La discussione collettiva: un’occasione per espletare il potenziale matematico delle fonti storiche

Abstract

Integrating the history of mathematics in class could be a hard task with young pupils. Indeed, the language of historical sources often poses problems for the modern reader.. Such texts represent cultural artefacts that can give access to mathematical knowledge. The teacher can exploit such potential by acting as a mediator between the mathematical signs of the source and those signs that are accessible to students. Through a case study, we investigate the role of the teacher in the process of semiotic mediation during a collective discussion. The intervention analysed is made up of two phases: firstly, the students work together and, secondly, the teacher mediates a discussion aimed at institutionalizing the knowledge gained. During the analysis of the discussion, working on a text from Tartaglia’s translation of Euclid’s Elements, a group of fifth graders construct a definition of prime numbers. Referring to Theory of Semiotic Mediation, we analyse the role of the teacher in building up semiotic chains linking the students’ productions to an institutionalized knowledge emerging from the discussion. We highlight how the teacher’s focalization on the students’ words facilitates the progress of the discussion, in other words, the potential of the historical text is exploited by fostering a definition that is close to culturally shared mathematics.