If we really want to close the achievement gap...

Perhaps the first step is simply making sure poor children receive adequate nutrition.

From Microeconomic Insights via Mark Thoma:

Adults who participated in the Food Stamp Program, renamed the Supplemental Nutrition Assistance Program (SNAP) in 2008, as children are healthier and better off financially than poverty-stricken families who did not have access to the program, according to findings in joint work with Douglas Almond and Diane Schanzenbach (this paper and a companion paper Almond, et al. 2011). Children with access were more likely as adults to graduate from high school, earn more, and rely less on government welfare programs as adults than impoverished children who did not have access to SNAP. Women, in particular, are substantially more likely to self-report they are in goffc905od health and are more economically self-sufficient in adulthood. We find no additional long-term health impacts for children from more exposure to the program during middle childhood, but individuals with access to food stamps before age 5 had measurably better health outcomes in adulthood with significant impacts for those in early childhood.