Graph Theory in Primary, Middle, and High School

In this paper we present an experimental teaching activity conduced in some primary, middle and high schools in Sicily. The activity concerned several topics of graph theory. Here we highlight, in particular, the approach to teaching Eulerian graphs. The aim of the whole project was to present a fun, easy approach to mathematics in order to promote a good attitude towards mathematics in primary school children and to improve it in middle school kids and in high school young people. This goal is pursued also by showing some connections of mathematics with real life, making mathematics less abstract than the topics too often taught in school. Through this activity we also reach mathematical knowledge and practical abilities (related to graph theory), and above all mathematical competencies related to reasoning and mathematization, in particular by the use of graphs in mathematical models to solve problems. The teaching experiments were different, according to the different school level, but unified by the method, based on laboratorial activities, by presenting a problem to be solved together with classmates, by manipulating objects and guided by the teacher. These activities were realized by the use of artefacts: in the sense of Vygotskijan semiotic mediation, we used signs, symbols, maps, language and, in many cases, new technology’s artefacts, to mediate mathematical concepts. Lessons involved also the body as a mean to learning, especially with children, according to embodied cognition theory.