alteacher, or alt-teacher, (or even alternative teacher) is a teacher who teaches using somewhat odd, original or indeed "alternative" methods, or even just holds views that could be defined as those things. They characteristically look for subtleties other teachers wouldn't think of. Often enjoy abstract work, making it easy to exploit them by doing rubbish work and claiming it has inner meaning.
"Did you do the art homework?" "Nah, I just drew a spiral and'll say it represents the world, me and my life in one simple gesture. Our teachers a total alteacher"