Review
Special Issue: Space, Time and Number
Neurocognitive start-up tools for symbolic number representations

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Attaching meaning to arbitrary symbols (i.e. words) is a complex and lengthy process. In the case of numbers, it was previously suggested that this process is grounded on two early pre-verbal systems for numerical quantification: the approximate number system (ANS or ‘analogue magnitude’), and the object tracking system (OTS or ‘parallel individuation’), which children are equipped with before symbolic learning. Each system is based on dedicated neural circuits, characterized by specific computational limits, and each undergoes a separate developmental trajectory. Here, I review the available cognitive and neuroscientific data and argue that the available evidence is more consistent with a crucial role for the ANS, rather than for the OTS, in the acquisition of abstract numerical concepts that are uniquely human.

Section snippets

Neurocognitive start-up tools

Current theories of cognitive development posit that knowledge acquisition is based on a limited set of ‘core knowledge’ systems, defined as domain-specific representational priors that guide and constrain the cultural acquisition of novel representations 1, 2. This notion fits well with a recent proposal that cultural learning occurs by a partial reconversion (‘cortical recycling’) of a few cerebral circuits initially selected to support evolutionary relevant functions, but sufficiently

The approximate number system

Approximate number, much like colour or shape, is a basic feature of the environment to which animals appear wired to attend to: spontaneous extraction of an approximate number of objects in sets is reported in several species, both in the wild and in more controlled laboratory settings (reviewed in [4]). For example, macaque monkeys spontaneously match the approximate number of individuals they see to the number of individuals’ voices that they hear [5]; they also sum up visual and auditory

The object tracking system

The OTS is a mechanism by which objects are represented as distinct individuals that can be tracked through time and space. This core system for representing objects centers on the spatio-temporal principles of cohesion (objects move as bounded wholes), continuity (objects move on connected, unobstructed paths), and contact (objects do not interact at a distance). These principles enable human infants, as well as other animals, to perceive object boundaries, and to predict when objects will

The role of the ANS and the OTS in the acquisition of symbolic number representations

Most existing proposals of the acquisition of symbolic number (here the term ‘symbolic numbers’ stands for positive integers) claim that the symbols for numbers acquire meaning by being mapped onto the pre-existing core quantity representations: some proposals highlight the role of the ANS 15, 17, 49, others the role of the OTS 2, 50, whereas others consider the combination of the two systems as crucial 1, 51 [see [52] for a concise review of the different positions, [53] for a proposal that

Traces of the ANS signature in symbolic number processing

Behavioral evidence Traces of the ANS signature in symbolic number processing appear to arise almost as soon as children acquire symbolic numbers. In a series of studies, Gilmore and colleagues showed that four- to five-year-old children, although they had not yet been taught the principles of exact calculation, solved simple arithmetical operations on large symbolic two-digit numbers relying on an approximate, ratio-dependent representation of quantity, and that they did so spontaneously [54].

Evidence for a foundational role of the OTS in symbolic number processing

Some theories of the acquisition of symbolic numbers propose that the OTS is foundational because it provides the notion of exact number and enables the endorsement of the successor [11] relations between adjacent numbers 2, 50, 51, 52 (Box 3). Indeed, it is often claimed that the ANS cannot provide semantic foundation to the representations of symbolic natural numbers because it lacks these two properties [50].

Concluding remarks

Humans are born with strong intuitions on approximate numerical quantities and their relations. There is evidence to suggest that culture-based acquisition of symbols representing exact numerical quantities is grounded on these pre-existing intuitions, whereas there is little evidence for a foundational role of the parallel individuation system. Current neuroimaging data suggest that representations of exact numbers emerge through important modifications of the pre-existing parietal coding

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