Cognition 106 (3):1221-1247 (2008)

Abstract
Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.
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DOI 10.1016/j.cognition.2007.06.004
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References found in this work BETA

On the Psychophysical Law.S. S. Stevens - 1957 - Psychological Review 64 (3):153-181.
A Law of Comparative Judgment.L. L. Thurstone - 1927 - Psychological Review 34 (4):273-286.

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Neurocognitive Start-Up Tools for Symbolic Number Representations.Manuela Piazza - 2010 - Trends in Cognitive Sciences 14 (12):542-551.

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