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Technical Report: UTEP-CS-15-79

Published in Proceedings of the 5th International Conference "Mathematics Education: Theory and Practice" MATHEDU'2015, Kazan, Russia, November 27-28, 2015, pp. 8-13.


For each mathematical object, there are usually several different equivalent representations: for example, a spatial object can be represented either in geometric terms, or by a function that describes its shape. The need for several representations comes from the fact that each of these representations is useful in solving some problems for which the use of other representations is less helpful. Thus, the more representations a student knows, the more capable this student is of solving mathematical problems. In this paper, we propose a general formal description of the corresponding notion of duality (and, more generally, "multi-ality"), and we explain the importance of duality and multi-ality in mathematics education.

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