On dialectic and dynamic links between the Mathematical Working Space model and practice in the teaching and learning of mathematics

In this communication, we address the specific relationships between the Mathematical Working Space model (MWS model) and practice in the teaching and learning of mathematics. The strong and positive interactions existing between these two aspects are illustrated with two examples from geometry and probability teaching. They show how some theoretical constructs as MWS diagram can enlighten practice and, conversely, how studies on practice nourish the model with new tools such as "comics", "complete mathematical work" or "emblematic tasks".