Examining the effects of different multiple representational systems in learning primary mathematics

Journal of the Learning Sciences

Volumn 11, Issue 1, 2002, Pages 25-61

  Ainsworth, Shaaron ^a   Bibby, Peter ^a   Wood, David ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036115588     PISSN: 10508406     EISSN: None     Source Type: Journal    
DOI: 10.1207/S15327809JLS1101_2     Document Type: Article

References (37)

1. Ainsworth, S. E. (1999). A functional taxonomy of multiple representations. Computers and Education, 33, 131-152.
2. Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Smith Reed, B., & Webb, D. (1997). The role of multiple representations in learning algebra. American Education Research Journal, 34, 663-689.
3. Chandler, P., & Sweller, J. (1992). The split-attention effect as a factor in the design of instruction. British Journal of Educational Psychology, 62, 233-246.
4. Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation in physics problems by experts and novices. Cognitive Science, 5, 121-152.
5. Clarke, H., & Shepherd, R. (1984) Think and solve mental maths. Cambridge, England: Cambridge University Press
6. Confrey, J. (1991). Function Probe©. Santa Barbara, CA: Intellimation Library for the Macintosh.
7. Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26, 135-164.
8. Confrey, J., Smith, E., Piliero, S., & Rizzuti, J. ( 1991). The use of contextual problems and multi-representational software to teach the concept of functions. Final Project Report to the National Science Foundation and Apple Computers Inc.
9. Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods. New York: Irvington.
10. de Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., Reimann, P., Sime, J., van Someren, M., Spada, H., & Swaak, J. (1998). Acquiring knowledge in science and math: the use of multiple representations in technology based learning environments. In M.W Van Someren, P. Reimann, H. Bozhimen, & T. de Jong (Eds.), Learning with multiple representations (pp 9-40). Amsterdam: Elsevier.
11. Dienes, Z. ( 1973). The six stages in the process of learning mathematics. Slough, UK: National Foundation for Education Research-Nelson.
12. Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45-55.
13. Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109-122). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
14. Howe, C. J., Rodgers, C., & Tolmie, A. (1990). Physics in the primary school: Peer interaction and the understanding of floating and sinking. European Journal of Psychology of Education, 4,459-475.
15. Kaput, J. J. ( 1987). Towards a theory of symbol use in mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 159-196). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
16. Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167-194). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
17. Kozma, R., Chin, C., Russel, J., & Marx, N. (2000). The roles of representations and tools in the chemistry laboratory and their implications for chemistry learning. The Journal of the Learning Sciences, 9, 105-143.
18. Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65-99.
19. LeFevre, J., Greenham, S. L., & Waheed, N. (1993). The development of procedural and conceptual knowledge in computational estimation. Cognition and Instruction, 11, 95-132.
20. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
21. Lohse, G. L., Biolsi, K., Walker, N., & Rueler, H. (1994). A classification of visual representations. Communication of the ACM, 37(12), 36-49.
22. Mayer, R. E., & Anderson, R. B. (1992). The instructive animation: Helping students build connections between words and pictures in multimedia learning. Journal of Educational Psychology, 84, 444-452.
23. Mayer, R. E., & Sims, V. K. ( 1994). For whom is a picture worth a thousand words? Extensions of a dual coding theory of multimedia learning. Journal of Educational Psychology, 86, 339-401.
24. Palmer, S. E. (1978). Fundamental aspects of cognitive representation. In E. Rosch & B. B. Lloyd (Eds.), Cognition and categorization (pp. 259-303). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
25. Reys, R. E., Rybolt, J. F., Bestgen, B. J., & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183-201.
26. Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology, volume 4 (pp. 55-175). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
27. Schwarte, B., & Dreyfus, T. (1993). Measuring integration of information in multi-representational software. Interactive Learning Environments, 3, 177-198.
28. Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on teaching and learning mathematics (pp. 371-389). New York: Macmillan.
29. Sowder, J. T., & Wheeler, M. M. (1989). The development of concepts and strategies used in computational estimation. Journal for Research in Mathematics Education, 20, 130-146.
30. Spiro, R. J., & Jehng, J-C. ( 1990). Cognitive flexibility and hypertext: Theory and technology for non-linear and multi-dimensional traversal of complex subject matter. In D. Nix & R. J. Spiro (Eds.), Cognition, education and multi-media: Exploring ideas in high technology (pp. 163-205). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
31. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12, 257-285.
32. Tabachneck, H. J. M., Koedinger, K. R., & Nathan, M. J. ( 1994). Towards a theoretical account of strategy use and sense making in mathematical problem solving. In A. Ram & K. Eiselt (Eds.), 16th Annual Conference of the Cognitive Science Society (pp. 836-841). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
33. Tabachneck, H. J. M., Leonardo, A. M., & Simon, H. A. (1994). How does an expert use a graph? A model of visual & verbal inferencing in economics. In A. Ram & K. Eiselt (Ed), 16th Annual Conference of the Cognitive Science Society, (pp. 842-847). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
34. Trafton, P. R. (1986). Teaching computational estimation: Establishing an estimation mind-set. In H. L. Schoen & M. Zweng (Eds.), Estimation and mental computation (pp. 16-30). Reston, VA: National Council of Teachers of Mathematics.
35. Watson, J. M., Campbell, K. J., & Collis, K. F. (1993). Multimodal functioning in understanding fractions. Journal of Mathematical Behavior, 12(1), 45-62.
36. Yerushalmy, M. (1991). Student perceptions of aspects of algebraic function using multiple representation software. Journal of Computer Assisted Learning, 7, 42-57.
37. Yerushalmy, M. (1997). Designing representations: Reasoning about functions of two variables. Journal for Research in Mathematics Education, 28(4), 431-466.