>> If schools really wanted to teach it, it would be well within fair use laws for them to show the whole thing.
>
> No, not a chance. Even a few paragraphs would likely get them smashed, especially if they're the most interesting of the speech.
>
Actually we had to memorize a significant portion of the speech for my eighth grade AP English class, in addition to watching the speech, and talking about the context. This was part of a larger section on civil rights coordinated with our History lessons.
I'm not a lawyer, but I'm fairly certain that educational programs are allowed to do whatever they want wrt. copyright as long as they can show educational value and aren't directly profiting off of reproducing the copyrighted work.
http://www.copyright.gov/fls/fl102.html