生成式AI在正弦型函数可视化教学的实践探索

Practical Research on Generative AI for Visual Teaching of Sinusoidal Functions

摘要: 随着人工智能技术的快速发展，AI协同教学已成为教育教学改革与创新的重要工具。本文聚焦高中数学《正弦型函数$y=Asin\left(\omega x+\phi \right)$ 的图像变换》这一教学难点，提出将生成式AI技术作为智能体辅助教师设计数形结合教学设计。利用AI技术快速生成基于Python的动态交互可视化图像，更有效地刺激学生的视觉直观，提升学生的空间想象力与代数变换理解度。该路径不仅弥补了传统几何软件的开发门槛，还催生了教师–学生–AI的三元互动教学模式，为数学数字化教学提供了一种全新的资源生成与课堂实施途径。

Abstract: With the rapid development of artificial intelligence technology, AI-assisted collaborative teaching has become an important instrument for the reform and innovation of education and instruction. Focusing on the difficult teaching point of senior high school mathematics—Image Transformation of Sinusoidal Function $y=Asin\left(\omega x+\phi \right)$ —this paper proposes adopting generative AI as an intelligent agent to assist teachers in designing teaching plans integrating numbers and shapes. AI technology is utilized to rapidly generate dynamic interactive visual graphics based on Python, which can better activate students’ visual intuition and improve their spatial imagination as well as their comprehension of algebraic transformations. This approach not only lowers the development barrier of traditional geometric software, but also fosters a ternary interactive teaching mode involving teachers, students and AI. It offers a brand-new pathway for resource generation and classroom implementation in digital mathematics teaching.