I honestly loathed homework in high school, but now just from being in college a few weeks or so, I am finding out quickly how important it is to have homework. I've found myself learning more from it then my professors so far, and banning homework in high school will just make you less prepared for doing homework in college(which you will end up spending more time doing then actually attending class btw).
Extending school would probably do no good.
From what I have heard many of the countries who are beating us education wise, I believe, not only have longer school days, but longer school years as well. Some of them just give kids a break in the middle of the day to rest their minds during lunch time and such.
