Three studies compared 98 children with spina bifida myelomeningocele (SBM)—a disorder associated with high rates of math disability and spatial deficits—to 94 typically developing children on multidigit subtraction and cognitive addition tasks. Children with SBM were classified into those with reading decoding and math disability, only math disability, and no reading or math disability. Study 1 showed that visual—spatial errors in multidigit arithmetic were not elevated in children with SBM. In Study 2, deficits in accuracy, speed, and strategy-use in single-digit addition characterized groups with math disability regardless of reading status. Accuracy and speed on single-digit addition was strongly related to performance on multidigit subtraction. A math-level matching design in Study 3 revealed less mastery of math facts by the group with SBM. The results are discussed with reference to cognitive and neuropsychological models of math disability.
Get full access to this article
View all access options for this article.
References
1.
Ashcraft, M. (1992). Cognitive arithmetic: A review of data and theory . Cognition, 44, 75—106.
2.
Ashcraft, M.H., Yamashita, T.S., & Aram, D.M. (1992). Mathematics performance in left and right brain-lesioned children and adolescents. Brain andCognition, 19, 208—252.
3.
Backman, J.E., Mamen, M., & Ferguson, H.B. (1984). Reading level design: Conceptual and methodological issues in reading research. Psychological Bulletin,96, 560—568.
4.
Barnes, M.A., & Dennis, M. (1998). Discourse after early-onset hydrocephalus: Core deficits in children of average intelligence. Brain andLanguage , 61, 309—334.
5.
Barnes, M.A., Dennis, M., & Hetherington, R. (2004). Reading and writing skills in young adults with spina bifida and hydrocephalus. Journal of the International Neuropsychological Society, 10, 680—688.
6.
Barnes, M.A., Faulkner, H., Wilkinson, M., & Dennis, M. (2004). Meaning construction and integration in children with hydrocephalus. Brain andLanguage, 89, 47— 56.
7.
Barnes, M.A., Pengelly, S., Dennis, M., Wilkinson, M., Rogers, T., & Faulkner, H. (2002). Mathematics skills in good readers with hydrocephalus . Journal of the International Neuropsychological Society , 8, 72—82.
8.
Barnes, M.A., & Smith-Chant, B. , & Landry, S. (2005). Number processing in neurodevelopmental disorders: Spina bifida myelomeningocele. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 299—314). New York: Psychology Press.
9.
Baroody, A.J., & Tiilikainen, S.H. (2003). Two perspectives on addition development. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: The construction of adaptive expertise (pp. 75—125). Mahwah, NJ: Erlbaum.
10.
Bull, R., & Johnston, R.S. (1997). Children's arithmetic difficulties: Contributions from processing speed, item identification, and short-term memory . Journal of Experimental Child Psychology, 65, 1—24.
11.
Butterworth, B. (1999). What counts: How every brain is hardwired for math. New York: Simon and Schuster .
12.
Campbell, J.I.D., & Graham, D.J. (1985). Mental multiplication skill: Structure, process, and acquisition. Canadian Journal of Psychology, 39, 338—366.
13.
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1—42.
14.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing . Cognitive Neuropsychology, 20, 487—506.
15.
del Bigio, M. (1993). Neuropathological changes caused by hydrocephalus . Acta Neuropathologica, 18, 573—585.
16.
Dennis, M., & Barnes, M.A. (2002). Math and numeracy in young adults with spina bifida and hydrocephalus. Developmental Neuropsychology, 21, 141—156.
17.
Fletcher, J.M., Dennis, M., Northrup, H., Barnes, M.A., Hannay, H.J., Landry, S.H., et al. (2004). Spina bifida: Genes, brain, and development . In L. M. Glidden (Ed.), Handbook of research on mental retardation (Vol. 28, pp. 63—117). San Diego, CA: Academic Press.
18.
Fuchs, L.S., & Fuchs, D. (2002). Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities . Journal of Learning Disabilities, 35, 563— 573.
Geary, D.C. (2003). Learning disabilities in arithmetic: Problem-solving differences and cognitive deficits. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Handbook of learning disabilities (pp. 199—212). New York: Guilford Press.
21.
Geary, D.C., Hamson, C.O., & Hoard, M.K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability . Journal of Experimental Child Psychology, 77, 236—263.
22.
Geary, D.C., Hoard, M.K., & Hamson, C.O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability . Journal of Experimental Child Psychology, 74, 213—239.
23.
Ginsburg, H.P., Klein, A., & Starkey, P. (1998). The development of children's mathematical thinking: Connecting research with practice. In I. E. Siegel & K. A. Renninger (Eds.), Handbook of child psychology: Vol. 4. Child psychology in practice (5th ed., pp. 401—476). New York : Wiley.
24.
Hanich, L., Jordan, N., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93, 615—626.
25.
Hartje, W. (1987). The effect of spatial disorders on arithmetical skills. In G. Deloche & X. Seron (Eds.), Mathematical disabilities: A cognitive neuropsychological perspective (pp. 121—135). Hillsdale, NJ: Erlbaum.
26.
Jordan, N.C., Hanich, L.B., & Kaplan, D. (2003a). A longitudinal study of mathematical competencies in children with specific math difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74, 834— 850.
27.
Jordan, N.C., Hanich, L.B., & Kaplan, D. (2003b). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103—119.
28.
Kosc, L. (1974). Developmental dyscalculia. Journal of Learning Disabilities, 7, 46—59.
29.
Mazzocco, M.M. (1998). A process approach to describing mathematics difficulties in girls with Turner syndrome. Pediatrics, 2, 492—496.
30.
Mazzocco, M.M. (2001). Math learning disability and math LD subtypes: Evidence from studies of Turner syndrome, fragile X syndrome, and neurofibromatosis type 1. Journal of Learning Disabilities, 34, 520— 533.
31.
McLean, J.F., & Hitch, G.J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74, 240—260.
32.
Morrison, S.R., & Siegel, L.S. (1991). Learning disabilities: A critical review of definitional and assessment issues. In J. E. Obrzut & G. W. Hynd (Eds.), Neuropsychological foundation of learning disabilities: A handbook of issues, methods, and practice (pp. 79—98). New York: Academic Press.
33.
Oakhill, J. (1993). Children's difficulties in reading comprehension . Educational Psychology Review, 5, 1—15.
34.
Rivera-Batiz, F.L. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. The Journal of Human Resources, 27, 313— 328.
35.
Rourke, B.P. (1993). Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. Journal of Learning Disabilities , 26, 214—226.
36.
Rovet, J., Szekely, C., & Hockenberry, M.N. (1994). Specific arithmetic calculation deficits in children with Turner syndrome. Journal of Clinical and Experimental Neuropsychology, 16, 820—839.
37.
Russell, R.L., & Ginsburg, H.P. (1984). Cognitive analysis of children's mathematical difficulties. Cognition and Instruction, 1, 217—244.
38.
Shalev, R.S., Auerbach, J., Manor, O., & Gross-Tsur, V. (2000). Developmental dyscalculia: Prevalence and prognosis. European Child & Adolescent Psychiatry, 9, 58—64.
39.
Share, D.L., Moffitt, T.E., & Silva, P.A. (1988). Factors associated with arithmeticand—reading disability and specific arithmetic disability. Journal of Learning Disabilities, 21, 313—320.
40.
Shrager, J., & Siegler, R.S. (1998). SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405—410.
41.
Siegel, L.S., & Ryan, E.B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60, 973—980.
42.
Siegler, R.S. (1987). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 117, 258—275.
43.
Siegler, R.S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258—275.
44.
Simon, T.J., Bearden, C.E., McDonald-McGinn, D., & Zackai, E. (2005). Visuospatial and numerical cognitive deficits in children with chromosome 22q11.2 deletion syndrome. Cortex , 41, 145—155.
45.
Stanovich, K.E., & Siegel, L.S. (1994). Phenotypic performance profile of children with reading disabilities: A regression-based test of the phonological-core variable-difference model. Journal of Educational Psychology, 86, 24—53.
46.
Strang, J.D., & Rourke, B.P. (1985). Arithmetic disability subtypes: The neuropsychological significance of specific arithmetical impairments in childhood. In B. P. Rourke (Ed.), Neuropsychology of learning disabilities: Essentials of subtype analysis (pp. 167—183). New York: Guilford Press.
47.
Swanson, H.L., & Sachse-Lee, C. (2001). Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology, 79, 294— 321.
Torgesen, J.K., Rashotte, C.A., & Alexander, A.W. (2001). Principles of fluency instruction in reading: Relationships with established empirical outcomes. In M. Wolf (Ed.), Dyslexia, fluency, and the brain (pp. 333—356). Timonium, MD: York Press.
50.
van Lehn, K. (1982). Bugs are not enough: Empirical studies of bugs, impasses and repairs in procedural skills. The Journal of Mathematical Behavior, 3, 3—71.
51.
Wechsler, D. (1991). Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corp.
52.
Wilkinson, G.S. (1993). Wide range achievement test (3rd ed.). San Antonio, TX: Psychological Corp.
53.
Wills, K.E. (1993). Neuropsychological functioning in children with spina bifida and /or hydrocephalus. Journal of Clinical Child Psychology, 22, 247—265.
