Skip to main content
SpringerLink
Log in

Mathematics and the brain: uncharted territory?

  • Published:
European Child & Adolescent Psychiatry Aims and scope Submit manuscript

Abstract

The prevalence of disorders of arithmetic skills in children of circa 6% calls for intensive consideration of the subject by health care providers and researchers. The necessity of interdisciplinary cooperation is evident. The current classifications by the ICD-10 (Specific disorder of arithmetic skills) and DSM-IV (Mathematics disorder) represent different viewpoints. A developmental dyscalculia is exclusively diagnosed according to clinical presentation. Arithmetic and its disorders are brain functions, determined and influenced by the (cerebral) human development. With modern neuroimaging techniques, a connectionistic model of distinct arithmetic functions has been specified. The results of single case descriptions of arithmetic disorders correspond well in that context with the concept of parallel cortico-subcortical and subcortico-cortical neuronal circuits. In comparison with dyslexia, there is intense need for research in the field of arithmetic disorders. Only through analysis and understanding of the complex cerebral connections in arithmetic can improved diagnostic as well as multidimensionally therapeutic approaches to arithmetic disorders be achieved, possibly opening new ways of academic and social integration of the affected individuals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aebli H (1998) Zwölf Grundformen des Lehrens. BD 1. Eine Allgemeine Didaktik. Medien und Inhalte didaktischer Kommunikation, der Lernzyklus. 10. Auflage. Stuttgart: Klett-Cotta

    Google Scholar 

  2. Anderson B, Harvey T (1996) Alterations in cortical thickness and neuronal density in the frontal cortex of Albert Einstein. Neuroscience Letters 210: 161–164

    Article  CAS  PubMed  Google Scholar 

  3. Assal G, Jacot-Descombes C (1984) Intitution arithmétique chez un acalculique. Revue Neurologique 140: 374–375

    CAS  PubMed  Google Scholar 

  4. Badian NA (1983) Dyscalculia and nonverbal disorders of learning. In: Myklebust HR (Ed) Progress in Learning Disabilities (pp 235–264). New York: Grune & Stratton

    Google Scholar 

  5. Berger H (1926) Über Rechenstörungen bei Herderkrankungen des Großhirns. Archiv für Psychiatrie 78: 238–263

    Article  Google Scholar 

  6. Black SE, Behrmann M (1994) Localisation in alexia. In: Kertesz A (ed) Localisation and Neuroimaging in Neuropsychology (pp 331–376). San Diego: Academic Press

    Google Scholar 

  7. Boller F (1983) Acalculia: historical development and current significance. Brain and Cognition 2: 205–223

    Article  CAS  PubMed  Google Scholar 

  8. Boller F, Grafman I (1985) Acalculia. In: Frederiks JAM (ed) Handbook of Clinical Neurology. Vol 1 (45): Clinical Neuropsychology (pp 473–481). Amsterdam: Elsevier Science Publishers B V

    Google Scholar 

  9. Bryant P (1995) Children and arithmetic. Journal of Child Psychology and Psychiatry 36: 3–32

    Article  CAS  PubMed  Google Scholar 

  10. Butterworth B (1999) A head for figures. Science 284: 928–929

    Article  CAS  PubMed  Google Scholar 

  11. Campbell JID, Clark JM (1988) An encoding-complex view of cognitive number processing: comment on McCloskey, Sokol, and Goodman (1986). Journal of Experimental Psychology: General 117: 204–214

    Article  Google Scholar 

  12. Cappa S, Wallesch CW (1994) Subcortical lesions and cognitive deficits. In: Kertesz A (ed) Localisation and Neuroimaging in Neuropsychology (pp 545–566). San Diego: Academic Press

    Google Scholar 

  13. Cohn R (1968) Developmental dyscalculia. Pediatric Clinics of North America 15: 651–668

    CAS  PubMed  Google Scholar 

  14. Dehaene S, Cohen L (1991) Two mental calculation systems: a case study of severe acalculia with preserved approximation. Neuropsychologia 29: 1045–1074

    Article  CAS  PubMed  Google Scholar 

  15. Dehaene S, Cohen L (1995) Towards an anatomical and functional model of number processing. Mathematical Cognition 1: 83–120

    Google Scholar 

  16. Dehaene S, Tzourio N, Frak V, Raynaud L, Cohen L, Mehler J, Mazoyer B (1996) Cerebral activitions during number multiplication and comparison: a PET study. Neuropsychologia 34: 1097–1106

    Article  CAS  PubMed  Google Scholar 

  17. Dehaene S, Cohen L (1997) Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33: 219–250

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  20. Diagnostic and Statistical Manual of Mental Disorders (1994). 4th ed (DSM-IV). Washington, D.C.: American Psychiatric Association

  21. Fisher SE, Marlow AJ, Lamb J, Maestrini E, Williams DF, Richardson AJ, Weeks DE, Stein JF, Monaco AP (1999) A quantitativetrait locus on chromosome 6p influences different aspects of developmental dyslexia. American Journal of Human Gentics 64: 146–156

    Article  CAS  Google Scholar 

  22. Giedd JN, Blumenthal J, Jeffries NO, Castellanos FX, Liu H, Zijdenbos A, Paus T, Evans AC, Rapoport JL (1999) Cerebral cortical gray matter changes during childhood and adolescence: a longitudinal MRI study. Nature Neuroscience 10: 861–863

    Article  Google Scholar 

  23. Gordon N, (1992) Children with developmental dyscalculia. Developmental Medicine and Child Neurology 34: 459–463

    CAS  PubMed  Google Scholar 

  24. Gross-Tsur V, Manor O, Shalev RS (1993) Developmental dyscalculia, gender and the brain. Archives of Disease in Childhood 68: 510–512

    Article  CAS  PubMed  Google Scholar 

  25. Gross-Tsur V, Manor O, Shalev RS (1996) Developmental dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology 38: 25–33

    Article  CAS  PubMed  Google Scholar 

  26. Guttmann E (1937) Congenital arithmetic disability and acalculia (Henschen). British Journal of Medical Psychology 16: 16–35

    Google Scholar 

  27. Hartje W, Dahmen W, Zeumer H (1981) Spezielle Schreib- und Rechenstörungen bei drei Patienten nach Läsion im linken parieto-okzipitalen Übergangsbereich. Der Nervenarzt 53: 159–163

    Google Scholar 

  28. Henschen SE (1919) Über Sprach-, Musik-und Rechenmechanismen und ihre Lokalisationen im Großhirn. Zeitschrift für die gesamte Neurologie und Psychiatrie 52: 273–298

    Article  Google Scholar 

  29. Hittmair-Delazer M, Semenza C, Denes G (1994) Concepts and facts in calculation. Brain 117: 715–728

    Article  PubMed  Google Scholar 

  30. Horwitz B, Rumsey JM, Donohue BC (1998) Functional connectivity of the angular gyrus in normal reading and dyslexia. Proceedings of the National Academy of Sciences of the United States of America 95: 8939–8944

    Article  CAS  PubMed  Google Scholar 

  31. Interagency Committee on Learning Disabilities. Learning disabilities: a report to the U.S. Congress (1987) Washington, D C: Government Printing Office

    Google Scholar 

  32. Internationale Klassifikation psychischer Störungen ICD-10. Kapitel V (F). Klinisch-diagnostische Leitlinien. Dilling H, Mombour W, Schmidt MH (eds) 2nd edition (1993) Bern, Göttingen, Toronto, Seattle: Huber

    Google Scholar 

  33. Kawai N, Matsuzawa T (2000) Numerical memory span in a chimpanzee. Nature 403: 39

    Article  CAS  PubMed  Google Scholar 

  34. Kiefer M, Dehaene S (1997) The time course of parietal activitation in single-digit multiplication: evidence from event-related potentials. Mathematical Cognition 3: 1–30

    Article  Google Scholar 

  35. Kigar DL, Witelson SF, Glezer II, Harvey T (1997) Estimates of cell number in temporal neocortex in the brain of Albert Einstein. Social Neurosciences Abstracts 23: No 89.9

  36. Kleist K (1934) Gehirnpathologie. Vornehmlich auf Grund von Kriegserfahrungen. Leipzig: J. A. Barth

    Google Scholar 

  37. Kosc L (1974) Developmental dyscalculia. Journal of Learning Disabilities 7: 46–59

    Article  Google Scholar 

  38. Kulak AG (1993) Parallels between math and reading disability: common issues and approaches. Journal of Learning Disabilities 26: 666–673

    Article  CAS  PubMed  Google Scholar 

  39. Leonhard K (1939) Die Bedeutung optischräumlicher Vorstellungen für das elementare Rechnen. Zeitschrift für die gesamte Neurologie und Psychiatrie 164: 321–351

    Article  Google Scholar 

  40. Leonhard K (1940) Vorstellungstypen des elementaren Rechmens. Zeitschrift für angewandte Psychologie und Charakterkunde 58: 193–212

    Google Scholar 

  41. Leonhard K (1952) Rechen- und zeitliche Orientierungsstörung bei Agraphie und konstruktiver Apraxie. Archiv für Psychiatrie und Nervenkrankheiten 188: 504–510

    Article  CAS  Google Scholar 

  42. Levin HS, Scheller J, Richard T, Grafman J, Martinkowski K, Winslow M, Mirvis S (1996) Dyscalculia and dyslexia after right hemisphere injury in infancy. Archives of Neurology 53: 88–96

    CAS  PubMed  Google Scholar 

  43. Lewandowsky M, Stadelmann E (1908) Über einen bemerkenswerten Fall von Hirnblutung und über Rechenstörungen bei Herderkrankung des Gehirns. Journal für Psychologie und Neurologie 11: 249–265

    Google Scholar 

  44. Lewis C, Hitch G, Walker P (1994) The prevalence of specific arithmetic difficulties and specific reading difficulties in 9-to 10-year-old boys and girls. Journal of Cognition Psychology and Psychiatry 35: 283–292

    Article  CAS  Google Scholar 

  45. Lucchelli F, De Renzi E (1993) Primary dyscalculia after a medical frontal lesion of the left hemisphere. Journal of Neurology, Neurosurgery, and Psychiatry 56: 304–307

    Article  CAS  PubMed  Google Scholar 

  46. Luria AR (1980) Higher Cortical Function in Man. Second edition. New York: Basic Books

    Google Scholar 

  47. McCloskey M, Caramazza A, Basili AG (1985) Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain and Cognition 4: 171–196

    Article  CAS  PubMed  Google Scholar 

  48. Ojeman G (1974) Mental arithmetic during thalamic stimulation. Neuropsychologia 12: 1–10

    Article  Google Scholar 

  49. Paulesu E, Frith U, Snowling M, Gallagher A, Morton J, Frackowiak RSJ, Frith CD (1996) Is developmental dyslexia a disconnection syndrome? Evidence from PET scanning. Brain 119: 143–157

    Article  PubMed  Google Scholar 

  50. Peritz G (1918) Zur Pathopsychologie des Rechnens. Deutsche Zeitschrift für Nervenheilkunde 61: 234–340

    Article  Google Scholar 

  51. Petersen SE, Fiez JA (1993) The processing of single words studied with positron emission tomography. Annual Review Neurosciences 16: 509–530

    Article  CAS  Google Scholar 

  52. Piaget J (1952) The Child’s Conception of Number. London: Routledge and Kegan Paul

    Google Scholar 

  53. Piaget J, Szeminska A (1965) Die Entwicklung des Zahlbegriffs beim Kinde. Stuttgart: Kohlhammer

    Google Scholar 

  54. Poeppel D, Rowley HA (1996) Magnetic source imaging and the neural basis of dyslexia. Annals of Neurology 40: 137–138

    Article  CAS  PubMed  Google Scholar 

  55. Pugh KR, Shaywitz BA, Shaywitz SE, Constable RT, Skudlarsky P, Fulbright, RK, Bronen RA, Shankweiler DP, Katz L, Fletcher JM, Gore JC (1996) Cerebral organization of component processes in reading. Brain 119: 1221–1238

    Article  PubMed  Google Scholar 

  56. Rapoport JL (2000) The Development of neurodevelopmental psychiatry. American Journal of Psychiatry 157: 159–161

    Article  Google Scholar 

  57. Remschmidt H, Schulte-Körne G, Warnke A, Propping P (eds) (1999) Genetics of dyslexia. European Child and Adolescent Psychiatry 8: suppl 3

  58. Rispens J, Yperen TA van (1997) How specific are “Specific developmental disorders”? The relevance of the concept of specific developmental disorders for the classification of childhood developmental disorders. Journal of Child Psychology and Psychiatry 38: 351–363

    Article  CAS  PubMed  Google Scholar 

  59. Rosenberger PB (1989) Perceptual-motor and attentional correlates of developmental dyscalculia. Annals of Neurology 26: 216–220

    Article  Google Scholar 

  60. Rutter M, Shaffer D, Shepherd M (1975) A Multi-axial Classification of Child Psychiatric Disorders. An Evaluation of a Proposal. Geneva: World Health Organisation

    Google Scholar 

  61. Shalev RS, Auerbach J, Gross-Tsur V (1995) Developmental dyscalculia behavioral and attentional aspects: a research note. The Journal of Child Psychology and Psychiatry 36: 1261–1268

    Article  CAS  Google Scholar 

  62. Shalev RS, Manor O, Amir N, Wertman-Elad R, Gross-Tsur V (1995) Developmental dyscalculia and brain laterality. Cortex 31: 357–365

    CAS  PubMed  Google Scholar 

  63. Shalev RS, Manor O, Auerbach J, Gross-Tsur V (1998) Persistence of developmental dyscalculia: what counts? Results from a 3-year prospective study. The Journal of Pediatrics 133: 358–362

    Article  CAS  PubMed  Google Scholar 

  64. Shaywitz SE (1998) Dyslexia. New England Journal of Medicine 338: 307–312

    Article  CAS  PubMed  Google Scholar 

  65. Shaywitz SE, Shaywitz BA, Pugh KR, Fulbright RK, Constable, RT, Mencl WE, Shankweiler DP, Liberman AM, Skudlarski P, Fletcher JM, Katz L, Marchione KE, Lacadie C, Gatenby C, Gore JC (1998) Functional disruption in the organization of the brain for reading in dyslexia. Proceedings of the National Academy of Sciences of the United States of America 95: 2636–2641

    Article  CAS  PubMed  Google Scholar 

  66. Shekim WO, Dekirmenjian H (1978) Catacholamine metabolites in nonhyperactive boys with arithmetic learning disability: a pilot study. The American Journal of Psychiatry 135: 490–491

    CAS  PubMed  Google Scholar 

  67. Slade PD, Russell GFM (1971) Developmental dyscalculia: a brief report on four cases. Psychological Medicine 1: 292–298

    Article  CAS  PubMed  Google Scholar 

  68. Sokoloff L, Mangold R, Wechsler RL, Kennedy C, Kety SS (1955) The effect of mental arithmetic on cerebral circulation and metabolism. Journal of Clinical Investigations 34: 1101–1108

    Article  CAS  Google Scholar 

  69. Stein J, Walsh V (1997) To see but not to read; the magnocellular theory of dyslexia. Trends in Neurosciences 20: 147–152

    Article  CAS  PubMed  Google Scholar 

  70. Takayama Y, Sugishita M, Akiguchi I, Kimura J (1994) Isolated Acalculia due to left parietal lesion. Archives of Neurology 51: 286–291

    CAS  PubMed  Google Scholar 

  71. Temple CM (1992) Developmental dyscalculia. In: Segalowitz SJ, Rapin I (vol eds) Handbook of Neuropsychology Vol. 6: Child psychology (pp 211–222). Amsterdam: Elsevier Science

    Google Scholar 

  72. Temple CM (1997) Cognitive neuropsychology and its application to children. The Journal of Child Psychology and Psychiatry 38: 27–52

    Article  CAS  Google Scholar 

  73. Weintraub S, Mesulam MM (1983) Developmental learning disabilities of the right hemisphere. Emotional, interpersonal, and cognitive components. Archives of Neurology 40: 463–468

    CAS  PubMed  Google Scholar 

  74. Witelson SF, Kigar DL, Harvey T (1999) The exceptional brain of Albert Einstein. The Lancet 353: 2149–2153

    Article  CAS  Google Scholar 

  75. Wynn K (1992) Addition and subtraction by human infants. Nature 358: 749–750

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Clinic of Child and Adolescent Psychiatry and Psychotherapy Charité Hospital, Campus Mitte Medical Faculty of, Humboldt-University of Berlin, Schumannstraße 20/21, 10098, Berlin, Germany

    Klaus-Jürgen Neumärker

Authors
  1. Klaus-Jürgen Neumärker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Klaus-Jürgen Neumärker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neumärker, KJ. Mathematics and the brain: uncharted territory?. European Child & Adolescent Psychiatry 9 (Suppl 2), S2–S10 (2000). https://doi.org/10.1007/s007870070002

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s007870070002

Key words

Search

Navigation