2～5岁儿童的数概念发展水平——理解者水平理论的视角

Two to Five-year-old Children's Levels of Number Concepts: A View from Knower-Levels Theory

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:4岁以后绝大部分儿童达到了数概念发展的最高水平即基数原则水平,该水平的儿童可以把后继函数的方向性和单位性变化对应到数数序列的数词上。而2～3岁的大部分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,子集水平的儿童也具有对较小数量的方向性和单位性的认识。

A basic challenge in understanding human cognitive development is to understand how children acquire number concepts. Number has been one of the most active areas of research in the field. One prominent current theory about the origin of integer concepts is the ＂knower-levels＂ theory （ Carey, 2001,2004 ; Carey ＆ Sar- necka, 2006; Condry ＆ Spelke, 2008; Le Corre ＆ Carey, 2007; Le Corre, Van de Walle, Brannon, ＆ Carey, 2006）. The knower- levels theory describes the development of children＇s number concepts from a new aspect and categorizes children into different knower levels. Moreover, Sarnecka and Carey （2008） proposed that the successor function was the very basic reason that can be used to ex- plain 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 was acquired step by step. 100 preschoolers of 2- to 5-years-olds, from two kindergartens in Hangzhou city, Zhejiang Province, participated in the study. The Give-N task, a commonly-used measure of young children＇s number knowledge, was used to divide the 2- to 5-year-olds into chil- dren who could give the right number of items for only a subset of the numerals in their count list （ ＂ subset-knowers＂ ） and those who could give the right number for all numerals tested （＂ cardinal-principle knowers＂ ）. We devised a series of simple measures （ the Direc- tion task, the Unit task and the Box task） to tap the children＇s understanding of how the direction and unit of numerical change were re- presented by moving forward or backward along the numeral list. The results of the study showed ： The cardinal number concepts of the 2- to 5-year-olds were developing continually. 2） From the view of the＂ knower-levels theory＂ , most 4-year-olds have already achieved the very high level of cardinal principle knowers, while the 2- to 3-year-olds were still on the pre-number level to the fourth level. Chi- nese preschoolers could be categorized into Carey＇s knower levels and the result somehow supported Carey＇s account. 3 ） From the view of the ＂successor function＂, performance on a series of novel numerical tasks supported the hypothesis that not only the cardinal-princi- ple-knowers understood how counting implemented the successor function, but also the subset-knowers understood the successor function in the condition of small sets. The successor function was acquired step by step.