The education entrepreneur Adam Robinson did his own survey a few decades ago. He found that while children of two immigrants did better on standardized tests than children of two non-immigrant parents, the "best" combination came from having an immigrant father and a non-immigrant mother. ("Best" when focusing solely on standardized test results)
That's curiously specific, as in the gender role and immigrant standing are tied together, but apparently that isn't the case. Googling around found the following editorialization of the source material [1] that gave a TL;DR faster than I can type it up:
Study of NYC school data and using custom questionnaires of teens across the world testing into Stuyvesant HS
Cutting to the conclusion: Groups that overcame socioeconomic factors to improve on tests (test improvement is more sensitive to those factors than outright performance) had the following factors:
immigrant father
US-born mother
Speculation to why this mattered? One parent to impart work ethic, one parent to impart language. The gender didn’t matter, it just turned out that the father typically tended to be the immigrant. This combo even outperformed both parents being born in the US.
> One parent to impart work ethic, one parent to impart language.
This at least passes the sniff test. I know plenty of 1.5 or 2nd Gen Indian Americans who seamlessly assimilate because they and/or their parents speak English, in an accent coded as classy (ie British-sounding)[1]. This is even true to some degree in the workplace: I work with some brilliant first gen Chinese immigrants, but there's a practical ceiling on their ability to work at higher levels because of the increasing importance of communication as you rise,and the way their thick accents and lack of vocabulary interact with that. A hypothetical kid of theirs with the same level of talent would shoot up the ranks.
[1] Note that this doesnt cover all Indian accents, only most traditionally upper-class ones.