Causing a cognitive conflict can be one way to make students aware of the inadequacy of the concepts that they possess and the methods that they use in solving a problem. Apart from discussions in a cooperative group and the use of mathematical games, the mathematical situations themselves have to possess certain characteristics to be able to provoke a conflict and furthermore facilitate the confrontation between the previous knowledge and new knowledge to be acquired. Moreover teachers need to have direct experiences at their level with this kind of activities, before they can employ them in their classes. In this paper we report the results of a study in which a cryptography activity was applied with a group of university and high school teachers, where the concepts of sets and binary operations came into play.
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