Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1

    Brannon, E. M. & Terrace, H. S. Ordering of the numerosities 1 to 9 by monkeys. Science 282, 746–749 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. 2

    Boysen, S. T. & Berntson, G. G. Numerical competence in a chimpanzee (Pan troglodytes). J. Comp. Psychol. 103, 23–31 (1989).

    Article  CAS  PubMed  Google Scholar 

  3. 3

    Cantlon, J. F. & Brannon, E. M. Shared system for ordering small and large numbers in monkeys and humans. Psychol. Sci. 17, 401–406 (2006).

    Article  PubMed  Google Scholar 

  4. 4

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. 5

    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).

    Article  CAS  PubMed  Google Scholar 

  6. 6

    Washburn, D. A. & Rumbaugh, D. M. Ordinal judgments of numerical symbols by macaques (Macaca mulatta). Psychol. Sci. 2, 190–193 (1991).

    Article  CAS  PubMed  Google Scholar 

  7. 7

    Koehler, O. Vom erlernen unbenannter anzahlen bei vögeln. Naturwissenschaften 29 (1941).

    Google Scholar 

  8. 8

    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).

    Article  CAS  PubMed  Google Scholar 

  9. 9

    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).

    Article  PubMed  PubMed Central  Google Scholar 

  10. 10

    Brannon, E. The representation of numerical magnitude. Curr. Opin. Neurobiol. 16, 222–229 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. 11

    Dehaene, S. Varieties of numerical abilities. Cognition 44, 1–42 (1992).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. 12

    Dehaene, S. The Number Sense: How The Mind Creates Mathematics (Oxford Univ. Press, Oxford, 1997).

    Google Scholar 

  13. 13

    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).

    Article  Google Scholar 

  14. 14

    Hubbard, E. M., Piazza, M., Pinel, P. & Dehaene, S. Interactions between number and space in parietal cortex. Nature Rev. Neurosci. 6, 435–448 (2005).

    Article  CAS  Google Scholar 

  15. 15

    Simon, T. J. The foundations of numerical thinking in a brain without numbers. Trends Cogn. Sci. 3, 363–365 (1999).

    Article  CAS  PubMed  Google Scholar 

  16. 16

    Fias, W. & Fischer, M. H. in Handbook of Mathematical Cognition (ed. Campbell, J. I. D.) 43–54 (Psychology Press, New York, 2005).

    Google Scholar 

  17. 17

    Moyer, R. S. & Landauer, T. K. Time required for judgements of numerical inequality. Nature 215, 1519–1520 (1967).

    Article  CAS  PubMed  Google Scholar 

  18. 18

    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).

    Article  CAS  PubMed  Google Scholar 

  19. 19

    Whalen, J., Gallistel, C. R. & Gelman, I. I. Nonverbal counting in humans: the psychophysics of number representation. Psychol. Sci. 2, 130–137 (1999).

    Article  Google Scholar 

  20. 20

    Barth, H., Kanwisher, N. & Spelke, E. The construction of large number representations in adults. Cognition 86, 201–221 (2003).

    Article  PubMed  Google Scholar 

  21. 21

    Feigenson, L., Dehaene, S. & Spelke, E. Core systems of number. Trends Cogn. Sci. 8, 307–314 (2004).

    Article  PubMed  PubMed Central  Google Scholar 

  22. 22

    Dehaene, S., Dehaene-Lambertz, G. & Cohen, L. Abstract representations of numbers in the animal and human brain. Trends Neurosci. 21, 355–361 (1998).

    Article  CAS  PubMed  Google Scholar 

  23. 23

    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).

    Article  PubMed  Google Scholar 

  24. 24

    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).

    Article  CAS  PubMed  Google Scholar 

  25. 25

    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).

    Article  Google Scholar 

  26. 26

    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).

    Article  CAS  PubMed  Google Scholar 

  27. 27

    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).

    Article  CAS  PubMed  Google Scholar 

  28. 28

    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).

    Article  PubMed  Google Scholar 

  29. 29

    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).

    Article  CAS  PubMed  Google Scholar 

  30. 30

    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).

    Article  PubMed  Google Scholar 

  31. 31

    Friston, K. J., Harrison, L. & Penny, W. Dynamic causal modelling. Neuroimage 19, 1273–1302 (2003).

    Article  CAS  PubMed  Google Scholar 

  32. 32

    Roebroeck, A., Formisano, E. & Goebel, R. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25, 230–242 (2005).

    Article  PubMed  Google Scholar 

  33. 33

    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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. 34

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. 35

    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).

    Article  PubMed  Google Scholar 

  36. 36

    Venkatraman, V., Ansari, D. & Chee, M. W. Neural correlates of symbolic and non-symbolic arithmetic. Neuropsychologia 43, 744–753 (2005).

    Article  PubMed  Google Scholar 

  37. 37

    Shuman, M. & Kanwisher, N. Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity. Neuron 44, 557–569 (2004).

    Article  CAS  PubMed  Google Scholar 

  38. 38

    Nieder, A. The number domain— can we count on parietal cortex? Neuron 44, 407–409 (2004).

    Google Scholar 

  39. 39

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. 40

    Cohen Kadosh, R. et al. Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia 43, 1238–1248 (2005).

    Article  PubMed  Google Scholar 

  41. 41

    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).

    Article  PubMed  PubMed Central  Google Scholar 

  42. 42

    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).

    Article  PubMed  Google Scholar 

  43. 43

    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).

    Article  CAS  Google Scholar 

  44. 44

    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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. 45

    Nieder, A., Diester, I. & Tudusciuc, O. Temporal and spatial enumeration processes in the primate parietal cortex. Science 313, 1431–1435 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. 46

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. 47

    Culham, J. C. & Kanwisher, N. G. Neuroimaging of cognitive functions in human parietal cortex. Curr. Opin. Neurobiol. 11, 157–163 (2001).

    Article  CAS  PubMed  Google Scholar 

  48. 48

    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).

    Article  CAS  PubMed  Google Scholar 

  49. 49

    Simon, O. et al. Automatized clustering and functional geometry of human parietofrontal networks for language, space, and number. Neuroimage 23, 1192–1202 (2004).

    Article  PubMed  Google Scholar 

  50. 50

    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).

    Article  PubMed  Google Scholar 

  51. 51

    Corbetta, M. & Shulman, G. L. Control of goal-directed and stimulus-driven attention in the brain. Nature Rev. Neurosci. 3, 201–215 (2002).

    Article  CAS  Google Scholar 

  52. 52

    Olesen, P. J., Westerberg, H. & Klingberg, T. Increased prefrontal and parietal activity after training of working memory. Nature Neurosci. 7, 75–79 (2004).

    Article  CAS  PubMed  Google Scholar 

  53. 53

    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).

    Article  PubMed  Google Scholar 

  54. 54

    Walsh, V. A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn. Sci. 7, 483–488 (2003).

    Article  PubMed  PubMed Central  Google Scholar 

  55. 55

    Nieder, A. Counting on neurons: the neurobiology of numerical competence. Nature Rev. Neurosci. 6, 177–190 (2005).

    Article  CAS  Google Scholar 

  56. 56

    Turconi, E., Campbell, J. I. & Seron, X. Numerical order and quantity processing in number comparison. Cognition 98, 273–285 (2006).

    Article  PubMed  Google Scholar 

  57. 57

    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).

    Article  CAS  PubMed  Google Scholar 

  58. 58

    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.

  59. 59

    Delazer, M. & Butterworth, B. A dissociation of number meanings. Cogn. Neuropsychol. 14, 613–636 (1997).

    Article  Google Scholar 

  60. 60

    Turconi, E. & Seron, X. Dissociation between order and quantity meaning in a patient with Gerstmann syndrome. Cortex 38, 911–914 (2002).

    Article  Google Scholar 

  61. 61

    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).

    Article  PubMed  Google Scholar 

  62. 62

    Jacob, S. N. & Nieder, A. The ABC of cardinal and ordinal number representations. Trends Cogn. Sci. 12, 41–43 (2008).

    Article  PubMed  Google Scholar 

  63. 63

    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.

    Article  PubMed  PubMed Central  Google Scholar 

  64. 64

    Dehaene, S. & Changeux, J. P. Development of elementary numerical abilities: a neuronal model. J. Cogn. Neurosci. 5, 390–407 (1993).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  65. 65

    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).

    Article  CAS  PubMed  Google Scholar 

  66. 66

    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'.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  67. 67

    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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  68. 68

    Gallistel, C. R. & Gelman, I. I. Non-verbal numerical cognition: from reals to integers. Trends Cogn. Sci. 4, 59–65 (2000).

    Article  CAS  PubMed  Google Scholar 

  69. 69

    Nieder, A. & Merten, K. A labeled-line code for small and large numerosities in the monkey prefrontal cortex. J. Neurosci. 27, 5986–5993 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. 70

    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).

    Article  CAS  PubMed  Google Scholar 

  71. 71

    Matsuzawa, T. Use of numbers by a chimpanzee. Nature 315, 57–59 (1985).

    Article  CAS  PubMed  Google Scholar 

  72. 72

    Diester, I. & Nieder, A. Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biol. 5, e294 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. 73

    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.

    Article  PubMed  Google Scholar 

  74. 74

    Kaufmann, L. et al. Neural correlates of the number-size interference task in children. Neuroreport 17, 587–591 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  75. 75

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. 76

    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).

    Article  CAS  PubMed  Google Scholar 

  77. 77

    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).

    Article  CAS  PubMed  Google Scholar 

  78. 78

    Dehaene, S. in Sensorimotor Foundation of Higher Cognition (eds Haggard, P., Rossetti, Y. & Kawato, M.) 527–574 (Harvard Univ.Press, Cambridge, Massachusetts, 2007).

    Google Scholar 

  79. 79

    Carey, S. Cognitive foundations of arithmetic: evolution and ontogenesis. Mind Lang. 16, 37–55 (2001).

    Article  Google Scholar 

  80. 80

    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.

    Article  CAS  PubMed  Google Scholar 

  81. 81

    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).

    Article  PubMed  Google Scholar 

  82. 82

    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).

    Article  PubMed  Google Scholar 

  83. 83

    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).

    Article  PubMed  Google Scholar 

  84. 84

    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).

    Google Scholar 

  85. 85

    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.

    Google Scholar 

  86. 86

    Henschen, S. L. On language, music and calculation. Mechanisms and their localization in the cerebrum. Z. Gesamte Neurol. Psychiatrie 52, 273–298 (1919).

    Article  Google Scholar 

  87. 87

    Gerstmann, J. syndrome of finger agnosia, disorientation for right and left, agraphia and acalculia - local diagnostic value. Arch. Neurol. Psychiatry 44, 398–408 (1940).

    Article  Google Scholar 

  88. 88

    Rueckert, L. et al. Visualizing cortical activation during mental calculation with functional MRI. Neuroimage 3, 97–103 (1996).

    Article  CAS  PubMed  Google Scholar 

  89. 89

    Dehaene, S. et al. Cerebral activations during number multiplication and comparison: a PET study. Neuropsychologia 34, 1097–1106 (1996).

    Article  CAS  PubMed  Google Scholar 

  90. 90

    Rickard, T. C. et al. The calculating brain: an fMRI study. Neuropsychologia 38, 325–335 (2000).

    Article  CAS  PubMed  Google Scholar 

  91. 91

    Gruber, O., Indefrey, P., Steinmetz, H. & Kleinschmidt, A. Dissociating neural correlates of cognitive components in mental calculation. Cereb. Cortex 11, 350–359 (2001).

    Article  CAS  Google Scholar 

  92. 92

    Price, C. J. The anatomy of language: contributions from functional neuroimaging. J. Anat. 197, 335–359 (2000).

    Article  PubMed  PubMed Central  Google Scholar 

  93. 93

    Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science 284, 970–974 (1999).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  94. 94

    Fayol, M., Barrouillet, P. & Marinthe, C. Predicting arithmetical achievement from neuro-psychological performance: a longitudinal study. Cognition 68, B63–B70 (1998).

    Article  CAS  PubMed  Google Scholar 

  95. 95

    Noel, M. P. Finger gnosia: a predictor of numerical abilities in children? Child Neuropsychol. 11, 413–430 (2005).

    Article  PubMed  Google Scholar 

  96. 96

    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).

    Article  PubMed  Google Scholar 

  97. 97

    Grabner, R. H. et al. Individual differences in mathematical competence predict parietal brain activation during mental calculation. Neuroimage 38, 346–356 (2007).

    Article  PubMed  Google Scholar 

  98. 98

    Ischebeck, A., Zamarian, L., Egger, K., Schocke, M. & Delazer, M. Imaging early practice effects in arithmetic. Neuroimage 36, 993–1003 (2007).

    Article  PubMed  Google Scholar 

  99. 99

    Zago, L. et al. Neural correlates of simple and complex mental calculation. Neuroimage 13, 314–327 (2001).

    Article  CAS  PubMed  Google Scholar 

  100. 100

    Gusnard, D. A. & Raichle, M. E. Searching for a baseline: functional imaging and the resting human brain. Nature Rev. Neurosci. 2, 685–694 (2001).

    CAS  Google Scholar 

  101. 101

    Raichle, M. E. et al. A default mode of brain function. Proc. Natl Acad. Sci. USA 98, 676–682 (2001).

    Article  CAS  PubMed  Google Scholar 

  102. 102

    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).

    Article  PubMed  Google Scholar 

  103. 103

    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).

    Article  PubMed  Google Scholar 

  104. 104

    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.

    Article  CAS  PubMed  Google Scholar 

  105. 105

    Delazer, M. et al. Learning by strategies and learning by drill—evidence from an fMRI study. Neuroimage 25, 838–849 (2005).

    Article  CAS  PubMed  Google Scholar 

  106. 106

    Ischebeck, A. et al. How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage 30, 1365–1375 (2006).

    Article  PubMed  Google Scholar 

  107. 107

    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.

    Article  CAS  PubMed  Google Scholar 

  108. 108

    Paulesu, E. et al. A cultural effect on brain function. Nature Neurosci. 3, 91–96 (2000).

    Article  CAS  PubMed  Google Scholar 

  109. 109

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  110. 110

    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).

    Article  PubMed  Google Scholar 

  111. 111

    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).

    Article  CAS  PubMed  Google Scholar 

  112. 112

    Lee, K. et al. Strategic differences in algebraic problem solving: neuroanatomical correlates. Brain Res. 1155, 163–171 (2007).

    Article  CAS  PubMed  Google Scholar 

  113. 113

    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.

    Article  CAS  Google Scholar 

  114. 114

    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).

    Article  PubMed  PubMed Central  Google Scholar 

  115. 115

    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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  116. 116

    Izard, V., Dehaene-Lambertz, G. & Dehaene, S. Distinct cerebral pathways for object identity and number in human infants. PLoS Biol. 6, e11 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  117. 117

    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).

    Article  Google Scholar 

  118. 118

    Dehaene, S. & Cohen, L. Cultural recycling of cortical maps. Neuron 56, 384–398 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  119. 119

    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).

    Google Scholar 

  120. 120

    Cohen Kadosh, R. & Walsh, V. Dyscalculia. Curr. Biol. 17, R946–R947 (2007).

    Article  CAS  PubMed  Google Scholar 

  121. 121

    Ansari, D. & Karmiloff-Smith, A. Atypical trajectories of number development: a neuroconstructivist perspective. Trends Cogn. Sci. 6, 511–516 (2002).

    Article  PubMed  Google Scholar 

  122. 122

    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).

    Article  PubMed  Google Scholar 

  123. 123

    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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  124. 124

    Rotzer, S. et al. Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage 39, 417–422 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. 125

    Kucian, K. et al. Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study. Behav. Brain Funct. 2, 31 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  126. 126

    Price, G. R., Holloway, I., Rasanen, P., Vesterinen, M. & Ansari, D. Impaired parietal magnitude processing in developmental dyscalculia. Curr. Biol. 17, R1042–R1042 (2007).

    Article  CAS  PubMed  Google Scholar 

  127. 127

    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.

    Article  CAS  PubMed  Google Scholar 

  128. 128

    Sekuler, R. & Mierkiewicz, D. Children's judgments of numerical inequality. Child Dev. 48, 630–633 (1977).

    Article  Google Scholar 

  129. 129

    Holloway, I. & Ansari, D. Domain-specific and domain-general changes in children's development of number comparison. Dev. Sci. (in the press).

  130. 130

    Xu, F. & Spelke, E. S. Large number discrimination in 6-month-old infants. Cognition 74, B1–B11 (2000).

    Article  CAS  PubMed  Google Scholar 

  131. 131

    Lipton, J. S. & Spelke, E. S. Origins of number sense. Large-number discrimination in human infants. Psychol. Sci. 14, 396–401 (2003).

    Article  PubMed  Google Scholar 

  132. 132

    Xu, F., Spelke, E. S. & Goddard, S. Number sense in human infants. Dev. Sci. 8, 88–101 (2005).

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Related links

Related links

FURTHER INFORMATION

Daniel Ansari's homepage

Numerical Cognition Laboratory

Numeracy and Literacy Research Group

Brannon Lab

Cognitive Neuroimaging Unit

Computational Cognitive Neuroscience Laboratory

Primate Neurocognition Laboratory

Laboratory for Developmental Studies

Cognitive & Systems Neuroscience Laboratory

Number Processing and Calculation Research Group

Glossary

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.

Numerosity

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.

Modularity

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.

Ordinality

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).

Enculturation

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.

Rights and permissions

Reprints and Permissions

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

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing