Hi RockerGurl & welcome.
Well, I can't say what is going on in his mind, but I can suggest a possibility.
If he does like you, he may, by flirting noticeably with other girls in your presence, be trying to get your attention.
If he stares at you, then he has noticed you ~ he may want to make sure, now, that you have noticed him.
Perhaps there might be an opportunity in your shared lesson to talk to him about something ~ and see what happens???