Interpreting paintings and constructing geometric figures

In this article, we present a set of activities designed for a course in elementary geometry within a master's program in Education Sciences. These activities aim to foster active mathematical learning by seeking a dynamic balance between the concrete and the abstract. The unifying theme is the exploration of analogies between interpreting a painting through debating and geometrizing a figure through geometric construction. The goal of the paper is to show how the search for suitable analogies between the two processes can be employed to clarify the delicate transition from intuitive to rational geometry and to help students retrace the main stages of this crucial evolution autonomously.