This article should be placed in the frame work of a research about the appropriation of natural numbers by the pupil of cours préparatoire (C.P. : first year of compulsory school - attendance in France; concerning 6 to 7 years old children).
The general aims of this research are :
- to show up the different conceptions of number in the pupil’s mind at a certain moment and for a certain number's size.
- try to understand how work these conceptions regarding the tasks proposed to the child.
These interrogations should allow to precise the conditions of a better appropriation of natural numbers by the pupil.
In this article the authors have choosed to present an analyse of pupil’s procedures and their evolution for a very precise task : in this task (consisting in the construction of a new-made collection, equipotent to a given one), the counting is not explicitely demanded, but on the contrary putted in concurrence with others procedures. The analyse of evolutions is made vis-à-vis two fundamental variables : the size of numbers and the specific moment of the scholastic year. This analyse states particularly, the existence of procedures, more or less pertinent to the task, relaying counting when this last one is failing.