There are a lot of reasons unrelated to school quality that affect the performance of children. In particular there are many issues affecting poor children. I highly recommend that you read A Framework for Understanding Poverty, by Ruby K. Payne, Ph.D.
Furthermore, as far as directly comparing school district expenditures per student, don't forget to compensate for the relative cost of living as that can mean that a district that is spending twice as much as another is really spending less in terms of how far those dollars can go in that location. Since good schools cause localized inflation, the better the school the more money they need to buy the same goods and services.
Also there are still significant impacts from environmental pollution, in particular lead poisoning. Lead exposure has recently been shown to lower IQ even at levels previously thought to be acceptable. The DC area still has lots of problems with lead exposure. Many problems in society are exacerbated by lead poisoning. One of the most important things we can do as a society to improve the intelligence and education of the populace is to reduce lead exposure.
"exposing children to toxic lead --
even at levels below 10 mcg per deciliter -- causes some of
them to become impulsive, aggressive, antisocial, delinquent
and violent. The more lead, the worse the behavior. Herbert L.
Needleman has recently suggested that this may turn out to be
the most important effect of exposing children to lead."
http://www.organicconsumers.org/school/lead081004.cfm
http://www.bridges4kids.org/news/10-02/Sun5-9-02.html
http://www.allheadlinenews.com/articles/7009027052
http://www.leadsafedc.com/
http://www.washingtonpost.com/...6/AR2007081602586.html
http://www.ehw.org/Lead/LEAD_CommunityAgenda.htm