The authors observe that, while black students enter the school system substantially behind white students as judged by tests of reading and mathematics, the difference vanishes if you control for a small number of environment variables such as socio-economic status of parents and number of books in the home (the authors are not entirely clear about which variables are used where, but those are two of the ones they mention). That result appears to support the conventional belief that racial differences in outcome are due to environment, not to innate differences.
As the children move through the first few grades of school, however, that situation changes. Black students fall behind white students at about a tenth of a standard deviation a year; that remains true even after controlling for the environmental variables that eliminated the initial difference.
The article is in large part about the authors' search for an explanation. In an earlier piece they had conjectured that the difference was in school quality; in this one, with more data, they are able to reject that explanation. The pattern exists for black and white students in the same school, even in the same classroom. It does not exist for hispanic and white students and it reverses for asian and white students. After exploring a variety of alternative explanations, the authors conclude that they cannot explain the data.
Having eliminated all of the possible environmental causes that they can think of, one might expect them to next consider the obvious alternative explanation: Innate differences between the races. That is not the only possibity, of course; I can think of a few more environmental explanations, such as different treatment of blacks and whites by schoolteachers and others or differences in peer group pressures. If, as I think likely, black students tend to socialize with black students and white students with white students, and if black youth culture is less friendly to education, or differs in other relevant ways, from white youth culture, that also might explain the observed pattern.
Nonetheless, insofar as the results are evidence in the controversy over racial differences, they are evidence in favor of such differences, since they are the results one would expect if blacks were on average innately worse, and east asians innately better, at certain things than whites. That explanation is not on the authors' list of conjectures to be tested. The authors try every environmental explanation they can think of a way to test, are unable to explain the data, and, instead of considering a non-environmental explanation, throw up their hands.
Their discussion of the omitted possibility is limited to a single footnote, which reads:
"This theory, if true, also re-introduces the possibility that genetics could play a role. Because we have little evidence on this either way, we choose to exclude it while noting that it is a possibility."
Including that footnote marks the authors, in my view, as more courageous than the typical academic. Nonetheless, it translates as "our results support a view not to be discussed in polite society, so we won't discuss it."
Which tells us something about to what degree the beliefs, at least the stated beliefs, of polite society are based on open enquiry into the evidence, and to what degree on prejudice.
I should probably add that the one discussion of the question of racial differences I have seen that actually provided real evidence against them was by Thomas Sowell in Ethnic America: A History. It was possible only because Sowell, being more courageous still, was willing to seriously consider the possibility that different racial outcomes might reflect genetic differences. He offered the economic performance of West Indian immigrants as evidence that the poor economic performance of American blacks is due to neither genetics not prejudice. West Indians are blacker than Afro-Americans, in terms of both genetics and appearance, yet their family income gets up to the U.S. average in a single generation. Readers curious about his explanation of the difference are invited to read his (very interesting, for many other reasons as well) book.