Abstract
Two types of elementary mathematics word problems involving different linguistic structures were devised to examine the understanding and solution of these problems by 91 Grade 3, 4, and 5 children divided into “more able” and “less able” subgroups. One task consisted of 12 consistent and 12 inconsistent language problems on the basic processes of addition, subtraction, multiplication and division. Another task consisted of a total of 36 word problems with 12 items each containing adequate, inadequate, and redundant information, respectively, for problem solution. Subsidiary tasks of general ability, vocabulary, reading comprehension, mathematics concepts, reflection on mathematics learning, and working memory were also administered to provide estimates of the contribution of these “nonmathematics” tasks to the solution of elementary mathematics problems. Analyses of variance and covariance of group data showed significant main effects of grade, consistency, and adequacy of linguistic information in problem solution. Word problems containing inconsistent information were more difficult than those with consistent information. Further, word problems containing inadequate and redundant information were more difficult to classify, and for the children to explain, than those items with just enough information. Interviews with 12 individual children provided further insight into their strategies for problem solutions. Both cognitive and developmental perspectives are important for mathematics learning and teaching for children with or without learning disabilities.
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References
Ackerman, P. T., & Dykman, R. A. (1995). Reading-disabled students with and without comorbid arithmetic disability. Developmental Neuropsychology, 11, 351–371.
Badian, N. A. (1999). Persistent arithmetic, reading, or arithmetic and reading disability. Annals of Dyslexia, 49, 45–70.
Bransford, J., Zech, L., Schwartz, D., Barron, B., Vye, N., & the Cognition and Technology Group at Vanderbilt (CTGV). (2000). Designs for environments that invite and sustain mathematical thinking. In P. Cobb, E. Yackel, & K. McClain (eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (pp. 275–324). Mahwah, NJ: Lawrence Erlbaum Associates.
Briars, D. J., & Larkin, J. H. (1984). An integrated model of skill in solving elementary word problems. Cognition and Instruction, 1, 245–296.
Cooney, J. B., & Swanson, H. L. (1990). Individual differences in memory for mathematical story problems: Memory span and problem perception. Journal of Educational Psychology, 82, 570–577.
Elliott, C. D., Murray, D. J., & Pearson, L. S. (1978). British ability scales: Manual 3; Directions for administration and scoring/Manual 4: Tables of abilities and norms. Windsor, Berks: National Foundation for Educational Research.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345–362.
Geary, D. C. (1996). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetic cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77, 236–263.
Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetic cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74, 213–239.
Ginsburg, H. P. (1977). Children’s arithmetic: The learning process. New York: D. van Nostrand.
Ginsburg, H. P. (1997). Mathematics learning disabilities: A view from developmental psychology. Journal of Learning Disabilities, 30, 20–33.
Goldman, S. R., Hasselbring, T. S., & the Cognition and Technology Group at Vanderbilt (1997). Achieving meaningful mathematics literacy for students with learning disabilities. Journal of Learning Disabilities, 30, 198–208.
King, E. M. (Ed.). (1982). Canadian tests of basic skills: Multilevel edition: Levels 9-12/Forms 5 & 6. Toronto: Nelson.
Leong, C. K. (1999). Phonological coding and children’s spelling. Annals of Dyslexia, 49, 195–220.
Low, R., & Over, R. (1993). Gender differences in solution of algebraic word problems containing irrelevant information. Journal of Educational Psychology, 85, 331–339.
McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107–157.
Miles, T. R., & Miles, E. (Eds.). (1992). Dyslexia and mathematics. London: Routledge.
Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164–177.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Nunes, T., & Bryant, P. (1996). Children doing mathematics. Oxford, UK: Blackwell.
Rivera, D. P. (Ed.). (1997). Mathematics education and students with learning disabilities: Introduction in the special series (Special series Part I & II). Journal of Learning Disabilities, 30 (1 & 2).
Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press.
Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and bahavior, Journal for Research in Mathematics Education, 20, 338–355.
Swanson, H. L. (1992). Generality and modifiability of working memory among skilled and less skilled readers. Journal of Educational Psychology, 84, 473–488.
Thornton, C. A., Langrall, C. W., & Jones, G. A. (1997). Mathematics instruction for elementary students with learning disabilities. Journal of Learning Disabilities, 30, 142–150.
Verschaffel, L. (1994). Using retelling data to study elementary school children’s representations and solutions of compare problems. Journal for Research in Mathematics Education, 25, 141–165.
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Leong, C.K., Jerred, W.D. Effects of consistency and adequacy of language information on understanding elementary mathematics word problems. Ann. of Dyslexia 51, 275–298 (2001). https://doi.org/10.1007/s11881-001-0014-1
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DOI: https://doi.org/10.1007/s11881-001-0014-1