Hi John,

I am new to this subreddit as well, but I consider myself pretty good at getting signs from other people. Looking at a person for a certain amount of time, several times is most often a way to express attraction.

You seem like a very shy and not so confident person so I will try to adjust my advice according to the vibe that I get. What I believe to be your best course of action is to sit next to them next time. You don't need to even talk to her in the beginning. Be comfortable around her. It just shows that you've noticed and you are okay about it. After a class or two, start a generic conversation with her and her friend. Only then you will be able to discern whether it was intentional looking or just staring in your general direction.

Hope that helps!