Immigrants who have poor educational attainment themselves tend to raise children who go on to also have fairly poor educational attainment, regardless of income.
Immigrants who have (on average) fairly high levels of educational attainment (such as modern Asian parents, or Jewish ones of the past) parent those children differently.
That's not (at least not totally) true. I knew a man who came to US to give his kids good future. He is just a handyman (he finished his HS only) and could not afford to live in good school district. But he always push his kids to study hard. Now both of his kids recieved scholarships are in medical school.
With regard to SES:
Dr. Ben Carson (Neurosurgeon from JH) came from poor SES. (His mother did not even read well but she wanted her kids to read 2 books a week and always on their back to study.)
Academic success depends on both
1) the kids' inherent ability (IQ)
2) motivation and support (school, parents, environment)
If we have both, SES does not matter. Of course, high SES means you can move to the good school district and provide top notch education and tutoring if needed.
The problem is the attitude of the parents. Unfortunately many parents are passionate into their kids sports activity than the education. One of the high school voted to build $ 10 million stadium but did not do anything about losing 10 teachers (half of them in special education) due to Federal and State budget cut.
But I do agree that educated parents encourage better education and advocate for their kids than their counterparts and therfore the children of educated parents are MOST LIKELY to find success academically than their counterparts.