APOS理论视角下高中数学概念的深度学习教学设计研究
APOS Theory Perspective on High School Mathematics Concepts: A Study on Instructional Design for Deep Learning

数学概念是构建数学理论大厦的基石，在整个高中教学中具有举足轻重的地位。鉴于数学概念自身的抽象性和复杂性，如何实现高中生数学概念深度学习仍是目前亟需解决的难题。APOS理论为数学概念教学提供了经典的理论模型，本研究在探讨APOS理论与深度学习理论的基础上，分析了二者结合的可行性。选用人教版高中数学“基本不等式”教学为例，基于APOS理论的四个阶段展开具体的教学设计，分步论证了如何利用APOS理论促进高中生数学概念深度学习。
Mathematical concepts are the building blocks of mathematical theory and play a pivotal role in the teaching of mathematics in senior secondary schools. In view of the abstraction and complexity of mathematical concepts, how to realize the deep learning of mathematical concepts among high school students is still an urgent problem to be solved at present. The APOS theory provides a classical theoretical model for teaching mathematical concepts, and this study analyses the feasibility of combining APOS theory and deep learning theory. Using the teaching of “Basic Inequalities” in senior secondary mathematics of the Humanities Education Edition as an example, this study develops a specific teaching design based on the four stages of APOS theory and demonstrates how to use APOS theory to promote the deep learning of mathematical concepts among senior secondary students in a step-by-step manner.