The Achievement Gap report (prepared by an outside consultant a couple of years ago) says,
Note the almost off-hand way that the parent role is glossed over. If one put the emphasis on the qualification inside the school building, it might make us read that sentence differently. Say, like this--'inside the school, which, realistically, has constraints to deal with, teacher quality matters, but good parent involvement might be an equal or even more significant factor.'
We can't really tell, though. As the report acknowledges on page 15,