Attualità delle riflessioni di Guido Castelnuovo sulla formazione dell'insegnante di matematica

In his courses at the University of Rome, Guido Castelnuovo confronted the idea of extensive and intensive teaching of Mathematics. According to him, extensive teaching is more suitable for perspective teachers while intensive teaching is more suitable perspective researchers. Nowadays many universities combine intensive teaching with courses on methodological didactical issues for the preparation of perspective teachers. We think that this is not enough. We should give also proper space to extensive teaching, in the sense explained in this paper.