儿童在数及数学上对部分与整体关系认识的发展

THE DEVELOPMENT OF CHILDREN’S COGNITION OF THE PART-WHOLE RELATIONSHIP CONCERNING NUMBER AND ARITHMETIC

本文概括了九个有关数和数概念的实验研究结果。作者在最早的四个实验的基础上,提出了儿童对部分与整体关系认识的十二项指标,再以之通过正整数,几何图形和分数三个方面进行探讨,探讨结果由两个数学试验验证应用。根据研究总结果,作者讨论了揭示认识对象的内在规律对于主体认识活动的作用,部分与整体关系认识的年龄特点,阶段性及激进时期以及认识这个关系的心理过程。也对数的部分与整体关系的掌握对小学数学教学的应用提出了意见。

This is a comprehensive report of 9 experiments we did during the pastthree years. From our previous 4 experiments, we put forword 12 criteria forthe comprehension of part-whole relationship. The same 12 criteria were usedin the 3 experiments (integers, geometrical figures and fraction) designed toinvestigate the reaction of children to part-whole relationship, after which 2teaching experiments were carried out to apply and check the results obtained.On thebasis of the results of these 9 experiments, the authors discussed howthe understanding of the intrinsic nature of the objects to be known (numberand arithmetical concepts in these studies) facilitates the knowing processes ofthe knower, the age characteristics, developmental levels and periods of acceler-ated growth during the process of comprehension of part-whole relationship.That the children’s cognition of part-whole relationship may be effectively ap-plied to the learning of arithmetic was also discussed.