Abstract
The acquisition of counting is a major milestone for children. A central question is how children’s non-verbal number concepts change as they learn to count. We assessed children’s verbal counting knowledge using the Give-N task and identified children who had acquired the cardinal principle (Cardinal Principle Knowers, or CP-knowers) and those who had not (Subset-Knowers, or SS-knowers). We compared their performance on two tests of nonverbal numerical cognition. We report comparable performance between SS- and CP-knowers for matching and tracking small sets of objects up to four, but disparate performance for sets between five and nine, with CP-knowers outperforming SS-knowers. These results indicate that the difference between CP- and SS-knowers extends beyond their knowledge of the verbal number system to their non-verbal quantitative reasoning. The findings provide support for the claim that children’s induction of cardinality represents a conceptual transition with concurrent, qualitative changes in numerical representation.
Highlights
The acquisition of counting is a major milestone for children
We found that no SS-knowers were able to map large number words onto large numerosities
CP-knowers gave increasing responses for larger targets in the high-number range, while SS-knowers did not show differential responses for caterpillars that had a large number of feet
Summary
The acquisition of counting is a major milestone for children. A central question is how children’s non-verbal number concepts change as they learn to count. In one sense, counting is clearly a feat of word learning: Children need to learn words for highly abstract number concepts and grasp how the structure of the count list gives meaning to the number words (i.e., going up one word in the list represents adding one item to the set; Gallistel & Gelman, 1992; Gelman & Gallistel, 1978) In another sense, counting is a feat of conceptual development: Children build an explicit symbolic representation that enables them to determine, track, and remember exact quantities (Carey, 2009; Carey & Sarnecka, 2006; Frank, Everett, Fedorenko, & Gibson, 2008; Gordon, 2004). These studies show that CP-knowers differ from SS-knowers with regard to their knowledge of how number words relate to cardinalities of sets of objects, for sets greater than four
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