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Effects of development and enculturation on number representation in the brain

Key Points

  • Behavioural studies have revealed that the processing and representation of numerical magnitude are qualitatively similar across species and across human development. Reliable effects such as the distance effect (numbers that are close together being harder to compare than those that are separated by a large numerical difference) have been used to characterize the representation of numerical magnitude.

  • Evidence from functional neuroimaging studies with humans and from single-cell neurophysiological recordings from the monkey cortex has indicated that bilateral regions of the intraparietal sulcus (IPS) are critical for the representation and processing of numerical magnitude.

  • Recently there has been substantial debate over the extent to which the IPS houses a domain-specific representation of numerical magnitude — a 'number module'. Data from single-cell and fMRI studies suggest that representations of numerical and non-numerical (length, size, luminosity, et cetera) magnitude overlap in the IPS, indicating that the IPS contains a distributed representation of numerical magnitude with local biases for particular categories, rather than neatly segregated modules.

  • fMRI studies have also shown similar activation in the IPS for judgments of numerical (which number is numerically larger?) and non-numerical (for example, which letter comes first in the alphabet?) order. These findings suggest that during numerical magnitude tasks the activity of the IPS might reflect access to an abstract representation or order rather than representations of numerical magnitude.

  • Although animals share with humans the ability to process non-symbolic numerical magnitude, the use of abstract symbols (such as number words or Arabic numerals) is uniquely human. These new mental tools are the products of cultural history, which raises the question of how they are processed in the brain and how they are related to non-symbolic representations of numerical magnitude.

  • Some computational models and theories posit that symbolic representations of numerical magnitude are acquired through mapping onto pre-existing non-symbolic representations. However, other data suggest that symbolic representations of magnitude might be qualitatively different from non-symbolic ones. To date, the precise neural mechanisms that allow for the processing of abstract, symbolic representations of numerical magnitude are not well understood.

  • The left temporoparietal cortex has been strongly linked with mental arithmetic. Recent fMRI studies have started to reveal the effects of learning and culture on the brain processes that subserve calculation. Specifically, different types of arithmetic training and problems shift activation from areas of the parietal lobe that are involved in magnitude processing (the IPS) to those that are thought to support arithmetic fact retrieval (the angular gyrus) to different degrees.

  • Cross-cultural studies have shown that culture has a significant and powerful effect on the neural correlates of calculation and even on basic symbolic-magnitude processing, such as the comparison of Arabic numerals. In addition, different methods of teaching lead to different patterns of brain activation during mathematical problem solving.

  • Developmental studies provide a tool for studying how cultural representations of numerical magnitude come to be represented in the brain. Recent evidence suggests that age-related increases occur in the activation of the left temporoparietal cortex during mental arithmetic and in the IPS during basic numerical-magnitude processing. Other evidence, however, suggests that there are similarities in the neural correlates of number processing in adults and children.


A striking way in which humans differ from non-human primates is in their ability to represent numerical quantity using abstract symbols and to use these 'mental tools' to perform skills such as exact calculations. How do functional brain circuits for the symbolic representation of numerical magnitude emerge? Do neural representations of numerical magnitude change as a function of development and the learning of mental arithmetic? Current theories suggest that cultural number symbols acquire their meaning by being mapped onto non-symbolic representations of numerical magnitude. This Review provides an evaluation of this contention and proposes hypotheses to guide investigations into the neural mechanisms that constrain the acquisition of cultural representations of numerical magnitude.

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Figure 1: Ontogenetic and phylogenetic continuity in basic signatures of numerical-magnitude representation.
Figure 2: Neural correlates of basic numerical-magnitude representation in the human and monkey brain.
Figure 3: Distributed and overlapping representations of numerical and non-numerical quantity in the intraparietal sulcus.
Figure 4: Different processing pathways for symbolic and non-symbolic numerical magnitude.
Figure 5: The calculating brain changes dynamically as a function of learning.
Figure 6: Ontogenetic differences and similarities in the neural correlates of mental arithmetic and magnitude processing.


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I would like to thank three anonymous reviewers for their valuable comments on an earlier version of this manuscript. I would like to thank I. Lyons, G. Price, I. Holloway and M. Zorzi for helpful discussions of many of the issues discussed in the paper. I would like to thank L. van Eimeren for help with the figures. This research was supported by grants from the Natural Science and Engineering Council of Canada, the Canada Research Chairs Program, The Canada Foundation for Innovation and the Ontario Ministry of Research and Innovation.

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Numerical magnitude

The total number of items in a set. It can be either exact or approximate, depending on whether the sets are counted or the total number of items is estimated.

Numerical distance

The difference between two numbers. For example, the numerical distance between eight and five is three. Many studies show that numerical distance has a profound effect on the time it takes to make a relative-numerical-magnitude judgement.


A term used to describe non-symbolic representations of numerical magnitude (such as arrays of dots or squares).

Cardinal number

The last number in a sequence; cardinal numbers represent the total number of items in a set.

Mental number line

A metaphor for the mental representation of numerical quantity, based on findings that support an association between space and number.

Tuning curve

How single neurons or, in the case of fMRI, large populations of cells are tuned to respond to a particular stimulus rather than to other, similar stimuli. A neuron might respond preferentially to three items but also fire during the presentation of one or two items.

Domain specificity

When brain regions respond more to a stimulus from one domain of cognitive processing (for example, faces) than they do to another (for example, houses). Regions that exhibit such domain-specific response properties are thought to be biologically determined to represent and process stimulus categories from a particular cognitive domain.


A term from cognitive science that refers to the notion that different cognitive domains (for example, language, visuo-spatial cognition and social cognition domains) have distinct organizational principles and are represented in encapsulated modules.

Multi-voxel pattern analysis

fMRI data are typically analysed using voxel-wise statistics; multi-voxel pattern analysis uses pattern-classification algorithms to decode fMRI activity that is distributed across multiple voxels.


The rank–order relationships between numbers (for example, the third in line).

Accumulator model of numerical-magnitude representation

A model of numerical-magnitude processing in which enumeration involves the passing of impulses through a gate into a summed representation. This summed representation can be likened to a measuring cup: in this analogy the level of the accumulated impulses represents the total number of enumerated impulses. This is also referred to as 'summation coding'.

fMRI adaptation

A phenomenon whereby repeated presentation of a particular stimulus leads to reductions in the fMRI signal in brain regions that are involved in representing and processing that stimulus. It is also referred to as 'repetition suppression'.

Finger agnosia

Impairment of the ability to distinguish between fingers. It is associated with damage to the left angular gyrus and frequently co-occurs with calculation deficits.

Two-operant problem

An arithmetic problem involving two numbers (for example, 12 x 45).


The process (encompassing language development, education, learning, et cetera) by which an individual becomes a fully functioning member of his or her culture.

Cross-sectional experiments

Experiments that compare different groups of participants (for example, children of different ages) rather than longitudinally following individuals in a single group.

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Ansari, D. Effects of development and enculturation on number representation in the brain. Nat Rev Neurosci 9, 278–291 (2008).

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