Simple:
let the market rule.
Let folks see the differences in the standard of living and job opportunities between states with well-educated workforces and say, Arkansas.
They'll then demand better schools.
And with the federal government out of the way, schools will be free to teach.
Consider that the problem was not nearly as bad when the federal government was not in the education business, beyond providing research money which in addition to it's stated purposes, also provided for the education of engineering, science and math (and occasionally economics and other social sciences) graduate students. Given that, I'd say we "include" the federal government as the Constitution allows, which is to say by getting them out of the business. Much of the problem is federal $$ and the strings that go along with them. Then there are all those federal mandates which no longer even have federal $$ attached to them. Many of those are from the unelected federal courts, but many come from Congress and the Executive Branch bureaucracy as well.
According to the Supreme Court (in the Gun Free School Zones case) education is not commerce, and thus the federal government has no power or authority in that areas.
It's a fallacy to say that just because a problem exists in most or all states, that automatically the feds must be involved. When they are involved they tend to run the train, and devise "one size fits all" solutions. Let each state and each school district find it's own solutions, or not, as the case may be. I think that without the carrot of federal dollars, and the stick of federal mandates, states and local school districts will find solutions that work for them, and will copy things that work for others.