中美数学思维观的比较研究

A Comparative Study of the Ideas of Mathematics Thinking in the US and the P.R.C

中美两国数学教育界对学生数学思维的发展都非常重视。我国学者从形象思维、抽象思维、直觉思维等角度对之进行研究和探索;美国学者从儿童生活实际出发,认为学生数学思维包括:匹配与区分、分类、排序、顺序、建模。在论述思维发展时,都结合学生的实际,以案例的方式进行描述。两国在研究的逻辑方法上存在显著差异。我国研究体现出从一般到特殊的特点,而美国的研究则体现出从特殊到一般的特点。比较两国的研究,吸取各自所长,有利于促进我国基础教育数学课程改革的健康发展。

The mathematical education circles of both the US and P.R.C attach importance to the development of students＇ mathematical thinking.Scholars of the P.R.C study mathematical thinking from image thinking,Abstract thinking and intuition thinking;while scholars of the U S study mathematical thinking from children＇s daily life and they think the mathematical thinking of children includes： matching and discriminating,classifying,ordering,sequencing and patterning.When discussing the thinking development of children,both sides picture it with students＇ practice cases,but there is salient difference in studying logical method between two sides.Study in the P.R.C has the characteristic of deduction to induction,while the study in the U S has the characteristic of induction to deduction.It is beneficial to develop our mathematical curriculum reform in compulsory education by comparing these two theories and absorbing their strong points.