Title: The nature of the teachers’ and students’ Geometric Working Spaces (GWS)
Organization: Braconne – Michoux, Annette / Henríquez – Rivas, Carolina / Michael – Chrysanthou, Paraskevi

Misunderstanding occurs when students’ views of what they need to do in class deviate from their teachers’ expectations. For instance, mathematics teachers are convinced that the students must know the theorems in order to use them in geometrical proofs; subsequently, depending on the curriculum or the country, the students learn them more or less by heart. But for a teacher, knowing a theorem necessarily implies being able to apply it. In doing so, teachers and students are working in different geometrical paradigms potentially leading to some misunderstandings, even, in some cases, to a total lack of comprehension.
Based on the above, the main questions to be addressed in this workshop rely on the nature of the teachers’ personal Geometric Working Spaces, through their epistemological and cognitive conceptions about the geometry they teach, their didactic conception about building an appropriate GWS for their students. This workshop aims to make the participants familiar with the different geometrical paradigms (GI, GII, GIII) and aware of the distance between the teachers’ and the students’ Geometrical Working Spaces. To do so, the participants will have the chance to analyze pupils’ written works from different countries translated in the three languages (7th to 10th grades pupils) using the theories of the geometrical paradigms and the GWS as reference frameworks (personal, appropriate GWSs).
As a conclusion, we hope that, being more familiar with the different geometrical paradigms and the different aspects of WGS (the process of visualization, the use of instruments or discursive reasoning) participants will be able to analyze their students’ answers or to refer to these in their research studies.