Role of Cognitive Theory in the Study of Learning Disability in Mathematics

Abstract

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.

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References

Badian, N.A. (1983). Dyscalculia and non-verbal disorders of learning . In H. R. Myklebust (Ed.), Progress in learning disabilities (Vol. 5, pp. 235—264). New York: Stratton.

Barrouillet, P. , Fayol, M. , & Lathulière, E. (1997). Selecting between competitors in multiplication tasks: An explanation of the errors produced by adolescents with learning disabilities. International Journal of Behavioral Development, 21, 253—275.

Briars, D. , & Siegler, R.S. (1984). A featural analysis of preschoolers' counting knowledge. Developmental Psychology, 20, 607— 618.

Fuchs, L.S. , Fuchs, D. , & Prentice, K. (2004). Responsiveness to mathematical problem-solving instruction: Comparing students at risk for mathematics disability with and without risk for reading disability. Journal of Learning Disabilities , 37, 293—306.

Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363—383.

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

Geary, D.C. (1995). Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. The American Psychologist, 50, 24—37.

Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4—15.

Geary, D.C. (in press). Development of mathematical understanding. In D. Kuhl & R. S. Siegler (Vol. Eds.), W. Damon (Gen. Ed.), Handbook of child psychology (6th ed.), Vol 2. Cognition, perception, and language. New York: Wiley.

10.

Geary, D.C. , & Brown, S.C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27, 398— 406.

11.

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.

12.

Geary, D.C. , & Hoard, M.K. (2002). Learning disabilities in basic mathematics: Deficits in memory and cognition. In J. M. Royer (Ed.), Mathematical cognition (pp. 93—115). Greenwich, CT: Information Age Publishing.

13.

Gelman, R. , & Meck, E. (1983). Preschooler's counting: Principles before skill . Cognition, 13, 343—359.

14.

Jordan, N.C. , Hanich, L.B. , & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103—119.

15.

Kosc, L. (1974). Developmental dyscalculia. Journal of Learning Disabilities, 7, 164—177.

16.

Ostad, S.A. (1998). Comorbidity between mathematics and spelling difficulties . Log Phon Vovol, 23, 145—154.

17.

McCloskey, M. , Aliminosa, D. , & Macaruso, P. (1991). Theory-based assessment of acquired dyscalculia. Brain and Cognition, 17, 285—308.

18.

Russell, R.L. , & Ginsburg, H.P. (1984). Cognitive analysis of children's mathematical difficulties. Cognition and Instruction, 1, 217—244.

19.

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 phonologically-based intervention. Biological Psychiatry, 55, 926—933.

20.

Shalev, R.S. , Manor, O. , & Gross-Tsur, V. (1993). The acquisition of arithmetic in normal children: Assessment by a cognitive model of dyscalculia. Developmental Medicine and Child Neurology, 35, 593—601.

21.

Siegler, R.S. , & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229—293). Hillsdale, NJ: Erlbaum.

22.

Tronsky, L.N. , & Royer, J.M. (2002). Relationships among basic computational automaticity, working memory, and complex mathematical problem solving: What we know and what we need to know. In J. M. Royer (Ed.), Mathematical cognition (pp. 117—146). Greenwich, CT: Information Age Publishing.