教学理解说及其理论与课程意义

Mathematics Understanding and Its Theoretical and Curriculum Significance

关于教学理解，学者们提出三种观点：一是网络联系说，即理解是表征网络的生成；二是表征转化说，即理解是实现表征之间的转化和建立表征之间的联系；三是类型层次说，即理解有直观理解、程序理解、抽象理解和形式理解等类型层次。这三种观点都基于认知心理学的表征内涵，深化了对数学理解的认识；而它的课程意义在于，可以而且应该基于学生的理解水平，制定适切的课程目标，促进有理解地教与学。

There are three theories about mathematics understanding. First， a mathematical knowledge is understood if it is linked to existing networks. Second， understanding is reflected in the ability to make connections and translation within and between various representations. Third， understanding includes intuitive understanding， procedural understanding， abstract understanding， and formal understanding. These theories are based on cognitive psychology， and think that understanding is a continual dynamic process. Using these theories， we can construct an understanding model and investigate students’ understanding levels. On the basis of understanding levels， appropriate curriculum objectives can be designed.