The Development of Number Concepts

该研究调查了人类婴儿如何表征数字概念以及学习口头计数和语言前数字表征之间的关系。 具体来说，目的是确定婴儿是否有两种数字表示，一种是小数字（1，2，3，也许是4），另一种是大数字（大于3或4的数字）。 此外，我们迈出了第一步，研究如何学习英语的整数列表（即，1、2、3、4、5等）可能会改变孩子后来的数字概念。 以往关于婴儿和学龄前儿童数字表征的研究表明，当婴儿在3至3.5岁左右获得数字词的含义时，他们的数字表征可能会发生重大的发展变化。 幼儿可能开始有两种数字表示系统，一种表示小数字（1、2和3），一种表示大数字（例如，8、16等）。 拟议的研究测试的假设，这两个代表是不同的，口头计数允许儿童联合收割机这两个代表产生成人一样的数字表示。 换句话说，因为口头计数列表（1，2，3等）由于对概念表征施加了某些限制，儿童必须同时使用小数和大数表征才能理解计数列表。 这些假设将与几种方法进行调查，包括违反预期的婴儿注视时间的方法，训练，然后转移的方法与幼儿，和有多少和给一个数字的任务，广泛用于评估儿童的理解数字的话。 这些实验的结果应该导致更详细和更深入地了解数的前语言表征和儿童学习计数之间的关系。 这项研究将为数字表征领域中语言与认知的关系提供基本的线索。

The research investigates how human infants represent numerical concepts and the relationship between learning to count verbally and pre-linguistic number representations. Specifically, the objective is to determine if there are two representations of number in infants, one for small numbers (1, 2, 3, and perhaps 4) and one for large numbers (numbers larger than 3 or 4). Furthermore, we take the first step in investigating how learning the integer list of English (i.e., 1, 2, 3, 4, 5, etc.) may change children's later numerical concepts. Previous studies on number representations in infants and preschool children have shown that there may be a major developmental change in infants' number representations when they have acquired the meaning of the number words at around 3 to 3.5 years of age. Young infants may begin with two systems of number representations, one for small number (1, 2, and 3) and one for large numbers (e.g., 8, 16, etc.). The proposed study tests the hypothesis these two representations are distinct and that verbal counting allows the child to combine these two representations to yield adult-like numerical representations. In other words, because the verbal counting list (1, 2, 3, etc.) imposes certain constraints on conceptual representations, the child has to use both the small number and the large number representations in order to make sense of the counting list. These hypotheses will be investigated with several methods, including a violation of expectancy looking time method with infants, a training-then-transfer method with toddlers, and the how-many and give-a-number tasks widely used in assessing children's understanding of number words. The results of these experiments should lead to a more detailed and deeper understanding of the relationship between pre-linguistic representations of number and children's learning to count. The proposed research will shed basic light on the relationship between language and cognition in the domain of number representations.