Situations et processus didactiques dans l’étude des nombres rationnels positifs

Abstract

This paper is a presentation of a classroom study on three situation-problems in the field of positive rational numbers. One of the main difficulties in understanding the epistemological status of rational numbers is that they can be considered as operators as such. Furthermore, looked upon as operators they can be used to clarify the correspondence between measure spaces (functional procedures) and express the relationship between two results in the same measure space (scalar procedures) (4).
After a presentation of the theoretical framework we give an analysis of the three situation-problems that were used in a secondary school with 13 to 15 years old aged pupils. This analysis is developped in three directions:

• a detailed introduction of successive questions
• a rather large focus on children behaviour
• a trial to interpret in terms of situation analysis the reasons for such or such behaviour.

So, this paper tries to bring a contribution to the field of teaching rational number theory and to the relation between mathematics and their applications in the classroom.