After the presentation of an issue related to curricula and study programs organized in terms of competencies, this article proposes an analysis of reference documents designed for teaching and assessing mathematics in primary school, in the French speaking part of Switzerland and in the Canton of Geneva. It underlines the bottom up transposition processes, departing from classroom practices concerning assessment which are mediated via in-service training and finally formalized in official texts. It highlights tensions, sometimes contradictory, between various curricular documents and conceptualizes the relationship between the notions of objective and competence, which are not opposed to each other in the Geneva context.