Cadre

"Disons qu'un cadre est constitué des objets d'une branche des mathématiques, des relations entre les objets, de leurs formulations éventuellement diverses et des images mentales associées à ces objets et ces relations. Ces images jouent un rôle essentiel dans le fonctionnement comme outil, des objets du cadre. Deux cadres peuvent comporter les mêmes objets et différer par les images mentales et la problématique développée. [...] Nous concevons la notion de cadre comme une notion dynamique." (Douady 1986 p.11)

• English : Setting

"The notion of setting has at least 3 dimensions: mathematical dimension, a socio-cultural one and an individual one. In its mathematical dimension, a setting is constituted by objects in a given mathematical domain with various levels of complexity, by relations between these objects and by their various formulations. [...] Many other objects are to be included in such a setting, but it would not be possible to make an exhaustive list because this list has a cultural character. That is where the socio-cultural dimension comes in the picture. Persons with the same culture or the same background, embedded in the same environment, facing the same problem, will usually mobilize the same objects, or at least in the same categories [...] The individual dimension is involved insofar as the constitution of a culture is not only the fruit of a social education [...] individuals sharing a wide common field of reference, build for themselves representations and personal mental images and life experiences, including cognitive experiences." (Douady 1991 p.117)