Teacher’s choices as the cause of misconceptions in the learning of the concept of angle.

In this research, we highlight that pupil’s misconceptions about the concept of angle, extensively treated in literature, depend also on the didactic choices made by the teachers in didactic transposition of knowledge and in the educational design. It is often driven by unique and binding choices which do not take into account that mathematical objects usually have various definitions elaborated in the history of mathematics. Mathematical objects are usually imposed by the teacher, instead of being the result of mediation and negotiation within a community of practices, with the aim of reaching a shared knowledge by the pupils. Another important cause of difficulty, on which this research specifically concentrates, consists in the incoherencies in the intentionality of the teachers deriving from a limited and unaware use of the semiotic means of objectification with respect to the conceptual and cultural aspect of the knowledge they want pupils to reach.