As Mother Jones put it, "If you're born poor, you'll probably stay that way."
The bit that particularly is important for education is this:
Alexander found that education, rather than giving kids a fighting chance at a better life, simply preserved privilege across generations.That's a tough thing to hear, but it would make a real difference in our policies on a lot of things if we got that into our heads and acted accordingly. It has to be broader than going after schools all of the time.
Johns Hopkins summarizes many of the findings here.