This exploratory study extends the research on schema-based strategy instruction by investigating its effects on the mathematical problem solving of 4 middle school students with learning disabilities who were low-performing in mathematics. A multiple-probe-across-participants design included baseline, treatment, generalization, and maintenance. During treatment, students received schema strategy training in problem schemata (conceptual understanding) and problem solution (procedural understanding). Results indicated that the schema-based strategy was effective in substantially increasing the number of correctly solved multiplication and division word problems for all 4 participants. Maintenance of strategy effects was evident for 10, 51/2, and 21/2 weeks following the termination of instruction for Sara, Tony, and Percy, respectively. In addition, the effects of instruction generalized to novel word problems for all 4 participants.
Get full access to this article
View all access options for this article.
References
1.
Anderson, J.R. (1989). A theory of the origins of human knowledge. Artificial Intelligence, 40, 313—351.
2.
Baroody, A.J., & Hume, J. (1991). Meaningful mathematics instruction: The case of fractions. Remedial and Special Education,12(3), 54—68.
3.
Bottge, B.A. (1999). Effects of contextualized math instruction on problem solving of average and below-average achieving students. The Journal of Special Education, 33, 81—92.
4.
Briars, D.J., & Larkin, J.H. (1984). An integrated model of skill in solving elementary problems. Cognition and Instruction, 1, 245—296.
5.
Butterfield, E.C., & Nelson, G.D. (1989). Theory and practice of teaching for transfer. Educational Technology Research and Development, 37, 5—38.
6.
Carpenter, T.P., & Moser, J.M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179—202.
7.
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.
8.
Cawley, J.F., & Parmar, R.S. (1992). Arithmetic programming for students with disabilities: An alternative. Remedial and Special Education, 12(2), 19—35.
9.
Chi, M.T.H., Glaser, R., & Rees, E. (1982). Expertise in problem solving. In R. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 1, pp. 7—75). Hillsdale, NJ: Erlbaum.
10.
Davis-Dorsey, J., Ross, S.R., & Morrison, G.R. (1991). The role of rewording and context personalization in the solving of mathematical word problems. Journal of Educational Psychology, 83(1), 61—68.
11.
DeCorte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. Berliner & R. Calfee (Eds.), Handbook of educational psychology (pp. 491—549). New York: Macmillan.
12.
Fennema, E., Carpenter, T.P., & Peterson, P.L. (1989). Learning mathematics with understanding: Cognitively guided instruction. In J. E. Brophy (Ed.), Advances in research on teaching (pp. 195—221). Greenwich, CT: JAI.
13.
Fraivillig, J.L., Murphy, L.A., & Fuson, K.C. (1999). Advancing children's mathematical thinking in Everyday Mathematics classrooms. Journal of Research in Mathematics , 30(2), 148—170.
14.
Fuson, K.C., & Willis, G.B. (1989). Second graders' use of schematic drawings in solving addition and subtraction word problems. Journal of Educational Psychology, 81, 514—520.
15.
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.
16.
Greer, B. (1992). Multiplication and division models of situations . In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276—295). Old Tappan, NJ: Macmillan.
17.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics . Hillsdale, NJ: Erlbaum.
18.
Hofmeister, A.M. (1993). Elitism and reform in school mathematics. Remedial and Special Education, 14(6), 8—13.
19.
Hutchinson, N.L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disability Quarterly, 16, 34—63.
20.
Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Erlbaum.
21.
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.
22.
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— 432.
23.
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.
24.
Jitendra, A.K., & Xin, Y. (1997). Mathematical word problem solving instruction for students with mild disabilities and students at risk for math failure: A research synthesis. The Journal of Special Education, 30, 412—438.
25.
Kintsch, W., & Greeno, J.G. (1985). Understanding and solving word arithmetic problems . Psychological Review, 92, 109—129.
26.
Maccini, P., & Hughes, C.A. (2000). Effects of a problem solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research & Practice, 15(1), 10—21.
27.
Marshall, S.P. (1995). Schemas in problem solving. New York: Cambridge University Press.
28.
Marshall, S.P., Barthuli, K.E., Brewer, M.A., & Rose, F.E. (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 .
29.
Marshall, S., Pribe, C.A., & Smith, J.D. (1987). Schema knowledge structures for representing and understanding arithmetic story problems (Tech. Rep. Contract No. N00014-85-K-0061) . Arlington, VA: Office of Naval Research.
30.
Mercer, C.D., & Miller, S.P. (1992). Teaching students with learning problems in math to acquire, understand, and apply basic math facts. Remedial and Special Education, 13(3), 19—61.
31.
Montague, M. (1995). Cognitive instruction and mathematics: Implications for students with learning disorders. Focus on Learning Problems in Mathematics, 17(2), 39—49.
32.
Montague, M. (1997a). Student perception, mathematical problem solving, and learning disabilities. Remedial and Special Education ,18, 46—53.
33.
Montague, M. (1997b). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164—177.
34.
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
35.
National Council of Teachers of Mathematics. ( 2000). Principles and standards for school mathematics electronic versionhttp://standards.nctm.org/
36.
National Education Goals Panel. (1997). National education goals report summary, 1997. Washington, DC: Author.
37.
Parmar, R.S., & Cawley, J.F. (1991). Challenging the routines and passivity that characterize arithmetic instruction for children with mild handicaps. Remedial and Special Education,12, 23—32.
38.
Parmar, R.S., Cawley, J.F., & Frazita, R.R. (1996). Word problem solving by students with and without mild disabilities. Exceptional Children, 62, 415—429.
39.
Parmar, R.S., Cawley, J.F., & Miller, J.H. (1994). Differences in mathematics performance between students with learning disabilities and students with mild retardation. Exceptional Children, 60, 549—563.
40.
Patton, J.R., Cronin, M.E., Bassett, D.S., & Koppel, A.E. (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, 178—187.
41.
Richard, T.J. (1997). SRA spectrum math (4th ed.). Columbus, OH: McGraw-Hill .
42.
Riley, M.S., Greeno, J.G., & Heller, J.I. (1983). Development of children's problem-solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153—196). New York: Academic Press.
43.
Rosenshine, B. (1986). Synthesis of research on explicit teaching. Educational Leadership, 43, 60—69.
44.
Rosenshine, B., & Stevens, R. (1984). Classroom instruction in reading. In P. D. Pearson (Ed.), Handbook of reading research (pp. 745—798). New York: Longman .
45.
Silver, E.A., & Marshall, S.P. (1990). Mathematical and scientific problem solving: Findings, issues, and instructional implications. In B. F. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction . Hillsdale, NJ: Erlbaum.
46.
Torgesen, J.K. (1982). The learning disabled child as an inactive learner . Topics in Learning and Language Disabilities, 2, 45—52.
47.
Van de Walle, J.A. (1998). Elementary and middle school mathematics: Teaching developmentally (3rd ed.). New York: Longman.
48.
Wechsler, D. (1991). Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corp.
49.
Wechsler, D. (1992). Wechsler individual achievement test. San Antonio, TX: Psychological Corp.
50.
Wood, D.K., Frank, A.R., & Wacker, D.P. (1998). Teaching multiplication facts to students with learning disabilities. Journal of Applied Behavior Analysis , 31, 323—338.
51.
Woodward, J., & Montague, M. (2000, April). Meeting the challenge of mathematics reform for students with learning disabilities. Paper presented at the annual meeting of the Council for Exceptional Children, Vancouver, Canada.
52.
Xin, Y.P., & Jitendra, A.K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32, 207—225.
53.
Zawaiza, T.B.W., & Gerber, M.M. (1993). Effects of explicit instruction on community college students with learning disabilities. Learning Disability Quarterly , 16, 64—79.
