Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T21:15:56.408Z Has data issue: false hasContentIssue false
  • English
  • Français

The Role of a Graphic Representational Technique on the Mathematical Problem Solving Performance of Fourth Graders: An Exploratory Study

Published online by Cambridge University Press:  26 February 2016

Asha Jitendra ,
Caroline M. DiPipi  and
Ed Grasso
Asha Jitendra*
Affiliation:
Lehigh University
Caroline M. DiPipi
Affiliation:
Lehigh University
Ed Grasso
Affiliation:
Lehigh University
*
Address for: Asha Jitendra, Lehigh University, College of Education, lacocca Hall, 111 Research Driva, Bethlehem PA 18015 United States of America. Email: AKJIZ@lehigh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this within‐subject comparisons exploratory study was to examine the influence of a graphic representational strategy on the problem solving performance of fourth graders, including special education students with learning problems. We employed a preliminary design experiment, prior to conducting a formal experimental or quasi‐experimental study, to gain insights into factors that may inhibit or enhance implementation of the intervention, especially in the context of real world of classroom (Gersten, Baker, & Lloyd, 2000). Students received teacher‐led strategy instruction in problem solving using a whole group (8 to 9 students) format followed by guided practice in applying the strategy during cooperative groups. Results indicate that students’ word problem solving performance increased from the pretest to posttest on multiplication and division problems. In addition, some students were able to generalise the skill to untaught problems. Implications of the representational strategy for solving word problems by elementary students and special education students with learning problems are discussed.

Type
Research Article
Information
Australasian Journal of Special Education , Volume 25 , Issue 1-2 , 2001 , pp. 17 - 33
Copyright
Copyright © The Australian Association of Special Education 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, J. (1989). A theory of the origins of human knowledge. Artificial Inteligence, 40, 313–351.Google Scholar
Bana, J., & Chapman, A. (Eds.) (July 2000). Mathematics education beyond 2000: Proceedings of the annual meeting of the mathematics education research group of Australasia (23rd Fremantle, Western Australia, Australia). ERIC Document Reproduction Service No. 444873.Google Scholar
Bransford, J., Delclos, V., Vye, N., Burns, M., & Hasselbring, T. (1987). State of the art and future directions. In Lidz, C. S. (Ed.), Dynamic assessment: An interactional approach to evaluating learner potential (pp. 479–496). New York: Guilford Press.Google Scholar
Briars, D., & Larkin, J. (1984). An integrated model of skill in solving elementary problems. Cognition and Instruction, 1, 245–296.Google Scholar
Brown, V., Cronin, M., McEntire, E. (1994). Test of mathematical abilities. Austin, TX: Pro-Ed.Google Scholar
Burton, G., Maletskky, E., Bright, G., Helton, S., Hollis, L., Johnson, H., McLeod, J., Neufeld, E., Newman, V., Perdante, T., Schultz, K., & Thatcher, M. (1998). Math advantage. Orlando, FL: Harcourt Brace.Google Scholar
Carpenter, T., & Moser, J. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202.CrossRefGoogle Scholar
Carpenter, T., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In Fenema, E. and Romberg, T. A. (Eds.) Mathematics classrooms that promote understanding (pp. 19–32). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Cawley, J., & Parmar, R. (1992). Arithmetic programming for students with disabilities: An alternative. Remedial and Special Education, 13(3), 6–18.CrossRefGoogle Scholar
Cawley, J., Parmar, R., Yan, W., & Miller, J. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research & Practice, 13, 68–74.Google Scholar
Chi, M., Glaser, R., & Rees, E. (İ981). Expertise in problem solving. In Sternberg, R. (Ed.), Advances in the psychology of human intelligence (Vol. 1, pp. 7–75). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Fennema, E., Carpenter, T., & Peterson, P. (1989). Learning mathematics with understanding: Cognitively guided instruction. In Brophy, J. E. (Ed.) Advances in research on teaching (pp. 195–221). Greenwich, CT: JAI press.Google Scholar
Fraivillig, J., Murphy, L., & Fuson, K. (1999). Advancing children’s mathematical thinking in Everyday Mathematics classrooms. Journal of Research in Mathematics 30(2), 148–170.Google Scholar
Fuson, K., & Willis, G. (1989). Second graders’ use of schematic drawings in solving addition and subtraction problems. Journal of Educational Psychology 81(4), 514–520.Google Scholar
Gersten, R., Baker, S., & Lloyd, J. (2000). Designing high-quality research in special education: Group experimental designs. Journal of Special Education, 34, 2–19.Google Scholar
Goldman, S., Hasselbring, T., & the Cognition and Technology Group at Vanderbilt. (1997). Achieving meaningful mathematics literacy for students with learning disabilities. Journal of Learning Disabilities 30(2), 198–208.CrossRefGoogle ScholarPubMed
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In Hiebert, J. (Ed.), Conceptual and procedural knowledge: The case of mathematics. Hillsdale, New Jersey: Lawrence Erlbaum.Google Scholar
Hutchinson, N. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disabilities Quarterly, 16, 34–63.CrossRefGoogle Scholar
Jitendra, A., Griffin, C., McGoey, K., Gardill, C., Bhat, P., & Riley, T. (1998). Effects of mathematical problem solving by students at risk or with mild disabilities. Journal of Educational Research 91(6), 345–356.Google Scholar
Jitendra, A., & Hoff, K. (1996). The effects of schema-based instruction on mathematical problem solving performance of students with learning disabilities. Journal of Learning Disabilities, 29(4), 422–431.Google Scholar
Jitendra, A., Hoff, K., & Beck, M. (1999). Teaching middle school students with learning disabilities to solve multistep problems using a schema-based approach. Remedial and Special Education, 20(1), 50–64.Google Scholar
Jitendra, A., & Xin, Y. (1997). Mathematical problem solving instruction for students with mild disabilities and students at risk for math failure: A research synthesis. The Journal of Special Education, 30(4), 412–438.CrossRefGoogle Scholar
Kaufman, A., & Kaufman, N. (1997). K-TEA: Kaufman test of educational achievement. Circle Pines, MN: American Guidance Service.Google Scholar
Kelly, B., & Camine, D. (1996). Teaching problem-solving strategies for word problems to students with learning disabilities. LD forum 21(3), 5–9.Google Scholar
Kintsch, W., & Greeno, J. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109–129.CrossRefGoogle ScholarPubMed
Marshall, S. (1990). The assessment of schema knowledge for arithmetic story problems: A cognitive science perspective. In Kulm, G. (Ed.), Assessing higher order thinking in mathematics. Washington, DC: American Association for the Advancement of Science.Google Scholar
Marshall, S. (1995). Schemas in problem solving. New York: Cambridge University Press.CrossRefGoogle Scholar
Marshall, S., Barthuli, K., Brewer, M., & Rose, F. (1989). STORY PROBLEM SOLVER: A schema-based system of instruction (CRMSE Tech. Rep. No. 89-01). San Diego, CA: Center for Research in Mathematics and Science Education.Google Scholar
Mastropieri, M., Scruggs, T., & Shiah, S. (1991). Mathematics instruction for learning disables students: A review of research. Learning Disabilities Research and Practice, 6, 89–98.Google Scholar
Miller, S., Butler, F., & Lee, K. (1998). Validated practices for teaching mathematics to students with learning disabilities: A review of literature. Focus on Exceptional Children, 31 (1), 1–24.Google Scholar
Montague, M., Applegate, B., & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disabilities Research and Practice, 8, 223–232.Google Scholar
National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics electronic version 1.0: Discussion draft htpp//standards-e.nctm.org/1.0/normal/indexCONTENT.html.Google Scholar
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics electronic version http://standards.nctm.org/.Google Scholar
Patton, J., Cronin, M., Bassett, D., & Koppel, A. (1997). A life skills approach to mathematics instruction: Preparing students with learning disabilities for the real-life math demands of adulthood. Journal of Learning Disabilities 30(2), 178–187.CrossRefGoogle ScholarPubMed
Pereira, J., & Winton, A. (1991). Teaching and remediation of mathematics: A review of behavioral research. Journal of Behavioral Education, 1, 1991, 5–36.Google Scholar
Riley, M., Greeno, J., & Heller, J. (1983). Development of children’s problem-solving ability in arithmetic. In Ginsburg, H. P. (Ed.), The development of mathematical thinking (pp. 153–196). New York: Academic Press.Google Scholar
Rivera, D. (1997). Mathematics education and students with learning disabilities: Introduction to the special series. Journal of Learning Disabilities, 30, 2–19.Google Scholar
Shafer, M., & Ramberg, T. (1999). Assessment ¡n classrooms that promote understanding. In Fenema, E. and Romberg, T. A. (Eds.) Mathematics classrooms that promote understanding (pp. 159–184). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Silver, E., & Marshal!, S. (1990). Mathematical and scientific problem solving: Findings, issues, and instructional implications. In Jones, B. F. & Idol, L. (Eds.), Dimensions of thinking and cognitive instruction. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Sternberg, R., & Ben-Zeev, T. (1996). Preface. In Sternberg, R. J. & Ben-Zeev, T. (Eds.), The nature of mathematical thinking. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Sweller, J., Chandler, P., Tierney, P., Cooper, M. (1990). Cognitive load as a factor in the structuring of technical material. Journal of Experimental Psychology: General 19(2), 176–192.Google Scholar
Van de Walle, J. (1998). Elementary and middle school mathematics: Teaching developmentally (3rd ed.). New York: Longman.Google Scholar
Wechsler, D. (1991). WISC - III. Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corporation.Google Scholar
Woodward, J., & Baxter, J. (1997). The effects of an innovative approach to mathematics , on academically low-achieving students in inclusive settings. Exceptional Children, 63, 373–388.Google Scholar
Xin, Y., & Jitendra, A. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32(4), 207–225.Google Scholar
Zawaiza, T., & Gerber, M. (1993). Effects of explicit instruction on community college students with learning disabilities. Learning Disabilities Quarterly, 16, 64–79.Google Scholar