This paper is dedicated to the numerical knowledge at pre-elementary and elementary school (pupils 4 to 7 years old. At these levels, observing pupils' numerical activities is quite difficult, because often the knowledge at stake is not recognised as mathematical knowledge. Following Briand, we will study different situations, focusing on the counting of movable objects. This study leads to the determination of two different spaces: the space attached to the collection and the space attached to the process.
