Developmental cognitive neuropsychology of number processing and calculation: varieties of developmental dyscalculia

Abstract

This article provides a brief overview about the current state of cognitive developmental neuropsychology of developmental dyscalculia (DD) as well as results from a Zurich study that investigates different subtypes of DD according to various aspects of numerical abilities that are impaired or preserved. The differential effects of impairments of one particular numerical area on the development of other numerical abilities are highlighted in the case of a 17 year old boy with severe DD and Developmental Gerstmann Syndrome. A comprehensive model of developmental dynamics of number processing and calculation abilities will be proposed in the last section with respect to the development of intelligence theory.

Key words

Number processing calculation development information processing developmental dyscalculia subtypes theory of intelligence 

References

  1. 1.
    Anderson M (1992) Intelligence and Development. A Cognitive Theory. Oxford: BlackwellGoogle Scholar
  2. 2.
    American Psychiatric Association (1994). Diagnostic and Statistical manual of Mental Disorders (4th edn) Washington, DC: APAGoogle Scholar
  3. 3.
    Ashcraft MH, Faust MW (1994) Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion 8: 97–125CrossRefGoogle Scholar
  4. 4.
    Baumert Y, Lehmann R (1997) TIMMS: Mathematisch-naturwissenschaftlicher Unterricht im Internationalen Vergleich. Opladen: Leske und BudrichGoogle Scholar
  5. 5.
    Benbow CP (1988) Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences 11: 169–232CrossRefGoogle Scholar
  6. 6.
    Benson DF, Geschwind N (1970) Developmental Gerstmann syndrome. Neurology 20: 293–298PubMedGoogle Scholar
  7. 7.
    Benton AL (1987) Mathematical disability and the Gerstmann syndrome. In: Deloche G, Seron X (eds) Mathematical Disabilities. A cognitive neuropsychological perspective. Hillsdale, New Jersey: ErlbaumGoogle Scholar
  8. 8.
    Brandys CF, Rourke BP (1991) Differential memory abilities in reading- and arithmetic-disabled children. In: Rourke BP (ed) Neuropsychological Validation of Learning Disability Subtypes. New York: Guilford PressGoogle Scholar
  9. 9.
    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: 204–214CrossRefGoogle Scholar
  10. 10.
    Dahmen W, Hartje W, Büssing A, Sturm W (1982) Disorders of calculation in aphasic patients. Spatial and verbal components. Neuropsychologia 20: 145–153CrossRefPubMedGoogle Scholar
  11. 11.
    De Corte E, Verschaffel L (1987) The effect of semantic structure on first graders strategies for solving addition and subtraction word problems. J Res Mathematics Education 18: 363–381CrossRefGoogle Scholar
  12. 12.
    Dehaene S (1992) Varieties of numerical abilities. Cognition 44: 1–42CrossRefPubMedGoogle Scholar
  13. 13.
    Dehaene S, Spelke E, Pinel P, Stanescu R, Tsivkin S (1999) Sources of mathematical thinking: behavioural and brain-imaging evidence. Science 284: 970–973CrossRefPubMedGoogle Scholar
  14. 14.
    Dellatolas G, von Aster MG, Willadino Braga L, Meier M, Deloche G (2000) Number processing and mental calculation in school children aged 7 to 10 years: a transcultural comparison. European Child and Adolescent Psychiatry (Suppl) (this issue)Google Scholar
  15. 15.
    Deloche G, Willmes K (2000) Cognitive neuropsychological models of adult calculation and number processing: on the role of the surface format of numbers. European Child and Adolescent Psychiatry (Suppl) (this issue)Google Scholar
  16. 16.
    Deloche G, Seron X, Larroque C, Magnien C, Metz-Lutz MN, Noel MN, Riva I, Schils JP, Dordain M, Tzavaras A, Vendrell J, Bergego C (1994) Calculation and number processing: assessment battery: role of demographic factors. Journal of Clinical and Experimental Neuropsychology 16: 195–208CrossRefPubMedGoogle Scholar
  17. 17.
    Deloche G, von Aster MG, Dellatolas G, Gaillard F, Tièche C, Azema D (1995) Traitement des nombres et calcul en CE 1 et CE2. Approche Neuropsychologique des Apprentissages chez l’Enfant (A.N.A.E.), Hors Série, 42–52Google Scholar
  18. 18.
    Deloche G (1995) EC301R: Batterie standardisée d’evaluation du calcul et du traitement des nombres. Salvador: Editora Sarah LetrasGoogle Scholar
  19. 19.
    Donlan C (ed) (1998) The Development of mathematical Skills. East Sussex: Psychology PressGoogle Scholar
  20. 20.
    Esser G (1991) Was wird aus Kindern mit Teilleistungsschwächen? Der langfristige Verlauf umschriebener Entwicklungsstörungen. Stuttgart. EnkeGoogle Scholar
  21. 21.
    Esser G, Schmidt MH (1994) Children with specific reading retardation — early determinants and long-term outcome. Acta Paedopsychoatrica 56: 229–239Google Scholar
  22. 22.
    Fodor JA (1983) The Modularity of Mind. Cambridge: MIT PressGoogle Scholar
  23. 23.
    Fuson KC, Richards J, Briars DJ (1982) The acquisition and elaboration of the number word sequence. In: Brainerd CJ (ed) Children’s Logical and Mathematical Cognition: Progress in Cognitive Developmental Research (pp 33–92). New York: Springer VerlagGoogle Scholar
  24. 24.
    Geary DC (1994) Children’s Mathematical Development. Washington DC: American Psychological AssociationGoogle Scholar
  25. 25.
    Geary DC (2000) From infancy to adulthood: the development of numerical abilities. European Child and Adolescent Psychiatry (Suppl) (this issue)Google Scholar
  26. 26.
    Gelman R, Gallistel CR (1978) The Child’s Understanding of Number. Cambridge, Mass: Harvard University PressGoogle Scholar
  27. 27.
    Grigsby JP, Kemper MB, Hagermann RJ (1987) Developmental Gerstmann syndrome without aphasia in fragile X syndrome. Neuropsychologia 25: 881–891CrossRefGoogle Scholar
  28. 28.
    Gross-Tsur V, Shalev RS, Manor O, Amir N (1995) Developmental right hemisphere syndrome: clinical spectrum of the non-verbal learning disability. Journal of Learning Disabilities 28: 80–86CrossRefPubMedGoogle Scholar
  29. 29.
    Gross-Tsur V, Manor O, Shalev RS (1996) Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine and Child Neurology 38: 25–33PubMedCrossRefGoogle Scholar
  30. 30.
    Halpern DF (1997) Sex differences in intelligence. American Psychologist 52: 1091–1102CrossRefPubMedGoogle Scholar
  31. 31.
    Haskell SH (2000) The determinants of Arithmetic skills in young children: Some observations. European Child and Adolescent Psychiatry (Suppl) (this issue)Google Scholar
  32. 32.
    Hembree R (1990) The nature effects and relief of mathematics anxiety. Journal of Research in Mathematics Education 21: 33–46CrossRefGoogle Scholar
  33. 33.
    Husen T (1967) International Study of Achievement in Mathematics: A Comparison of Twelve Countries. Vol 2 Stockholm: Almquist & WiksellGoogle Scholar
  34. 34.
    International Association for the Evaluation of Education Achievement (IEA) (1996) Mathematics Achievement in the Middle School Years: IEA’s Third International Mathematics and Science Study (TIMSS). Chestnut Hill: Boston collegeGoogle Scholar
  35. 35.
    Karmiloff-Smith A (1992) Beyond Modularity Cambridge: MIT PressGoogle Scholar
  36. 36.
    Kim KH, Relkin NR, Lee KM, Hirsch J (1997) Distinct cortical areas associated with native and second languages. Nature, 388: 171–174CrossRefPubMedGoogle Scholar
  37. 37.
    Kinsbourne M (1968) Developmental Gerstmann syndrome. Pediatric Clinics of North America 15: 771–778PubMedGoogle Scholar
  38. 38.
    Klauer KJ (1992) In Mathematik mehr leistungsschwache Mädchen, im Rechnen und Rechtschreiben mehr leistungsschwache Jungen? Zur Diagnostik von Teilleistungsschwächen. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie 24: 48–65Google Scholar
  39. 39.
    Klin A, Volkmar FR, Sparrow SS, Cicchetti DV & Rourke BP (1995) Validity and neuropsychological characterisation of Asperger Syndrome: convergence with nonverbal learning disability syndrome. Journal of Child Psychology and Psychiatry and Allied Disciplines 36: 1127–1140CrossRefGoogle Scholar
  40. 40.
    Kipera-Frye K, Dehaene S, Streissguth AP (1996) Impairments of number processing induced by prenatal alcohol exposure. Neuropsychologia 34: 1187–1198CrossRefGoogle Scholar
  41. 41.
    Kosc L (1974) Developmental dyscalculia. Journal of Learning Disabilities 7: 164–177CrossRefGoogle Scholar
  42. 42.
    Mattson AJ, Sheer DE, Fletcher JM (1993) Electrophysiological evidence of lateralised disturbances in children with learning disabilities. Journal of Clinical and Experimental Neuropsychology 14: 707–716CrossRefGoogle Scholar
  43. 43.
    McCloskey M, Caramazza A, Basili A (1985) Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain and Cognition 4: 171–196CrossRefPubMedGoogle Scholar
  44. 44.
    Mirura JT, Kim CC, Chang C-M, Okamoto Y (1988) Effects of language characteristics on children’s cognitive representation of number: cross-national comparisons. Child Development 59: 1445–1450CrossRefGoogle Scholar
  45. 45.
    Miura JT, Okamoto Y, Kim CC, Chang C-M, Steere M, Fayol M (1994) Comparisons of children’s cognitive representation of number: China, France, Japan, Korea, Sweden and the United States. International Journal of Behavioral Development 17: 401–411Google Scholar
  46. 46.
    Morris HH, Lüders H, Lesser RP, Dinner DS, Hahn JH (1984) Transient neuropsychological abnormalities (including Gestmann’s syndrome) during cortical stimulation. Neurology 34: 877–883PubMedGoogle Scholar
  47. 47.
    Ozols EJ, Rourke BP (1988) Characteristics of young learning-disabled children classified according to patterns of academic achivement: auditory-perceptual and visual-perceptual disabilities. Journal of Clinical Child Psychology 17: 44–52CrossRefGoogle Scholar
  48. 48.
    PeBenito R (1987) Developmental Gerstmann syndrome: case report and review of the literature. Journal of Developmental Behavioral Pediatrics 8: 229–232Google Scholar
  49. 49.
    Poeck K, Orgass B (1975) Gerstmann syndrome without aphasia: comments on the paper by Strub and Geschwind. Cortex 11: 291–295PubMedGoogle Scholar
  50. 50.
    Reusser K (2000) Success and failure in school mathematics: effects of instruction and school environment. European Child and Adolescent Psychiatry (Suppl) (this issue)Google Scholar
  51. 51.
    Rourke BP (1989) Nonverbal Learning Disabilities. The Syndrome and the Model. New York: Guilford PressGoogle Scholar
  52. 52.
    Rourke BP (1993) Arithmetic disabilities, specific and otherwise: a neuropsychological perspective. Journal of Learning Disabilities 26: 214–226CrossRefPubMedGoogle Scholar
  53. 53.
    Rourke BP & Finlayson MAJ (1978) Neuropsychological significance of variations in patterns of academic performance: verbal and visual-spatial abilities. Journal of Abnormal Child Psychology 6: 121–133CrossRefPubMedGoogle Scholar
  54. 54.
    Rourke BP, Fuerst DR (1991) Learning Disabilities and Psychosocial Functioning. New York: Guilford PressGoogle Scholar
  55. 55.
    Rourke BP, Strang JD (1978) Neuropsychological significance of variations in patterns of academic performance: motor, psychomotor, and tactile-perceptual abilities. Journal of Pediatric Psychology 3: 62–66CrossRefGoogle Scholar
  56. 56.
    Schwank I (1990) Untersuchungen algorithmischer Denkprozesse bei Mädchen. Osnabrück: Forschungsinstitut für MathematikdidaktikGoogle Scholar
  57. 57.
    Schwank I (1992) Cognitive Structures and Cognitive Strategies in Algorithmic Thinking. Osnabrück: Forschungsinstitut für MathematikdidaktikGoogle Scholar
  58. 58.
    Shalev RS, Gross-Tsur V (1993) Developmental dyscalculia and medical assessment. Journal of Learning Disabilities 26: 134–137CrossRefPubMedGoogle Scholar
  59. 59.
    Shalev RS, Auerbach J, Gross-Tsur V (1995) Developmental dyscalculia: attentional and behavioral aspects. Journal of Child Psychology and Psychiatry 35: 1261–1268CrossRefGoogle Scholar
  60. 60.
    Share DL, Moffit TE, Silva PA (1988) Factors associated with arithmetic and reading disability and specific arithmetic disability. Journal of Learning Disabilities 21: 313–320CrossRefPubMedGoogle Scholar
  61. 61.
    Slade PD, Russel GFM (1971) Developmental dyscalculia: a brief report on four cases. Psychological Medicine 1: 292–298CrossRefPubMedGoogle Scholar
  62. 62.
    Spellacy F, Peter B (1978) Dyscalculia and elements of the developmental Gerstmann syndrome in school children. Cortex 14: 197–206PubMedGoogle Scholar
  63. 63.
    Starkey P, Spelke ES, Gelman R (1990) Numerical abstraction by human infants. Cognition 36: 97–127CrossRefPubMedGoogle Scholar
  64. 64.
    Strang JD, Rourke BP (1983) Conceptformation/non-verbal reasoning abilities of children who exhibit specific academic problems with arithmetic. Journal of Clinical Child Psychology 12: 33–39CrossRefGoogle Scholar
  65. 65.
    Temple C (1989) Digit dyslexia: a category-specific disorder in developmental dyscalculia. Cognitive Neuropsychology 6: 93–116CrossRefGoogle Scholar
  66. 66.
    Temple C (1997) Developmental Cognitive Neuropsychology. East Sussex: Psychology PressGoogle Scholar
  67. 67.
    Tiedemann J, Faber G (1995) Mädchen im Mathematikunterricht: Selbstkonzept und Kausalattributionen im Grundschulalter. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie 27: 61–71Google Scholar
  68. 68.
    Towse J, Saxton M (1998) Mathematics across national boundaries: cultural and linguistic perspectives on numerical competence. In: Donlan C (ed) The Development of Mathematical Skills. East Sussex: Psychology PressGoogle Scholar
  69. 69.
    von Aster MG (1993) Developmental and acquired dyscalculias in children. In Stachowiak FJ (ed) Development in the Assessment and Rehabilitation of Braindamaged Patients. Tübingen: NarrGoogle Scholar
  70. 70.
    von Aster MG (1994) Developmental dyscalculia in children: review of the literature and clinical validation. Acta Paedopsychiatrica 56: 169–178Google Scholar
  71. 71.
    von Aster MG (1996) Psychopathologische Risiken bei Kindern mit umschriebenen schulischen Entwicklungsstörungen. Kindheit und Entwicklung 5: 53–59Google Scholar
  72. 72.
    von Aster MG (1997) Die Störungen des Rechnens und der Zahlenverarbeitung in der kindlichen Entwicklung. Unveröffentlichte Habilitationschrift. Universität ZürichGoogle Scholar
  73. 73.
    von Aster MG, Deloche G, Dellatolas G, Meier M (1997) Number processing and calculation in 2nd and 3rd grade school children: a comparative study of French-speaking and German-speaking children. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie 24: 151–166Google Scholar
  74. 74.
    World Health Organization (1992) The ICD-10 Classification of Mental and Behavioral Disorders — Clinical Descriptions and Diagnostic Guidelines. WHO GenevaGoogle Scholar
  75. 75.
    Witelson SF (1979) Geschlechtsspezifische Unterschiede in der Neurologie der kognitiven Funktionen und ihre psychologischen, sozialen, edukativen und klinischen Implikationen. In: Sullerot EE (Ed) Die Wirklichkeit der Frau. München: SteihausenGoogle Scholar

Copyright information

© Steinkopff-Verlag 2000

Authors and Affiliations

  1. 1.Department of Child and Adolescent PsychiatryUniversity of ZurichMaennedorf/ZurichSwitzerland

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