Strongly didactic contracts and mathematical work

This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in probability. It is particularly focused on the reality of mathematical work performed by students and teachers. For this research, classroom sessions were developed in an in-service teacher training course designed (and adapted) according to the Japanese Lesson Study model. Through the combined use of the Theory of Didactical Situations (TDS) and the Theory of Mathematical Working Spaces (ThMWS), a coding of the sessions observed was developed. Based on this coding, different patterns emerged which gave each session a specific rhythm and identity from which it was possible to recognize and characterize different strongly didactic contracts. The study highlights the difference between the potential contracts intended by the teachers and those observed in practice. The tools, and especially the coding, developed for the study could be used for future research on instructional situations or in-service teacher training.