One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

Corre, Mathieu Le; Carey, Susan

doi:10.1016/j.cognition.2006.10.005

Cited by 575 publications

(786 citation statements)

References 66 publications

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“…This suggests that children's understanding of number symbols may emerge independently of the AMS (for a similar proposal, see, e.g, Le Corre & Carey, 2007;Carey, 2011). At minimum, our results suggest that the SNS is only indirectly linked to the AMS early in development, which is difficult to reconcile with the view that approximate representations of quantity serve as the semantic building blocks of their symbolic counterparts (e.g., Feigenson et al, 2004Feigenson et al, , 2013Verguts & Fias, 2004;Piazza et al, 2007;Dehaene, 2008;Piazza, 2010).…”

Section: Evidence For the Sns→ams Viewmentioning

confidence: 59%

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Lyons

Bugden

Zheng³

et al. 2018

Developmental Psychology

106

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There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial debate and study of the relationship between approximate, nonverbal (approximate magnitude system, AMS) and exact, symbolic (symbolic number system, SNS) representations of number. Here we examined several hypotheses concerning whether, in the earliest stages of formal education, AMS abilities predict growth in SNS abilities, or the other way around. In addition to tasks involving symbolic (Arabic numerals) and non-symbolic (dot arrays) number comparisons, we also tested children's ability to translate between the two systems (i.e., mixed-format comparison). Our data included a sample of 539 Kindergarten children (mean=5.17yrs, SD=0.29yrs), with AMS, SNS and mixed comparison skills assessed at the beginning and end of the academic year. In this way, we provide, to the best of our knowledge, the most comprehensive test to date of the direction of influence between the AMS and SNS in early formal schooling. Results were more consistent with the view that SNS abilities at the beginning of Kindergarten lay the foundation for improvement in both AMS abilities and the ability to translate between the two systems. Importantly, we found no evidence to support the reverse. We conclude that, once one acquires a very basic grasp of exact number symbols, it is this understanding of exact number (and perhaps repeated practice therewith) that facilitates growth in the AMS. Though the precise mechanism remains to be understood, these data challenge the widely held view that the AMS scaffolds the acquisition of the SNS.

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Section: Evidence For the Sns→ams Viewmentioning

confidence: 59%

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Lyons

Bugden

Zheng³

et al. 2018

Developmental Psychology

106

View full text Add to dashboard Cite

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“…For instance two-knowers might have a mental model of "one" as {X} and "two" as {X, X}. These representations rely on children's ability for enriched parallel individuation, a representational capacity that Le Corre and Carey (2007) argue can individuate objects, manipulate sets, and compare sets using 1-1 correspondence. Subset-knowers can, for instance, check if "two" applies to a set S by seeing if S can be put in 1-1 correspondence with their mental model of two, {X, X}.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping in a language of thought: A formal model of numerical concept learning

Piantadosi¹,

Tenenbaum²,

2012

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In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a recursive system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful representational system. We provide an implemented model that is powerful enough to learn number word meanings and other related conceptual systems from naturalistic data. The model shows that bootstrapping can be made computationally and philosophically well-founded as a theory of number learning. Our approach demonstrates how learners may combine core cognitive operations to build sophisticated representations during the course of development, and how this process explains observed developmental patterns in number word learning.

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“…In her groundbreaking studies of children's numeral acquisition, Wynn (1990Wynn ( , 1992 developed a system of "number knower" levels that has since been used extensively in the literature (see Barner, et al, 2009;Condry & Spelke, 2008;LeCorre & Carey, 2007;LeCorre, Brannon, Van deWalle, & Carey, 2006;Sarnecka et al, 2007; for a contrasting view, see Dehaene, 1997;Gallistel, 1990;Gallistel & Gelman, 1992). Wynn's key contribution was to suggest that children's acquisition of numeral meanings proceeds in distinct stages.…”

Section: Early Numeral Meanings and Implicaturementioning

confidence: 99%

“…Their research has instead focused on the other problem of exactness -i.e., how exact meanings originate in development, given the apparent lack of exact representations in pre-linguistic cognition (for examples see Gallistel & Gelman, 1992;Gelman & Gallistel, 1978; LeCorre, Van deWalle, Brannon, & Carey, 2006;LeCorre & Carey, 2007;Mix, Huttenlocher, & Levine, 2002;Schaeffer, Eggleston, & Scott, 1974;Wynn, 1990Wynn, , 1992. The core problem for psychologists is how this special representational capacity, not found in other animals, emerges from the process of acquiring a linguistic counting system and mapping this system to non-linguistic representations.…”

Section: U {X : S(x) λ W(x)}| =mentioning

confidence: 99%

Inference and exact numerical representation in early language development

Barner¹,

Bachrach²

2016

Preprint

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How do children as young as 2 years of age know that numerals, like one, have exact interpretations, while quantifiers and words like a do not? Previous studies have argued that only numerals have exact lexical meanings. Children could not use scalar implicature to strengthen numeral meanings, it is argued, since they fail to do so for quantifiers (Papafragou & Musolino, 2003). Against this view, we present evidence that children's early interpretation of numerals does rely on scalar implicature, and argue that differences between numerals and quantifiers are due to differences in the availability of the respective scales of which they are members.Evidence from previous studies establishes that (1) children can make scalar inferences when interpreting numerals, (2) children initially assign weak, non-exact interpretations to numerals when first acquiring their meanings, and (3) children can strengthen quantifier interpretations when scalar alternatives are made explicitly available.

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One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles

Cited by 575 publications

References 66 publications

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Symbolic number skills predict growth in nonsymbolic number skills in kindergarteners.

Bootstrapping in a language of thought: A formal model of numerical concept learning

Inference and exact numerical representation in early language development

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