Ok so I have the training aspect done...
But how would combat work?
It wouldn't be a straight up fighting or action game. So how would you create a strategic game based around martial arts without outright copying other games.
And these are POSSIBLY 1 on 1 fights (Though I will outright admit... A Turn based strategy game where you train your pupils who fight on a grid would be interesting).
I think it would be about positioning, "Pro-Wrestling" style is the easiest to do an example for, it's big moves are all done if you manage to knock an enemy down close to the sides of the arena. While Boxing's finishing moves is when you knock an enemy back into the wall.
At the same time each martial art comes in two styles (though some have obvious leanings). Boxing is in the big punch strong style and the lightning jab quick style.
Well at the risk of the "outright copying other games" thing, there is something pretty similar to this in flash form, called "My Pet Protector"
You can find that on Kongregate and possibly get some ideas from it.
Although I must ask if you think the combat should be done by the player or if your students should be "programmable" I.E. are you taking control or are they just doing what you taught them to in certain situations?
Also you could have it so that at the start of the game your "master" is only really teaching one style, and as the game progresses you can integrate other styles that you have seen others use in tournaments and such, while giving them your own flavor.
The actual "running of the dojo" thing is another point of possible interest, where you can have your apprentices do chores and such to keep it tidy/upgrade it while getting them stats karate kid style.
Also it can bring up things like "will you focus on training the supa-prodigy or will you give everyone a balanced education" and also have events pop up like "rich guy wants to pay you to accept/focus on his totally inept son, do you sell out or keep true to code (and poverty)?"