基于APOS理论的数学史融入教学设计案例——以“椭圆及其标准方程”为例

A Case Study of Teaching Design for Integrating the History of Mathematics Based on APOS Theory—Taking the “Ellipse and Its Standard Equation” as an Example

摘要: 椭圆的发现与发展是人类探索几何规律的重要历程，每一次理论突破都是对原有认知的革新与完善。经过漫长历史的积淀，椭圆的相关知识形成了系统且稳定的理论体系。本文以“椭圆及其标准方程”为研究对象进行教学设计，立足学生已有的几何认知经验，深入分析学情与教学内容，设计了一系列层层递进的教学活动。教学过程中充分凸显学生的主体地位，注重逻辑思维的引导与训练，让学生亲历椭圆概念的发生、发展全过程，挖掘几何知识的本质内涵，自主构建椭圆相关知识的网络体系。同时，让学生在知识传递中感受数学文化的浸润，领略数学史的教育价值与文化内涵，构建一套完整的示范案例，为今后数学史融入几何概念课堂教学提供参考样例与实施方案。

Abstract: The discovery and development of the ellipse represent a pivotal chapter in humanity’s exploration of geometric principles, with each theoretical breakthrough representing an innovation and refinement of prior understanding. Through centuries of historical accumulation, knowledge about ellipses has evolved into a systematic and robust theoretical framework. This paper presents a teaching design centered on the “Ellipse and Its Standard Equation”, building upon students’ existing geometric knowledge and conducting an in-depth analysis of learning contexts and instructional content to develop a series of progressively structured teaching activities. The instructional approach fully emphasizes student-centered learning, prioritizes the guidance and cultivation of logical thinking, and enables students to witness firsthand the emergence and evolution of the ellipse concept. This approach helps students uncover the essential nature of geometric knowledge and independently construct a coherent knowledge network related to ellipses. Additionally, students are immersed in mathematical culture during knowledge transmission, appreciate the educational and cultural value of mathematical history, and benefit from a comprehensive set of exemplary cases that serve as reference models and implementation guidelines for integrating mathematical history into geometry classroom instruction.