TPACK框架下GeoGebra动态参数提升高中三角函数直观想象能力的研究

A Study on Enhancing High School Students’ Visual Imagination Ability of Trigonometric Functions Using Dynamic Parameters with GeoGebra under the TPACK Framework

摘要: 本研究聚焦高中三角函数教学中直观想象能力培养的抽象性难题，基于TPACK框架，探究GeoGebra动态参数工具对学生理解三角函数图象变换规律的作用机制。通过理论建构、教学设计案例分析与实证研究发现，GeoGebra的动态参数功能，能够将三角函数中振幅(A)、频率(ω)、初相(φ)等抽象参数转化为可视化、可操作的动态对象，支持学生通过“猜想–调节参数–观察图象–归纳规律”的探究路径，建立“解析式–图象–性质”的深度关联。

Abstract: This study focuses on the challenge of cultivating visual imagination ability in high school trigonometry teaching, particularly the abstract nature of teaching trigonometric function image transformations. Based on the TPACK framework (Technology-Pedagogy-Content Knowledge), this research explores the mechanism of GeoGebra’s dynamic parameters in helping students understand the transformation rules of trigonometric function images. Through theoretical construction, teaching design case analysis, and empirical research, it is found that GeoGebra’s dynamic parameter function can transform abstract parameters in trigonometric functions, such as amplitude (A), frequency (ω), and initial phase (φ), into visual and operable dynamic objects. This supports students in establishing a deep connection among “analytical expressions-image-properties” through an inquiry path of “conjecture-parameter adjustment-image observation-law induction”.