Here's my bias, up front: I despise modern schools. Schools, especially public K-12 schools, aren't hallowed institutions of learning. They're part-time prison camps. The Prussian model, from which all modern systems descend, was designed to condition and indoctrinate soldiers, factory workers and housewives--to turn children into docile and reliable units in an industrial economy. Human machine parts. The most important lessons they convey are how to sit in one place for long periods of time, how to carry out dull, repetitive and essentially meaningless tasks, and how to knuckle under to authority.
Burn the fucking mausoleums to the ground and start over.
How I Would Reform K-12 and Undergraduate Education
1) Phase out in-person lectures, replace with Khan academy-style videos.
Lectures suck twice over. First, they're a lousy instructional format. Second, in the Internet age, there's no need to have them constructed and delivered artisan-style by fifty thousand individual lecturers of varying (and mostly poor) ability, any more than we need all music to be performed by local chamber ensembles. If we have to deliver information in the lecture format, let's find the best one, or the best hundred (to match individual learning styles and preferences).
What about hands-on interaction, the back-and-forth of true personal teaching, you may ask? That's not lecturing, that's something that disrupts lecturing. Let's talk about that separately.
2) Fire the useless teachers, have the decent teachers become well-paid, prestigious tutor/guides, for live one-on-one consultation.
This is how many ancient academies actually worked, and it's how a handful of the greatest, like Oxford and Cambridge, still do. There's no substitute for discussion, but the modern lecture system doesn't support discussion, it crowds it out, especially in high schools.
3) Arrange the essential curriculum in the form of skill trees and gamify the hell out of it.
Again, Khan academy does this already. So do MMOs. Give students well-defined paths to follow in the essentials, and give them immediate and continuous feedback on their progress. You mastered the unit on factoring quadratic polynomials? Level up!
4) Pay children to progress.
Adults bitterly resent forced work without compensation, but we expect children to labor for thirteen years with little concrete feedback and less reward. So here's how I'd do it differently. Earned 1000 progression points? Get an hour on the Nintendo, in the school game room, or three hours reading/exploration time in the library, or two hours scheduled team sports, or what have you. Remake half the school into a rec center. This isn't necessarily a big change; make the library and sports fields places students actually go by choice, rather than another regimented mandatory-or-forbidden space in which to be ordered about.
5) Kill the clock.
We have to accept the industrial-economy constraint, provisionally, that students have to be contained for eight hours a day. OK. But with lectures-on-demand via video, asynchronous curriculum progression via computer testing, and one-on-one tutoring, it will be actually desirable to deschedule and destructure a lot of school activity. Let kids find their natural rhythm.
6) Adaptive difficulty.
This is already done with things like the computerized SAT--the program feeds easier or harder problems until it finds the natural level a student is challenged but not overwhelmed at. Smarter kids will find the curriculum getting harder, slower kids will find it getting easier, until each finds their own level.
The real point is that you tell a kid, "OK, here's your work block, get it done and you can be FREE for a while." I don't know about you guys, but that would have motivated the shit out of me. Some kids could crank out work in the morning & rest in the afternoon, others could take it easy in the morning and work in the afternoon. Some kids might save karma points up for a week and then take a couple days off. Adaptive difficulty means smart kids don't do a year's work in a month and then sleep the rest of the year, and slow kids aren't crushed.
I'm mostly trying to design a system that isn't a fucking prison farm for children. Education is secondary. I don't think that's a drawback, because it's not like the current system is any good at education.
A note on the currently fashionable problem of bullying: Consider the possibility that children are so horrible because they're thrown together in prison conditions, like rats in an overcrowded cage resorting to cannibalism. Kids don't do much of that shit outside school. Give the shy kids room to be alone, give the social kids room to be social outside a pressure cooker. Give them all a sense that they're doing something they find meaningful.
That's my attempt at 'how to fix schools'. What are my qualifications to advance a critique like this? Bitter former mathematics professor, and vastly more bitter victim of the public school system. HTH, HAND.