Early Approach to Theoretical Thinking: Gears in Primary School

Gears are part of everyday experience from very early childhood. This paper analyses a teaching experiment conducted with 4th graders in the field of experience of gears. The aim is to identify the characteristics which, given a suitable sequence of tasks and proper teacher guidance, have enabled the pupils to approach theoretical thinking, and in particular mathematical theorems.We have focused on the relationships between the epistemological analysis of some pieces of mathematical knowledge brought into play in tasks concerning gears, cognitive analysis of pupil construction of those pieces of mathematicalknowledge, and didactic analysis of the teacher’s role in designing tasks and in offering cultural mediation. This paper presents the early findings of the teaching experiments, both at the external level of interpersonal classroom processes and at the inner level of individual mental processes.