Education is a commodity, just like groceries, dry cleaning, gasoline, and lawn care. We wouldn't tolerate government managing other commodities (can you imagine a government-run auto-repair shop? government-run appliance store?) - so why do we surrender when it comes to something as important as education?
Education should be provided by the private sector, albeit with tax-sponsored vouchers (this is America; we want everyone to have a chance at an education). Parents should decide which school their children should attend, just as they decide which cell-phone carrier to use. Poor schools will no more survive than do poor restaurants.
Teachers' unions would no longer monopolize education because a free market is in charge.