I have to agree with Gary DeMar on this issue. We need to abandon the idea of government run schools entirely.
"Instead of wasting time and money fighting for scraps, why don’t Christians remove their children from these atheistic schools and teach them at home or set up their own schools? How many more times and in how many ways does God have to tell Christian parents to get their children out of public schools?" —
Gary DeMar, American VisionWell, the root is the problem IS not that the public schools are government agencies but that education is a political rather than private and religious matter. Frederick the Great started state schools to inculcate loyalty to the regime. The French revolutionaries followed his example, and it has spread to the rest of the western world.