The milieu is here defined as the set of external conditions within which a human being behaves and grows. Il plays an important role in the determination of the knowledge that the subject – its antagonist – must develop in order to control a situation for action. Recent theoretical developments give it a fundamental role in learning processes. From this point of view, a large part of teaching activities seems to consist of the reorganisation of the milieu in order to favour a-didactical adaptations. But for this purpose, it is necessary to know which didactical conditions are required for the devolution process in order to allow students to enter such a contract. In a situation for validation, the milieu becomes the place where functions the corresponding knowledge, as well as its – implicit or explicit – reference. For this reason it becomes both a cultural and an epistemological object to be taught.
The first part of the article aims at reminding the reader about the théorie des situations didactiques which constitutes the framework for the introduction of the notions of milieu and of contract. The second part shows how some didactical enginery allows to solve the devolution problem in an a-didactical milieu. It consists of asking pupils of the second grade to solve equations as a preliminary to the introduction of the substraction computation. This example shows the functionning of the milieu and the necessity for its construction as a content to be known from pupils.