Check out this post from Joy about her recent public school job, job search. Despite having 2 years of experience, she's having a hard time because schools seem to want to hire someone with a teaching or English degree or something similar.
My thoughts? Good for you Korea! It's about time you stopped giving jobs to people with a BA in computer science (or something of the sort) and a pulse. Not that I'm qualified as a "real teacher" but at least my degrees are in the social sciences, I had to write papers and take English classes.