The effect of schema-based instruction in solving mathematics word problems: An emphasis on prealgebraic conceptualization of multiplicative relations

Journal for Research in Mathematics Education

Volumn 39, Issue 5, 2008, Pages 526-551

  Xin, Yan Ping ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Conceptual knowledge; Elementary, K 8; Instructional intervention; Learning disabled; Mathematical model; Multiplication, division; Prealgebra; Problem solving

Indexed keywords

EID: 56049087994     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (72)

1. Anderson, J. R. (1989). A theory of the origins of human knowledge. Artificial Intelligence, 40, 313-351.
2. Baxter, J., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction in five third grade classrooms. Elementary School Journal, 101, 529-548.
3. Bednarz, N., & Janvier, B. (1996). Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp. 115-136). London: Kluwer Academic Publishers.
4. Bloom, B. S. (1976). Human characteristics and school learning. New York: McGraw-Hill.
5. Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F., & Schmittau, J. (2004, April). The development of students' algebraic thinking in earlier grades: A cross-cultural comparative perspective. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.
6. Carnine, D., Jones, E., & Dixon, R. (1994). Mathematics: Educational tools for diverse learners. School Psychology Review, 23, 406-427.
7. Carpenter, T. P., Hiebert, J., & Moser, J. (1979, April). The effect of problem structure in first graders' initial solution process for simple addition and subtraction problems. Paper presented at the annual meeting of the American Education Research Association, San Francisco.
8. Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2006). Learning mathematics in elementary and middle schools: A learner-centered approach (4th ed). Upper Saddle River, NJ: Person Merrill Prentice Hal.
9. Cawley, J., & Parmar, R. S. (2003). Mathematics assessment for students with mild disabilities, frameworks and practices. Learning Disabilities: A Contemporary Journal, I(1), 20-26.
10. Cawley, J., Parmar, R., Foley, T. E., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Implications for standards and programming. Exceptional Children, 67, 311-328.
11. Charbonneau, L. ( 1996). From Euclid to Descartes: Algebra and its relation to geometry. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 15-37). Dordrecht, Netherlands: Kluwer.
12. Chen, Z. (1999). Schema induction in children's analogical problem solving. Journal of Educational Psychology, 91, 703-715.
13. Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37-46.
14. Curcio, F., & Schwartz, S. L. (1997). What does algebraic thinking look like and sound like with preprimary children? Teaching Children Mathematics, 3, 296-300.
15. Davis, R. B., Jockusch, E., & McKnight, C. (1978). Cognitive process in learning algebra. Journal of Children's Mathematical Behavior, 2, 310-320.
16. Didierjean, A., & Cauzinille-Marmeche, E. (1998). Reasoning by analogy: Is it schema-mediated or cased based? European Journal of Psychology of Education, 13, 385-398.
17. Fennell, F., Ferrini-Mundy, J., Ginsburg, H. P., Greenes, C., Murphy, S. J., & Tate, W. (1998). Mathematics. Madison, WI: Silver Burdett Ginn.
18. 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.
19. Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., et al. (2003). Explicitly teaching for transfer: Effects on third-grade students' mathematical problem solving. Journal of Educational Psychology, 95, 293-305.
20. 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.
21. Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276-295). New York: MacMillan.
22. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.
23. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan.
24. 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.
25. Hinsley, D., Hayes, J., & Simon, H. (1977). From words to equations meaning and representation in algebra word problems. In P. Carpenter & M. Just (Eds.), Cognitive processes in comprehension (pp. 89-108). Hillsdale, NJ: Lawrence Erlbaum Associates.
26. Horner, R. D., & Baer, D. M. (1978). Multiple-probe technique: A variation of the multiple baseline. Journal of Applied Behavior Analysis, 11, 189-196.
27. Indiana Department of Education. (2004). Indiana Statewide Testing for Educational Progress-Plus. Center for Assessment, Research, and Information Technology: Author.
28. Jitendra, A. K. (2002). Teaching students math problem-solving through graphic representations. Teaching Exceptional Children, 34(4), 34-38.
29. Jitendra. A., DiPipi, C. M., & Grasso, E. (2001). The role of a graphic representational technique on the mathematical problem solving performance of fourth graders: An exploratory study. Australasian Journal of Special Education. 25(1&2), 17-33.
30. Jitendra, A., Griffin, C., Deatline-Buchman, A., DiPipi-Hoy, C., Sczesniak, E., Sokol, N., et al. (2005). Adherence to NCTM standards and instructional design criteria for problem-solving in mathematics textbooks. Exceptional Children. 71, 319-338.
31. 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.
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., 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.
34. Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford.
35. Kriegler, S. (2000). Mathematics content programs for teachers. UCLA, Department of Mathematics. Retrieved July, 8, 2008, from http://www.learner.org/channel/courses/learningmath/algebra/session1/part_a/ index.html
36. Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics intervention for children with special educational needs: A meta-analysis. Remedial and Special Education, 24, 97-114.
37. Larkin, J. (1980). Skilled problem solving in physics: A hierarchical planning model. Journal of Structural Learning, 6, 271-297.
38. Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81, 521-531.
39. Maccini, P., McNaughton, D., & Ruhl, K. L. (1999). Algebra instruction for students with learning disabilities: Implications from a research review. Learning Disability Quarterly, 22, 113-126.
40. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.
41. Moses, B. (1997). Algebra for a new century. Teaching Children Mathematics, 3, 264-265.
42. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
43. National Council of Teachers of Mathematics. (2007). Results and interpretation of the 2003 math assessment of the NAEP. Reston, VA: Author.
44. National Education Goals Panel. (1997). The national education goals report summary 1997: Mathematics and science achievement for the 21st century. Washington, DC: Author.
45. National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
46. th ed.). San Antonio, TX: Psychological Corporation.
47. Owen, R. L., & Fuchs, L. S. (2002). Mathematical problem solving strategy instruction for third-grade students with learning disabilities. Remedial and Special Education, 23, 268-278.
48. Pressley, M. (1986). The relevance of the good strategy user model to the teaching of mathematics. Educational Psychologist, 21, 139-161.
49. Richards, S. B., Taylor, R. L., Ramasamy, R., & Richards, R. Y. (1999). Single subject research: Applications in education and clinical settings. San Diego, CA: Singular Publishing Group, Inc.
50. 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.
51. Psychological Corporation. (2001). Wechsler individual achievement test (2nd ed.). San Antonio, TX: Author.
52. Schmidt, S., & Weiser, W. (1995). Semantic structures of one-step word problems involving multiplication or division. Educational Studies in Mathematics, 28, 55-72.
53. Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.
54. Scruggs, T. E., & Mastropieri, M. A. (1998). Summarizing single-subject research: Issues and applications. Behavior Modification, 22, 221-242.
55. Sherin, B. (2001). How students understand physics equations. Cognition and Instruction, 19, 479-541.
56. Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181-198). Hillsdale, NJ: Erlbaum.
57. Simon, D. P., & Simon, H. A. (1978). Individual differences in solving physics problems. In R. Siegler (Ed.), Children's thinking: What develops? (pp. 325-348). Hillsdale, NJ: Erlbaum.
58. Sowder, L. (1988). Children's solutions of story problems. Journal of Mathematical Behavior, 7, 227-238.
59. Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3, 153-171.
60. 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.
61. Thompson, P. (1989). Artificial intelligence, advanced technology, and learning and teaching algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 135-161). Reston, VA: National Council of Teachers of Mathematics.
62. Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). Boston: Allyn & Bacon.
63. Wagner, J. (2006). Transfer in pieces. Cognition and Instruction, 24, 1-71.
64. Wang, J., & Lin, E. (2005). Comparative studies on U.S. and Chinese mathematics learning and the implications for standards-based mathematics teaching reform. Educational Researcher, 34(5), 3-13.
65. Wechsler, D. (1991). Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corp.
66. Wechsler, D. (2003). Wechsler intelligence scale for children (4th ed.). San Antonio, TX: Psychological Corp.
67. Wheeler, D. (1996). Backwards and forwards: Reflections on different approaches to algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 317-325). Dordrecht, Netherlands: Kluwer.
68. Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). WJ-III tests of achievement. Itasca, IL: Riverside Publishing Company.
69. Woodward, J., & Brown, C. (2006). Meeting the curricular needs of academically low-achieving students in middle grade mathematics. Journal of Special Education, 40, 151-159.
70. Xin, Y. P. (2003). A comparison of two instructional approaches on mathematical word problem solving by students with learning problems. Unpublished doctoral dissertation, Lehigh University, Bethlehem, PA.
71. Xin, Y. P. (2005, April). Mathematics word-problem-solving skills profile and its relation to textbooks' instructional features: A cross-cultural comparison. Paper presented at the annual meeting of the American Educational Research Association, Montréal, Canada.
72. Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 100, 347-359.