Functions in algebraic and graphical environments

Abstract. In this paper we discuss the results of a questionnaire on the concept of function given to students aged from 14 to 19. The findings suggest different observations: here we consider the various students’ behaviour in relation to the graphical and algebraic representation of functions. We relate these differences to the students’ ages (namely the extent and type of mathematics studied) and to the teachers’ expectation. The questionnaire is one of the products of an undertaking of teacher re-training carried out by a team of teachers of a Genoese school.