Crossing the divide: Infants discriminate small from large numerosities.

Abstract

Although young infants have repeatedly demonstrated successful numerosity discrimination across large sets when the number of items in the sets changes twofold (E. M. Brannon, S. Abbott, & D. J. Lutz, 2004; J. N. Wood & E. S. Spelke, 2005; F. Xu & E. S. Spelke, 2000), they consistently fail to discriminate a twofold change in number when one set is large and the other is small (<4 items; F. Feigenson, S. Carey, & M. Hauser, 2002; F. Xu, 2003). It has been theorized that this failure reflects an incompatibility in representational systems for small and large sets. The authors investigated the ability of 7-month-old infants to compare small and large sets over a variety of conditions. Results reveal that infants can successfully discriminate small from large sets when given a fourfold change, but not a twofold change, in number. The implications of these results are discussed in light of current theories of number representation.

Core mathematical abilities in infants

“…For instance, infants fail to discriminate a 1:2 ratio numerical difference between one small and one large set (Lipton and Spelke, 2004;Wood and Spelke, 2005b;Xu, 2003). Nevertheless, other studies have shown that infants can use analog magnitudes for both small and large numbers, with successful discrimination of 2 vs 4 (Coubart et al, 2015;Starr et al, 2013a;vanMarle and Wynn, 2009), and an ability to compare small and large numbers provided the ratio between them is generous enough (eg, 2 vs 8 dots; Cordes and Brannon, 2009), consistent with the idea of a unique nonverbal system for representing number (eg, Gallistel and Gelman, 1992). In fact, small numbers might be represented both by the OTS and by the ANS.…”

“…What appears to drive the type of system, and therefore the representation and signature that is observable in a given task, is the context. For instance, reaching tasks might privilege the OTS due to its higher precision and enhanced attention to individual objects (Feigenson and Carey, 2003), while tasks in which a small number of objects is contrasted with a large set of objects might prompt the ANS for representing both sets provided a critical change threshold is exceeded (Cordes and Brannon, 2009). Another critical aspect that has been recently proposed is that precision in quantity discrimination (involving both small and large sets) is determined in part by the regularities and redundancy across the numerical displays, so that when the signal is made clear by reducing variations in the stimuli (Cantrell et al, 2015), or when the magnitude changes are redundant across dimensions (Cordes and Brannon, 2009;Suanda et al, 2008), infants' numerical competence is enhanced.…”

Impaired Numerical Ability Affects Supra-Second Time Estimation

“…This idea is consistent with the proposition that dyscalculics would be more impaired when bigger numbers are involved (but see But-terworth, 2010), and also with the fact that DDs are not significantly impaired in sub-sec timings (Cappelletti et al, 2011a). Furthermore, the transition between sub-second ('automatic' or 'sensory-motor' timing, Bueti et al, 2012;Buhusi & Meck, 2005;Buonomano, 2007;Lewis & Miall, 2003;Macar et al, 2006;Naatanen et al, 2004;Wiener et al, 2010) and supra-second ('cognitive') timing mechanisms occurs at around 3 s (Gilaie-Dotan et al, 2011;Poppel, 1997), which might parallel the transition between mechanisms supporting small and larger numerosities (Agrillo et al, 2012;Buhusi & Cordes, 2011;Cordes & Brannon, 2009), although there is no consensus about this idea (see Buhusi & Cordes, 2011 for review). While a distinction between 'small' and 'large' numerosities can be dichotomised, one might also consider it on a magnitude continuum.…”

Do infants have a sense of numerosity? A p-curve analysis of infant numerosity discrimination studies

“…Consistent with Weber's law, large numerosity discrimination is ratio dependent whereby the accuracy or precision with which two numerosities can be discriminated is inversely correlated with their numerical ratio (Nieder & Dehaene, 2009). Put differently, there is a large literature showing that individuals of all ages are more accurate at discriminating numerosities with comparatively, a small vs. a large ratio (Cordes & Brannon, 2009;Lipton & Spelke, 2004;Lipton & Spelke, 2003;Starr, Libertus, & Brannon, 2013;Wood & Spelke, 2005;Xu & Arriaga, 2007;Xu & Spelke, 2000;Xu, Spelke, & Goddard, 2005). Indeed, the first study of infant large numerosity discrimination (Xu & Spelke, 2000) reported that 6-month old infants could discriminate between numerosities with a ratio of 0.…”