In this article, we present some results of a longitudinal research program which started at the pre-school level. In the first section, we discuss the longitudinal part of a program inspired by Head Start and implanted at the pre-school level for children living in urban areas. We examine its influence on the linguistic competence of children belonging to ethnic minorities. At the end of pre-school, these children show a greater improvement in their linguistic competence than their French-speaking peers. Despite the inter-group difference at the end of kindergarten in favour of French-speaking children, over the long term there is a continuation of increasing linguistic competence among children from ethnic minorities, to such an extent that there is no longer a perceptible difference between the two groups at the end of the first year of elementary school. This improvement is due in part to the efforts made by parents and pre-school teachers to help these students overcome the challenges of school. In the second section, we discuss the experimental aspect of the program, describing the positive impact of a pre-arithmetic program based on knowledge of mathematical precursors, which was established at the pre-kindergarten level, and the results of an enrichment program established at the kindergarten level.