Signal clarity: an account of the variability in infant quantity discrimination tasks

Abstract

Infants have shown variable success in quantity comparison tasks, with infants of a given age sometimes successfully discriminating numerical differences at a 2:3 ratio but requiring 1:2 and even 1:4 ratios of change at other times. The current explanations for these variable results include the two-systems proposal - a theoretical framework that suggests that there are multiple systems at play and that these systems do not communicate early in infancy, leading to failure in certain numerical comparisons. An alternative proposal is that infants may be attending to continuous extent dimensions in these tasks rather than number per se. However, neither of these two main proposals is independently capable of accounting for the previously published data. Recently the Signal Clarity Hypothesis was proposed to account for and predict the variability (Cantrell & Smith, 2013). According to this hypothesis, infants' variable success may be understood from a framework of statistical learning taken together with the signal-to-noise ratio generated by control procedures in habituation tasks. Here we test specific predictions made by the Signal Clarity Hypothesis. Across four experiments assessing 9-month old discriminations of small and large sets (2 vs. 4 and 3 vs. 4), we demonstrate that infant success can be predicted by this novel approach and, further, that infants may discriminate smaller ratios of change than previously believed (3:4 numerical change and 2:3 cumulative area change).

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

“…On this view, infants might discover number by noticing more intense perceptual stimulation and eventually realizing this intensity is correlated with other percepts. Indeed, when the consistency of these correlations was varied, infants demonstrated greater acuity for both number and area when the correlations were maximally correlated (Cantrell et al 2015a). This line of inquiry demonstrates the insight gained by viewing quantitative perception as a complex system of interrelated signals, rather than a collection of isolated streams.…”

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

“…Newcombe, Levine, and Mix (2015) offer support for this theory by highlighting evidence supporting the idea that at least space and number representations are first represented by a single system. The signal clarity hypothesis, which suggests that in infancy all quantities are seen as a single dimension, and thus the confounded nature of quantity facilitates infants' understanding of quantity, is also consistent with the developmental divergence model (Cantrell & Smith, 2013;Cantrell, Boyer, Cordes, & Smith, 2015). In this article, we review the evidence for and against a common magnitude system and conclude that, while not conclusive, the data provide the strongest support for the developmental divergence model (Newcombe, 2014).…”

Core mathematical abilities in infants

“…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.…”