FOSTERING PRESERVICE TEACHERS’ MWS-INTERPRETATIVE KNOWLEDGE THROUGH EPISTEMOLOGICAL TAXICAB PERTURBATIONS

One of the most discussed issues in teacher education research is the one concerning the mathematical knowledge acquired in university courses and the mathematical knowledge a teacher should have to teach, known in the literature as Klein's discontinuity. To define the designed mathematics teacher knowledge and to study how to reach it is the main issue of the research in mathematics teaching. Furthermore, working to reduce this gap is the aim of mathematics teacher training activities. In this paper, we investigate graduated prospective teachers’ perception and interpretation of the geometric work carried out by peers who were asked to perform a geometric task going back and forth between Euclidean geometry and Taxicab geometry. We analyse prospective teachers’ productions through the combination of two theoretical constructs: Interpretative Knowledge (IK) and Mathematical Working Spaces (MWS).