The Irish are an obvious illustration, it taking them several generations to work out of the situation. Much was the same with the Germans in Minnesota. My father-in-law had a difficult time in school because he had such a hard time with English. He was third generation but the first generation never learned English. His father learned some and mother refused to learn it. A very common situation in that area at the time but not anymore.
In this area we had a lot of Norwegian and Swedish immigrants who went through similar situations but again, it's not a factor today.