基于CPFS结构理论的初中数学教学探究——以“三角形”单元为例

Research on Junior Middle School Mathematics Teaching Based on CPFS Structure Theory—Taking “Triangle” Unit as an Example

摘要: CPFS结构是数学学习特有的认知结构，是在认知发展理论基础上发展而来的更为实用的结构理论，对初中生的数学各方面能力都能提升，用它来研究数学知识教学是十分有必要的。三角形知识作为初中阶段十分重要的知识板块，由于教材编排方式和本身抽象性、逻辑性强等特点，导致学生对三角形这块的知识掌握不太理想，从数学学习的本质和教学的根本任务上来看，形成一个良好的数学认知结构是解决三角形数学知识内化问题的关键。本文将从课标、三角形的知识结构与分布特点及CPFS结构理论的优势结合提出利用CPFS理论在三角形教学中的实际应用的对策，如采用变式教学、引导式教学、分层教学等。

Abstract: CPFS structure is a unique cognitive structure of mathematics learning, and it is a more practical structural theory developed on the basis of cognitive development theory. It can improve the mathematical ability of junior high school students in all aspects, and it is very necessary to use it to study mathematical knowledge teaching. As a very important knowledge block in junior high school, triangular knowledge is not well mastered by students due to the arrangement of teaching materials and its strong abstract and logical characteristics. From the perspective of the essence of mathematics learning and the fundamental task of mathematics teaching, forming a good mathematical cognitive structure is the key to solving the problem of triangular mathematical knowledge teaching. This paper will combine the characteristics of curriculum standard, triangle knowledge structure and distribution, and the advantages of CPFS structure theory to put forward the practical application of CPFS theory in triangle teaching, such as variable teaching, guided teaching, hierarchical teaching and so on.