In many Western countries the pressure exerted on immigrants to integrate has become intense in recent years. Efforts to preserve their ethnic identity through multicultural recognition has now been replaced by the requirements of active civic participation and assimilation. Of course integration is considered important not only for the immigrant parents but also for their children. The central question in this article is whether there is a relationship between the degree of integration of the immigrant parents and the generation of their children on the one hand and the level of language and numeracy achievement of the children on the other. To answer this question we use data collected in 2008 from the Dutch COOL5-18 cohort study. The information comes from more than 9000 immigrant and 16,000 indigenous children and their parents. The results show that as immigrant parents are better integrated and their children are of later generations, the language and numeracy skills of the children improve, though there remain large differences in achievement between different ethnic groups. (Contains 3 tables.)