This article provides a synthesis of word-problem-solving intervention research with samples of students with learning problems (i.e., mild disabilities and at risk for mathematics failure). The effectiveness of word-problem-solving instruction in 25 outcome studies was examined across student characteristics (e.g., grade, IQ); instructional features (e.g., intervention approach, treatment length); methodological features; skill maintenance; and generalization components. Separate analyses were performed for group-design studies and single-subject studies using standardized mean change and percentage of nonoverlapping data (PND), respectively. The overall mean weighted effect size (d) and PND for word-problem-solving instruction were positive across the group-design studies (ES = +.89) and single-subject studies (PND = 89%). In addition, positive effects for skill maintenance and generalization were found for group design (ES = +.78 and +.84, respectively) and single-subject studies (PND = 100%). Computer-assisted instruction was found to be most effective for group-design studies. Effects for representation techniques and strategy training were found to be significantly higher than the "other" approach for both group-design and single-subject studies. Long-term (> 1 month) intervention effects were significantly higher than short- or intermediate-term interventions for group-design studies, whereas both long-term and intermediate treatments were seen to be more effective than short-term treatments for single-subject studies. Other significant effects found for group-design studies only in terms of student characteristics, instructional features, and methodological features are reported. Finally, implications of the current analysis for future research in the area of word-problem solving are discussed.
Get full access to this article
View all access options for this article.
References
1.
Allinder, R.M. (1996). When some is not better than none: Effects of differential implementation on curriculum-based measurement. Exceptional Children, 62, 525-536.
2.
Allison, D.B., & Gorman, B.S. (1993). Calculating effect sizes for meta-analysis: The case of the single case. Behavior Research and Therapy, 31, 621-631.
3.
Anrig, G.R., & LaPointe, A.E. (1989). What we know about what students don't know. Educational Leadership, 47(3), 4-9.
4.
*Baker, D.E. (1992). The effect of self-generated drawings on the ability of students with learning disabilities to solve mathematical word problems. Unpublished doctoral dissertation, Texas Technology University , Lubbock.
5.
Becker, B.J. (1988). Synthesizing standardized mean-change measures . British Journal of Mathematical Psychology, 41, 257-278.
6.
Bender, W. (1992). Learning disabilities: Characteristics, identification, and teaching strategies. Boston: Allyn & Bacon.
7.
*Bennett, K.K. (1981). The effect of syntax and verbal mediation on learning disabled students' verbal mathematical problem scores. Unpublished doctoral dissertation, Northern Arizona University, Flagstaff.
8.
*Bottge, B.A., & Hasselbring, T.S. (1993). A comparison of two approaches for teaching complex, authentic mathematics problems to adolescents in remedial math classes. Exceptional Children, 59, 556-566.
9.
Busk, P.L., & Serlin, R.C. (1992). Meta-analysis for single-case research. In T. R. Kratochwill & J. R. Levin (Eds.), Single-case research design and analysis (pp. 187-212). Hillsdale, NJ: Erlbaum.
10.
Busse, R.T., Kratochwill, T.R., & Elliott, S.N. (1995). Meta-analysis for single-case consultation outcomes: Applications to research and practice. Journal of School Psychology , 33, 269-286.
11.
Carnine, D. (1994). Introduction to the mini-series: Educational tools for diverse learners. School Psychology Review, 23, 341-350.
12.
Carnine, D., Jitendra, A.K., & Silbert, J. (1997). A descriptive analysis of mathematics curricula materials from a pedagogical perspective: A case study of fractions. Remedial and Special Education, 18, 66-81.
13.
Carnine, D., Jones, E.D., & Dixon, R. (1994). Mathematics: Educational tools for diverse learners . School Psychology Review, 3, 406-427.
14.
Carpenter, R.L. (1985). Mathematics instruction in resource rooms: Instruction time and teacher competence. Learning Disability Quarterly , 8, 95-100.
15.
**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.
16.
**Cassel, J., & Reid, R. (1996). Use of self-regulated strategy intervention to improve word problem-solving skills of students with mild disabilities. Journal of Behavioral Education, 6, 153-172.
17.
Cawley, J.F., & Miller, J.H. (1989). Cross-sectional comparisons of the mathematical performance of children with learning disabilities: Are we on the right track toward comprehensive programming? Journal of Learning Disabilities , 23, 250-254, 259.
18.
Darch, C.B. (1982). A comparison of two approaches in teaching math word story problem solving to skill deficient fourth graders. Unpublished doctoral dissertation, University of Oregon, Eugene.
19.
Dunlap, W.F. (1982). Readiness for solving story problems. Academic Therapy, 17, 581-587.
20.
Englert, C.S., Culatta, B.E., & Horn, D.G. (1987). Influence of irrelevant information in addition word problems on problem solving. Learning Disability Quarterly , 10, 29-36.
21.
Frankenberger, W., & Franzaglio, K. (1991). A review of states' criteria and procedures for identifying children with learning disabilities. Journal of Learning Disabilities, 8, 495-500.
22.
Fuchs, L.S. (1988). Effects of computer-managed instruction on teachers' implementation of systematic monitoring programs and student achievement. Journal of Educational Research, 81, 294-304
23.
Glass, G.V. (1977). Integrating findings: The meta-analysis of research . Review of Research in Education, 5, 351-379.
24.
*Gleason, M., Carnine, D., & Boriero, D. (1990). Improving CAI effectiveness with attention to instructional design in teaching story problems to mildly handicapped students . Journal of Special Education Technology, 10, 129-136.
Gray, C.B., & Kemp, E.J., Jr. (1993, September 19). Flunking testing: Is too much fairness unfair to school kids? The Washington Post, Section C, p. 3.
27.
Hedges, L.V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.
28.
Hunter, J.E., & Schmidt, F.L. (1990). Methods of meta-analysis. Newbury Park, CA: Sage.
29.
**Huntington, D.J. (1994). Instruction in concrete, semi-concrete, and abstract representation as an aid to the solution of relational problems by adolescents with learning disabilities. Unpublished doctoral dissertation, University of Georgia, Athens.
30.
a*Hutchinson, N.L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disability Quarterly, 16, 34-63.
31.
Jitendra, A.K., Carnine, D., & Silbert, J. (1996). A descriptive analysis of fifth grade division instruction in basal mathematics programs: Violations of pedagogy. Journal of Behavioral Education, 6, 381-403.
32.
**Jitendra, A., & Hoff, K. (1996). The effects of schema-based instruction on mathematical word-problem-solving performance of students with learning disabilities. Journal of Learning Disabilities, 29, 422-431.
33.
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.
34.
Johnson, B.T. (1989). DSTAT: Software for the meta-analytic review of research literature. Hillsdale, NJ: Erlbaum.
35.
Kameenui, E.J., & Griffin, C.C. (1989). The national crisis in verbal problem solving in mathematics: A proposal for examining the role of basal mathematics programs . The Elementary School Journal, 89, 575-593.
36.
Kavale, K.A. (1984). Potential advantages of the meta-analysis technique for research in special education. The Journal of Special Education, 18, 61-72.
37.
Kavale, K.A., & Glass, G.V. (1984). Meta-analysis and policy decisions in special education. In B. K. Keogh (Ed.), Advances in special education (Vol. IV, pp. 195-247). Greenwich, CT: JAI.
38.
Kulik, C.C., & Kulik, J.A. (1991). Effectiveness of computer-based instruction: An updated analysis. Computers in Human Behavior, 7, 75-94.
39.
Kulik, J.A., & Kulik, C.C. (1987). Review of recent research literature on computer-based instruction. Contemporary Educational Psychology, 12, 222-230.
40.
LaPointe, A.E., Mead, N.A., & Phillips, G.W. (1989). A world of difference: An international assessment of mathematics and science. Prince-ton, NJ: Educational Testing Service.
41.
*Lee, J.W. (1992). The effectiveness of a novel direct instructional approach on math word problem solving skills of elementary students with learning disabilities. Unpublished doctoral dissertation, Ohio State University, Columbus.
42.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving research. In C. Janvier (Ed.), Problems of representation in teaching and learning of mathematics (pp. 207-214). Hillsdale, NJ: Erlbaum.
43.
Liedtke, W. (1984). Learning difficulties: Dealing with problem solving skills in mathematics. Special Education in Canada, 58(3), 82-85.
44.
**Marsh, L.G. (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities. Learning Disabilities Research and Practice, 11, 58-65.
45.
*Marzola, E.S. (1987). An arithmetic verbal problem solving model for learning disabled students. Unpublished doctoral dissertation, Columbia University, New York.
46.
Mastropieri, M.A., Bakken, J.P., & Scruggs, T.E. (1991). Mathematics instruction for individuals with mental retardation: A perspective and research synthesis. Education and Training in Mental Retardation, 26, 115-129.
47.
Mastropieri, M.A., Scruggs, T.E., & Shiah, S. (1991). Mathematics instruction for learning disabled students: A review of research. Learning Disabilities Research & Practice, 6, 89-98.
48.
Mercer, C.D., Jordan, L., & Miller, S.P. (1994). Implications of constructivism for teaching math to students with moderate to mild disabilities. The Journal of Special Education, 28, 290-306.
49.
Miller, S.P., & Mercer, C.D. (1993). Using graduated word problem sequence to promote problem-solving skills. Learning Disabilities Research & Practice, 8, 169-174.
50.
**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.
51.
Montague, M. (1993). Student-centered or strategy-centered instruction: What is our purpose? Journal of Learning Disabilities, 26, 433-437, 481.
52.
Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164-177.
53.
*Montague, M., Applegate, B., & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disabilities Research & Practice, 8, 223-232.
54.
**Montague, M., & Bos, C.S. (1986). The effect of cognitive strategy training on verbal math problem solving performance of learning disabled adolescents. Journal of Learning Disabilities, 19, 26-33.
55.
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.
56.
*Moore, L.J., & Carnine, D. (1989). Evaluating curriculum design in the context of active teaching. Remedial and Special Education, 10, 28-37.
57.
Mostert, M.P. (1996). Reporting meta-analysis in learning disabilities . Learning Disabilities Research & Practice, 11, 2-14.
58.
National Assessment of Educational Progress. ( 1992). NAEP 1992 mathematics report card for the nation and the states. Washington, DC: National Center for Educational Statistics, Report No. 23-ST02.
59.
National Center for Education Statistics. ( 1991). The digest of education statistics 1991. Washington, DC: U.S. Department of Education.
60.
National Center for Education Statistics. ( 1992). Condition of education 1992. Washington, DC: U.S. Department of Education.
61.
Niemiec, R., & Walberg, H.J. (1987). Comparative effects of computer-assisted instruction: A synthesis of reviews. Journal of Educational Computing Research , 3, 19-37.
62.
*Noll, R.S. (1983). Effects of verbal cueing and a visual representation on percent problem-solving performance of remedial adults. Unpublished doctoral dissertation, Fordham University, New York.
63.
**Nuzum, M. (1983). The effects of an instructional model based on the information processing paradigm on the arithmetic problem solving performance of four learning disabled students. Unpublished doctoral dissertation, Columbia University, New York.
64.
Nuzum, M. (1987). Teaching the arithmetic story problem process . Reading, Writing and Learning Disabilities, 3, 53-61.
65.
Parmar, R.S. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. Diagnostique, 17, 227-243.
66.
Parmar, R.S., Cawley, J.F., & Frazita, R.R. (1996). Word problem-solving by students with and without mild disabilities. Exceptional Children, 62, 431-450.
67.
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, 549-566.
68.
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.
69.
Pereira, J.A., & Winton, A.S.W. (1991). Teaching and remediation of mathematics: A review of behavioral research. Journal of Behavioral Education, 1, 5-36.
70.
Prawat, R.S. (1989). Promoting access to knowledge, strategy, and disposition in students: A research synthesis. Review of Educational Research , 59(1), 1-41.
71.
Pressley, M., Harris, K.R., & Marks, M.B. (1992). But good strategy instructors are constructivists!Educational Psychology Review, 4, 3-33.
72.
Resnick, L.B., & Omanson, S.F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology (pp. 41-95). Hillsdale, NJ: Erlbaum.
73.
Rivera, D.P. (1997). Mathematics education and students with learning disabilities: Introduction to the special series. Journal of Learning Disabilities, 30, 2-19.
74.
Schmidt, M., Weinstein, T., Niemic, R., & Walberg, H.J. (1985-1986). Computer-assisted instruction with exceptional children. The Journal of Special Education , 19, 493-501.
75.
Scruggs, T.E., Mastropieri, M.A., & Casto, G. (1987). The quantitative synthesis of single-subject research: Methodology and validation. Remedial and Special Education , 8(2), 24-33.
76.
Scruggs, T.E., Mastropieri, M.A., Cook, S., & Escobar, C. (1986). Early intervention for children with conduct disorders: A quantitative synthesis of single-subject research. Behavioral Disorders, 11, 260-271.
77.
Shiah, R., Mastropieri, M.A., & Scruggs, T.E. (1995). Computer-assisted instruction and students with learning disabilities: Does research support the rhetoric? In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (Vol. 9, 163-194). Greenwich, CT: JAI Press.
78.
*Shiah, R., Mastropieri, M.A., Scruggs, T.E., & Fulk, B.J.M. (1995). The effects of computer-assisted instruction on the mathematical problem solving of students with learning disabilities. Exceptionality, 5, 131-161.
79.
**Smith, E.M. (1981). The effect of teaching sixth graders with learning difficulties a strategy for solving verbal mathematical problems. Unpublished doctoral dissertation, University of Kansas, Lawrence.
80.
Stedman, L.C. (1994). Incomplete explanations: The case of U.S. performance in the international assessments of education. Educational Researcher, 23(7), 24-32.
81.
Stein, M., Silbert, J., & Carnine, D. (1997). Designing mathematics instruction: A direct instruction approach (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
82.
Swanson, H.L., Carson, C., & Saches-Lee, C.M. (1996). A selective synthesis of intervention research for students with learning disabilities. School Psychology Review, 25, 370-391.
83.
Swing, S., Stoiber, K., & Peterson, P.L. (1988). Thinking skills versus learning time: Effects of alternative classroom-based interventions on students' mathematics problem solving. Cognition and Instruction, 5, 123-191.
84.
**Tippins, C.H. (1987). A training program for adolescent learning disabled students in the use of mathematical word problem solving strategies. Unpublished doctoral dissertation, University of South Carolina, Columbia.
85.
*Walker, D.W., & Poteet, J.A. (1989). A comparison of two methods of teaching mathematics story problem-solving with learning disabled students. National Forum of Special Education Journal, 1, 44-51.
86.
**Watanabe, A.K. (1991). The effects of a mathematical word problem solving strategy on problem solving performance by middle school students with mild disabilities. Unpublished doctoral dissertation, University of Florida, Gainesville.
87.
Wheeler, L.J., & McNutt. G. (1983). The effect of syntax on low-achieving students' abilities to solve mathematical word problems. The Journal of Special Education, 17, 309-315.
*Wilson, C.L., & Sindelar, P.T. (1991). Direct instruction in math word problems: Students with learning disabilities. Exceptional Children, 57, 512-519.
90.
*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.
91.
Zentall, S.S. (1990). Fact-retrial automatization and math problem solving by learning disabled, attention disordered, and normal adolescents. Journal of Educational Psychology, 82, 856-865.
92.
Zentall, S.S., & Ferkis, M.A. (1993). Mathematical problem solving for youth with ADHD, with and without learning disabilities. Learning Disability Quarterly, 16, 6-18.
