“超回归”数学理解模型的引介与思考

Progress and Implications of the Research on“Transcendent Recursive”Mathematical Understanding Model

数学理解是国际数学教育研究研究的重要主题.在国际数学教育界,“超回归”数学理解模型的应用范围广、持续时间长、影响深远.该模型具有以下特征:返回原处、活动与表达的互补、不需要边界、通过干预促进学生理解发展.该模型的启示有:一是对数学理解研究方面重视每一个理解层级的价值,基于此针对性展开教学;其次,学生数学理解是一个折回往返过程,要重点研究学生数学理解中的折回和增厚现象;再次,充分发挥活动与表达在学生数学理解中的互促作用;最后,教师要学会借助不同干预手段解决学生理解困难点,打通学与教的关系.

Mathematical understanding is an important topic in international mathematical education research.In the international mathematics education community,the“transcendent recursive”mathematical understanding model has a wide range of applications,a long duration and far-reaching influence.This model has the following characteristics:returning to the original place,complementing activities and expressions,not requiring boundaries,and promoting the development of students’understanding through intervention.The model brings us the following insights:Firstly,pay attention to the value of each level of understanding in the study of mathematical understanding and carry out targeted teaching based on it.Secondly,Students’mathematical understanding is a fold-back and round-trip process,and we should focus on the phenomenon of fold-back and thickening in students’mathematical understanding.Then,to give full play to the reciprocal role of activity and expression in students’mathematical understanding.Finally,teachers should learn to use different intervention methods to solve students’difficulties in understanding and open up the relationship between learning and teaching.