A non-euclidean clockwork orange: from reality to mathematics and back

This paper presents a teaching experience in non-Euclidean geometry involving the use of artefacts and physical experiences. The teaching practice was set up for a group of 25 4th-year high-school students. The aim of this activity was to encourage the “process of translation from ‘reality’ to mathematics and back”. Further, the students were stimulated to evaluate the authenticity of the proposed context, which was designed for learning about spherical geometry and its value in helping students understand and organise the abstract key facts of the topic. The overall aim was to shift back to the starting point and apply the acquired theoretical knowledge in order to interpret a real-world problem.