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.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Brannon, E. M. & Terrace, H. S. Ordering of the numerosities 1 to 9 by monkeys. Science 282, 746–749 (1998).
Boysen, S. T. & Berntson, G. G. Numerical competence in a chimpanzee (Pan troglodytes). J. Comp. Psychol. 103, 23–31 (1989).
Cantlon, J. F. & Brannon, E. M. Shared system for ordering small and large numbers in monkeys and humans. Psychol. Sci. 17, 401–406 (2006).
Cantlon, J. F. & Brannon, E. M. Semantic congruity affects numerical judgments similarly in monkeys and humans. Proc. Natl Acad. Sci. USA 102, 16507–16511 (2005).
Brannon, E. M. & Terrace, H. S. Representation of the numerosities 1–9 by rhesus macaques (Macaca mulatta). J. Exp. Psychol. Anim. Behav. Process. 26, 31–49 (2000).
Washburn, D. A. & Rumbaugh, D. M. Ordinal judgments of numerical symbols by macaques (Macaca mulatta). Psychol. Sci. 2, 190–193 (1991).
Koehler, O. Vom erlernen unbenannter anzahlen bei vögeln. Naturwissenschaften 29 (1941).
Brannon, E. M., Wusthoff, C. J., Gallistel, C. R. & Gibbon, J. Numerical subtraction in the pigeon: evidence for a linear subjective number scale. Psychol. Sci. 12, 238–243 (2001).
Uller, C., Jaeger, R., Guidry, G. & Martin, C. Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim. Cogn. 6, 105–112 (2003).
Brannon, E. The representation of numerical magnitude. Curr. Opin. Neurobiol. 16, 222–229 (2006).
Dehaene, S. Varieties of numerical abilities. Cognition 44, 1–42 (1992).
Dehaene, S. The Number Sense: How The Mind Creates Mathematics (Oxford Univ. Press, Oxford, 1997).
McComb, K., Packer, C. & Pusey, A. Roaring and numerical assessment in contests between groups of female lions, Panthera lei. Anim. Behav. 47, 379–387 (1994).
Hubbard, E. M., Piazza, M., Pinel, P. & Dehaene, S. Interactions between number and space in parietal cortex. Nature Rev. Neurosci. 6, 435–448 (2005).
Simon, T. J. The foundations of numerical thinking in a brain without numbers. Trends Cogn. Sci. 3, 363–365 (1999).
Fias, W. & Fischer, M. H. in Handbook of Mathematical Cognition (ed. Campbell, J. I. D.) 43–54 (Psychology Press, New York, 2005).
Moyer, R. S. & Landauer, T. K. Time required for judgements of numerical inequality. Nature 215, 1519–1520 (1967).
Dehaene, S., Dupoux, E. & Mehler, J. Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. J. Exp. Psychol. Hum. Percept. Perform. 16, 626–641 (1990).
Whalen, J., Gallistel, C. R. & Gelman, I. I. Nonverbal counting in humans: the psychophysics of number representation. Psychol. Sci. 2, 130–137 (1999).
Barth, H., Kanwisher, N. & Spelke, E. The construction of large number representations in adults. Cognition 86, 201–221 (2003).
Feigenson, L., Dehaene, S. & Spelke, E. Core systems of number. Trends Cogn. Sci. 8, 307–314 (2004).
Dehaene, S., Dehaene-Lambertz, G. & Cohen, L. Abstract representations of numbers in the animal and human brain. Trends Neurosci. 21, 355–361 (1998).
Fias, W., Lammertyn, J., Reynvoet, B., Dupont, P. & Orban, G. A. Parietal representation of symbolic and nonsymbolic magnitude. J. Cogn. Neurosci. 15, 47–56 (2003).
Pesenti, M., Thioux, M., Seron, X. & De Volder, A. Neuroanatomical substrates of arabic number processing, numerical comparison, and simple addition: a PET study. J. Cogn. Neurosci. 12, 461–479 (2000).
Le Clec, H. G. et al. Distinct cortical areas for names of numbers and body parts independent of language and input modality. Neuroimage 12, 381–391 (2000).
Chochon, F., Cohen, L., van de Moortele, P. F. & Dehaene, S. Differential contributions of the left and right inferior parietal lobules to number processing. J. Cogn. Neurosci. 11, 617–630 (1999).
Pinel, P., Dehaene, S., Riviere, D. & LeBihan, D. Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage 14, 1013–1026 (2001).
Ansari, D., Garcia, N., Lucas, E., Hamon, K. & Dhital, B. Neural correlates of symbolic number processing in children and adults. Neuroreport 16, 1769–1773 (2005).
Menon, V., Rivera, S. M., White, C. D., Glover, G. H. & Reiss, A. L. Dissociating prefrontal and parietal cortex activation during arithmetic processing. Neuroimage 12, 357–365 (2000).
Ansari, D., Fugelsang, J. A., Dhital, B. & Venkatraman, V. Dissociating response conflict from numerical magnitude processing in the brain: an event-related fMRI study. Neuroimage 32, 799–805 (2006).
Friston, K. J., Harrison, L. & Penny, W. Dynamic causal modelling. Neuroimage 19, 1273–1302 (2003).
Roebroeck, A., Formisano, E. & Goebel, R. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25, 230–242 (2005).
Nieder, A., Freedman, D. J. & Miller, E. K. Representation of the quantity of visual items in the primate prefrontal cortex. Science 297, 1708–1711 (2002). This single-unit neurophysiological study provided the first demonstration that there are single cells in the monkey prefrontal cortex that are sensitive to specific numerosities. Importantly, the response properties of these 'number neurons' were found to exhibit psychophysical effects (such as the size and distance effects) that had previously been found in human behavioural and neuroimaging studies.
Nieder, A. & Miller, E. K. A parieto-frontal network for visual numerical information in the monkey. Proc. Natl Acad. Sci. USA 101, 7457–7462 (2004).
Cohen Kadosh, R., Lammertyn, J. & Izard, V. Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Prog. Neurobiol. 84, 132–147 (2008).
Venkatraman, V., Ansari, D. & Chee, M. W. Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia 43, 744–753 (2005).
Shuman, M. & Kanwisher, N. Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity. Neuron 44, 557–569 (2004).
Nieder, A. The number domain— can we count on parietal cortex? Neuron 44, 407–409 (2004).
Pinel, P., Piazza, M., Le Bihan, D. & Dehaene, S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 41, 983–993 (2004).
Cohen Kadosh, R. et al. Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia 43, 1238–1248 (2005).
Norman, K. A., Polyn, S. M., Detre, G. J. & Haxby, J. V. Beyond mind-reading: multi-voxel pattern analysis of fMRI data. Trends Cogn. Sci. 10, 424–430 (2006).
Peelen, M. V. & Downing, P. E. Using multi-voxel pattern analysis of fMRI data to interpret overlapping functional activations. Trends Cogn. Sci. 11, 4–5 (2007).
Downing, P. E., Wiggett, A. J. & Peelen, M. V. Functional magnetic resonance imaging investigation of overlapping lateral occipitotemporal activations using multi-voxel pattern analysis. J. Neurosci. 27, 226–233 (2007).
Tudusciuc, O. & Nieder, A. Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proc. Natl Acad. Sci. USA 104, 14513–14518 (2007). This study made recordings from single neurons in the monkey IPS while the animal performed comparisons of both discrete (arrays of dots) and continous (length) magnitude. The results suggest that some cells code for either continuous or discrete magnitude whereas a third group responds to both, which in turn suggests that there is a highly distributed representation of numerical and non-numerical quantity at the single-cell level in the IPS.
Nieder, A., Diester, I. & Tudusciuc, O. Temporal and spatial enumeration processes in the primate parietal cortex. Science 313, 1431–1435 (2006).
Castelli, F., Glaser, D. E. & Butterworth, B. Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proc. Natl Acad. Sci. USA 103, 4693–4698 (2006).
Culham, J. C. & Kanwisher, N. G. Neuroimaging of cognitive functions in human parietal cortex. Curr. Opin. Neurobiol. 11, 157–163 (2001).
Simon, O., Mangin, J. F., Cohen, L., Le Bihan, D. & Dehaene, S. Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron 33, 475–487 (2002).
Simon, O. et al. Automatized clustering and functional geometry of human parietofrontal networks for language, space, and number. Neuroimage 23, 1192–1202 (2004).
Culham, J. C. et al. Visually guided grasping produces fMRI activation in dorsal but not ventral stream brain areas. Exp. Brain Res. 153, 180–189 (2003).
Corbetta, M. & Shulman, G. L. Control of goal-directed and stimulus-driven attention in the brain. Nature Rev. Neurosci. 3, 201–215 (2002).
Olesen, P. J., Westerberg, H. & Klingberg, T. Increased prefrontal and parietal activity after training of working memory. Nature Neurosci. 7, 75–79 (2004).
Olesen, P. J., Macoveanu, J., Tegner, J. & Klingberg, T. Brain activity related to working memory and distraction in children and adults. Cereb. Cortex 17, 1047–1054 (2007).
Walsh, V. A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn. Sci. 7, 483–488 (2003).
Nieder, A. Counting on neurons: the neurobiology of numerical competence. Nature Rev. Neurosci. 6, 177–190 (2005).
Turconi, E., Campbell, J. I. & Seron, X. Numerical order and quantity processing in number comparison. Cognition 98, 273–285 (2006).
Fias, W., Lammertyn, J., Caessens, B. & Orban, G. A. Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. J. Neurosci. 27, 8952–8956 (2007).
Ischebeck, A. et al. Are numbers special? Comparing the generation of verbal materials from ordered categories (months) to numbers and other categories (animals) in an fMRI study. Human Brain Mapp. 17 Aug 2007 (doi:10.1002/hbm.20433). This paper and reference 57 are two independently published fMRI studies that show that both numerical and non-numerical ordering tasks activate areas of the IPS (the anterior portion) that have previously been associated with numerical-quantity processing. These data suggest that there is an abstract representation of numerical order in the IPS and they thereby question the degree to which IPS activation during numerical tasks only reflects magnitude processing.
Delazer, M. & Butterworth, B. A dissociation of number meanings. Cogn. Neuropsychol. 14, 613–636 (1997).
Turconi, E. & Seron, X. Dissociation between order and quantity meaning in a patient with Gerstmann syndrome. Cortex 38, 911–914 (2002).
Turconi, E., Jemel, B., Rossion, B. & Seron, X. Electrophysiological evidence for differential processing of numerical quantity and order in humans. Brain Res. Cogn. Brain Res. 21, 22–38 (2004).
Jacob, S. N. & Nieder, A. The ABC of cardinal and ordinal number representations. Trends Cogn. Sci. 12, 41–43 (2008).
Verguts, T. & Fias, W. Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16, 1493–1504 (2004). This was the first computational model of the development of both symbolic and non-symbolic representations of numerical magnitude. The model proposes that symbolic representations develop by being mapped onto pre-existing non-symbolic representations and suggests that there are format-specific pathways from input to place coding on the mental number line.
Dehaene, S. & Changeux, J. P. Development of elementary numerical abilities: a neuronal model. J. Cogn. Neurosci. 5, 390–407 (1993).
Meck, W. H. & Church, R. M. A mode control model of counting and timing processes. J. Exp. Psychol. Anim. Behav. Process. 9, 320–334 (1983).
Roitman, J. D., Brannon, E. M. & Platt, M. L. Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biol. 5, e208 (2007). In this single-unit neurophysiology study, monkeys completed a delayed-saccade task while being presented with task-irrelevant numerosities of different numerical magnitude. Single cells in the monkey LIP were found to monotonically increase or decrease as a function of the numerical magnitude of the task-irrrelevant numerosity, thus providing single-cell evidence for the notion of accumulators or 'summation coding'.
Piazza, M., Pinel, P., Le Bihan, D. & Dehaene, S. A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53, 293–305 (2007). Using fMRI adaptation, this study shows that following adaptation to symbolic numerosity there is recovery of bilateral activity in the IPS during the presentation of non-symbolic deviants (and vice versa). However, hemispheric differences in adaptation and deviant-response suggest that there is more precise tuning to symbolic representations of numerical magnitude in the left IPS.
Gallistel, C. R. & Gelman, I. I. Non-verbal numerical cognition: from reals to integers. Trends Cogn. Sci. 4, 59–65 (2000).
Nieder, A. & Merten, K. A labeled-line code for small and large numerosities in the monkey prefrontal cortex. J. Neurosci. 27, 5986–5993 (2007).
Xia, L., Emmerton, J., Siemann, M. & Delius, J. D. Pigeons (Columba livia) learn to link numerosities with symbols. J. Comp. Psychol. 115, 83–91 (2001).
Matsuzawa, T. Use of numbers by a chimpanzee. Nature 315, 57–59 (1985).
Diester, I. & Nieder, A. Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biol. 5, e294 (2007).
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. Three parietal circuits for number processing. Cogn. Neuropsychol. 20, 487–506 (2003). This meta-analysis and review of fMRI and PET studies of numerical-magnitude processing and mental arithmetic suggests that there are three parietal regions that subserve different functions during these processes.
Kaufmann, L. et al. Neural correlates of the number-size interference task in children. Neuroreport 17, 587–591 (2006).
Piazza, M., Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44, 547–555 (2004).
Cohen Kadosh, R., Cohen Kadosh, K., Kaas, A., Henik, A. & Goebel, R. Notation-dependent and -independent representations of numbers in the parietal lobes. Neuron 53, 307–314 (2007).
Barth, H., La Mont, K., Lipton, J. & Spelke, E. S. Abstract number and arithmetic in preschool children. Proc. Natl Acad. Sci. USA 102, 14116–14121 (2005).
Dehaene, S. in Sensorimotor Foundation of Higher Cognition (eds Haggard, P., Rossetti, Y. & Kawato, M.) 527–574 (Harvard Univ.Press, Cambridge, Massachusetts, 2007).
Carey, S. Cognitive foundations of arithmetic: evolution and ontogenesis. Mind Lang. 16, 37–55 (2001).
Polk, T. A., Reed, C. L., Keenan, J. M., Hogarth, P. & Anderson, C. A. A dissociation between symbolic number knowledge and analogue magnitude information. Brain Cogn. 47, 545–563 (2001). This reference reports a patient who, following damage to the left supramarginal gyrus, lost the ability to process numerical information when it was presented in symbolic format; non-symbolic number competence was left intact. These findings reveal that there is a dissociation between the neural representation of symbolic and non-symbolic numerical magnitude.
Roux, F. E., Lubrano, V., Lauwers-Cances, V., Giussani, C. & Demonet, J. F. Cortical areas involved in Arabic number reading. Neurology 70, 210–217 (2008).
Le Corre, M. & Carey, S. One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition 105, 395–438 (2007).
Rousselle, L. & Noel, M. P. Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing. Cognition 102, 361–395 (2007).
Zorzi, M., Campbell, J. I. D. & Umilta, C. in Handbook of Mathematical Cognition (ed. Campbell, J. I. D.) 67–83 (Psychology Press, New York, 2005).
Zorzi, M. & Butterworth, B. in Twenty First Annual Conference of the Cognitive Science Society (eds Hahn, M. & Stoness, S. C.) 778–783 (Erlbaum, New Jersey, 1999). This paper contains a computational model of number comparison that, in contrast to other models, proposes that the distance effect is the function of nonlinear decision processes rather than a noisy approximate representation of numerical magnitude with either scalar variability or compressive logarithmic coding. The model predicts that numerical magnitude is represented discretely in the form of summation codes.
Henschen, S. L. On language, music and calculation. Mechanisms and their localization in the cerebrum. Z. Gesamte Neurol. Psychiatrie 52, 273–298 (1919).
Gerstmann, J. syndrome of finger agnosia, disorientation for right and left, agraphia and acalculia - local diagnostic value. Arch. Neurol. Psychiatry 44, 398–408 (1940).
Rueckert, L. et al. Visualizing cortical activation during mental calculation with functional MRI. Neuroimage 3, 97–103 (1996).
Dehaene, S. et al. Cerebral activations during number multiplication and comparison: a PET study. Neuropsychologia 34, 1097–1106 (1996).
Rickard, T. C. et al. The calculating brain: an fMRI study. Neuropsychologia 38, 325–335 (2000).
Gruber, O., Indefrey, P., Steinmetz, H. & Kleinschmidt, A. Dissociating neural correlates of cognitive components in mental calculation. Cereb. Cortex 11, 350–359 (2001).
Price, C. J. The anatomy of language: contributions from functional neuroimaging. J. Anat. 197, 335–359 (2000).
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science 284, 970–974 (1999).
Fayol, M., Barrouillet, P. & Marinthe, C. Predicting arithmetical achievement from neuro-psychological performance: a longitudinal study. Cognition 68, B63–B70 (1998).
Noel, M. P. Finger gnosia: a predictor of numerical abilities in children? Child Neuropsychol. 11, 413–430 (2005).
Rusconi, E., Walsh, V. & Butterworth, B. Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia 43, 1609–1624 (2005).
Grabner, R. H. et al. Individual differences in mathematical competence predict parietal brain activation during mental calculation. Neuroimage 38, 346–356 (2007).
Ischebeck, A., Zamarian, L., Egger, K., Schocke, M. & Delazer, M. Imaging early practice effects in arithmetic. Neuroimage 36, 993–1003 (2007).
Zago, L. et al. Neural correlates of simple and complex mental calculation. Neuroimage 13, 314–327 (2001).
Gusnard, D. A. & Raichle, M. E. Searching for a baseline: functional imaging and the resting human brain. Nature Rev. Neurosci. 2, 685–694 (2001).
Raichle, M. E. et al. A default mode of brain function. Proc. Natl Acad. Sci. USA 98, 676–682 (2001).
Shulman, G. L., Astafiev, S. V., McAvoy, M. P., d'Avossa, G. & Corbetta, M. Right TPJ deactivation during visual search: functional significance and support for a filter hypothesis. Cereb. Cortex 17, 2625–2633 (2007).
Ansari, D., Lyons, I. M., van Eimeren, L. & Xu, F. Linking visual attention and number processing in the brain: the role of the temporo-parietal junction in small and large symbolic and nonsymbolic number comparison. J. Cogn. Neurosci. 19, 1845–1853 (2007).
Delazer, M. et al. Learning complex arithmetic—an fMRI study. Brain Res. Cogn. Brain Res. 18, 76–88 (2003). This fMRI study compared brain activation during the solving of trained and untrained arithmetic problems. Whereas trained problems showed greater activation of the left angular gyrus, untrained problems were found to activate the IPS, suggesting a neural shift from the use of quantitative strategies to verbal retrieval as a function of arithmetic training.
Delazer, M. et al. Learning by strategies and learning by drill—evidence from an fMRI study. Neuroimage 25, 838–849 (2005).
Ischebeck, A. et al. How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage 30, 1365–1375 (2006).
Tang, Y. et al. Arithmetic processing in the brain shaped by cultures. Proc. Natl Acad. Sci. USA 103, 10775–10780 (2006). This fMRI study compared the brain activation of native English and Chinese speakers while they carried out mental arithmetic and made relative-magnitude judgements of Arabic numerals. It was the first investigation into the effects of culture on the neural correlates of number processing, and it revealed that culture has an effect on even the most basic aspects of the neural representation of number.
Paulesu, E. et al. A cultural effect on brain function. Nature Neurosci. 3, 91–96 (2000).
Kobayashi, C., Glover, G. H. & Temple, E. Cultural and linguistic effects on neural bases of 'Theory of Mind' in American and Japanese children. Brain Res. 1164, 95–107 (2007).
Goh, J. O. et al. Age and culture modulate object processing and object-scene binding in the ventral visual area. Cogn. Affect. Behav. Neurosci. 7, 44–52 (2007).
Sohn, M. H. et al. Behavioral equivalence, but not neural equivalence—neural evidence of alternative strategies in mathematical thinking. Nature Neurosci. 7, 1193–1194 (2004).
Lee, K. et al. Strategic differences in algebraic problem solving: neuroanatomical correlates. Brain Res. 1155, 163–171 (2007).
Rivera, S. M., Reiss, A. L., Eckert, M. A. & Menon, V. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb. Cortex 15, 1779–1790 (2005). This reference is a cross-sectional, developmental fMRI study of the neural correlates of mental arithmetic. It shows that there is an age-related shift from the engagement of frontal regions by mental arithmetic to increasing activation of the left supramarginal gyrus. The study suggests that left temporoparietal activation during mental arithmetic is the outcome of a process of developmental specialization.
Ansari, D. & Dhital, B. Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study. J. Cogn. Neurosci. 18, 1820–1828 (2006).
Cantlon, J. F., Brannon, E. M., Carter, E. J. & Pelphrey, K. A. Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biol. 4, e125 (2006). This reference reported the first fMRI study with 4-year-old children. Through the use of fMRI adaptation, it was shown that 4-year-old children and adults show similar responses to numerical deviants in the right IPS, suggesting that there are similar neural circuits for the representation of non-symbolic numerical magnitude in adults and 4-year-old children.
Izard, V., Dehaene-Lambertz, G. & Dehaene, S. Distinct cerebral pathways for object identity and number in human infants. PLoS Biol. 6, e11 (2008).
Miller, K. F., Smith, C. M., Zhu, J. & Zhang, H. Preschool origins of cross-national differences in mathematical competences: the role of number naming systems. Psychol. Sci. 6, 56–60 (1995).
Dehaene, S. & Cohen, L. Cultural recycling of cortical maps. Neuron 56, 384–398 (2007).
Shalev, R. S. in Why Is Math So Hard for Some Children? (eds Berch, D. B. & Mazzocco, M. M. M.) 49–60 (Brookes Publishing, Baltimore, 2007).
Cohen Kadosh, R. & Walsh, V. Dyscalculia. Curr. Biol. 17, R946–R947 (2007).
Ansari, D. & Karmiloff-Smith, A. Atypical trajectories of number development: a neuroconstructivist perspective. Trends Cogn. Sci. 6, 511–516 (2002).
Landerl, K., Bevan, A. & Butterworth, B. Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students. Cognition 93, 99–125 (2004).
Isaacs, E. B., Edmonds, C. J., Lucas, A. & Gadian, D. G. Calculation difficulties in children of very low birthweight: a neural correlate. Brain 124, 1701–1707 (2001).
Rotzer, S. et al. Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage 39, 417–422 (2008).
Kucian, K. et al. Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study. Behav. Brain Funct. 2, 31 (2006).
Price, G. R., Holloway, I., Rasanen, P., Vesterinen, M. & Ansari, D. Impaired parietal magnitude processing in developmental dyscalculia. Curr. Biol. 17, R1042–R1042 (2007).
Cohen-Kadosh, R. et al. Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing. Curr. Biol. 17, 689–693 (2007). This transcranial magnetic stimulation (TMS) study showed that the application of TMS to the right parietal lobe induces performance deficits on a 'number stroop' paradigm that are similar to those that are found in adult participants with developmental dyscalculia. The experiment implicates the right IPS as the region that is crucial for the automatic activation of numerical magnitude.
Sekuler, R. & Mierkiewicz, D. Children's judgments of numerical inequality. Child Dev. 48, 630–633 (1977).
Holloway, I. & Ansari, D. Domain-specific and domain-general changes in children's development of number comparison. Dev. Sci. (in the press).
Xu, F. & Spelke, E. S. Large number discrimination in 6-month-old infants. Cognition 74, B1–B11 (2000).
Lipton, J. S. & Spelke, E. S. Origins of number sense. Large-number discrimination in human infants. Psychol. Sci. 14, 396–401 (2003).
Xu, F., Spelke, E. S. & Goddard, S. Number sense in human infants. Dev. Sci. 8, 88–101 (2005).
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.
- 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.
About this article
Cite this article
Ansari, D. Effects of development and enculturation on number representation in the brain. Nat Rev Neurosci 9, 278–291 (2008). https://doi.org/10.1038/nrn2334
Neurocognitive modeling of latent memory processes reveals reorganization of hippocampal-cortical circuits underlying learning and efficient strategies
Communications Biology (2021)
npj Science of Learning (2021)
A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving
Bootstrapping of integer concepts: the stronger deviant-interpretation challenge (and how to solve it)
Fostering number sense in low SES children: a comparison between low- and high-intensity interventions
Mathematics Education Research Journal (2021)