Children's multiplicative transformations of discrete and continuous quantities
Children's multiplicative transformations of discrete and continuous quantities
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DOI：
10.1016/j.jecp.2009.01.014
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发表时间：
2009-08-01
影响因子：
2.6
通讯作者：
Carey, Susan
中科院分区：
文献类型：
--
作者：
Barth, Hilary;Baron, Andrew;Carey, Susan
最近的研究证明了一种进化上原始的、早期出现的关于数字心理表征的认知系统(模拟量系统)。对非人类灵长类动物、人类婴儿和学龄前儿童的研究表明，在算术训练之前，该系统支持涉及整数概念的数字排序、加法和减法计算。在这里，我们报告的证据表明，这个系统支持儿童对将转变减半甚至加倍的结果的预测。共有138名幼儿园学生和一年级学生被要求对初始数量加倍或减半(一组点)或初始长度(条形)所产生的数量进行推理。对网点大小、总网点面积和网点密度的控制确保儿童对阵列中网点的数量做出反应。在符号乘法、除法或有理数的正式教学之前，减半(也许是加倍)计算似乎是在离散的、可能是连续的数量上进行的。将简单的乘法变换应用于数量的模拟幅度表示的能力可能构成儿童用来构建后来的有理数概念的工具包的一部分。(C)2009 Elsevier Inc.保留所有权利。
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. (C) 2009 Elsevier Inc. All rights reserved.