基于APOS理论的椭圆及其标准方程教学设计

Teaching Design of Ellipse and Its Standard Equation Based on APOS Theory

摘要: 概念是思维的基本单位，数学概念的理解是一切数学思维活动的基石，学生对数学概念理解不充分会导致其它数学活动的实施变得困难。在高中数学教学中，圆锥曲线的概念较为抽象，而椭圆又是学习圆锥曲线的起始，如何合理引导学生学习椭圆及其标准方程至关重要。APOS理论将数学概念学习划分为操作、过程、对象和图式四个环节，旨在通过活动辅助获得数学概念，加深理解。本文基于APOS理论对高中椭圆及其标准方程内容进行了教学设计，探究该理论在教学实践中的可行性，旨在为提升高中数学教学水平提出建议。

Abstract: A concept is the fundamental unit of thought, and the understanding of mathematical concepts serves as the cornerstone for all mathematical thinking activities. Inadequate understanding of mathematical concepts by students can render the implementation of other mathematical activities difficult. In high school mathematics teaching, the concept of conic sections is relatively abstract, and the ellipse marks the beginning of studying conic sections. Therefore, it is crucial to guide students in learning about ellipses and their standard equations in a reasonable manner. The APOS theory divides the learning of mathematical concepts into four stages: action, process, object, and schema, aiming to facilitate the acquisition and deepening of understanding of mathematical concepts through activities. Based on the APOS theory, this paper designs a teaching plan for the content of ellipses and their standard equations in high school mathematics, exploring the feasibility of this theory in teaching practice. The aim is to propose suggestions for enhancing the teaching quality of high school mathematics.