The Logo in the teaching of Mathematics: problems, experiences and requests

In this paper we linger on some of our choices for the innovation of the teaching and learning of Mathematics in pupils aged 11-14 through the use of the computer as "a machine for thinking". In particular we relate on some experiences by us carried out in the realm of our research group (the GREM) concerning Arithmetics, Verbal Problems, Geometric Transformations. We underline the features of the strategy adopted to manage the classroom activity, in particular we linger on the role of the teacher, who prepares the situation for introducing the problem chosen in order to gain the attention of the pupils, solicits and helps these to analyse a solutory algorithm suitable for the computer by using tables to higthlight its functioning and then acts as an interpreter between pupils and computer by giving a translation of the proposed algorithms as "litterally" as possible.From the point of view of Computer Science important themes such as the beginning of algorithmic thought, recursive thought and structured programming are compared. In such experiences the contribution of the computer was fundamental both for the mathematical argument in itself and for the awareness induced in the pupils of their own thinking processes. Finally we conclude with some requests for LOGO suggested by our experience.