Children’s mappings between number words and the approximate number system

Odic, Darko; Corre, Mathieu Le; Halberda, Justin

doi:10.1016/j.cognition.2015.01.008

Cited by 80 publications

(119 citation statements)

References 68 publications

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“…Subset-knowers used larger number gestures in response to 9 or 10 objects than in response to 5 or 6 objects, but did not distinguish these set sizes using number words. Subset-knowers' failure to distinguish these set sizes in the verbal modality is consistent with previous work (Gunderson et al, 2015;Le Corre & Carey, 2007;Odic, Le Corre, & Halberda, 2015). Researchers have argued that subset-knowers have difficulty producing large enough number words to label these large set sizes (Gunderson et al, 2015;Wagner & Johnson, 2011).…”

Section: Discussionsupporting

confidence: 74%

Gesture as a window onto children’s number knowledge

et al. 2015

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Section: Discussionsupporting

confidence: 74%

Gesture as a window onto children’s number knowledge

et al. 2015

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“…Two violations have been of especially high interest: whether the participants counted, rather than estimated, the stimulus presented (Cordes et al, 2001;Frank et al, 2008;Grondin, Meilleur-Wells, & Lachance, 1999;Odic, Le Corre, & Halberda, 2015) and whether the σ value changes with high or low intensities (Bizo, Chu, Sanabria, & Killeen, 2006;Grondin, 2012;Lejeune & Wearden, 2006;Wearden & Lejeune, 2008). For example, in the time literature, evidence for changes in the σ value have been used as evidence for multiple independent clock mechanisms, each for a different scale of duration (Gibbon, Malapani, Dale, & Gallistel, 1997;Grondin, 2012;Lewis & Miall, 2009).…”

Section: Extending Psimle(βσ) To Test Model Violationsmentioning

confidence: 96%

PsiMLE: A maximum-likelihood estimation approach to estimating psychophysical scaling and variability more reliably, efficiently, and flexibly

Odic

Eisinger

et al. 2015

Behav Res

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A simple and popular psychophysical model-usually described as overlapping Gaussian tuning curves arranged along an ordered internal scale-is capable of accurately describing both human and nonhuman behavioral performance and neural coding in magnitude estimation, production, and reproduction tasks for most psychological dimensions (e.g., time, space, number, or brightness). This model traditionally includes two parameters that determine how a physical stimulus is transformed into a psychological magnitude: (1) an exponent that describes the compression or expansion of the physical signal into the relevant psychological scale (β), and (2) an estimate of the amount of inherent variability (often called internal noise) in the Gaussian activations along the psychological scale (σ). To date, linear slopes on log-log plots have traditionally been used to estimate β, and a completely separate method of averaging coefficients of variance has been used to estimate σ. We provide a respectful, yet critical, review of these traditional methods, and offer a tutorial on a maximum-likelihood estimation (MLE) and a Bayesian estimation method for estimating both β and σ [PsiMLE(β,σ)], coupled with free software that researchers can use to implement it without a background in MLE or Bayesian statistics (R-PsiMLE). We demonstrate the validity, reliability, efficiency, and flexibility of this method through a series of simulations and behavioral experiments, and find the new method to be superior to the traditional methods in all respects.

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“…However, if any difference were found between SS-and CP-knowers' performance on the non-verbal matching task, it could be alternately explained by children's ability to generate verbal estimates corresponding to the number of items in the set. Therefore, we also assessed children's estimation knowledge, and the quality of children's mapping between verbal numerals and approximate representations of quantity in the ANS, using an estimation task-"Fast Cards"-used in previous studies (Le Corre & Carey, 2007;Odic, Le Corre, & Halberda, 2015;Shusterman et al, 2016). In this task, children were shown sets of items flashed quickly on the screen and were asked to guess the number of dots.…”

Section: The Present Studymentioning

confidence: 99%

Conceptual correlates of counting: Children’s spontaneous matching and tracking of large sets reflects their knowledge of the cardinal principle

et al. 2017

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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.

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Children’s mappings between number words and the approximate number system

Cited by 80 publications

References 68 publications

Gesture as a window onto children’s number knowledge

Gesture as a window onto children’s number knowledge

PsiMLE: A maximum-likelihood estimation approach to estimating psychophysical scaling and variability more reliably, efficiently, and flexibly

Conceptual correlates of counting: Children’s spontaneous matching and tracking of large sets reflects their knowledge of the cardinal principle

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