Abstract: Study on children’s number concept have occupied important position in the research on children’s cognitive development. However there are conflicts in this field. Susan Carey（2006, 2007, 2008）and colleagues have proposed a “knower-levels account” to describe the development of children’s number concept from a new aspect and also categorized children into different knower levels. Moreover, they proposed that successor function was the very basic reason that can be used to explain the difference between “subset-knowers” and “cardinal-principle knowers”. The present study was to explore the development of number concepts and examine whether the successor function were acquired step by step or all-or-none. 100 preschoolers of 2- to 5-year-olds, from two kindergartens in Hangzhou city, Zhejiang Province, participated in the study. The Give-N task was used to separate 2- to 5-year-olds into children who could give the right number of items for only a subset of the numerals in their count list (“subset-knowers”) and children who could give the right number for all numerals tested (“cardinal-principle knowers”). The results of the study showed: 1) The developmental pattern of preschoolers’ number concept was as follows: the cardinal number concept of 2- to 5-year-olds was developing continually. 3- to 4-year-old was the critical period of cardinal number concept. 2) From the view of “knower-levels account”, most 4-year-olds have already achieved the very high level of cardinal principle knower, while 2- to 3-year-olds were still on the pre-number level to the third level. Children of 2- to 3-year-old were the subset knowers. Chinese preschoolers could also be categorized into Carey’s knower levels and the result somehow supported Carey’s account. 3) From the view of “successor function”, performance on a series of novel numerical tasks supported the hypothesis that not only the cardinal-principle-knowers understood how counting implemented the successor function, but also subset-knowers understood the successor function in the condition of small sets. The successor function was acquired step by step, not all-or-none.

Key words: preschoolers, number concept, knower-levels account, successor function

摘要： 本研究从儿童数概念发展的理解者水平模型的理论视角，对100名2～5岁学前儿童的数概念发展水平进行划分，并比较不同水平儿童对后继函数的理解和掌握，探讨儿童数概念的发展过程。结果表明：儿童在4岁时基本达到了数概念发展的最高水平即基数原则水平，已经理解了后继函数，能够把它的方向性和单位性的变化，对应到数数序列的数词上。而2～3岁的儿童还处于子集水平，该水平的儿童和基数原则水平的儿童相比，对后继函数的理解存在差异。但后继函数的发展不是全或者无的，儿童积累的数词越多，后继函数发展得越好。

关键词: 学前儿童, 数概念, 理解者水平模型, 后继函数