My wife is Asian. Her elder relatives have assimilated very little - they hold on to their language, their customs, and their values. The go "back home" at least once a year, and tend to speak only their natal language.
The people of my wife's generation have assimilated more, but only those customs that are advantageous to their lives and careers. At home, they are very much their parents' children, with the same linguistic skills, the same customs, and the same mannerisms. At work, they are Americans, albeit with an accent and some odd mannerisms.
The third generation, however, has grown up in America, and have taken on just about every American custom that is not of their grandparents' native land. Most do not speak their grandparents' native language, nor do they seem interested in visiting their relative "back home" (as their parents and grandparents call it). If you could only listen to them, they would sound exactly like any American kids of the same age.
It may be safe to assume that by the fourth generation, these people will be as assimilated as they're going to get - for better or for worse.
"Should" they assimilate? It seems inevitable, but only as they generations go by.
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