The process of proof in the geometric work space: Initial training teachers

Teaching and learning of proof often are explicit aims of the high school curriculum. Nevertheless, the same does not happen in the teachers' training curricula; i.e., neither teaching nor learning of proof are considered to be mathematical objects subject to didactic transposition. Here we use the Theory of Paradigms and Geometric Work Space to analyze, in novel Chilean teachers, obstacles that generate because the roles and status of the proof in the institution high school differ from those in the university as a teachers' training institution. Thus, we give evidence of geometric conceptions and the lack of transpositions facing the process of proof in geometry. This in turn manifests an epistemological, didactic and cognitive break usually found in the teaching of geometry.