Learning difficulties in mathematical problem solving with computers

The paper presents some observations made regarding the students of the classes involved in a project elaborated by the Didactic Research Group of Pavia for the teaching of a programming language (BASIC) and its use in implementation of arithmetical algorithms and in solving simple problems of applied mathematics by computers with 11 - 14 year old students. Some of the difficulties connected with programming activities in this age group are analysed, in particular those linked to the concept of variable, and some examples of error analysis and of consequent didactic interventions are presented. The results of this activity have been verified by means of tests that are discussed here. The outcome of the work can be considered positive but the detailed analyses carried out in this research on the abilities requested pose the problems of the adequacy of requested formalization for the age group and of the effects of this kind of work outside the field of computer science.