Low numeracy and dyscalculia: Identification and intervention

ZDM - International Journal on Mathematics Education

Volumn 42, Issue 6, 2010, Pages 527-539

  Butterworth, Brian ^a,b   Laurillard, Diana ^b,c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b University College London   (United Kingdom)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867560338     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-010-0267-4     Document Type: Article

References (68)

1. Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2009). Use of number by fish. PLoS One, 4(3), e4786.
2. Alarcon, M., Defries, J., Gillis Light, J., & Pennington, B. (1997). A twin study of mathematics disability. Journal of Learning Disabilities, 30, 617-623.
3. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278-291.
4. Ansari, D., & Karmiloff-Smith, A. (2002). Atypical trajectories of number development: A neuroconstructivist perspective. Trends in Cognitive Sciences, 6(12), 511-516.
5. Bruandet, M., Molko, N., Cohen, L., & Dehaene, S. (2004). A cognitive characterization of dyscalculia in Turner syndrome. Neuropsychologia, 42, 288-298.
6. Butterworth, B. (2000). The mathematical brain. London: Macmillan.
7. Butterworth, B. (2001). What makes a prodigy? Nature Neuroscience, 4(1), 11-12.
8. Butterworth, B. (2005a). Developmental dyscalculia. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 455-467). Hove: Psychology Press.
9. Butterworth, B. (2005b). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3-18.
10. 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.
11. 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.
12. 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.
13. Butterworth, B., & Yeo, D. (2004). Dyscalculia guidance. London: nferNelson.
14. Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-yold children. Public Library of Science Biology, 4(5), e125.
15. 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.
16. Cappelletti, M., Butterworth, B., & Kopelman, M. (2001). Spared numerical abilities in a case of semantic dementia. Neuropsychologia, 39, 1224-1239.
17. 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.
18. 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.
19. Cipolotti, L., Butterworth, B., & Denes, G. (1991). A specific deficit for numbers in a case of dense acalculia. Brain, 114, 2619-2637.
20. 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.
21. 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.
22. Dehaene, S., Molko, N., & Cohen, L. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14, 218-224.
23. 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.
24. 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.
25. Dowker, A. (Ed.). (2008). Mathematical difficulties: Psychology and intervention. London: Academic Press.
26. Dowker, A. (2009). What works for children with mathematical difficulties? The effectiveness of intervention schemes. London: Department for Children, Schools and Familieso. Document Number.
27. 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.
28. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314.
29. Gathercole, S. (1995). Nonword repetition: More than just a phonological output task. Cognitive Neuropsychology, 12(8), 857-861.
30. 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.
31. Geary, D. C. (1993). Mathematical disabilities: Cognition, neuropsychological and genetic components. Psychological Bulletin, 114, 345-362.
32. 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.
33. 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.
34. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665-668.
35. Healy, L., & Kynigos, C. (2010). Charting the microworld territory over time: Design and construction in mathematics education. ZDM Mathematics Education, 42, 63-76.
36. Henschen, S. E. (1920). Klinische und Anatomische Beitrage zu Pathologie des Gehirns. Stockholm: Nordiska Bokhandeln.
37. 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.
38. 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.
39. 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.
40. 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.
41. 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.
42. 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.
43. 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.
44. Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM Mathematics Education, 41, 427-440.
45. McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetical difficulties. Journal of Experimental Child Psychology, 74, 240-260.
46. 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.
47. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520.
48. 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.
49. 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.
50. 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.
51. Noss, R., & Hoyles, C. (1996). Windows on mathematical meaning: Learning cultures and computers. Dordrecht: Kluwer.
52. 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.
53. 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.
54. 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.
55. 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.
56. 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.
57. 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.
58. 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.
59. Shalev, R. S., Manor, O., & Gross-Tsur, V. (1997). Neuropsychological aspects of developmental dyscalculia. Mathematical Cognition, 3(2), 105-120.
60. 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.
61. Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78(3), 427-515.
62. 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.
63. Varma, S., McCandliss, B. D., & Schwartz, D. L. (2008). Scientific and pragmatic challenges for bridging education and neuroscience. Educational Researcher, 37(3), 140-152.
64. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
65. Warrington, E. K., & James, M. (1967). Tachistoscopic number estimation in patients with unilateral lesions. Journal of Neurology, Neurosurgery and Psychiatry, 30, 468-474.
66. 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.
67. 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.
68. 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.