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The Massachusetts General Hospital Guide to Learning Disabilities pp 39–58Cite as

Mathematics Disorders

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Abstract

The prevalence of math disorders is similar to that of developmental dyslexia and ADHD. However, there is no agreed-upon core cognitive deficit in mathematics disorder. In this chapter, subtypes of math disorders are outlined and explained based on developmental delays in skills such as number representation, language processing, working memory and executive functions, and spatial or nonverbal reasoning. Both typical and atypical developments of math skills are explained to help clinicians who work with children to recognize and flag the need to refer for additional testing. Identifying, via comprehensive neuropsychological assessment, the pattern of cognitive processing strengths and weaknesses that contribute to an individual’s underachievement in math provides the best path to implementing effective intervention. A number of common measures of math skills as well as of the cognitive skills that underlie math reasoning are listed and described. Finally, potential comorbidities of and interventions for math disorders are discussed and an illustrative case study presented.

Keywords

  • Math disorders
  • Dyscalculia
  • Math learning disability

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References

  1. Alloway TP. Working memory, reading, and mathematical skills in children with developmental coordination disorder. J Exp Child Psychol. 2007;96(1):20–36. https://doi.org/10.1016/j.jecp.2006.07.002.

    CrossRef  PubMed  Google Scholar 

  2. Alloway TP, Archibald L. Working memory and learning in children with developmental coordination disorder and specific language impairment. J Learn Disabil. 2008;41(3):251–62. https://doi.org/10.1177/0022219408315815.

    CrossRef  PubMed  Google Scholar 

  3. Alloway TP, Temple KJ. A comparison of working memory skills and learning in children with developmental coordination disorder and moderate learning difficulties. Appl Cogn Psychol. 2007;21(4):473–87. https://doi.org/10.1002/acp.1284.

    CrossRef  Google Scholar 

  4. American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 5th ed. Washington, DC: American Psychiatric Association; 2013.

    CrossRef  Google Scholar 

  5. Ashkenazi S, Rosenberg-Lee M, Metcalfe AW, Swigart AG, Menon V. Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition. Neuropsychologia. 2013;51(11):2305–17.

    CrossRef  PubMed  PubMed Central  Google Scholar 

  6. Bernstein BE. Mathematics learning disorder: practice essentials, background, epidemiology. Medscape. 2016. Retrieved 3/12/2017 from http://emedicine.medscape.com/article/915176-overview#a0199.

  7. Boller F, Grafman J. Acalculia: historical development and current significance. Brain Cogn. 1983;2(3):205–23. https://doi.org/10.1016/0278-2626(83)90010-6.

    CrossRef  CAS  PubMed  Google Scholar 

  8. Butterworth B. Foundational numerical capacities and the origins of dyscalculia. Trends Cogn Sci. 2010;14(12):534–41.

    CrossRef  PubMed  Google Scholar 

  9. Dehaene S. Varieties of numerical abilities. Cognition. 1992;44(1–2):1–42.

    CAS  PubMed  Google Scholar 

  10. Dehaene S, Cohen L. Towards an anatomical and functional model of number processing. Math Cogn. 1995;1:83–120.

    Google Scholar 

  11. Dehaene S, Cohen L. Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex J Devoted Study Nerv Syst Behav. 1997;33(2):219–50.

    CrossRef  CAS  Google Scholar 

  12. Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol. 2003;20(3):487–506.

    CrossRef  PubMed  Google Scholar 

  13. DeSmedt B, Noel MP, Gilmore C, Ansari D. 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 Neurosci Educ. 2013;2:48–55.

    CrossRef  Google Scholar 

  14. Dickhauser O, Reinhard M-A. The effects of affective states on the formation of performance expectancies. Cognit Emot. 2008;22(8):1542–54. https://doi.org/10.1080/02699930801906900.

    CrossRef  Google Scholar 

  15. Docherty SJ, Davis OSP, Kovas Y, Meaburn EL, Dale PS, Petrill SA, Schalkwyk LC, Plomin R. A genome-wide association study identifies multiple loci associated with mathematics ability and disability. Genes Brain Behav. 2010;9:234–47. https://doi.org/10.1111/j.1601-183X.2009.00552.x.

    CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

  16. Feifer SG. The neuropsychology of mathematics: an introduction to the FAM. Sparta: School Neuropsych Press, LLC; 2017.

    Google Scholar 

  17. Feigensohn L, Dahaene S, Spelke E. Core systems of number. Trends Cogn Sci. 2004;8(7):307–14.

    CrossRef  Google Scholar 

  18. Fennema E, Romberg TA. In: Fennema E, Romberg TA, editors. Mathematics classrooms that promote understanding. Mahwah: Lawrence Erlbaum Associates Publishers; 1999.

    CrossRef  Google Scholar 

  19. Fias W, Menon V, Szucs D. Multiple components of developmental dyscalculia. Trends Neurosci Educ. 2013;2:43–7.

    CrossRef  Google Scholar 

  20. Fias W, Lammertyn J, Reynvoet B, Dupont P, Orban GA. Parietal representation of symbolic and nonsymbolic magnitude. J Cogn Neurosci. 2003;15(10):47–56.

    CrossRef  PubMed  Google Scholar 

  21. Geary. Mathematics and learning disabilities. J Learn Disabil. 2004;37(1):4–15.

    CrossRef  PubMed  Google Scholar 

  22. Gelman R. Counting in the preschooler: what does and does not develop. In: Siegler RS, editor. Children’s thinking: what develops? Hillsdale: Lawrence Erlbaum Associates, Inc; 1978. p. 213–41.

    Google Scholar 

  23. Gordon P. Numerical cognition without words: evidence from Amazonia. Sci Spec Issue Cogn Behav. 2004;306(5695):496–9.

    CAS  Google Scholar 

  24. Hale J, Alfonso V, Berninger V, Bracken B, Christo E, Clark M, Cohen AD, Decker S, Denckla M, Dumont R, Elliott C, Feifer S, Fiorello C, Flanagan D, Fletcher-Janzen E, Geary D, Gerber M, Gerner M, Goldstein S, Gregg N, Hagin R, Jaffe L, Kaufman A, Kaufman N, Keith T, Kline F, Kochhar-Bryant C, Lerner J, Marshall G, Mascolo J, Mather N, Mazzocco M, McCloskey G, McGrew K, Miller D, Miller J, Mostert M, Naglieri J, Ortiz S, Phelps L, Podhajski B, Reddy L, Reynolds C, Riccio C, Schrank F, Schultz E, Semrud-Clikeman M, Shaywitz S, Simon J, Silver L, Swanson L, Urso A, Wasserman T, Willis J, Wodrich D, Wright J, Yalof J. Critical issues in response-to-intervention, comprehensive evaluation, and specific learning disabilities identification and intervention. Learn Disabil Q. 2010;33:223–36.

    CrossRef  Google Scholar 

  25. Hopko DR, Ashcraft MH, Gute J, Ruggiero KJ, Lewis C. Mathematics anxiety and working memory: support for the existence of a deficient inhibition mechanism. J Anxiety Disord. 1998;12(4):343–55.

    CrossRef  CAS  PubMed  Google Scholar 

  26. Kaufman L, Kucian K, von Aster M. Development of the numerical brain. In: Dowker A, Cohen Kadosh R, editors. Oxford handbook of numerical cognition. Oxford: Oxford University Press; 2014.

    Google Scholar 

  27. Kellogg JS, Hopko DR, Ashcraft MH. The effects of time pressure on arithmetic performance. J Anxiety Disord. 1999;13(6):591–600.

    CrossRef  CAS  PubMed  Google Scholar 

  28. Kucien K, von Aster M. Developmental dyscalculia. Eur J Pediatr. 2015;174:1–13. https://doi.org/10.10007/s00431-014-2455-7.

    CrossRef  Google Scholar 

  29. Kucien K, Grond U, Rotzer S, Henzi B, Schonmann C, Plangger F, Gälli M, Martin E, von Aster M. Mental number line training in children with developmental dyscalculia. NeuroImage. 2011;57(3):782–95.

    CrossRef  Google Scholar 

  30. Lindsay RL, Tomazic T, Levine MD, Accardo PJ. Attentional function as measured by a continuous performance task in children with dyscalculia. Dev Behav Pediatr. 2001;22(5):287–92.

    CrossRef  CAS  Google Scholar 

  31. Mazzocco MM, Feigenson L, Halberda J. Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Dev. 2011;82(4):1224–37.

    CrossRef  PubMed  PubMed Central  Google Scholar 

  32. Nicolson R, Fawcett AJ, Dean P. Developmental dyslexia: the cerebellar deficit hypothesis. Trends Neurosci. 2001;24(9):508–11.

    CrossRef  CAS  PubMed  Google Scholar 

  33. Parsons S, Brynner J. Does numeracy matter more: national research and development centre for adult literacy and numeracy. London: Institute of Education; 2005.

    Google Scholar 

  34. Pica P, Lemer C, Izard V, Dehaene S. Exact and approximate arithmetic in an Amonian indigene group. Science. 2004;306(5695):499–503.

    CrossRef  CAS  PubMed  Google Scholar 

  35. Piazza M, Facoetti A, Trussardi AN, Berteletti I, Conte S, Lucangeli D, Dehaene S, Zorzo M. Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition. 2010;116:33–41.

    CrossRef  PubMed  Google Scholar 

  36. Pieters S, Desoete A, Van Waelvelde H, Vanderswalmen R, Roeyers H. Mathematical problems in children with developmental coordination disorder. Res Dev Disabil. 2012;33:1128–35.

    CrossRef  PubMed  Google Scholar 

  37. Rotzer S, Loenneker T, Kucian K, Martin E, Klaver P, von Aster M. Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia. 2009;47(13):2859–65.

    CrossRef  CAS  PubMed  Google Scholar 

  38. Shalev RS, Auerbach J, Manor O, Gross-Tsur. Developmental dyscalculia: prevalence and prognosis. Eur Child Adolesc Psychiatry. 2000;9(2):II58.

    CrossRef  PubMed  Google Scholar 

  39. Shalev RS, Manor O, Kerem B, Ayali M, Badichi N, Friedlander Y, Gross-Tsur V. Developmental dyscalculia is a familial learning disability. J Learn Disabil. 2001;34(1):59–65.

    CrossRef  CAS  PubMed  Google Scholar 

  40. Szucs D, Devine A, Soltesz F, Nobes A, Gabriel F. Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex. 2013;49:2674–88.

    CrossRef  PubMed  PubMed Central  Google Scholar 

  41. Toll SWM, Van der Ven SHG, Kroesbergen EH, Van Luit JEH. Executive functions as predictors of math learning disabilities. J Learn Disabil. 2011;44(6):521–32. https://doi.org/10.1177/0022219410387302.

    CrossRef  PubMed  Google Scholar 

  42. Tosto MG, Hanscombe KB, Haworth CMA, Davis OS, Petrill SA, Dale PS, Malykh, Plomin R, Kovas Y. Why do spatial abilities predict mathematical performance? Dev Sci. 2014;17(3):462–70.

    CrossRef  PubMed  PubMed Central  Google Scholar 

  43. Venneri A, Cornoldi C, Garuti M. Arithmetic difficulties in children with visuospatial learning disability (VLD). Child Neuropsychol. 2003;9(3):175–83.

    CrossRef  PubMed  Google Scholar 

  44. Verdine BN, Irwin CM, Golinkoff RM, Hirsh-Pasek K. Contributions of executive function and spatial skills to preschool mathematics achievement. J Exp Child Psychol. 2014;126:37–51.

    CrossRef  PubMed  PubMed Central  Google Scholar 

  45. Visser J. Developmental coordination disorder: a review of research on subtypes and comorbidities. Hum Mov Sci. 2003;22:479–93.

    CrossRef  CAS  PubMed  Google Scholar 

  46. Willmes K. Acalculia. In: Goldenberg G, Miller BL, editors. Handbook of clinical neurology, vol. 88 (3rd series) neuropsychology and behavioral neurology. Amsterdam: Elsevier B.V; 2008. p. 339–58.

    Google Scholar 

  47. Baker JM, Reiss AL. A meta-analysis of math performance in Turner syndrome. Developmental Medicine and Child Neurology. 2016;58(2):123–30. https://doi.org/10.1111/dmcn.12961.

    Google Scholar 

  48. Pierpont EI, Pierpont ME, Mendelsohn NJ, Roberts AE, Tworog-Dube E, Seidenberg MS. Genotype differences in cognitive functioning in Noonan syndrome. Genes, Brain, and Behavior. 2009;8(3):275–82. https://doi.org/10.1111/j.1601-183X.2008.00469.x.

    Google Scholar 

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Authors and Affiliations

  1. Department of Child Psychiatry, Massachusetts General Hospital, Boston, MA, USA

    Ellen H. O’Donnell

  2. Harvard Medical School, Boston, MA, USA

    Ellen H. O’Donnell

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  1. Ellen H. O’Donnell
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Correspondence to Ellen H. O’Donnell .

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Editors and Affiliations

  1. Massachusetts General Hospital, Boston, MA, USA

    Ph.D. H. Kent Wilson

  2. Harvard Medical School, Boston, MA, USA

    Ellen B. Braaten

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O’Donnell, E.H. (2019). Mathematics Disorders. In: Wilson, H., Braaten, E. (eds) The Massachusetts General Hospital Guide to Learning Disabilities. Current Clinical Psychiatry. Humana Press, Cham. https://doi.org/10.1007/978-3-319-98643-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-98643-2_3

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