A case study of dynamic visualization and problem solving

International Journal of Mathematical Education in Science and Technology

Volumn 38, Issue 8, 2007, Pages 1075-1092

  Lavy, Ilana ^a  

^a THE MAX STERN YEZREEL VALLEY COLLEGE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36248989103     PISSN: 0020739X     EISSN: 14645211     Source Type: Journal    
DOI: 10.1080/00207390601129196     Document Type: Article

References (30)

1. Presmeg, N., 1986a, Visualization in high-school mathematics. For the Learning of Mathematics, 6(3), 42-46.
2. Presmeg, N., 1986b, Visualization and mathematical giftedness. Educational Studies in Mathematics, 17(3), 297-311.
3. Kent, L.B., 2000, Connecting integers of meaningful context. Mathematics Teaching in the Middle School, 6(1), 62-66.
4. Mariotti, M.A., 2000, Introduction to proof: the mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1-2), 25-53.
5. Slovin, H., 2000, Moving to proportional reasoning. Mathematics Teaching in the Middle School, 6(1), 58-60.
6. Kosslyn, S.M., 1983, Ghosts in the Mind's Machine: Creating and Using Images in the Brain (New York: W.W.Norton);
7. Hershkowitz, R., 1989, Visualization in geometry - two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61-76.
8. Mayer, R.E., 1992, Thinking, Problem Solving, Cognition, 2nd edn (New York: W.H. Freeman).
9. Lowrie, T. and Hill, D., 1996, The development of a dynamic problem-solving model. Journal of Science and Mathematics Education in Southeast Asia, XXIX(1), 1-11.
10. Hoyles, C., Noss, R. and Adamson, R., 2002, Rethinking the microworlds idea. Journal of Educational Computing Research, 27(1&2), 29-53.
11. Hoyles, C. and Noss, R., 1987, Synthesizing mathematical conceptions and their formalization through the construction of a Logo-based school mathematics curriculum. International Journal of Mathematics Education, Science, and Technology, 18, 581-595.
12. Papert, S., 1980, Mindstorms: Children, Computers, and Powerful Ideas. (New York: Basic Books).
13. diSessa, A., 1982, Unlearning Aristotelian physics: a study of knowledge-based learning. Cognitive Science, 6, 37-75.
14. Edwards, L., 1992, A Logo microworld for transformation geometry. In: C. Hoyles and R. Noss (Eds) Learning Logo and Mathematics (Cambridge, MA: MIT Press), pp. 127-155.
15. Sendova, E. and Sendov, B., 1993, Learning to speak mathematically and speaking mathematically to learn in the Logo-based environment "Geomland". 4th European Logo Conference, Athens Greece, pp. 281-288.
16. Noss, R., Healy, L. and Hoyles, C., 1997, The construction of mathematical meanings: connecting the visual with the symbolic. Educational Studies in Mathematics, 33(2), 202-231.
17. Hoyles, C. and Healy, L., 1997, Unfolding meanings for reflective symmetry. International Journal of Computers for Mathematics Learning, 2(1), 27-59.
18. Sinclair, N., Zazkis, R. and Liljedahl, P., 2003, Number worlds: visual and experimental access to elementary number theory concepts. International Journal of Computers for Mathematical Learning, 8(3), 235-263.
19. Edwards, L.D., 1995, Microworlds as representations. In: A.A. diSessa, C. Hoyles and R. Noss (Eds) Computers and Exploratory Learning, NATO ASI Series (VIII: Springer Verlag), pp. 127-154.
20. Presmeg, N., 1989, Visualization in multicultural mathematics classrooms. Focus on Learning Problems in Mathematics, 11(1-2), 17-24.
21. Presmeg, N., 1992, Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595-610.
22. Hershkowitz, R., 1990, Psychological aspects of learning geometry. In: P. Nesher and J. Kilpatrick (Eds) Mathematics and Cognition (Cambridge: Cambridge University Press), pp. 70-95.
23. Dreyfus, T., 1991, On the status of visual reasoning in Mathematics and Mathematics Education. Proceedings of the 15th International Conference for the Psychology of Mathematical Education, Vol. 1, pp. 33-48.
24. 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 (Hillsdale, NJ: Lawrence Erlbaum Associates), pp. 159-195.
25. Kaput, J.J., 1989, Supporting concrete visual thinking in multiplicative reasoning: difficulties and opportunities. Focus on Learning Problems in Mathematics, 11(1), 35-47.
26. Janvier, C., 1987, Representation and understanding: the notion of function as an example. In: C Janvier (Ed.) Problems of Representation in the Teaching and Learning of Mathematics (Hillsdale, NJ: Lawrence Erlbaum Associates), pp. 67-71.
27. Janvier, C., Girardon, C and Morand, J.-C., 1993, Mathematical symbols and representations. In: P.S. Wilson (Ed.) Research Ideas for the Classroom, High School Mathematics (New York: Macmillan), pp. 79-102.
28. Arcavi, A., 2003, The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
29. Presmeg, N., (1991), Classroom aspects which influence use of visual imagery in high school mathematics. In: F. Furunghetti (Ed.) Proceedings of Fifteenth International Conference on the Psychology of Mathematics Education (PME) Conference, Assisi, Italy, Vol". 3, pp. 191-198.
30. Zimmermann, W. and Cunningham, S., 1991, What is mathematical visualization? In: W. Zimmermann and S. Cunningham (Eds) Visualization in Teaching and Learning Mathematics (Washington: Mathematical Association of America), pp. 1-8.