Spontaneous analog number representations in 3‐year‐old children

Abstract

When enumerating small sets of elements nonverbally, human infants often show a set-size limitation whereby they are unable to represent sets larger than three elements. This finding has been interpreted as evidence that infants spontaneously represent small numbers with an object-file system instead of an analog magnitude system (Feigenson, Spelke, and Dehaene, 2004). In contrast, non-human animals and adult humans have been shown to rely on analog magnitudes for representing both small and large numbers (Brannon & Terrace, 1998; Cantlon & Brannon, 2007; Cordes et al., 2001). Here we demonstrate that, like adults and non-human animals, children as young as three years of age spontaneously employ analog magnitude representations to enumerate both small and large sets. Moreover, we show that children spontaneously attend to numerical value in lieu of cumulative surface area. These findings provide evidence of young children’s greater sensitivity to number relative to other quantities and demonstrate continuity in the process they spontaneously recruit to judge small and large values.

The spatial–numerical congruity effect in preschoolers

“…For numerosities above 4, left hemisphere activation was expected, which promoted right-side choices. This was not necessary when a numerosity range did not exceed 4 elements (a number range that allows exact nonverbal comparison [e.g., Cantlon, Safford, & Brannon, 2010]), so for small numbers the SNC effect was preserved. Other explanations could also be possible, but all in all, this effect was restricted to the CP-knowers only and does not affect the validity of the demonstration of an SNC-indicating pattern of results in preliterate and precounting children.…”

Relationships between approximate number system acuity and early symbolic number abilities

“…It should be noted however that, at this age, almost half of children performed below chance level when discriminating numerosities. Previous studies have reported high drop-out rates when preschool children had to complete the same kind of task (e.g., [4,15]). Instead of excluding these participants as was done elsewhere, we interpreted their low performance in numerosity comparison as an index of difficulties to isolate numerical information from other non-numerical factors, which could be linked to their poor mastery of cardinality.…”

Child proportional scaling: Is 1/3=2/6=3/9=4/12?

“…The cognitive cost of scaling may be more apparent when participants use intuitive perceptual processes to solve proportional equivalence problems than when they use more formal mathematical approaches (i.e., division and multiplication) because the former are more likely than the latter to activate visual-perceptual processes. It is possible, however, that a trace of the cost of scaling may remain even when proportional problems are solved using mathematical symbols and operations, similar to what has been shown for numerical comparisons involving arrays of both dots and numerals (e.g., Cantlon, Safford, & Brannon, 2009;Dehaene & Akhavein, 1995).…”