基于APOS理论和RMI原则融合模型的概念教学研究——以“函数的概念”的教学为例

A Study of Concept Teaching Based on the Integrated Model of APOS Theory and RMI Principle—A Case Study of the Teaching of “The Concept of Function”

摘要: 数学概念是数学知识的重要组成部分，但其高度的抽象性和复杂性，给学生带来了显著的认知障碍，教学效果并不理想。针对这一现状，提出了以APOS理论的认知阶段为学习认知依据、RMI原则的思想为方法指导的双理论融合教学模型。通过梳理APOS理论和RMI原则并分析其在数学教育中的作用，以概念形成这一数学概念获得方式为重要桥梁，将RMI原则融入APOS理论的四个阶段，构建融合教学模型。根据融合教学模型设计《函数的概念》教学案例，旨在推动学生形成对函数概念的深层次认知，同时领悟数学思想方法，落实核心素养，为一线教学提供直观参考。

Abstract: Mathematical concepts constitute a fundamental component of mathematical knowledge. However, their high degree of abstraction and complexity pose significant cognitive obstacles for students, resulting in unsatisfactory teaching effectiveness. To address this issue, this paper proposes a dual-theory integrated teaching model that takes the cognitive stages of APOS theory as the cognitive foundation for learning and the methodology of the RMI principle as the methodological guidance. By sorting out the APOS theory and the RMI principle and analyzing their roles in mathematics education, and taking the concept formation, a way of acquiring mathematical concepts, as an important bridge, the RMI principle is integrated into the four stages of the APOS theory to construct an integrated teaching model. Based on the integrated teaching model, a teaching case for “The Concept of Function” is designed, aiming to promote students’ in-depth understanding of the function concept, enable them to comprehend mathematical thinking methods, and foster core mathematical competencies, thereby providing practical reference for teaching practice.