Does schooling equalize achievement disparities among students with and without a migrant background? This question remains largely unanswered in sociology. We hypothesized that children of migrants would benefit more from schooling, thereby making schools engines of educational integration. Our study tests this hypothesis in the context of German primary schooling using data from the National Educational Panel Study. We compared the achievements of students from native families and those with Western, non-Western (including Turkey), and former Soviet Union migrant backgrounds. Using the differential exposure approach, we decomposed learning into two causally distinct components: learning due to school exposure and learning due to being older at the time of testing. Our findings do not support the notion that schooling equalizes migrant-native achievement gaps. Instead, our results suggest that school exposure may widen the gap between the two largest groups of migrants in Germany, with students from the former Soviet Union disproportionally benefiting from school compared to other non-Western students. We conclude that German primary schools are not functioning as engines of educational integration because schooling does not reduce the migrant-native achievement gap and migrant groups with the greatest educational disadvantage benefit the least from schooling.