Produrre matematica

[Autom. eng. transl.] The famous statement "A mathematician is a machine for transforming coffee into theorems" is due to a conversation between Paul Erdős and Alfréd Rényi, two Hungarian mathematicians active in the last century: a description of their point of view not only on the exciting effects of caffeine , but also on the purpose of doing mathematics. With this intervention we intend to propose an analogy between the sense of mathematics and the operative phase of a Situated Learning Episode. As we know, in the second phase of the EAS students are required to work in a small group to create an artifact to be shared later with the rest of the class and on which to reflect. It is the heart of EAS, centered on the logic of learning by doing: a necessary phase to then move on to reflective learning. A profound and authentic learning is achieved precisely through the “dismantling” of cultural objects, in order to then reconstruct them. At the same time, however, an EAS cannot disjoin the epistemology of disciplines, that is, their way of generating and operating on knowledge. The teacher, "didactic engineer", must create a fertile ground through which students can generate knowledge. The teacher then creates the conditions through which pupils are at the center of their own learning process, become architects of a product and are able to express and argue the processes put in place for its realization. In this article we will illustrate some examples of artifacts that the teacher who works for EAS (but not only) can propose to the class: objects that are created in the way in which "mathematics is produced". To do this, let's first see the ways in which mathematics generates and produces entities and relationships, and the consequent models and reflections.