Core systems of number

doi:10.1016/j.tics.2004.05.002

Trends in Cognitive Sciences

Volume 8, Issue 7, July 2004, Pages 307-314

https://doi.org/10.1016/j.tics.2004.05.002 Get rights and content

Abstract

What representations underlie the ability to think and reason about number? Whereas certain numerical concepts, such as the real numbers, are only ever represented by a subset of human adults, other numerical abilities are widespread and can be observed in adults, infants and other animal species. We review recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number. Performance signatures common across development and across species implicate one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human.

Section snippets

Core system 1 in infants

Even in infancy, children exhibit numerical knowledge. Xu and Spelke tested 6-month-old infants' discrimination of the numerosities 8 vs. 16 using a habituation paradigm [2]. Infants first saw repeated presentations of either 8 or 16 dots (Figure 1a). Careful controls for non-numerical dimensions ensured that infants responded to numerosity only (see Box 1). When tested with alternating arrays of 8 and 16 dots, infants looked longer at the numerically novel test arrays regardless of whether

Core system 2 in infants

The approximate system is not our only source of numerical information. Infants and adults have a second system for precisely keeping track of small numbers of individual objects and for representing information about their continuous quantitative properties.

In one experiment, 10- and 12-month-old infants chose between two quantities of hidden crackers (Figure 1c) [20]. Infants watched an experimenter sequentially hide, for example, one cracker in a bucket on the left, and 1+1=2 crackers in a

The core systems' shared heritage

Core representations of number are common across many species. When given tasks comparable with those presented to human infants and adults, animals show the same signature limits, suggesting that core knowledge of number depends on mechanisms with a long phylogenetic history.

Cerebral bases of the core systems

Recently, neuroimaging and neurophysiological techniques have begun to provide access to the neuronal underpinnings of the core number systems. The system for representing approximate numerical magnitudes has become well characterized and is associated by a convergent series of results with the bilateral horizontal segment of the intraparietal sulcus (HIPS; for a review see [40]). This brain region is implicated by both event-related potentials 41, 42 and fMRI 43, 44 as the source of the

Conclusion

Why is number so easy and yet so hard? Although studies of human infants have not definitively answered this question (see Box 2), they offer several suggestions. First, number is easy because it is supported by core systems of representation with long ontogenetic histories. One system serves to represent approximate numerical magnitudes independently of non-numerical quantities. Because this system is active early in infancy, humans are attuned to the cardinal values of arrays from the

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Trends in Cognitive Sciences

Language and Conceptual Development seriesCore systems of number

Abstract

Section snippets

Core system 1 in infants

Core system 2 in infants

The core systems' shared heritage

Cerebral bases of the core systems

Conclusion

Cognition

Cognition

Cognition

Cognition

Trends Cogn. Sci.

Trends Cogn. Sci.

Cogn. Psychol.

Cogn. Psychol.

Cognition

Cognition

Cognition

Learn. Motiv.

Cogn. Psychol.

Cortex

Cortex

Neuropsychologia

Neuron

Neuron

Neuropsychologia

Cognition

Cogn. Psychol.

Trends Cogn. Sci.

The Number Sense

A probabilistic model for the discrimination of visual number

Percept. Psychophys.

Origins of number sense: large number discrimination in human infants

Psychol. Sci.

Nonverbal counting in humans: the psychophysics of number representation

Psychol. Sci.

Development of elementary numerical abilities: a neuronal model

J. Cogn. Neurosci.

A mode control model of counting and timing processes

J. Exp. Anal. Behav.

Variability signatures distinguish verbal from nonverbal counting for both small and large numbers

Psychonomic Bull. Rev

Preschoolers' magnitude comparisons are mediated by a preverbal analog mechanism

Psychol. Sci.

Brain mechanisms of quantity are similar in 5-year-olds and adults

Proc. Natl. Acad. Sci. U. S. A.

Time required for judgments of numerical inequality

Nature

Language and Conceptual Development series
Core systems of number