Machines as tools in teacher education

The aim of this chapter is to present some issues concerning teacher education, at both primary and secondary school levels, drawing on the activity of the Laboratory of Mathematical Machines at the Department of Mathematics of the University of Modena and Reggio Emilia (MMLab: www.mmlab.unimore.it). After having defined what are mathematical machines (geometrical and arithmetical machines, as well), we shall illustrate shortly the theoretical framework of semiotic mediation after Vygotsky, where the activity for prospective and practising school teachers is situated. We shall offer two examples. The first concerns arithmetical machines related to the meaning of place value in primary school and the second geometrical machines related to the meaning of axial symmetry in secondary school. Activity takes place in small size (25–30 students) laboratory settings for prospective and practising school teachers, according to the Italian standards for teacher education and to the implementation realized at the Faculty of Education of the University of Modena and Reggio Emilia.