The term "First" or "Second Generation", omits the obvious, first or second generation "American". If we say that those who immigrated are the 1st, then by definition their children are 2nd. But that poses a problem, not everyone who immigrates becomes an "American" (11 million are not even legal residents). Although a bit confusing because many of them (I am one of them) do end up becoming American, for clarity, we need to start calling only those who are born here the First Generation.