A geometry that lets you soar while keeping your feet on the ground: from a STEAM approach to abstraction in Taxicab geometry

This paper reports on a teaching experiment conducted with prospective mathematics teachers (PMTs), within a university geometry seminar for teaching framed around Taxicab geometry. The activity, structured in four episodes moving from real-world modelling to formal proof and activity designing, was designed to foster a STEAM approach and to promote advanced levels of geometric reasoning. PMTs worked in groups at vertical whiteboards, used GeoGebra for dynamic exploration, and interacted with the generative AI tool ChatGPT. Their written productions and classroom interactions are analysed through the lens of the Van Hiele model of geometric reasoning. The study provides evidence that Taxicab geometry, combined with digital tools and AI interaction, offers a powerful context for integrating interdisciplinary thinking, supporting student agency, as solvers and as designers, and reaching high levels of mathematical abstraction.