In this communication we will discuss some preliminary results of a large study, named "Teachers and new competencies in primary mathematics1" which main goals are: to characterize primary pupils' mathematical knowledge; to investigate the development on primary pupils of concept models; to identify the obstacles that are placed on what concerns that are placed on what concerns to concept construction and study ways to overcome them; to identify the teachers' practices that favor or inhibit the pupils development of concepts; to identify social aspects (school, class, family) that favor or inhibit mathematical learning. Specifically we will present results related with how children construct concepts, in particular, how third and fourth grades' children deal with division concept and rational numbers in a problem solving context.