Activities with graphs for gifted students

Abstract

We present a didactic proposal designed to work graph theory, intended for Primary Education students with high skills in Mathematics. We want to provide students motivational mathematical contents outside school curriculum to promote the development of their abilities, as well as providing them with a simple and powerful tool for representing and solving real-life problems. The proposal is structured in four phases based on the Dienes methodology, in which we follow the Pólya problem-solving model, with a variable number of sessions in each phase, according to the students’ needs. Our approach starts with coloring maps as a natural context to introduce graphs, followed by the layout of paths and Eulerian cycles. We apply graphs to the resolution of a combinatorial problem by induction, and finally, we decompose the graphs appeared in star polygons and stars. In a forthcoming publication, we will present the results of the implementation of this proposal.