A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving

Journal of Educational Psychology

Volumn 99, Issue 1, 2007, Pages 115-127

  Jitendra, Asha K ^a   Griffin, Cynthia C ^b   Haria, Priti ^c   Leh, Jayne ^a   Adams, Aimee ^a   Kaduvettoor, Anju ^a  

^a LEHIGH UNIVERSITY   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

^c UNIVERSITY OF DELAWARE   (United States)

Author keywords

Mathematical word problem solving; Mathematics achievement; Schema based instruction; Strategy instruction; Third grade students

Indexed keywords

EID: 33847627985     PISSN: 00220663     EISSN: None     Source Type: Journal    
DOI: 10.1037/0022-0663.99.1.115     Document Type: Article

References (58)

1. Briars, D. J., & Larkin, J. H. (1984). An integrated model of skill in solving elementary word problems. Cognition and Instruction, 1, 245-296.
2. 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, 179-202.
3. Charles, R. I., Crown, W., & Fennell, F. (2004). Mathematics. Glenview, IL: Pearson Education.
4. Chen, Z. (1999). Schema induction in children's analogical problem solving. Journal of Educational Psychology, 91, 703-715.
5. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
6. CTB/McGraw-Hill. (1986). California Achievement Tests: Forms E and F. Technical Bulletin 2. Monterey, CA: Author.
7. CTB/McGraw-Hill. (2001). TerraNova. Monterey, CA: Author.
8. Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Pyschology, 20, 405-438.
9. De Corte, E., Verschaffel, L., & De Win, L. (1985). Influence of rewording verbal problems on children's problem representations and solutions. Journal of Educational Psychology, 77, 460-470.
10. De Corte, E., Verschaffel, L., & Op't Eynde, P. O. (2000). Self-regulation: A characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687-726). San Diego, CA: Academic Press.
11. Desoete, A., Roeyers. H., & De Clercq, A. (2003). Can offline metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95, 188-200.
12. Fuchs, L. S., Fuchs, D., Finelli, R., Courey, S. J., & Hamlett, C. L. (2004). Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems. American Educational Research Journal, 41, 419-445.
13. Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Allinder, R. (1989). The reliability and validity of skills analysis within curriculum-based measurement. Diagnostique, 14, 203-221.
14. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., et al. (2003a). Explicitly teaching for transfer: Effects on third-grade students' mathematical problem solving. Journal of Educational Psychology, 95, 293-305.
15. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., & Schroeter, K. (2003b). Enhancing third-grade students' mathematical problem solving with self-regulated learning strategies. Journal of Educational Psychology, 95, 306-315.
16. Fuchs, L. S., Fuchs, D., Prentice, K., Hamlett, C. L., Finelli, R., & Courey, S. J. (2004). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96, 635-647.
17. Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1998). Monitoring basic skills progress: Basic math computational manual (2nd ed.). Austin, TX: Pro-Ed.
18. Glass, G., McGaw, B., & Smith, M. (1981). Meta-analysis and social research. Beverly Hills, CA: Sage.
19. Goldman, S. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12, 43-55.
20. Harcourt Brace & Company. (1996). Stanford Achievement Tests (9th ed.). San Antonio, TX: Harcourt Brace Educational Measurement.
21. Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press.
22. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684-689.
23. Hegarty, M., Mayer, R. H., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18-32.
24. Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
25. Hutchinson, N. L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disabilities Quarterly, 16, 34-63.
26. 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. Journal of Special Education, 36, 23-38.
27. Jitendra, A. K., & Griffin, C. (2004, April). Results of design studies to understand teaching and learning of mathematical problem-solving in inclusive classrooms: Findings from two sites. Paper presented at the Council for Exceptional Children Annual Convention, New Orleans, LA.
28. 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. Journal of Educational Research, 91, 345-355.
29. Jitendra, A. K., Griffin, C., Deatline-Buchman, A., DiPipi-Hoy, C., Sczesniak, E., Sokol, N. G., & Xin, Y. P. (2005). Adherence to mathematical professional standards and instructional design criteria for problem-solving in mathematics textbooks. Exceptional Children, 71, 319-337.
30. Jitendra, A. K., Griffin, C., Deatline-Buchman, A., & Scresniak, E. (2004, April). Results of design studies to understand teaching and learning of mathematical problem-solving in inclusive classrooms: Findings from two sites. Paper presented at the Council for Exceptional Children Annual Convention. New Orleans, LA.
31. Jitendra, A. K., & 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.
32. 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.
33. Jonassen, D. H. (2003). Designing research-based instruction for story problems. Educational Psychology Review, 15, 267-296.
34. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.
35. Leinhardt, G., Putnam, R., & Hattrup, R. (1992). Analysis of arithmetic for mathematics teaching. Hillsdale, NJ: Erlbaum.
36. Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp. 75-88). New York: Springer-Verlag.
37. Lucangeli, D., Tressoldi, P. E., & Cendron, M. (1998). Cognitive and metacognitive abilities involved in the solution of mathematical word problems: Validation of a comprehensive model. Contemporary Educational Psychology, 23, 257-275.
38. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
39. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.
40. Marshall, S. P., 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.
41. Mayer, R. E. (1992). Thinking, problem solving, and cognition. New York: Freeman.
42. Mayer, R. E. (1999). The promise of educational psychology: Vol. 1. Learning in the content areas. Upper Saddle River, NJ: Merrill Prentice Hall.
43. Mayer, R. E., & Hegarty, M. (1996). The process of understanding mathematics problems. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29-53). Hillsdale, NJ: Erlbaum.
44. Mayer, R. E., Lewis, A. B., & Hegarty, M. (1992). Mathematical misunderstandings: Qualitative reasoning about quantitative problems. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 137-154). Amsterdam: Elsevier.
45. Nathan, M. J., Long, S. D., & Alibali, M. W. (2002). The symbolic precedence view of mathematical development: A corpus analysis of the rhetorical structure of textbooks. Discourse Processes, 33, 1-21.
46. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
47. No Child Left Behind Act of 2001, Pub. L. No. 107-110, 115 Stat. 1425 (2002).
48. Pennsylvania State Department of Education. (2000). Mathematics assessment handbook 2000-2001. The Pennsylvania System of School Assessment. Harrisburg, PA: Bureau of Curriculum and Academic Services.
49. Prawat, R. S. (1989). Promoting access to knowledge, strategy, and disposition in students: A research synthesis. Review of Educational Research, 59, 1-41.
50. Quilici, J. L., & Mayer, R. E. (1996). Role of examples in how students learn to categorize statistics word problems. Journal of Educational Psychology, 88, 144-161.
51. 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.
52. Schurter, W. A. (2002). Comprehension monitoring: An aid to mathematical problem solving. Journal of Developmental Education, 26(2), 22-33.
53. StatSoft. (1998). Analysis of covariance (ANCOVA). Retrieved March 19, 2005. from http://sunsite.univie.ac.at/textbooks/statistics/stanman, html#analysis
54. 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, 119, 176-192.
55. Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). Boston: Allyn & Bacon.
56. Woodward, J. (2006). Making reformed based mathematics work for academically low achieving middle school students. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning difficulties (pp. 29-50). New York: Guildford Press.
57. Xin, P. Y., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem solving instruction on students with learning problems. Journal of Special Education, 39, 181-192.
58. Zawaiza, T. B. W., & Gerber, M. M. (1993). Effects of explicit instruction on community college students with learning disabilities, Learning Disabilities Quarterly, 16, 64-79.