Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor multiplication fact mastery and calculation fluency and general working memory discriminated children with MLD from typically achieving age-matched peers. Furthermore, children with MLD were slower in executing backup procedures than typically achieving age-matched peers. The performance of children with MLD on multiple measures of multiplication skill and knowledge was most similar to that of ability-matched younger children. MLD may be due to difficulties in computational skills and working memory. Implications for the diagnosis and remediation of MLD are discussed.
American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders (4th 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 (5th 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.
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. BiologicalPsychiatry, 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. BiologicalPsychiatry, 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 andLanguage, 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 (3rd 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.
