We taught a group of experienced in-service primary school mathematics teachers the notion of mathematical model, in order to foster the interdisciplinary mathematics teaching in primary school. In particular, we developed an exercise in which they were supposed to construct a mathematical model on the basis of primary school mathematics. We found out that the formal mathematical knowledge needed to perform the exercise was not sufficient to successfully cope with it. The main factor that influences the ability of the teachers to cope with this type of activity is the depth of their mathematical knowledge which we identify with a person's mathematical insight. [For the complete proceedings, see ED597799.]