Journal du Nombre: Medium and tool for the conceptualization of mathematical knowledge
This article relates an experiment on the construction of the number at the level of the preparatory course and the elementary course (pupils aged 6 to 8). We focus our analysis on one of the engineering and elements. It is a personal and collective copybook, called the Journal du Nombre, which aims to a better understanding of mathematics. One of its particularities is the exclusion of all evaluation in order to favor the construction of a time knowledge to develop a personal connection to mathematical objects, especially for less advanced students. Our theoretical framework is the Theory of Joint Action in Didactics-TJAD, which is the continuation of the work of Brousseau (1970) and Sensevy (1996). We retained some theoretical categories such as the defining and strategic rules, the middle contract, the joint action, the collective productive incentive, the dialectic of the expression reluctance and the less advanced students. The methodology consists of the analysis of a small sample of work in the Journal du Nombre done by less advanced students. The results show that the Journal du Nombre is a device that links the institutional time and the personal duration of the student for a better acquisition of mathematical knowledge.