APOS理论在高中幂函数概念教学中的应用

The Application of APOS Theory in the Concept Teaching of Power Functions in Senior High School

摘要: 传统的数学教学常因机械的公式记忆而忽视概念本质，导致学生对幂函数等抽象数学概念理解不足。文章基于APOS理论，以高中幂函数教学为例设计分层递进的教学活动。通过“活动–过程–对象–图式”四阶段，从几何实例的具体操作切入，引导学生在感知幂函数形式的基础上，逐步抽象归纳出一般定义，深化对指数参数与定义域的理解，最终实现跨学科应用与知识整合。从而突破机械学习带来的局限，为数学概念教学提供可操作的实践路径。

Abstract: Traditional mathematics teaching often neglects the essence of concepts due to mechanical memorization of formulas, resulting in students’ insufficient understanding of abstract mathematical concepts such as power functions. Based on the APOS theory, this paper designs a hierarchical and progressive teaching activity with the teaching of power functions in high school as an example. Through the four stages of “activity-process-object-schema”, starting from the specific operation of geometric examples, it guides students to perceive the form of power functions, gradually abstract and generalize the general definition, deepen the understanding of the index parameter and the domain, and ultimately achieve cross-disciplinary application and knowledge integration. Thus, it breaks through the limitations brought by mechanical learning and provides an operational, practical path for the teaching of mathematical concepts.