I think that English 1, 2, and a half semester of American Literature is needed.
Algebra 1 and 2 definitely. As for Trig, though, there's no need unless you go into mathematics. Just the other day I was asking a teacher the practical purpose of providing proof of identities. Is there something like algebra in business for trig? She said there really was no practical use. That kind of stuff pisses me off. I have no taste or desire for math (although, I'm rather good at it.) Don't feed me this stuff when I could be getting other classes done.
Government and history should always be mandatory--these classes create educated and informed citizens.
Physical fitness stays; we're too damn fat.
Then you have your vocational classes along with the fine arts.
I think a small
test should be taken every year for students to see what they are good at. It's ultimately up to them, though.
If you're really wanting to reform education, scrap No Child Left Behind. As the son of two educators, I can attest to their despise of it: federal regulations without federal funding. Plus, kids who just hinder the system are forced to be there. If they're making a mess and don't want to be there, kick em.
Another thing I'd do is have mix-schedules. Not a pure block and not a pure standard. It works in many schools.
Budget wise, four day weeks, longer days. Scrap paper standardized testing. Making it digital. We use something called NWEA, and teachers love it.
After that, I've got nothing else. If I think of something, I'll put it down.