基于APOS理论的初中数学概念探究——以分式为例
Inquiry into Middle School Mathematics Concepts Based on APOS Theory—Taking Fraction as an Example

本文基于APOS理论，以初中数学中的分式概念为例，对数学概念教学进行了深入探究。文章首先系统梳理了APOS理论的核心要点，并指出了当前数学概念教学中存在的一些普遍问题。随后，结合分式的教学实际，详细分析了学生在掌握分式概念过程中可能经历的四个阶段，包括活动阶段(Action)、过程阶段(Process)、对象阶段(Object)和图式阶段(Schema)，从而揭示分式概念形成和发展的内在规律，并设计相应教学过程。依据所设计的教学过程进行教学实践，课后通过调查问卷与测试成绩分析调查学生分式概念学习情况，数据分析表明，基于APOS理论的分式概念教学过程能达到较好的效果。通过这一探究，本文旨在帮助教师更好地理解分式概念的教学过程，把握学生在不同阶段的学习特点和难点，从而采取针对性的教学策略，提升教学质量。同时，引导学生更有效地掌握分式概念，提高数学学习的效果。
This paper conducts an in-depth exploration of mathematics concept teaching, taking the concept of fractions in junior high school mathematics as an example, based on the APOS theory. It first systematically outlines the core points of the APOS theory and points out some common issues in current mathematics concept teaching. Subsequently, combining the practical teaching of fractions, the paper analyzes in detail the four stages that students may experience in mastering the concept of fractions, including the Action stage, Process stage, Object stage, and Schema stage. This analysis reveals the internal laws governing the formation and development of the fraction concept and designs a corresponding teaching process. Teaching practice is carried out according to the designed teaching process, and a post-class survey is conducted to investigate students’ learning of the fraction concept through questionnaires and test score analysis. Data analysis shows that the fraction concept teaching process based on the APOS theory can achieve good results. Through this exploration, this paper aims to help teachers better understand the teaching process of the fraction concept, grasp the learning characteristics and difficulties of students at different stages, and thereby adopt targeted teaching strategies to improve teaching quality. At the same time, it guides students to more effectively grasp the fraction concept and enhance the effectiveness of mathematics learning.