There's a flaw on jdizzy001's argument about taxes that need to be pointed out. I'm not american, but of course, I beleive tax systems are not THAT different than those from Brazil, which means I have a small grasp on how it works, having studied it in Law.
While, yes, property taxes are used to fund the school system, those are based on neighborhood and property value (correct me if I'm wrong, as I said, I'm applying the logic of our system), which means that, in a nutshell, those with more money pay more (which is the fundamental of tax law), which also means that some people that pay such taxes do no need to use said system, as they can (and will) afford private schools for their children.
Because of this, if the school system were to be privatized, the amount of money left over for the poorest families from not having to pay the appropriate amount of property tax (probably a PART of it, not the thing as a whole) wouldn't be enough, on its own, to make it possible to afford their children's education. Also, lest us not forget the government would probably simply apply the tax elsewhere, I mean, people are "used to paying it anyway", so, why not direct the money somewhere else (even if "somewhere else" means "their pockets")?
I'm not saying the system should stand as is, since it's really messed up (and to this, I again apply the logic of our system of Public Education here, although ours is not as bad as yours, so I hear). One thing that COULD be done is looking at our Public University systems (in Brazil, people compete to get into PUBLIC Universities, they are better than Private ones by a fair margin, having better students, due to the rough selection process, and having better teachers, due to the whole career plan they have), which, while ALSO a bit flawed, still works. In our Federal Universities, for instance, people compete for a spot in, say, Med School at a rate of 130 people for each spot, rising to close to (or even over) 300 in the best Med School we have in a Federal University. For instance, Law, where I live, has the overall 3rd or 4th course in the country (all Federal Universities, also), and it closes in on 80 people per spot. Seeing as we have a #$&*@! of a 3-day test to get it, and there's no such thing as an "application" that will be read by a Board (we do write an essay, but those are univesal for all courses and unidentified, so the people grading it have no idea even in which course that person is trying to get in, let alone who it is), you have to study pretty hard to get in, meaning the Private Universities, basically (there are exceptions, I know a few), get what is "left over" from those students, meaning, the ones that were not smart enough or that were too lazy to try and get into one of the Public ones, meaning the Federal and State (heck, even City ones where they exist) Universities get better human material to work with from the get go, meaning we post higher gradings on national tests and stuff, not to mention we tend to do better in tests to get into great jobs (where competition is even more dire), resulting in yet another plus for the public system (and it looks awesome in your resumé, as well, it alone can get you some jobs). Funny, though, how we can't get this across to Public Schools, it simply does not work. Used to, some 20+ years ago, but has simply stopped. I could name a few reasons why I believe this happened, but it would generate a whole other discussion.