一种面向差错控制的认知观测系统模型——平面向量概念理解差错模式实证研究

A Sort of Error Cognitive Observation System Model Demonstrate Investigation of the Misunderstanding of Plane Vectors

结合认知理论和系统控制理论,构造了一种面向数学概念理解差错的观测分析模型,建立了对平面向量概念体系的理解进行实证研究的观测分析流程.通过对平面向量概念理解差错进行统计分析,认为数学概念学习中的理解差错,主要有两种模式:一类是概念模板差错,另一类是认知过程差错.基于观测分析,提出了改进设想:概念的表述;在练习中理解;重视教学的整体性;加强相关学科间的联系.

According to the cognitive theory and controlling theory, the observing model had been created to encounter misunderstandings on mathematical concepts. After clustering analysis on the misunderstanding of plane vectors, there was a common sense that the misunderstandings from the mathematical learning mainly derive from two models. The first one was the error of conceptual framework, including the external framework error, the internal framework error, and the maintenance framework error. The second model was the error on cognitive process, mainly including the assimilation bias in the internalization of concepts, as well as the structural mistake in the framework construction.