ESCAPING THE MAZE: A HANDS-ON INTRODUCTION TO GRAPH THEORY

In mathematics education, bridging the gap between active and embodied experiences and abstract mathematical reasoning remains a persistent challenge. This paper presents a hands-on activity designed to introduce fundamental ideas of graph theory through active exploration. The laboratory presented here invites groups of students from primary and secondary school to navigate a walkable maze on the floor, made up of rooms connected by doors. In the first phase, participants are challenged to find an “optimal walk,” defined as the path that crosses the greatest number of doors while ensuring that each door is traversed at most once. In the second phase, students analyze multiple mazes, visualized as graphs, on paper to collaboratively identify invariants across different settings and deduce the general rules governing the existence of the paths that cross every door exactly once. The activity guides students from embodied interaction toward mathematical principles related to Eulerian graphs, inspired by the classic problem of the Seven Bridges of Königsberg.