σπουδαζω ελληνικα I believe means the same thing, no?
What's wrong with μαθαίνω Ελληνικά?
On a side note, μαθαίνω as 'learn' can be used as 'teach' or to 'learn to someone'
The site wants ´ελληνική' and says ´ελληνικά' is a typo. It´s not; it´s correct, as your line above demonsrates.