CPFS结构视域下的平面向量教学实践与探索

The Practice and Exploration of Flat Vector Teaching from the Perspective of CPFS Structure

摘要: CPFS结构是数学学科特有的、优良的个体数学认知结构，它对数学学习尤其是数学问题解决能力有直接的影响，基于CPFS结构理论以及CPFS结构理论相关研究，采用文献分析法，探究CPFS结构对问题解决能力的影响，研究表明CPFS结构对问题解决有正向的影响。根据以上分析，选取“平面向量”知识模块，发现并总结目前高中平面向量教学中存在的问题，并结合CPFS结构理论提出合理的平面向量教学实践建议，包括教学中重点体现概念的形成，帮助学生建立概念域与概念系；教学中重点体现命题之间的联系，帮助学生建立命题域与命题系；改善教学模式，引导学生自主建构与完善平面向量CPFS结构。

Abstract: The CPFS structure is a unique and excellent individual mathematical cognitive structure in mathematics. It has a direct impact on mathematics learning, especially the ability to solve mathematical problems. Based on the CPFS structure theory and related researches on the CPFS structure theory, this paper uses the method of literature analysis to explore the impact of CPFS structure on problem-solving ability. Research shows that CPFS structure has a positive impact on problem-solving. According to the above analysis, the knowledge module of “plane vector” is selected to discover and summarize the problems existing in the current high school plane vector teaching, and combine the CPFS structure theory to put forward reasonable practical suggestions for plane vector teaching, including the formation of key concepts in teaching, to help students establish concept domain and concept department; focus on the relationship between propositions in teaching, help students establish proposition domain and proposition system; improve teaching mode, guide students to independently construct and perfect the plane vector CPFS structure.