Credits : All modules are presented by Claire Margolinas (Clermont-Auvergne University) and Annie Bessot (Grenoble-Alpes University), except Module 0 by Jean-Luc Dorier (University of Geneva). All videos are produced by IPPA (Clermont-Auvergne University).
Claire Margolinas and Annie Bessot, have worked within the theoretical framework of the Theory of didactical situations in mathematics and they have a deep understanding of Brousseau’s works. They have been faced with the very difficult task of selecting some aspects of Brousseau’s work. This selection was necessary because Brousseau’s work is very subtle and has many aspects.
This first module is devoted to the introduction of the principles of Brousseau’s theory: didactics of mathematics as a field of theoretical and experimental scientific research, in relationship with engineering as a “phenomenotechnique”.
This second module is devoted to one of the most important concepts of the Theory of Mathematical situations namely the dual aspect of knowledge: situational knowledge (“connaissance” in French) and institutional knowledge (“savoir” in French). This module is the basis for the other modules and can be considered as an introduction.
In this module, we also introduce the example of cars and garages situation which will be developed in the following modules.
This third module is dedicated to the characterization of mathematical situations. We will consider Brousseau’s question: “Why study situations if what is at stake is to acquire institutional knowledge?”
This module includes the distinction made by Brousseau between ‘problem’ and ‘situation”. The example of the race to twenty situation is introduced and will be developed in other modules. We introduce the properties and components of mathematical situations: milieu, stake and action situation as a general model.
This fourth module is dedicated to the concept of action situation, including milieu, stake and situational knowledge studying the car garage situation that we have introduced in module 2. We will develop the first status of knowledge: situational knowledge in action situation.
This fifth module is dedicated to the concept of formulation situation.
Implicit situational knowledge has been recognized as useful for action. For a formulation to occur, one has to encounter a new situation during which formulation is necessary. The status of the situational knowledge changes when some aspects of knowledge are formulated, as we will develop in this module.
This sixth module is dedicated to the concept of validation situation.
Implicit situational knowledge and explicitly formulated situational knowledge has been encountered in the previous situations. However, in mathematics, validation is an essential dimension: formulations have to become statements and then conjectures and those conjectures have to resist contradiction. We will thus explore the conditions and constraints of the validation situations.
This unit is not yet complete, modules 7 to 10 are in preparation.
Module 7 – Fundamental situation: principles
Module 8 – Is there a fundamental situation for natural numbers?
Module 9 – Is the race to twenty a fundamental situation and for which institutional knowledge?
Module 10 – An introduction to the theory of didactical situation