Advanced Search

Journal Navigation

Journal Home

Subscriptions

Archive

Contact Us

Table of Contents

Click here to sign up for SAGE Journal Email Alerts today!

Sign In to gain access to subscriptions and/or personal tools.
Journal of Learning Disabilities
This Article
Right arrow Abstract Freely available
Right arrow Free Full Text (Free PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by van Garderen, D.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by van Garderen, D.
Social Bookmarking
 Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?

Teaching Students With LD to Use Diagrams to Solve Mathematical Word Problems

Delinda van Garderen

University of Missouri-Columbia, vangarderend{at}missouri.edu

This study examined the effectiveness of instruction focused on teaching students with learning disabilities (LD) to solve 1- and 2-step word problems of varying types. Three students with LD in Grade 8 participated in the study. During the treatment, students received instruction in diagram generation and a strategy that incorporates diagrams as a part of the procedure to solve word problems. The results indicated that all students improved in the number of diagrams they used and in their ability to generate diagrams. Their word problem solving performance increased. Moreover, the students generated and used diagrams to solve other types of problems. Overall, the students were very satisfied with the instruction and would continue to use the diagrams and the strategy to solve word problems in other classroom settings.

References

  • Alexander, P.A. (2006). Psychology in learning and instruction. Prentice Hall.
  • Barratt, P.E. (1953). Imagery and thinking. Australian Journal of Psychology, 5, 154— 164.
  • Brown, D.L., & Presmeg, N.C. (1993, July). Types of imagery used by elementary and secondary school students in mathematical reasoning. In Proceedings of the 17th Annual Meeting of the International Group for the Psychology of Mathematics Education, Tsukuba, Japan (Vol. II, pp. 137— 144).
  • Campbell, K.J., Collis, K.F., & Watson, J.M. (1995). Visual processing during mathematical problem solving. Educational Studies in Mathematics, 28, 177—194.[CrossRef]
  • Case, L.P., Harris, K.R., & Graham, S. (1992). Improving the mathematical problem-solving skills of students with learning disabilities: Self-regulated strategy development. The Journal of Special Education, 26, 1—19.
  • Davis, R.B., & Maher, C.A. (1997). How students think: The role of representations. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 93—115). Mahwah, NJ: Erlbaum.
  • Diezmann, C.M., & English, L.D. (2001). Promoting the use of diagrams as tools for thinking. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics: 2001 yearbook (pp. 77— 89). Reston, VA: National Council of Teachers of Mathematics.
  • Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109—122). Hillsdale, NJ: Erlbaum.
  • Geary, D.C. (1996). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
  • Goldman, S.R. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12, 43—55.[CrossRef][Web of Science]
  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual—spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684—689.[CrossRef][Web of Science]
  • Hutchinson, N.L. (1993). Effects of cognitive strategy instruction on algebra problem solving with adolescents. Learning Disability Quarterly, 16, 34—63.[CrossRef][Web of Science]
  • Janvier, C. (1987). Representation and understanding: The notion of function as an example. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 67—71). Hillsdale, NJ: Erlbaum.
  • Jitendra, A., DiPipi, C.M., & Perron-Jones, N. (2002). An exploratory study of schema-based word-problem—solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36, 23—38.
  • Jitendra, A.K., Griffin, C.C., McGoey, K., Gardill, M.C., Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. The Journal of Educational Research, 91, 345—355.
  • Jitendra, A.K., & Hoff, K. (1996). The effects of schema-based instruction on the mathematical word-problem—solving performance of students with learning disabilities. Journal of Learning Disabilities, 29, 422—431.[Abstract/Free Full Text]
  • Jitendra, A.K., Hoff, K., & Beck, M.M. (1999). Teaching middle school students with learning disabilities to solve word problems using a schema-based approach. Remedial and Special Education, 20, 50—64.[Abstract/Free Full Text]
  • Kazdin, A.E. (1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford University Press.
  • Kozhevnikov, M., Hegarty, M., & Mayer, R.E. (2002). Revising the visualizer— verbalizer dimension: Evidence for two types of visualizers. Cognition and Instruction, 20, 47—77.[CrossRef]
  • Lean, G., & Clements, M.A.K. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267—299.[CrossRef]
  • Lowrie, T. (1996). The use of visual imagery as problem-solving tool: Classroom implementation. Journal of Mental Imagery, 20, 127—140.
  • Mayer, R.E., & Hegarty, M. (1996). The process of understanding mathematical problems. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29—53). Mahwah, NJ: Erlbaum.
  • Meltzer, L., & Montague, M. (2001). Strategic learning in students with learning disabilities: What have we learned? In D. P. Hallahan & B. K. Keogh (Eds.), Research and global perspectives in learning disabilities: Essays in honor of William M. Cruickshank (pp. 111—130). Mahwah, NJ: Erlbaum.
  • Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25, 230—248.[Abstract/Free Full Text]
  • Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164—177.[Abstract/Free Full Text]
  • Montague, M. (2003). Solve it! A practical approach to teaching mathematical problem solving skills. Reston, VA: Exceptional Innovations.
  • Montague, M. (2006). Self-regulation strategies for better math performance in middle school. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning di ficulties (pp. 72—88). New York: Guilford Press.
  • Montague, M., & Applegate, B. (1993a). Mathematical problem-solving characteristics of middle school students with learning disabilities. The Journal of Special Education, 27, 175—201.
  • Montague, M., & Applegate, B. (1993b). Middle school students' mathematical problem solving: An analysis of think-aloud protocols. Learning Disability Quarterly, 16, 19—32.[CrossRef][Web of Science]
  • Montague, M., Bos, C., & Doucette, M. (1991). Affective, cognitive, and metacognitive attributes of eighth-grade mathematical problem solvers. Learning Disabilities Research & Practice, 6, 145—151.
  • Montague, M., Warger, C., & Morgan, T.H. (2000). Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research & Practice, 15, 110—116.[CrossRef]
  • Moses, B.E. (1980). The relationship between visual thinking tasks and problem-solving performance. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA.
  • Novick, L.R., Hurley, S.M., & Francis, M. (1999). Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory & Cognition, 27, 288—308.[Medline] [Order article via Infotrieve]
  • Owens, K.D., & Clements, M.A.K. (1998). Representations in spatial problem solving in the classroom. The Journal of Mathematical Behavior, 17, 197—218.[CrossRef]
  • Pape, S.J., & Tchoshanov, M.A. (2001). The role of representation(s) in developing mathematical understanding. Theory Into Practice, 40, 118-127.[CrossRef]
  • Parmar, R.S. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. Diagnostique, 17, 227—243.
  • Presmeg, N.C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299—312). Mahwah, NJ: Erlbaum.
  • Presmeg, N.C. (1986a). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297—311.[CrossRef]
  • Presmeg, N.C. (1986b). Visualization in high school mathematics. For the Learning of Mathematics, 6, 42—46.
  • Van de Walle, J.A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). New York: Longman.
  • van Garderen, D. (2006). Teaching visual representation for mathematics problem solving. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning di ficulties (pp. 72—88). New York: Guilford Press.
  • van Garderen, D., & Montague, M. (2003). Visual—spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18, 246—254.[CrossRef]
  • Walker, D.W., & Poteet, J.A. (1989—1990). A comparison of two methods of teaching mathematics story problem-solving with learning disabled students. National Forum of Special Education Journal, 1, 44— 51.
  • Wechsler, D. (1991). Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corp.
  • Woodcock, R.W., McGrew, K.S., & Mather, N. (2001). Woodcock-Johnson—III tests of cognitive abilities. Itasca, IL: Riverside.
  • Woodward, J., & Montague, M. (2002). Meeting the challenge of mathematics reform for students with LD. The Journal of Special Education, 36, 89—101.[CrossRef]

Journal of Learning Disabilities, Vol. 40, No. 6, 540-553 (2007)
DOI: 10.1177/00222194070400060501


Add to CiteULike CiteULike   Add to Complore Complore   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us   Add to Digg Digg   Add to Reddit Reddit   Add to Technorati Technorati   Add to Twitter Twitter    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Free Full Text (Free PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to Saved Citations
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow Request Reprints
Right arrow Add to My Marked Citations
Citing Articles
Right arrow Citing Articles via Google Scholar
Right arrow Citing Articles via Scopus
Google Scholar
Right arrow Articles by van Garderen, D.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by van Garderen, D.
Social Bookmarking
 Add to CiteULike   Add to Complore   Add to Connotea   Add to Del.icio.us   Add to Digg   Add to Reddit   Add to Technorati   Add to Twitter  
What's this?