Knowledge of numerical relationships in infants

本研究的目的是探讨婴儿期数字思维的发展。数字，就像时间和空间一样，似乎是成人认知的基本组成部分之一。最近的数据表明，婴儿也对他们所处环境的数字特性很敏感（参见Wynn，1998年的综述）。婴儿的数字能力可能与成年人和非人类动物的模拟数字表示是同源的（参见Dehaene等人，1998年）。为了确定婴儿的数字能力是否真的是成人数字能力的前身，了解婴儿时期数字表征的性质是很重要的。目前，很少有人知道的格式的数字表示在婴儿期或类型的数学运算，可以执行这些表示。这项建议旨在寻找证据，证明婴儿有两种数学运算：数字排序和数字的比率比较。提出了两组实验。在第一组实验中，将在婴儿中测试数字顺序的知识。一个新的范例是发展中国家的一系列数字将提出在下降或上升的顺序，直到婴儿习惯于序列。然后，婴儿将被测试与新的数字序列的升序和降序。如果婴儿代表数字之间的顺序关系，那么他们应该在新的顺序方向上看更长的数字序列。结果将与从类似的实验中获得的那些在大小而不是数量上不同的刺激进行比较。在第二组实验中，婴儿将习惯于以特定数字比率不同的数位对（例如，1：2）。然后，他们将被测试与新的数字，不同的相同比例或一个新的比例。如果婴儿欣赏数字之间的比例关系，那么他们应该更长时间地观察具有新比例的数字对。这些实验的结果将提供一个更好的理解的方式之间的相似性和差异的婴儿，成年人和非人类动物处理的数字方面的环境。此外，了解婴儿如何在没有语言的情况下处理数字可能对儿童语言介导的算术计算教学具有重要意义。

The goal of the proposed research is to investigate the development of numerical thinking in infancy. Number, like time, and space, appears to be one of the fundamental building blocks of adult cognition. Recent data suggests that infants too are sensitive to numerical properties of their environments (see Wynn, 1998 for a review). It is possible that the numerical abilities of infants are homologous to the analog numerical representations hypothesized for adult humans and non-human animals (see Dehaene, et al., 1998). To determine whether the numerical abilities of infants really are the precursors of adult numerical abilities it is important to understand the properties of numerical representations in infancy. Currently, little is known about the format of numerical representations in infancy or of the types of mathematical operations that can be performed on these representations. This proposal seeks evidence for two types of mathematical operations in infants: numerical ordering and ratio comparisons of numerosities. Two sets of experiments are proposed. In the first set of experiments, knowledge of numerical order will be tested in infants. A new paradigm is developed where a sequence of numerosities will be presented in descending or ascending order until the infant habituates to the sequences. Infants will then be tested with sequences of new numerosities in ascending and descending order. If infants represent ordinal relationships between numerosities then they should look longer at the numerical sequences presented in the new ordinal direction. Results will be compared to those obtained from an analogous experiment with stimuli that vary in size rather than number. In a second set of experiments, infants will be habituated to pairs of numerosities that differ by a specific numerical ratio (e.g., 1:2). They will then be tested with new numerosities that differ by the same ratio or a new ratio. If infants appreciate ratio relations between numbers then they should look longer at pairs that have a new ratio. The results of these experiments will provide a better understanding of the similarities and differences between the way infants, adults, and non-human animals process the numerical aspects of their environments. Moreover, understanding how infants process number without language may have important implications for teaching children linguistically-mediated arithmetic computations.