Why would a guy make prolonged eye contact across a college classroom, but not smile?

Mistywrites
This guy in my college algebra class seems quiet and shy, but I am unsure. We have only been in this particular class together for two weeks, but I keep catching him looking at me for longer periods of time each class. We sit on completely opposite corners of the room, diagonally, from each other; he at the front left corner, and I in the back, right corner. Our professor favors teaching at the board on my side of the classroom, to the right, but towards the front, away from me. The weird thing about this is that he always, without fail, faces his entire body towards the side of room where I am. Even before class has started and when she is teaching from the board in front of him, his body remains angled mainly towards my side. He is always in class early, and whenever I enter the room he is turned around completely backwards in his seat, facing the door where I enter and he watches me come in and then rotates slightly to talk to a few people behind him quietly with his body towards my table. Whenever class is over, he packs slowly if I do, then when he sees me walk towards the door, he walks out too, usually right in front of me, then three out of the four classes we have had, he holds the door open for a few people, then continues holding the door until I come, even if it takes me a while to get there, but never looks at me when he does. The last class we had, a few nights ago, he watched me enter the room, then actually leaned around the few people blocking our view of each other and locked eyes with mine for an uninterrupted 8 to 10 seconds, then turned around like nothing happened. He repeated this long eye contact with me a few more times during the class. Is this guy painfully shy, or what is with all the staring and other unusual behavior? I always meet his gaze, but if he's interested, why hasn't he spoken to me or smiled yet?
Why would a guy make prolonged eye contact across a college classroom, but not smile?
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