像的平移、伸缩、对称变换核心逻辑，设计“动态演示–自主探究–验证归纳–迁移应用”的教学流程，重点展示GeoGebra在变换参数可视化、图像同步生成、动态交互操作、错题即时辨析等环节的应用策略。实践表明，该教学模式能有效降低学生对变换规律的理解难度，提升学生的数形结合能力与课堂参与度，为高中三角函数教学提供了可复制的数字化教学方案，同时也为数学学科核心素养的落地提供了实践参考。

Abstract: To solve the pain points in the teaching of trigonometric function image transformation in senior high school, such as abstract comprehension, lack of intuition, and students’ difficulty in establishing the combination of number and shape, this paper takes GeoGebra dynamic mathematical software as the core tool. Combined with the requirements of the new senior high school mathematics curriculum standard and students’ cognitive rules, it explores its application paths in the teaching of trigonometric function image transformation. By sorting out the core logic of translation, scaling and symmetry transformation of sine, cosine and tangent function images, this paper designs a teaching procedure of “dynamic demonstration-independent exploration-verification and induction-transfer and application”. It focuses on demonstrating the application strategies of GeoGebra in parameter visualization, synchronous image generation, dynamic interactive operation and instant error analysis. Practice shows that this teaching mode can effectively reduce students’ difficulty in understanding transformation rules, improve students’ ability of combining number with shape and classroom participation. It provides a replicable digital teaching scheme for senior high school trigonometric function teaching, and also offers practical reference for the implementation of core literacy in mathematics discipline.