1. look at any competitor's press releases.
2. if your competitors have investors then they may have already justified the market size. Those documents maybe lying around in whitepapers on their site.
3. search "total addressable market" (or maybe TAM) - this is commonly used in investor docs. I googled ("distance learning" or elearning) "total addressable market" - no idea if its useful.
4. I remember there was an aussie elearning company called "Harvest Road" that listed publicly, you could:
a) look through linkedin and reach out to someone ex there
b) sniff around old documents they would have produced for IPO etc (you may need wayback for that!)
Of course data out of date but might point to references.
5. If you are cash-limited rather than case-strapped:
a) Ask and pay for a question on Mahalo (or similar) - you never know!
b) Hire someone on Odesk to research for the 10 hours you don't have - it might cost $100. As an example - some providers from Philippines have excellent english skills people and are likely to understand the nuances of your mission.
I have err, borrowed from analyst reports, in my field 451, Gartner, Forrestor. But somehow they have appeared without paying for them. Those reports don't don't have a startup-friendly pricetag. You may find by engaging in a forum, linkedin group with people in that fields/segment will get you some pointers.
I'm guessing your are doing all this as part of a CA grant application - just make sure you make the project large enough to cover the application costs!