Resumen

We designed a set of activities on one real variable functions, based on various semiotic registers of representation (Duval, 2000), expecting to answer the following research question: “Can the individual concept image (Tall & Vinner, 1981) of function be enriched by the use of various functions and their associate ones, using verbal texts, algebraic laws and graphs?”. Seven in-service Mathematics teachers from Brazil carried out these activities, during six two and a half hours sessions. In this paper, we ocused on protocols and observers’ written notes of one teacher from the group, which were analysed in the light of the theoretical framework of The Three Worlds of Mathematics (Tall, 2004a, 2004b). We found that this teacher had, in his concept image, notions related with only first and seconddegree polynomial functions, and used mostly the embodied world to justify his answers. The activities seemed useful for him to broaden his concept image.