For students from 5 to 8 years old, the spatial and geometrical learning concern mainly the control of its relations to real space (tracking, travelling), the recognition of objects and shapes, and their representation by drawings using straight lines. The ERMEL team, in France, is experimenting teaching situations on space and geometric learning in the 2nd cycle of primary education (5–8 years old student) and is building complete engineering to teach math in elementary school. Our methodology involves an analysis of the student’s way to solve problems and thus their abilities. Experiments conducted in a great number of classrooms allow us to better understand the components of this learning in terms of knowledge and abilities. Thanks to these results, our hypothesis and choices have evolved.