基于APOS理论的初中数学概念教学实践初探——初中“直线和圆的位置关系”教学

Elementary Study on the Practice of Mathematics Concept Teaching in Junior Middle School Based on APOS Theory—Teaching “the Position Relation between Line and Circle” in Junior Middle School

摘要: 数学概念是数学学习的知识基础和逻辑起点，对学生数学学习有非常重要的作用。APOS理论属于建构主义理论，强调数学概念教学是构建学生心智的过程，能有效揭示数学的本质。为了更好地指导教师进行概念教学，笔者基于APOS理论设计了一次直线与圆的位置关系的概念教学，分析了APOS理论下操作或活动阶段、过程阶段、对象阶段、模型阶段中教学过程的呈现，期待在该APOS理论的指导下，数学概念实践中能有效提升教学效率，提高学习积极性，学生的身心发展和学习能力得到更大的提升。

Abstract: The concept of mathematics is the knowledge base and logical starting point of mathematics learning, which plays a very important role in students’ mathematics learning. APOS theory be-longs to constructivism theory, which emphasizes that the teaching of mathematical concepts is the process of constructing students’ minds and can effectively reveal the essence of mathematics. In order to better guide teachers in concept teaching, the author designs a concept teaching based on the APOS theory of the position relationship between the line and the circle, analyzes the presentation of the teaching process in the operation or activity stage, process stage, object stage and model stage under the APOS theory. It is expected that the practice of mathematical concepts can effectively improve the teaching efficiency under the guidance of the APOS theory. Learning enthusiasm is improved, and students’ physical and mental development and learning ability are enhanced.