APOS理论视角下初中数学概念教学探究——以“反比例函数”为例

An Exploration of Junior High School Mathematics Concept Teaching from the Perspective of APOS Theory —Taking the “Inverse Proportional Function” as an Example

摘要: 数学概念是学好数学的基础，更是教师教学的核心，能够帮助学生实现从感性认识到理性认识的飞跃。APOS理论基于数学概念的抽象性，将数学概念的学习概括为“活动阶段——过程阶段——对象阶段——图式阶段”四个阶段。此研究以初中数学“反比例函数”的教学为例，设计出基于APOS理论为框架的概念教学设计：设置情境，温故探新；类比探究，感知建构；问题驱动，辨析概念；拓展深化，丰富认知。阐明三则教学反思，旨在提高教师概念教学，帮助学生感悟概念的本质和内涵，落实数学核心素养培养。

Abstract: Mathematical concepts are the foundation of learning mathematics well, and they are the core of teachers’ teaching, which can help students make the leap from perceptual to rational understanding. Based on the abstraction of mathematical concepts, the APOS theory summarizes the learning of mathematical concepts into four stages: “activity stage, process stage, object stage and schema stage”. Taking the teaching of “inverse proportional function” in junior high school mathematics as an example, this study designs a conceptual teaching design based on the framework of APOS theory: setting up the situation, reviewing the past and exploring the new; Analogical inquiry, perceptual construction; Problem-driven, discerning concepts; expanding and deepening and enriching cognition. The purpose of clarifying the three teaching reflections is to improve teachers’ concept teaching, help students understand the essence and connotation of concepts, and implement the cultivation of mathematics core literacy.