Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America.
Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America.
Cognition. 2022 Jan;218:104952. doi: 10.1016/j.cognition.2021.104952. Epub 2021 Nov 19.
Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a "set-matching" task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children's ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.
人类在精确表示数字和用符号表示这些表示的能力方面是独一无二的。这种相关性引发了关于符号数字系统是否有必要表示大的精确数字的争论。以前在无法计算的成年人和半计算的儿童中解决这个问题的工作受到相互矛盾的结果和不同方法的限制，并没有得出明确的答案。我们通过改编在无法计算的人群中使用的方法（“集匹配”任务）来解决这个争论，该方法适用于处于不同符号数字习得阶段的 3 至 5 岁美国儿童。在五项研究中，我们发现儿童精确匹配集的能力不仅与了解几个数字词的含义有关，而且还与理解如何使用计数来生成集（即基数原则）有关。然而，尽管孩子们在获得基数原则后更有可能匹配集，但他们仍然表现出失败，这与这样一种假设是一致的，即精确相等的推理能力在稍后的某个时间出现。这些发现为精确数字概念的起源提供了重要数据，并指出了计数系统的知识，而不是一般的数字语言，是推理大精确数字的能力的关键因素。
