### Séminaire de Recherche en Didactique et Epistémologie des Mathématiques

vendredi 24 mars 2017 à 09:00 - Campus Triolet- Bâtiment 9 - salle 109

Laura BRANCHETTI (*Politecnico de Milano (Italie))*

#### The epistemological and didactical complexity of real numbers and continuum and how it affects teachers' choices in the high school

Since '70s a lot of researches in Mathematics education have stressed the difficulties that students have learning real numbers, with particular attention to irrational numbers and decimal representation. The epistemological complexity of real numbers and continuum are well known so the difficulties could be easily interpreted as a direct cause of it. Nowadays several researches have showed that a large part of the difficulties are due to the didactical choices of teachers; in particular not suitably complex activities hide the meaning of the most used representations, making students' learning even more difficult. In my PhD I investigated the role of different factors in teachers' decision-making processes involving teaching and learning of real numbers and continuum. In particular I showed that, also in the cases in which teachers are good mathematicians, the lack of awareness of the epistemological complexity and the lack of knowledge in Mathematics education might affect teachers' choices in a negative way, driving them to make unsuitable choices.