Theory of Didactical Situations

The theory of didactical situations, developed from the 1970s by the French mathematics educator Guy Brousseau, is a framework for designing and analyzing the teaching and learning of mathematics by modeling the classroom as a kind of game played among the student, the teacher and the milieu, the material and social environment surrounding the problem at hand. In Brousseau's framework, a didactical situation is one the teacher deliberately sets up to bring about the devolution of a problem, the process by which responsibility for solving it is handed over to the student, so that the student takes ownership of the problem rather than simply following the teacher's lead; an adidactical situation is the phase within that setup where the student works on the problem largely on their own, interacting directly with the milieu and constructing knowledge through that interaction rather than being told the answer. Brousseau describes a full didactic process as unfolding through a sequence of situation types, moving the student from informal action on the problem toward more explicit formulation, validation and eventually institutionalization of the resulting knowledge as recognized mathematics. The theory draws on Gaston Bachelard's notion of epistemological obstacles, points in a subject where a learner's existing ways of thinking actively resist a needed conceptual change, and on Jean Piaget's ideas of disequilibration and accommodation, and although it was developed for mathematics education it has since been applied to the teaching of other subjects, including physics.