From Archimedes and the oxen problem to Pell's equation

Abstract

As part of the laboratory activities designed for the students of the second year of the Mathematical High School by the research group in Mathematics Education of the Department of Mathematics of the University of Salerno, the theme “From Archimedes and the oxen problem to Pell’s equation” has been designed. The course has not yet been delivered to students and in this paper the didactic path to be developed in the classroom will be described. The students initially will retrace the various solution approaches proposed over the centuries. Subsequently, with a heuristic approach, they will tackle the resolution of the proposed problem by exploiting properties related to the theory of numbers. With the help of some schedules, provided by the teachers-tutors, they will conjecture and argue by answering questions aimed at stimulating didactic reflection. This workshop path involves processes such as exploring and conjecturing through the articulation of different ways of working (individual and in groups), manual and digital.