Knowledge of numerical relationships in infants

这项拟议的研究的目标是调查婴儿期数值思维的发展。与时间和空间一样，数字似乎是成人认知的基本组成部分之一。最近的数据表明，婴儿对环境的数字特性也很敏感(参见Wynn，1998)。婴儿的数字能力可能与成人和非人类动物的模拟数字表征相同(见Dehaene等人，1998)。要确定婴儿的数字能力是否真的是成人数字能力的前驱，重要的是要了解婴儿期数字表征的性质。目前，关于婴儿期数字表示的格式或可以对这些表示执行的数学运算的类型知之甚少。这项建议为婴儿的两种数学运算寻找证据：数字排序和数值的比率比较。提出了两套实验方案。在第一组实验中，数字顺序知识将在婴儿身上进行测试。一种新的范式被开发出来，其中一系列数字将以降序或升序呈现，直到婴儿习惯于这些序列。然后，婴儿将接受按升序和降序排列的新数字序列的测试。如果婴儿代表数字之间的顺序关系，那么他们应该更长时间地观察新的顺序方向上呈现的数字序列。结果将与类似的实验结果进行比较，这些刺激的大小不同，而不是数量不同。在第二组实验中，婴儿将习惯于以特定的数字比例(例如，1：2)不同的数字对。然后，它们将用不同于相同比率或新比率的新数字进行测试。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关注具有新比例的配对。这些实验的结果将更好地理解婴儿、成年人和非人类动物处理环境数字方面的异同。此外，了解婴儿如何在没有语言的情况下处理数字，可能对教授儿童通过语言进行算术计算具有重要意义。

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.