Definition as a teaching object: a preliminary study

In this paper we consider mathematical definition as a teaching object to be understood and used to perform mathematical tasks. There are studies on the way students define, but it seems to us that it is less considered how students perceive definitions, how they are able to work on them. In this paper we give a short account of ideas expressed by authors of the past and of the present on problematic features of definition. Afterwards we report an experiment with students aged 15 on defining trapezia. Since this experiment dealt with concepts not problematic for students it allowed to focus our study rather on the concept to be defined than on students’ concept image of definition itself.