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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.
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Exact Number Concepts Are Limited to the Verbal Count Range
Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., “one, two, three . . .”). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population—the Tsimane’ of Bolivia—in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants ( N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants’ verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.
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- Award ID(s):
- 1901262
- PAR ID:
- 10364053
- Publisher / Repository:
- SAGE Publications
- Date Published:
- Journal Name:
- Psychological Science
- Volume:
- 33
- Issue:
- 3
- ISSN:
- 0956-7976
- Page Range / eLocation ID:
- p. 371-381
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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