This issue presents two ways of reading the data from a didactic experiment about teaching "the division" at school. This dialog allows the emergence of its management characteristics, as the experiment permits the creation of a collective memory of the didactic system that pupils call for on their own initiative. The various functionalities of these phenomenons within the creation process of numerical knowledge are analyzed through the concept of schema as presented in the Theory of the Conceptual Fields, as this theory could not explain teacher's work.

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions and on the didactic memory from both the teacher perspective and the learner perspective: in particular, it not only investigates how didactic memory is managed by the teacher, but also how students recall past events or reread those events in a-didactic situations.

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions and on the didactic memory from both the teacher perspective and the learner perspective: in particular, it not only investigates how didactic memory is managed by the teacher, but also how students recall past events or reread those events in a-didactic situations.KEY WORDS: concepts-in-action, didactical engineering, didactical memory, division problems, operational invariant, numerical knowledge, theory of conceptual fields, theory of didactical situations, schemes Educational Studies in Mathematics (2005) 59: 59-84

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Dans ce texte nous présentons une recherche visant à analyser le rapport que des enseignants ou futurs enseignants ont à l'égard des mathématiques. Nous avons expérimenté avec 14 binômes (6 d'étudiants et 8 de professeurs plus confirmés) un dispositif consistant, dans un premier temps pour un enseignant généraliste du primaire et un enseignant de mathématiques du secondaire de Genève à répondre par écrit à un questionnaire de mathématiques, puis dans un deuxième temps à confronter leurs réponses en présence d'un expérimentateur. Nous analysons tout d'abord ce qui émerge dans chacun des 4 groupes de questions, puis nous faisons une analyse en termes de postures lors de l'entretien, avant de conclure sur l'intérêt, les limites et les perspectives de ce dispositif.