基于APOS理论的高中数学教学案例——以余弦定理为例

High School Mathematics Teaching Case Based on APOS Theory—Taking “Cosine Theorem” as an Example

摘要: APOS理论是一种数学教育理论，强调通过操作、过程、对象和图式四个阶段促进学生的数学概念建构。余弦定理作为高中数学的核心内容，具有深刻的数学内涵和丰富的物理背景，是数形结合的良好载体和有效的解题工具。本研究以高中数学“余弦定理”相关内容为研究对象，采用文献研究法和案例分析法对APOS理论的来源、内涵与特点进行分析，结合余弦定理的教材内容与《普通高中数学课程标准(2017版)》解读，分析以APOS理论为指导的高中数学教学案例，提出余弦定理的教学策略和具体的教学设计案例。

Abstract: APOS theory is a kind of mathematics education theory, which emphasizes the promotion of students’ mathematical concept construction through the four stages of operation, process, object and schema. As the core content of high school mathematics, cosine theorem has profound mathematical connotation and rich physical background. It is a good carrier and effective problem-solving tool for the combination of number and shape. This study takes the relevant content of high school mathematics “cosine theorem” as the research object, uses literature research method and case analysis method to analyze the source, connotation and characteristics of APOS theory, combines the textbook content of cosine theorem with the interpretation of “Ordinary High School Mathematics Curriculum Standard (2017 Edition)”, analyzes the high school mathematics teaching cases guided by APOS theory, and puts forward the teaching strategies and specific teaching design cases of cosine theorem.