Abstract
Human mathematical abilities comprise both learned, symbolic representations of number and unlearned, non-symbolic evolutionarily primitive cognitive systems for representing quantities. However, the mechanisms by which our symbolic (verbal) number system becomes integrated with the non-symbolic (non-verbal) representations of approximate magnitude (supported by the Approximate Number System, or ANS) are not well understood. To explore this connection, forty-six children participated in a 6-month longitudinal study assessing verbal number knowledge and non-verbal numerical acuity. Cross-sectional analyses revealed a strong relationship between verbal number knowledge and ANS acuity. Longitudinal analyses suggested that increases in ANS acuity were most strongly related to the acquisition of the cardinal principle, but not to other milestones of verbal number acquisition. These findings suggest that experience with culture and language is intimately linked to changes in the properties of a core cognitive system.
Highlights
Number concepts in humans are supported in part by a universal, non-symbolic cognitive system for representing quantities, often referred to as the Approximate Number System (ANS)
Data from the first half of the study were sampled from Session 2 and data from the second half of the study were sampled from Session 5, with the midpoint session taken to be representative of each half of the larger study
While many animals share with humans a primitive Approximate Number System (ANS), only humans naturally acquire an understanding of number symbols and large exact cardinalities
Summary
Number concepts in humans are supported in part by a universal, non-symbolic cognitive system for representing quantities, often referred to as the Approximate Number System (ANS). The ANS is a well-characterized non-symbolic system for representing numerical magnitudes, present from birth in humans [1] and across a wide range of animal species (for review, see [2], [3]). Number concepts are represented by a learned, symbolic system of verbal counting [4], [5]. ANS representations are generally characterized on the basis of their internal variability, as manifested in the errors observers make in tasks believed to tap the ANS. ANS representations exhibit scalar variability—with increasing variability as a function of larger set sizes [6]. Numerical discrimination tasks yield performance that is a function of PLOS ONE | DOI:10.1371/journal.pone.0153072 April 14, 2016
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