Developing the use of diagrammatic representations in primary mathematics through professional development

Educational Research

Volumn 55, Issue 3, 2013, Pages 263-290

  Barmby, Patrick ^a   Bolden, David ^a   Raine, Stephanie ^a   Thompson, Lynn ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

diagrammatic representations; mathematics instruction; primary education; teacher professional development

Indexed keywords

EID: 84883406930     PISSN: 00131881     EISSN: 14695847     Source Type: Journal    
DOI: 10.1080/00131881.2013.825164     Document Type: Article

References (66)

1. Ainsworth, S. 1999. The functions of multiple representations. Computers & Education, 33: 131 - 152.
2. Back, J., De Geest, E., Hirst, C. and Joubert, M. 2009. Final report: Researching effective CPD in mathematics education (RECME), Sheffield: NCETM.
3. Ball, D. L., Thames, M. H. and Phelps, G. 2008. Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59 (5): 389 - 407.
4. Barmby, P., Bilsborough, L., Harries, T. and Higgins, S. 2009a. Primary mathematics: Teaching for understanding, Buckingham: Oxford University Press.
5. Barmby, P., Harries, T., Higgins, S. and Suggate, J. 2009b. The array representation and primary children's understanding and reasoning in multiplication. Educational Studies in Mathematics, 70: 217 - 241.
6. Barmby, P., and J. Milinkovic. 2011. "Pre-service teachers' use of visual representations of multiplication." In Proceedings of the 35th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2), edited by B. Ubuz, 105-112. Ankara, Turkey: PME.
7. Baturo, A. R., and T. J. Cooper. 1999. "Fractions, reunitisation and the number-line representation." In Proceedings of the 23rd Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2), edited by O. Zaslavsky, 81-88. Haifa, Israel: PME.
8. Behr, M. J., Lesh, R., Post, T. P. and Silver, E. A. 1983. " Rational-number concepts ". In Acquisition of mathematics concepts and processes, Edited by: Lesh, R. and Landau, M. 91 - 126. New York: Academic Press.
9. Behr, M. J., Wachsmuth, I., Post, T. R. and Lesh, R. 1984. Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15 (5): 323 - 341.
10. Borko, H. 2004. Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33 (8): 3 - 15.
11. Boulton-Lewis, G. M. 1998. Children's strategy use and interpretations of mathematical representations. Journal of Mathematical Behavior, 17 (2): 219 - 237.
12. Brophy, J. 1991. "Conclusion." In Advances in research on teaching (Vol. 2), edited by J. Brophy, 349-364. Greenwich, CT: JAI Press.
13. Burkhardt, H. and Schoenfeld, A. H. 2003. Improving educational research: Toward a more useful, more influential, and better-funded enterprise. Educational Researcher, 32 (9): 3 - 14.
14. Charalambous, C. Y. and Pitta-Pantazi, D. 2007. Drawing on a theoretical model to study student's understandings of fractions. Educational Studies in Mathematics, 64 (3): 293 - 316.
15. Cobb, P., Yackel, E. and Wood, T. 1992. A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23 (1): 2 - 33.
16. Cohen, L., Manion, L. and Morrison, K. 2000. Research methods in education, 5th ed., London: RoutledgeFalmer.
17. Creswell, J. W. 1994. Research design: Qualitative and quantitative approaches, London: Sage.
18. Desimone, L. M., Porter, A. C., Garet, M. S., Yoon, K. S. and Birman, B. F. 2002. Effects of professional development on teachers' instruction: Results from a three-year longitudinal study. Educational Evaluation and Policy Analysis, 24 (2): 81 - 112.
19. Duval, R. 1999. "Representation, vision and visualization: Cognitive functions in mathematical thinking." In Proceedings of the Twenty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, edited by F. Hitt, and M. Santos, 3-26. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
20. Flevares, L. M. and Perry, M. 2001. How many do you see? The use of nonspoken representations in first-grade mathematics lessons. Journal of Educational Psychology, 93 (2): 330 - 345.
21. Flick, U. 2009. An introduction to qualitative research, 4th ed., London: Sage.
22. Franke, M. L., Carpenter, T. P., Levi, L. and Fennema, E. 2001. Capturing teachers' generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38 (3): 653 - 689.
23. Garet, M. S., Porter, A. C., Desimore, L., Birman, B. F. and Yoon, K. S. 2001. What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38 (4): 915 - 945.
24. Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P. and Flojo, J. 2009. Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79 (3): 1202 - 1242.
25. Goldin, G. A. 1998. Representational systems, learning and problem solving in mathematics. Journal of Mathematical Behavior, 17 (2): 137 - 165.
26. Greeno, J. G. and Hall, R.P. 1997. Practicing representation: Learning with and about representational forms. The Phi Delta Kappan, 78 (5): 361 - 367.
27. Greer, B. 1992. " Multiplication and division as models of situations ". In Handbook of research on mathematics teaching and learning, Edited by: Grouws, D. A. 276 - 295. New York: Macmillan.
28. Hall, N. 1998. Concrete representations and procedural analogy theory. Journal of Mathematical Behavior, 17 (1): 33 - 51.
29. Hannula, M. S. 2003. "Locating fraction on a number line." In Proceedings of the 2003 Joint Meeting of the PME and PMENA (Vol. 3), edited by N. A. Pateman, B. J. Dougherty, and J. Zilliox, 17-24. CRDG, College of Education, University of Hawaii, Hawaii.
30. Hart, K. M., ed. 1981. Children's understanding of mathematics: 11-16, London: John Murray.
31. Hiebert, J. and Carpenter, T. P. 1992. " Learning and teaching with understanding ". In Handbook of research on mathematics teaching and learning, Edited by: Grouws, D. A. 65 - 97. New York: Macmillan.
32. Hiebert, J. and Wearne, D. 1992. Links between teaching and learning place value with understanding in first grade. Journal for Research in Mathematics Education, 23 (2): 98 - 122.
33. Hill, H. C. and Ball, D. L. 2004. Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35 (5): 330 - 351.
34. Kaestle, C.F. 1993. The awful reputation of education research. Educational Researcher, 22 (1) 23 and 26-31
35. Kamii, C. and Clark, F. B. 1995. Equivalent fractions: Their difficulty and educational implications. Journal of Mathematical Behavior, 14: 365 - 378.
36. Kaput, J. J. 1991. " Notations and representations as mediators of constructive processes ". In Radical constructivism in mathematics education, Edited by: von Glasersfeld, E. 53 - 74. Dordrecht: Kluwer.
37. Kerslake, D. 1986. Fractions: Children's strategies and errors, London: NFER Nelson.
38. Kieren, T. 1976. " On the mathematical, cognitive, and instructional foundations of rational numbers ". In Number and measurement: Papers from a research workshop, Edited by: Lesh, R. 101 - 144. Columbus, OH: ERIC/SMEAC.
39. Korthagen, F. A. J. and Kessels, J. P. A. M. 1999. Linking theory and practice: Changing the pedagogy of teacher education. Educational Researcher, 28 (4): 4 - 17.
40. Kvale, S. 2007. Doing interviews, London: Sage.
41. Lampert, M. 1986. Knowing, doing, and teaching multiplication. Cognition and Instruction, 3: 305 - 342.
42. Larkin, J. H. and Simon, H. A. 1987. Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11: 65 - 69.
43. Lean, G. and Clements, K. 1981. Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12 (3): 267 - 299.
44. Leinhardt, G., R. T. Putnam, M. K. Stein, and J. Baxter. 1991. "Where subject knowledge matters." In Advances in research on teaching: Vol. 2. Teachers' knowledge of subject matter as it relates to their teaching practice, edited by J. Brophy, 87-113. Greenwich, CT: JAI Press.
45. Lesh, R., Landau, M. and Hamilton, E. 1983. " Conceptual models and applied mathematical problem-solving research ". In Acquisition of mathematics concepts and processes, Edited by: Lesh, R. and Landau, M. 263 - 343. Orlando, FL: Academic Press.
46. Mack, N. K. 1990. Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21 (1): 16 - 32.
47. Muijs, D. 2004. Doing quantitative research in education with SPSS, London: Sage.
48. Ni, Y. 2001. Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26: 400 - 417.
49. Outhred, L., and M. Mitchelmore. 2004. "Student's structuring of rectangular arrays." In Proceedings 28th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 3), edited by M. J. Høines, and A. Fuglestad, 465-472. Bergen, Norway: PME.
50. Pape, S. J. and Tchoshanov, M. A. 2001. The role of representation(s) in developing mathematical understanding. Theory into Practice, 40 (2): 118 - 127.
51. Paivio, A. 1969. Mental imagery in associative learning and memory. Psychological Review, 76 (3): 241 - 263.
52. Peck, D. M. and Jencks, S. M. 1981. Conceptual issues in the teaching and learning of fractions. Journal for Research in Mathematics Education, 12 (5): 339 - 348.
53. Perkins, D. N. and Unger, C. 1994. A new look in representations for mathematics and science learning. Instructional Science, 22: 1 - 37.
54. Pitkethley, A. and Hunting, R. 1996. A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30 (1): 5 - 38.
55. Post, T. R. and Cramer, K. A. 1989. " Knowledge, representation, and quantitative thinking ". In Knowledge base for the beginning teacher, Edited by: Reynolds, M. C. 221 - 232. New York: Pergamon.
56. Presmeg, N. C. 1986. Visualisation and mathematical giftedness. Educational Studies in Mathematics, 17 (3): 297 - 311.
57. Punch, K. F. 2009. Introduction to research methods in education, London: Sage.
58. Rhodes, C. and Houghton-Hill, S. 2000. The linkage of continuing professional development and the classroom experience of pupils: Barriers perceived by senior managers in some secondary schools. Journal of In-Service Education, 26 (3): 423 - 435.
59. Robson, C. 2002. Real world research, 2nd ed., Oxford: Blackwell Publishing.
60. Skemp, R. R. 1986. The psychology of learning mathematics, Harmondsworth: Penguin Books.
61. Shulman, L. S. 1986. Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2): 4 - 14.
62. Sowell, E. J. 1989. Effects of manipulative materials in mathematics education. Journal for Research in Mathematics Education, 20 (5): 498 - 505.
63. Tashakkori, A. and Teddlie, C. 1998. Mixed methodology, London: Sage.
64. Teacher Training Agency. 1998. National standards for subject leaders, London: TTA.
65. Webb, N. M., K. Gold, and S. Qi. 1990. Mathematical problem-solving processes and performance: Translations among symbolic representations (CSE No. 316). Los Angeles, CA: UCLA Center for Research on Evaluation, Standards, and Student Testing.
66. Wilson, S. M. and Berne, J. 1999. Learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. Review of Research in Education, 24: 173 - 209.