Barth Hilary, Baron Andrew, Spelke Elizabeth, Carey Susan
Department of Psychology, Wesleyan University, Middletown, CT 06459, USA.
J Exp Child Psychol. 2009 Aug;103(4):441-54. doi: 10.1016/j.jecp.2009.01.014. Epub 2009 Mar 16.
Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving whole number concepts prior to arithmetic training. Here we report evidence that this system supports children's predictions about the outcomes of halving and perhaps also doubling transformations. A total of 138 kindergartners and first graders were asked to reason about the quantity resulting from the doubling or halving of an initial numerosity (of a set of dots) or an initial length (of a bar). Controls for dot size, total dot area, and dot density ensured that children were responding to the number of dots in the arrays. Prior to formal instruction in symbolic multiplication, division, or rational number, halving (and perhaps doubling) computations appear to be deployed over discrete and possibly continuous quantities. The ability to apply simple multiplicative transformations to analog magnitude representations of quantity may form a part of the toolkit that children use to construct later concepts of rational number.
最近的研究记录了一种进化上原始、早期出现的用于数字数量心理表征的认知系统（模拟数量系统）。对非人类灵长类动物、人类婴儿和学龄前儿童的研究表明，该系统在算术训练之前支持涉及整数概念的数字排序、加法和减法运算。在此，我们报告证据表明，该系统支持儿童对减半以及可能的加倍变换结果的预测。总共138名幼儿园儿童和一年级学生被要求对一组点的初始数量或一条线的初始长度加倍或减半后的数量进行推理。对点大小、总点面积和点密度的控制确保了儿童是根据数组中的点数做出反应。在正式学习符号乘法、除法或有理数之前，减半（以及可能的加倍）运算似乎可应用于离散量以及可能的连续量。将简单乘法变换应用于数量的模拟数量表征的能力可能构成儿童构建后来有理数概念所使用工具包的一部分。
