Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Low numeracy and dyscalculia: identification and intervention

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

One important factor in the failure to learn arithmetic in the normal way is an endogenous core deficit in the sense of number. This has been associated with low numeracy in general (e.g. Halberda et al. in Nature 455:665–668, 2008) and with dyscalculia more specifically (e.g. Landerl et al. in Cognition 93:99–125, 2004). Here, we describe straightforward ways of identifying this deficit, and offer some new ways of strengthening the sense of number using learning technologies.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. ‘Digital interventions for dyscalculia and low numeracy’, funded by Becta small research grants.

References

  • Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2009). Use of number by fish. PLoS One, 4(3), e4786.

    Article  Google Scholar 

  • Alarcon, M., Defries, J., Gillis Light, J., & Pennington, B. (1997). A twin study of mathematics disability. Journal of Learning Disabilities, 30, 617–623.

    Article  Google Scholar 

  • Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278–291.

    Article  Google Scholar 

  • Ansari, D., & Karmiloff-Smith, A. (2002). Atypical trajectories of number development: A neuroconstructivist perspective. Trends in Cognitive Sciences, 6(12), 511–516.

    Article  Google Scholar 

  • Bruandet, M., Molko, N., Cohen, L., & Dehaene, S. (2004). A cognitive characterization of dyscalculia in Turner syndrome. Neuropsychologia, 42, 288–298.

    Article  Google Scholar 

  • Butterworth, B. (2000). The mathematical brain. London: Macmillan.

    Google Scholar 

  • Butterworth, B. (2001). What makes a prodigy? Nature Neuroscience, 4(1), 11–12.

    Article  Google Scholar 

  • Butterworth, B. (2005a). Developmental dyscalculia. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 455–467). Hove: Psychology Press.

    Google Scholar 

  • Butterworth, B. (2005b). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3–18.

    Article  Google Scholar 

  • Butterworth, B. (2006). Mathematical expertise. In K. A. Ericsson, N. Charness, P. J. Feltovich, & R. R. Hoffmann (Eds.), Cambridge handbook of expertise and expert performance (pp. 553–568). Cambridge: Cambridge University Press.

    Google Scholar 

  • Butterworth, B., Granà, A., Piazza, M., Girelli, L., Price, C., & Skuse, D. (1999). Language and the origins of number skills: Karyotypic differences in Turner’s syndrome. Brain and Language, 69, 486–488.

    Google Scholar 

  • Butterworth, B., & Reigosa Crespo, V. (2007). Information processing deficits in dyscalculia. In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 65–81). Baltimore, MD: Paul H Brookes Publishing Co.

    Google Scholar 

  • Butterworth, B., & Yeo, D. (2004). Dyscalculia guidance. London: nferNelson.

    Google Scholar 

  • 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. Public Library of Science Biology, 4(5), e125.

    Google Scholar 

  • Cappelletti, M., Barth, H., Fregni, F., Spelke, E. S., & Pascuale-Leone, A. (2007). rTMS over the intraparietal sulcus disrupts numerosity processing. Experimental Brain Research, 179, 631–642.

    Article  Google Scholar 

  • Cappelletti, M., Butterworth, B., & Kopelman, M. (2001). Spared numerical abilities in a case of semantic dementia. Neuropsychologia, 39, 1224–1239.

    Article  Google Scholar 

  • Cappelletti, M., Kopelman, M., & Butterworth, B. (2002). Why semantic dementia drives you the dogs (but not to the horses): A theoretical account. Cognitive Neuropsychology, 19(6), 483–503.

    Article  Google Scholar 

  • Castelli, F., Glaser, D. E., & Butterworth, B. (2006). Discrete and analogue quantity processing in the parietal lobe: A functional MRI study. Proceedings of the National Academy of Science, 103(12), 4693–4698.

    Article  Google Scholar 

  • Cipolotti, L., Butterworth, B., & Denes, G. (1991). A specific deficit for numbers in a case of dense acalculia. Brain, 114, 2619–2637.

    Article  Google Scholar 

  • Cohen Kadosh, R., Cohen Kadosh, K., Schuhmann, T., Kaas, A., Goebel, R., Henik, A., et al. (2007). Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing. Current Biology, 17, 1–5.

    Article  Google Scholar 

  • Cowan, R., Donlan, C., Newton, E., & Lloyd, D. (2005). Number skills and knowledge in children with specific language impairment. Journal of Educational Psychology, 97, 732–744.

    Article  Google Scholar 

  • Dehaene, S., Molko, N., & Cohen, L. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14, 218–224.

    Article  Google Scholar 

  • Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284(5416), 970–974.

    Article  Google Scholar 

  • Donlan, C., Bishop, D. V. M., & Hitch, G. J. (1998). Magnitude comparisons by children with specific language impairments: Evidence of unimpaired symbolic processing. International Journal of Language & Communication Disorders, 33, 149–160.

    Article  Google Scholar 

  • Dowker, A. (Ed.). (2008). Mathematical difficulties: Psychology and intervention. London: Academic Press.

    Google Scholar 

  • Dowker, A. (2009). What works for children with mathematical difficulties? The effectiveness of intervention schemes. London: Department for Children, Schools and Familieso. Document Number.

  • Eden, G., Jones, K., Cappell, K., Gareau, L., Wood, F., Zeffiro, T., et al. (2004). Neural changes following remediation in adult developmental dyslexia. Neuron, 44, 411–422.

    Article  Google Scholar 

  • Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.

    Article  Google Scholar 

  • Gathercole, S. (1995). Nonword repetition: More than just a phonological output task. Cognitive Neuropsychology, 12(8), 857–861.

    Article  Google Scholar 

  • Gathercole, S. E., & Pickering, S. J. (2000). Working memory deficits in children with low achievements in the national curriculum at 7 years of age. British Journal of Educational Psychology, 70(2), 177–194.

    Article  Google Scholar 

  • Geary, D. C. (1993). Mathematical disabilities: Cognition, neuropsychological and genetic components. Psychological Bulletin, 114, 345–362.

    Article  Google Scholar 

  • Geary, D. C., Bailey, D. H., Littlefield, A., Wood, P., Hoard, M. K., & Nugent, L. (2009). First-grade predictors of mathematical learning disability: A latent class trajectory analysis. Cognitive Development, 24, 411–429.

    Google Scholar 

  • Griffin, S., Case, R., & Siegler, R. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom learning: Integrating cognitive theory and classroom practice (pp. 25–50). Boston: MIT Press.

    Google Scholar 

  • Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668.

    Article  Google Scholar 

  • Healy, L., & Kynigos, C. (2010). Charting the microworld territory over time: Design and construction in mathematics education. ZDM Mathematics Education, 42, 63–76.

    Article  Google Scholar 

  • Henschen, S. E. (1920). Klinische und Anatomische Beitrage zu Pathologie des Gehirns. Stockholm: Nordiska Bokhandeln.

    Google Scholar 

  • Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124, 1701–1707.

    Article  Google Scholar 

  • Isaacs, E. B., Gadian, D. G., Sabatini, S., Chong, W. K., Quinn, B. T., Fischl, B. R., et al. (2008). The effect of early human diet on caudate volumes and IQ. Pediatric Research, 63(3), 308–314.

    Article  Google Scholar 

  • Iuculano, T., Tang, J., Hall, C., & Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11(5), 669–680.

    Article  Google Scholar 

  • Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2(1), 1–23.

    Article  Google Scholar 

  • Kovas, Y., Haworth, C., Dale, P., & Plomin, R. (2007). The genetic and environmental origins of learning abilities and disabilities in the early school years. Monograph of the Society for Research in Child Development, 72(3), 1–144.

    Article  Google Scholar 

  • Kulik, J. (2003). Effects of using instructional technology in elementary and secondary schools: What controlled evaluation studies say. SRI Project Number P10446.001: SRI International.

  • Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8–9 year old students. Cognition, 93, 99–125.

    Article  Google Scholar 

  • Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM Mathematics Education, 41, 427–440.

    Article  Google Scholar 

  • McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetical difficulties. Journal of Experimental Child Psychology, 74, 240–260.

    Article  Google Scholar 

  • Molko, N., Cachia, A., Rivière, D., Mangin, J.-F., Bruandet, M., Le Bihan, D., et al. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40, 847–858.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mussolin, C., De Volder, A., Grandin, C., Schlögel, X., Nassogne, M.-C., & Noël, M.-P. (2009). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22(5), 860–874.

    Article  Google Scholar 

  • Nation, K., Adams, J. W., Bowyer-Crane, C. A., & Snowling, M. J. (1999). Working memory deficits in poor comprehenders reflect underlying language impairments. Journal of Experimental Child Psychology, 73(2), 139–158.

    Article  Google Scholar 

  • Noël, M. P., Seron, X., & Trovarelli, F. (2004). Working memory as a predictor of addition skills and addition strategies in children. Current Psychology of Cognition, 22, 3–25.

    Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meaning: Learning cultures and computers. Dordrecht: Kluwer.

    Google Scholar 

  • Pesenti, M., Zago, L., Crivello, F., Mellet, E., Samson, D., Duroux, B., et al. (2001). Mental calculation expertise in a prodigy is sustained by right prefrontal and medial-temporal areas. Nature Neuroscience, 4(1), 103–107.

    Article  Google Scholar 

  • Piazza, M., Mechelli, A., Price, C. J., & Butterworth, B. (2006). Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research, 1106, 177–188.

    Article  Google Scholar 

  • Pinel, P., Dehaene, S., Rivière, D., & Le Bihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. NeuroImage, 14, 1013–1026.

    Article  Google Scholar 

  • Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), R1042–R1043.

    Article  Google Scholar 

  • Rotzer, S., Kucian, K., Martin, E., Aster, M.v., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. NeuroImage, 39(1), 417–422.

    Article  Google Scholar 

  • Rusconi, E., Walsh, V., & Butterworth, B. (2005). Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia, 43(11), 1609–1624.

    Article  Google Scholar 

  • 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(51), 1–13.

    Google Scholar 

  • Shalev, R. S., Manor, O., & Gross-Tsur, V. (1997). Neuropsychological aspects of developmental dyscalculia. Mathematical Cognition, 3(2), 105–120.

    Article  Google Scholar 

  • Shalev, R. S., Manor, O., Kerem, B., Ayali, M., Badichi, N., Friedlander, Y., et al. (2001). Developmental dyscalculia is a familial learning disability. Journal of Learning Disabilities, 34(1), 59–65.

    Article  Google Scholar 

  • Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427–515.

    Article  Google Scholar 

  • Tang, J., Critchley, H. D., Glaser, D., Dolan, R. J., & Butterworth, B. (2006). Imaging informational conflict: An fMRI study of numerical stroop. Journal of Cognitive Neuroscience, 18, 2049–2062.

    Article  Google Scholar 

  • Varma, S., McCandliss, B. D., & Schwartz, D. L. (2008). Scientific and pragmatic challenges for bridging education and neuroscience. Educational Researcher, 37(3), 140–152.

    Article  Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Warrington, E. K., & James, M. (1967). Tachistoscopic number estimation in patients with unilateral lesions. Journal of Neurology, Neurosurgery and Psychiatry, 30, 468–474.

    Article  Google Scholar 

  • Wilson, A., Dehaene, S., Pinel, P., Revkin, S., Cohen, L., & Cohen, D. (2006). Principles underlying the design of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 19. doi:10.1186/1744-9081-2-19.

    Article  Google Scholar 

  • Wilson, A., Revkin, S., Cohen, D., Cohen, L., & Dehaene, S. (2006). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 20. doi:10.1186/1744-9081-2-20.

  • Zago, L., Pesenti, M., Mellet, E., Crivello, F., Mazoyer, B., & Tzourio-Mazoyer, N. (2001). Neural correlates of simple and complex mental calculation. NeuroImage, 13(2), 314–327.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Cognitive Neuroscience, University College London, 17 Queen Square, London, WC1N 3AR, UK

    Brian Butterworth

  2. Centre for Educational Neuroscience, London, UK

    Brian Butterworth & Diana Laurillard

  3. London Knowledge Lab, Institute of Education University of London, London, UK

    Diana Laurillard

Authors
  1. Brian Butterworth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diana Laurillard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brian Butterworth.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Butterworth, B., Laurillard, D. Low numeracy and dyscalculia: identification and intervention. ZDM Mathematics Education 42, 527–539 (2010). https://doi.org/10.1007/s11858-010-0267-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0267-4

Keywords

Search

Navigation