Students, mathematics, applications: an attempt at linking three different domains through the computer

In this paper we report the main lines of a project addressed to students aged 16-17 in which a didactic path is developed from theoretical mathematical aspects (in number theory) to applications (cryptography). The ambition of this work would be to make students reach awareness of the way of working of the mathematician (within limits of the school level involved); a particular emphasis is given to activities such as the production of conjectures, examples and counterexamples. All that is performed using the computer - spreadsheets, Derive, programming - in different situations. This scenario offers elements to study how informatics influences the students’ behaviour; positive and negative aspects are analysed and possible developments of research are outlined.