Cultivating intelligence through mathematical language.

Abstract

This paper sets out different contexts where mathematics helps create a thinking and reasoning habit, with special emphasis on problem solving. Intelligence is thought to be connected to problem solving ability and so we are interested in the relationship between intelligence and mathematical problem solving. These problems will be posed in a broad sense, not just considering classical written problems but also problems that appear in situations such as chess, magic tricks, and board games. These settings motivate students better, solving them requires different approaches, and they relate to other fields of knowledge. This paper reports on our experience of posing problems and reasoning with gifted students through magic tricks based on mathematical ideas and we give some examples of the activities we have done with them. We also present recreational mathematics as a discipline that promotes student motivation and increases curiosity and inquiry. We show some ideas from Miguel De Guzmán, Martín Gardner, and Raymond Smullyan that have been used in different frameworks. We describe some games that have been shown to be useful tools for creating reasoning schemas, presenting the particular case of chess as an educational tool. Finally, we set out some conclusions about the introduction of new materials, methods, and ideas for solving problems and we formulate a proposal for continuing this work and applying it in the classroom.