Homeschool, Home-school or Home School?

Just a few short years ago, I never much cared how a person wrote home-school. Actually, I never thought about it that much. But over the past year or so, as you might expect, I have been coming across the words (word?) quite frequently and have seen it written a number of ways and, honestly, it really has been bothering me to see so many incarnations of the same word. Surely one has to be correct.

Today, after a year of irritation, I decided to dig into some dictionaries as see what they had to say. I started with the Oxford English Dictionary. Under its noun/adjective entry for "home" there is a special section for "combinations and special collocations" which specifies its use with participial adjectives in sense '(for use) at home' and lists a number of popular examples (i.e. homebody, home-bred, home economics, homeland, homemaker and home stretch) and it writes the puzzling phrase as "home-school" and its definition for any interested parties as "verb trans. educate (a child, esp. one's own) at home.

I tend to trust the OED but, to be fair, I decided to dig a touch deeper.

Dictionary.com had it listed as one word, no hyphen (i.e. homeschool). At the end of the definition it said "also home-school."

Merrian-Webster on-line, like Dictionary.com, had the word listed as the verb "homeschool."

And then I stopped looking because, well, I got bored. Also, my embedded Firefox spell checker keeps underlining "homeschool" as an improperly spelled word. However, when I left click it for suggestions, the only suggestion that comes up is "home school." So, which dictionary are they using?

As for me, I've used all three, but tend to use "home school" the most. But now I'm starting to think "home-school" might be the most correct but, it seems safe to say, that none of the three versions listed here are patently incorrect.

This all still bothers me though. There should just be one, correct and proper way to write the word, and that's it.