for the learning of mathematics

Igor' Kontorovich ,  Rina Zazkis ,  John Mason - Vol. 41 Num. 1 (2021)
 From one kind of numbers to another: the metaphors of expansion and transition


Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an alternative approach, in which one transitions between different numerical domains, some subsets of which are isomorphic.


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