Connaissances géométriques et connaissances spatiales dans les situations didactiques avec la technologie

After a review of the research works about dynamic geometry over the last ten years, this text presents the most recent studies about the integration of digital technologies into a complex system of tools and didactical situations. Following Berthelot and Salin’s work, we consider spatial knowledge and geometrical knowledge as two different conceptual fields, with strong connections. We present the specific role of graphical space in the development of knowledge and relationship between these two conceptual fields. Moreover, we show that digital environments, like dynamic geometry, have specific and complementary, even necessary, properties for designing didactical situations for the learning of geometry. In this purpose, we introduce the idea of duo of artefacts to focus on the articulation of tangible and digital artefacts in the design of didactical situations and the studies of learning and teaching processes. We illustrate these theoretical developments with research about dynamic geometry, with spatial or geometrical concepts like setting positions and trajectories with a squared grid, symmetry, triangle construction and nets of cube