Starting from the constructs ‘cultural scripts’ and ‘social representations’, and on the basis of the empirical research we have been developing until now, we revisit the construct norms from a sociocultural perspective. Norms, both sociomathematical norms and norms of the mathematical practice, as cultural scripts influenced by social representations, mediate the learning of mathematics in multicultural classrooms. When taking into account the particular circumstances in which mediation occurs, there is a need for a move from a cultural perspective to a broader sociocultural one. THE SCENE Because of the important recent waves of migration into Spain, our educational system must face the needs of a society where the plurality of cultures and languages is, and will be, a reality. However, the Spanish school system has a limited understanding of the sociocultural and linguistic aspects linked to teaching mathematics in multicultural situations. In general, mathematics teachers are not prepared to teach in multiethnic classrooms, the mathematics curriculum is intended for the ‘native’ groups and, at most, language, understood as everyday language, is the only ‘problem to be solved’ in multiethnic mathematics classrooms. For more than six years now, we have been researching multiethnic mathematics classrooms in an effort to understand their complexity. The beginning of our project was the result of a request from the Catalan Ministry of Education. Its aims were a result of an initial negotiation with the educational administration, and they included, among others: a) to know more about the knowledge that immigrant students bring with them to school and how this knowledge can be linked with the curriculum and its development in the mathematics classroom;