The innateness of visual number: A case study using children’s counting books

Abstract

A brief glance at an apple tree is enough to form a surprisingly accurate impression of the number of apples on its branches. What is the basis of this capacity? Can our abstract numerical representations be directly traced back to primitive early visual representations of number, or must we learn to construct them from low-level non-numerical features (such as surface area, density, or convex hull) over the course of development? If cognitive representations of number must be constructed from non-numerical visual features, then it must be the case that the visual evidence available to us sufficiently determines the number of items in a display. Here, we explore this assumption by making use of a surprisingly underutilized resource: the visual images that children look at when learning number from counting books. If the non-numerical visual cues in these images fail to capture number, then children could not rely on them to learn how many items are on a page. This implies that vision must rely on a more direct number signal. Much work suggests that the concept number must be constructed from early visual features, so we analyzed how well such features track cardinality across 50 children’s counting books. We found that continuous features were at best weakly correlated with number (highest r2 = .32). A linear regression over the three most predictive features explained a modest amount of variability in the number of items, R2 = .33, p < .001. Further, a system of visual number that only uses evidence from non-numerical features will perform much worse than children do in typical number tasks. We show that children’s number abilities go beyond that which could be provided by low-level visual features and therefore must involve either a more direct numerical extraction or an inference beyond the evidence of non-numerical features.