The best way to educate children is to allow each state to use the food stamps model. Most state governments have decided that food stamps are a public benefit that the state should provide while you may agree or disagree with this notion, you should agree that the state governments allowing food stamp recipients to shop at private sector grocery stores is a much better solution than having the government actually take over the distribution of the food.
Education is similar. Parents should be allowed to open enroll their child into the school of their choice. The market effects of competition will drive down cost while increasing quality meaning everyone wins.