Abstract:

In mathematics education, bridging the gap between embodied experience and abstract mathematical reasoning is a persistent challenge.

This paper presents a hands-on laboratory experience designed to introduce fundamental ideas of graph theory through physical exploration and group activity. The workshop invites participants to navigate walkable mazes constructed on the floor using coloured tape. The mazes consist of “rooms” connected by “doors,” which participants traverse while completing a series of progressively challenging tasks.

In the first phase, participants move from a starting room to an ending room while passing through each door exactly once, within a limited time. In a second maze, where such a path does not exist, participants - still under time constraints - are challenged to find an “optimal walk,” defined as the path that crosses the greatest number of doors, and to justify its optimality, thus engaging in variation, trial and error, and discussion. In the final phase, with no time pressure, participants undertake guided exploration, analysing multiple mazes on paper and collaboratively identifying patterns and general rules ensuring the existence of a path that traverses every door exactly once.

Although structured as a game, the activity guides participants from concrete, embodied interaction toward general mathematical principles related to Eulerian graphs, inspired by the classical problem of the Seven Bridges of Königsberg. Special attention is given to collaborative problem solving, testing strategies, and recognising invariants across changing settings.

The workshop also shows how advanced mathematical notions can be meaningfully introduced in primary and secondary education using accessible and low-cost materials.

The paper includes some pedagogical reflections and practical guidelines for teachers to create new maze configurations exploring the same mathematical concepts.

Keywords:

Active learning, inquiry-based learning, collaborative learning, mathematical laboratory.