Neurobiological Origins of Mathematical Learning Disabilities or Dyscalculia: A Review of Brain Imaging Data

  • Bert De SmedtEmail author
  • Lien Peters
  • Pol Ghesquière


The first scientific reports of mathematical learning disabilities or dyscalculia indicated that these impairments originated from abnormalities in brain structures or functions related to mathematical processing. Due to the increasing availability of non-invasive brain imaging methods in the last decades, such as magnetic resonance imaging or MRI, there has been an increase in our knowledge about the brain networks that are relevant for mathematical performance. This research was originally limited to adult participants, but there is now a nascent body of developmental imaging studies in children as well. Research in typically developing children indicates that a frontoparietal network is consistently active during number processing and arithmetic. This network shows both communalities and differences with what is being observed in adults. Children with dyscalculia show functional as well as structural abnormalities in this network. In the absence of longitudinal data, it is currently unclear whether these abnormalities are a cause or consequence of this learning disorder. Future studies are needed to investigate this.


Dyscalculia Mathematical learning disabilities Arithmetic Number processing Intraparietal sulcus Frontoparietal network fMRI Biomarkers 



This paper has some text in common with De Smedt and Ghesquière (2016) and Peters and De Smedt (2018).


  1. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: Author.CrossRefGoogle Scholar
  2. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews. Neuroscience, 9, 278–291. CrossRefGoogle Scholar
  3. Ansari, D. (2010). Neurocognitive approaches to developmental disorders of numerical and mathematical cognition: The perils of neglecting the role of development. Learning and Individual Differences, 20(2), 123–129. CrossRefGoogle Scholar
  4. Ansari, D., & Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience, 18(2004), 1820–1828. CrossRefGoogle Scholar
  5. Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. Neuroreport, 16(16), 1769–1773. CrossRefGoogle Scholar
  6. Arsalidou, M., & Taylor, M. J. (2011). Is 2 + 2 = 4? Meta-analyses of brain areas needed for numbers and calculations. NeuroImage, 54(3), 2382–2393. CrossRefGoogle Scholar
  7. Ashkenazi, S., Rosenberg-Lee, M., Tenison, C., & Menon, V. (2012). Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia. Developmental Cognitive Neuroscience, 2, S152–S166. CrossRefGoogle Scholar
  8. Barrouillet, P., Mignon, M., & Thevenot, C. (2008). Strategies in subtraction problem solving in children. Journal of Experimental Child Psychology, 99(4), 233–251. CrossRefGoogle Scholar
  9. Barth, M. E., Landsman, W. R., & Lang, M. H. (2008). International accounting standards and accounting quality. Journal of Accounting Research, 46(3), 467–498.CrossRefGoogle Scholar
  10. Berteletti, I., Prado, J., & Booth, J. R. (2014). Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems. Cortex, 57, 143–155. CrossRefGoogle Scholar
  11. Black, J. M., Myers, C. A., & Hoeft, F. (2015). The utility of neuroimaging studies for informing educational practice and policy in reading disorders. New Directions in Child and Adolescent Development, 147, 49–56. CrossRefGoogle Scholar
  12. Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332(2011), 1049–1053. CrossRefGoogle Scholar
  13. Cacioppo, J. T., Berntson, G. G., & Nusbaum, H. C. (2008). Neuroimaging as a new tool in the toolbox of psychological science. Current Directions in Psychological Science, 17, 62–67. CrossRefGoogle Scholar
  14. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4(5), 844–854. CrossRefGoogle Scholar
  15. Chang, T., Metcalfe, A. W. S., Padmanabhan, A., Chen, T., & Menon, V. (2016). Heterogeneous and nonlinear development of human posterior parietal cortex function. NeuroImage, 126, 184–195. CrossRefGoogle Scholar
  16. Christodoulou, J., Lac, A., & Moore, D. S. (2017). Babies and math: A meta-analysis of infants’ simple arithmetic competence. Developmental Psychology, 53(8), 1405–1417. CrossRefGoogle Scholar
  17. Davis, N., Cannistraci, C. J., Rogers, B. P., Gatenby, J. C., Fuchs, L. S., Anderson, A. W., & Gore, J. C. (2009). Aberrant functional activation in school age children at-risk for mathematical disability: A functional imaging study of simple arithmetic skill. Neuropsychologia, 47(12), 2470–2479. CrossRefGoogle Scholar
  18. De Smedt, B., & Ghesquière, P. (2016). Neurowetenschappelijke inzichten in de ontwikkeling van rekenstoornissen en dyscalculie [Neuroscientific insights in the development of mathematical learning disabilities and dyscalculia]. In M. H. van Ijzendoorn & L. Rosmalen (Eds.), Pedagogiek in Beeld. Houten: Bohn Stafleu Van Loghum.Google Scholar
  19. De Smedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278–292. CrossRefGoogle Scholar
  20. De Smedt, B., Holloway, I. D., & Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771–781. CrossRefGoogle Scholar
  21. De Smedt, B., Noël, M. P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48–55. CrossRefGoogle Scholar
  22. De Visscher, A., Berens, S. C., Keidel, J. L., Noël, M. P., & Bird, C. M. (2015). The interference effect in arithmetic fact solving: An fMRI study. NeuroImage, 116, 92–101. CrossRefGoogle Scholar
  23. Dehaene, S., & Cohen, L. (1997). Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex: A Journal Devoted to the Study of the Nervous System and Behavior, 33, 219–250. CrossRefGoogle Scholar
  24. Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56(2), 384–398. CrossRefGoogle Scholar
  25. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. CrossRefGoogle Scholar
  26. Duncan, G. J., Dowsett, C. J., Claessense, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.CrossRefGoogle Scholar
  27. Eickhoff, S. B., Nichols, T. E., Laird, A. R., Hoffstaedter, F., Amunts, K., Fox, P. T., et al. (2016). Behavior, sensitivity, and power of activation likelihood estimation characterized by massive empirical simulation. NeuroImage, 137, 70–85.CrossRefGoogle Scholar
  28. Feigenson, L., Libertus, M. E., & Halberda, J. (2013). Links between the intuitive sense of number and formal mathematics ability. Child Development Perspectives, 7(2), 74–79. CrossRefGoogle Scholar
  29. Fuchs, D., Compton, D. L., Fuchs, L. S., Bryant, J., & Davis, N. G. (2008). Making “secondary intervention” work in a three tier responsiveness-to-intervention model: Findings from the first grade longitudinal reading study of the National Research Center on Learning Disabilities. Reading and Writing Quarterly: An Interdisciplinary Journal, 21(4), 413–436.CrossRefGoogle Scholar
  30. Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345–362. CrossRefGoogle Scholar
  31. Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552.CrossRefGoogle Scholar
  32. Gerstmann, J. (1940). Syndrome of finger agnosia, disorientation for right and left, agraphia and acalculia. Archives of Neurology and Psychiatry, 44(2), 398–408.CrossRefGoogle Scholar
  33. Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47, 604–608. CrossRefGoogle Scholar
  34. Grabner, R. H., Ansari, D., Reishofer, G., Stern, E., Ebner, F., & Neuper, C. (2007). Individual differences in mathematical competence predict parietal brain activation during mental calculation. NeuroImage, 38, 346–356. CrossRefGoogle Scholar
  35. Henschen, S. E. (1919). Über sprach-, musik- und rechenmechanismen und ihre lokalisationen im großhirn. Zeitschrift Für Die Gesmate Neurologie Und Psychiatrie, 52(1), 273–298.CrossRefGoogle Scholar
  36. Holloway, I. D., Price, G. R., & Ansari, D. (2010). Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: An fMRI study. NeuroImage, 49(1), 1006–1017. CrossRefGoogle Scholar
  37. Ifrah, G. (1998). The universal history of numbers. London: The Harvil Press.Google Scholar
  38. Imbo, I., & Vandierendonck, A. (2007). The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96(4), 284–309.CrossRefGoogle Scholar
  39. Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain: A Journal of Neurology, 124(Pt 9), 1701–1707. CrossRefGoogle Scholar
  40. Iuculano, T., Rosenberg-Lee, M., Richardson, J., Tenison, C., Fuchs, L., Supekar, K., & Menon, V. (2015). Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications, 6(September), 8453. CrossRefGoogle Scholar
  41. Johnson, M. H. (2011). Interactive specialization: A domain-general framework for human functional brain development? Developmental Cognitive Neuroscience, 1(1), 7–21. CrossRefGoogle Scholar
  42. Johnson, M. H., & de Haan, M. (2011). Developmental cognitive neuroscience (3rd ed.). London: Wiley.Google Scholar
  43. Jolles, D., Ashkenazi, S., Kochalka, J., Evans, T., Richardson, J., Rosenberg-Lee, M., et al. (2016). Parietal hyper-connectivity, aberrant brain organization, and circuit-based biomarkers in children with mathematical disabilities. Developmental Science, 19(4), 613–631. CrossRefGoogle Scholar
  44. Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103–119. CrossRefGoogle Scholar
  45. Karmiloff-Smith, A. (2010). Neuroimaging of the developing brain: Taking “developing” seriously. Human Brain Mapping, 31(6), 934–941. CrossRefGoogle Scholar
  46. Kaufmann, L., Kucian, K., von Aster, M., Cohen Kadosh, R., & Dowker, A. (2014). Brain correlates of numerical disabilities, (September), 1–11.
  47. Kaufmann, L., Wood, G., Rubinsten, O., & Henik, A. (2011). Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. Developmental Neuropsychology, 36(6), 763–787. CrossRefGoogle Scholar
  48. Kosc, L. (1974). Developmental dyscalculia. Journal of Learning Disabilities, 7(3), 164.CrossRefGoogle Scholar
  49. Kovas, Y., Giampietro, V., Viding, E., Ng, V., Brammer, M., Barker, G. J., et al. (2009). Brain correlates of non-symbolic numerosity estimation in low and high mathematical ability children. PLoS One, 4(2), 4. CrossRefGoogle Scholar
  50. Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., et al. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782–795. CrossRefGoogle Scholar
  51. Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional MRI study. Behavioral and Brain Functions: BBF, 2, 31. CrossRefGoogle Scholar
  52. Leibovich, T., Al-Rubaiey Kadhim, S., & Ansari, D. (2017). Beyond comparison: The influence of physical size on number estimation is modulated by notation, range and spatial arrangement. Acta Psychologica, 175(March), 33–41. CrossRefGoogle Scholar
  53. Leibovich, T., & Ansari, D. (2016). The symbol-grounding problem in numerical cognition: A review of theory, evidence, and outstanding questions. Canadian Journal of Experimental Psychology, 70(1), 12–23. CrossRefGoogle Scholar
  54. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. Journal of Experimental Psychology. General, 124(1), 83–97. CrossRefGoogle Scholar
  55. Matejko, A. a., & Ansari, D. (2015). Drawing connections between white matter and numerical and mathematical cognition: A literature review. Neuroscience & Biobehavioral Reviews, 48, 35–52. CrossRefGoogle Scholar
  56. Menon, V. (2015). Arithmetic in the child and adult brain. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford University Press.Google Scholar
  57. Menon, V. (2016). Working memory in children’s math learning and its disruption in dyscalculia. Current Opinion in Behavioral Sciences, 10, 125–132. CrossRefGoogle Scholar
  58. Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14–20. CrossRefGoogle Scholar
  59. Michels, L., O’Gorman, R., & Kucian, K. (2018). Functional hyperconnectivity vanishes in children with developmental dyscalculia after numerical intervention. Developmental Cognitive Neuroscience, 30, 291–303. CrossRefGoogle Scholar
  60. Mussolin, C., De Volder, A., Grandin, C., Schlögel, X., Nassogne, M.-C., & Noël, M.-P. (2010). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22, 860–874. CrossRefGoogle Scholar
  61. Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208. CrossRefGoogle Scholar
  62. Peters, L., & De Smedt, B. (2018). Arithmetic in the developing brain: A review of brain imaging studies. Developmental Cognitive Neuroscience, 30, 265–279.CrossRefGoogle Scholar
  63. Peters, L., De Smedt, B., & Op de Beeck, H. P. (2015). The neural representation of Arabic digits in visual cortex. Frontiers in Human Neuroscience, 9(September), 517. CrossRefGoogle Scholar
  64. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41. CrossRefGoogle Scholar
  65. Polspoel, B., Peters, L., Vandermosten, M., & De Smedt, B. (2017). Strategy over operation: Neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children. Human Brain Mapping, 38, 4657.CrossRefGoogle Scholar
  66. Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), 1042–1043. CrossRefGoogle Scholar
  67. Qin, S., Cho, S., Chen, T., Rosenberg-Lee, M., Geary, D. C., & Menon, V. (2014). Hippocampal-neocortical functional reorganization underlies children’s cognitive development. Nature Neuroscience, 17(9), 1263–1269. CrossRefGoogle Scholar
  68. Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24(7), 1301–1308. CrossRefGoogle Scholar
  69. Rivera, S. M., Reiss, a. L., Eckert, M. a., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15(November), 1779–1790. CrossRefGoogle Scholar
  70. Rosenberg-Lee, M., Ashkenazi, S., Chen, T., Young, C. B., Geary, D. C., & Menon, V. (2015). Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. Developmental Science, 18(3), 351–372. CrossRefGoogle Scholar
  71. Rosenberg-Lee, M., Chang, T. T., Young, C. B., Wu, S., & Menon, V. (2011). Functional dissociations between four basic arithmetic operations in the human posterior parietal cortex: A cytoarchitectonic mapping study. Neuropsychologia, 49(9), 2592–2608. CrossRefGoogle Scholar
  72. Rotzer, S., Kucian, K., Martin, E., von Aster, M., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. NeuroImage, 39(1), 417–422. CrossRefGoogle Scholar
  73. Rykhlevskaia, E., Uddin, L. Q., Kondos, L., & Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: Combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3(November), 51. CrossRefGoogle Scholar
  74. Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), 1–16. CrossRefGoogle Scholar
  75. Schwenk, C., Sasanguie, D., Kuhn, J. T., Kempe, S., Doebler, P., & Holling, H. (2017). Non-symbolic magnitude processing in children with mathematical difficulties: a meta-analysis. Research in Developmental Disabilities, 64, 152–167. CrossRefGoogle Scholar
  76. Siegler, R. S. (1996). Emerging minds: The process of change in children’s thinking. Oxford: Oxford University Press.Google Scholar
  77. Smith, C. N., & Squire, L. R. (2009). Medial temporal lobe activity during retrieval of semantic memory is related to the age of the memory. The Journal of Neuroscience, 29(4), 930–938. CrossRefGoogle Scholar
  78. Smyth, R., & Ansari, D. (2017, August 2). P-curve analysis of infant numerosity preference data. Retrieved from
  79. Sokolowski, H. M., Fias, W., Bosah Ononye, C., & Ansari, D. (2017). Are numbers grounded in a general magnitude processing system? A functional neuroimaging meta-analysis. Neuropsychologia, 105, 50–69. CrossRefGoogle Scholar
  80. Soltész, F., Szucs, D., Dékány, J., Márkus, A., & Csépe, V. (2007). A combined event-related potential and neuropsychological investigation of developmental dyscalculia. Neuroscience Letters, 417(2), 181–186. CrossRefGoogle Scholar
  81. Tsang, J. M., Dougherty, R. F., Deutsch, G. K., Wandell, B. A., & Ben-Shachar, M. (2009). Frontoparietal white matter diffusion properties predict mental arithmetic skills in children. Proceedings of the National Academy of Sciences, 106(52), 22546–22551. CrossRefGoogle Scholar
  82. Tschentscher, N., & Hauk, O. (2014). How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies. NeuroImage, 92, 369–380. CrossRefGoogle Scholar
  83. Uddin, L. Q., Supekar, K., Amin, H., Rykhlevskaia, E., Nguyen, D. A., Greicius, M. D., & Menon, V. (2010). Dissociable connectivity within human angular gyrus and intraparietal sulcus: Evidence from functional and structural connectivity. Cerebral Cortex, 20(11), 2636–2646. CrossRefGoogle Scholar
  84. Van Beek, L., Ghesquière, P., Lagae, L., & De Smedt, B. (2014). Left fronto-parietal white matter correlates with individual differences in children’s ability to solve additions and multiplications: A tractography study. NeuroImage, 90, 117–127. CrossRefGoogle Scholar
  85. Vandermosten, M., Boets, B., Wouters, J., & Ghesquière, P. (2012). A qualitative and quantitative review of diffusion tensor imaging studies in reading and dyslexia. Neuroscience and Biobehavioral Reviews, 36(6), 1532–1552. CrossRefGoogle Scholar
  86. Vandermosten, M., Hoeft, F., & Norton, E. S. (2016). Integrating MRI brain imaging studies of pre-reading children with current theories of developmental dyslexia: A review and quantitative meta-analysis. Current Opinion in Behavioral Sciences, 10, 155–161. CrossRefGoogle Scholar
  87. Zamarian, L., & Delazer, M. (2015). Arithmetic learning in adults: Evidence from brain imaging. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford University Press.Google Scholar
  88. Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic-evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews, 33(6), 909–925. CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Psychology and Educational Sciences, Parenting and Special Education Research UnitKU LeuvenLeuvenBelgium

Personalised recommendations