Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities

Journal of Learning Disabilities

Volumn 41, Issue 1, 2008, Pages 15-28

  Mabbott, Donald J ^a   Bisanz, Jeffrey ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Computational skill; Conceptual understanding; Dyscalculia; Mathematics learning disabilities; Multiplication; Working memory

Indexed keywords

AGE; ARTICLE; CHILD; COMPREHENSION; CONCEPT FORMATION; EDUCATION; EDUCATIONAL STATUS; FEMALE; HUMAN; LEARNING DISORDER; MALE; MATHEMATICS; PROBLEM SOLVING; PSYCHOLOGICAL ASPECT; SHORT TERM MEMORY;

AGE FACTORS; CHILD; COMPREHENSION; CONCEPT FORMATION; EDUCATION, SPECIAL; EDUCATIONAL STATUS; FEMALE; HUMANS; LEARNING DISORDERS; MALE; MATHEMATICS; MEMORY, SHORT-TERM; PROBLEM SOLVING;

EID: 41749101532     PISSN: 00222194     EISSN: None     Source Type: Journal    
DOI: 10.1177/0022219407311003     Document Type: Article

References (67)

1. American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders (4 th ed.). Washington, DC: Author.
2. Ardila, A., & Rosselli, M. (2002). Acalculia and dyscalculia. Neuropsychology Review, 12, 179 - 231.
3. Ashcraft, M.H., Donley, R.D., Halas, M.A., & Vakali, M. (1992). Working memory, automaticity, and problem difficulty. Amsterdam: Elsevier.
4. Baddeley, A.D. (1986). Working memory. New York: Oxford University Press.
5. Baddeley, A.D., & Hitch, G. (1974). Working memory (Vol. 8). New York: Academic Press.
6. 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.
7. Baroody, A.J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual knowledge and procedural knowledge. Mahwah, NJ: Lawrence Erlbaum.
8. Baroody, A.J., & Ginsburg, H.P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. Hillsdale, NJ: Lawrence Erlbaum.
9. Barrouillet, P., Fayol, M., & Lathuliere, E. (1997). Selecting between competitors in multiplication tasks: An explanation of the errors produced by adolescents with learning difficulties. International Journal of Behavioral Development, 21, 253 - 275.
10. Brown, R.T., Madan-Swain, A., Walco, G.A., Cherrick, I., Ievers, C.E., Conte, P.M., et al. (1998). Cognitive and academic late effects among children previously treated for acute lymphocytic leukemia receiving chemotherapy as CNS prophylaxis. Journal of Pediatric Psychology, 23, 333 - 340.
11. Bull, R., & Johnston, R.S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1 - 24.
12. Bull, R., Johnston, R.S., & Roy, J.A. (1999). Exploring the roles of the visual-spatial sketch pad and central executive in children's arithmetical skills: Views from cognition and developmental neuropsychology. Developmental Neuropsychology, 15, 421 - 442.
13. Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children's mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273 - 293.
14. Byrnes, J.P., & Wasik, B.A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777 - 786.
15. Dennis, M., & Barnes, M. (2002). Math and numeracy in young adults with spina bifida and hydrocephalus. Developmental Neuropsychology, 21, 141 - 155.
16. Dixon, J.A., & Moore, C.F. (1996). The developmental role of intuitive principles in choosing mathematical strategies. Developmental Psychology, 32, 241 - 253.
17. 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.
18. Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363 - 383.
19. Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4 - 15.
20. Geary, D.C., Bow-Thomas, C.C., & Yau, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54, 372 - 391.
21. Geary, D.C., Brown, S.C., & Samaranayake, V.A. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology, 27, 787 - 797.
22. 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.
23. Geary, D.C., Hoard, M.K., Byrd-Craven, J., & DeSoto, M.C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121 - 151.
24. Gersten, R., Jordan, N.C., & Flojo, J.R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293 - 304.
25. Ginsburg, H.P., Klein, A., & Starkey, P. (1998). The development of children's mathematical thinking: Connecting research with practice (5 th ed., Vol. 4). New York: Wiley.
26. Goldman, S.R., Pellegrino, J.W., & Mertz, D.L. (1988). Extended practice of basic addition facts: Strategy changes in learning-disabled students. Cognition and Instruction, 5, 223 - 265.
27. Gonzales, J.J., & Espinel, A.I. (2002). Strategy choice in solving arithmetic word problems: Are there differences between students with learning disabilities, G-V poor performance, and typical achievement students? Learning Disability Quarterly, 25, 113 - 122.
28. Gross-Tsur, V., Manor, O., & Shalev, R.S. (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine and Child Neurology, 38, 25 - 33.
29. Hanich, L.B., Jordan, N.C., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93, 615 - 626.
30. Hitch, G.J., & McAuley, E. (1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82, 375 - 386.
31. Hittmair-Delazer, M., Sailer, U., & Benke, T. (1995). Impaired arithmetic facts but intact conceptual knowledge-a single-case study of dyscalculia. Cortex, 31, 139 - 147.
32. 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.
33. Jordan, N.C., & Hanich, L.B. (2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33, 567 - 578.
34. Jordan, N.C., Hanich, L.B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74, 834 - 850.
35. Jordan, N.C., Levine, S.C., & Huttenlocher, J. (1995). Calculation abilities in young children with different patterns of cognitive functioning. Journal of Learning Disabilities, 28, 53 - 64.
36. Jordan, N.C., & Montani, T.O. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30, 624 - 634, 684.
37. Kesler, S.R., Menon, V., & Reiss, A.L. (2005). Neurofunctional differences associated with arithmetic processing in turner syndrome. Cerebral Cortex, 16, 849 - 856.
38. LeFevre, J. (1993). Individual differences in working memory. Unpublished manuscript, Carlton University.
39. Logie, R.H., Gilhooly, K.J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory and Cognition, 22, 395 - 410.
40. Lovett, M.W., Lacerenza, L., & Borden, S.L. (2000). Putting struggling readers on the phast track: A program to integrate phonological and strategy-based remedial reading instruction and maximize outcomes. Journal of Learning Disabilities, 33, 458 - 476.
41. Lovett, M.W., Steinbach, K.A., & Frijters, J.C. (2000). Remediating the core deficits of developmental reading disability: A double-deficit perspective. Journal of Learning Disabilities, 33, 334 - 358.
42. Mabbott, D.J., & Bisanz, J. (2003). Developmental change and individual differences in children's multiplication. Child Development, 74, 1091 - 1107.
43. 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.
44. 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.
45. Micallef, S., & Prior, M. (2004). Arithmetic learning difficulties in children. Educational Psychology, 24, 175 - 200.
46. Molko, N., Cachia, A., Riviere, 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. Ostad, S.A. (1997). Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children. British Journal of Educational Psychology, 67, 345 - 357.
48. Passolunghi, M.C., & Siegel, L.S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80, 44 - 57.
49. Passolunghi, M.C., & Siegel, L.S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88, 348 - 367.
50. Putnam, R.T., deBettencourt, L.U., & Leinhardt, G. (1990). Understanding of derived-fact strategies in addition and subtraction. Cognition and Instruction, 7, 245 - 285.
51. Rourke, B.P. (1989). Nonverbal learning disabilities: The syndrome and the model. New York: Guilford Press.
52. Russell, R., & Ginsburg, H.P. (1984). Cognitive analysis of children's mathematics difficulties. Cognition and Instruction, 1, 217 - 244.
53. Shaywitz, B.A., Shaywitz, S.E., Blachman, B.A., Pugh, K.R., Fulbright, R.K., Skudlarski, P., et al. (2004). Development of left occipitotemporal systems for skilled reading in children after a phonologically based intervention. Biological Psychiatry, 55, 926 - 933.
54. Shaywitz, S.E., Shaywitz, B.A., Fulbright, R.K., Skudlarski, P., Mencl, W.E., Constable, R.T., et al. (2003). Neural systems for compensation and persistence: Young adult outcome of childhood reading disability. Biological Psychiatry, 54, 25 - 33.
55. Shrager, J., & Siegler, R.S. (1998). Scads: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405 - 410.
56. 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.
57. Siegler, R.S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258 - 275.
58. Swanson, H.L. (1993). Working memory in learning disability subgroups. Journal of Experimental Child Psychology, 56, 87 - 114.
59. Swanson, H.L. (1994). Short-term memory and working memory: Do both contribute to our understanding of academic achievement in children and adults with learning disabilities? Journal of Learning Disabilities, 27, 34 - 50.
60. 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.
61. Torbeyns, J., Verschaffel, L., & Ghesquiere, P. (2004). Strategy development in children with mathematical disabilities: Insights from the choice/no-choice method and the chronological-age/ability-level- match design. Journal of Learning Disabilities, 37, 119 - 131.
62. Turner, M.L., & Engle, R.W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28, 127 - 154.
63. van der Sluis, S., van der Leij, A., & de Jong, P.F. (2005). Working memory in Dutch children with reading- and arithmetic-related LD. Journal of Learning Disabilities, 38, 207 - 221.
64. Wechsler, D. (1989). Wechsler Intelligence Scale for Children (3 rd ed.). San Antonio, TX: Psychological Corp.
65. Wilkinson, G.S. (1993). Wide Range Achievement Test-Revision 3. Wilmington, DE: Jastak Associates.
66. Wilson, K.M., & Swanson, H.L. (2001). Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit? Journal of Learning Disabilities, 34, 237 - 248.
67. Zentall, S.S. (1990). Fact-retrieval automatization and math problem solving by learning disabled, attention-disordered, and normal adolescents. Journal of Educational Psychology, 82, 856 - 865.