Using Italian data on language standardized tests for three different levels of schooling we investigate if the observed gap in educational attainments in 1st generation immigrants tends to lower the longer they stay in Italy, and if younger children tend to catch up faster than their older schoolmates. The analysis shows that the significant gap in language skills observed between 1st and 2nd generation immigrant students is mainly due to both the negative performance of immigrant children newly arrived in Italy, and the immigrant students' area of origin. Comparing the results across the different grades, we also find that this gap narrows at a different pace in the early or later years of an immigrant student's life. Overall, our results suggest the presence of a 'critical' age above which 1st generation immigrant students face a negative impact on their school performance, and that institutional and cultural factors play a role on immigrant language skills acquisition.