I feel like introductions aren't really a thing anymore. In my English class of 15 students, I've had a decent conversation with almost everyone at some point this semester. Yet, I feel like we aren't close enough to say a basic "hi, how are you?" when passing by each other in the hallways... especially since I haven't learned most of their names. This leads to some panic and sweaty hands on my part when approaching one of them outside of class. Do I say hi and try and engage even though I don't know their names? Or do I walk by and have them think I'm rude and then act like nothing happened when we see each other in class? About a dozen of the questions race through my mind in the matter of seconds when I see someone I "kind of know, but not really."
These little bursts of anxiety really don't make any sense. I just overthink the scenario until it isn't even realistic anymore. They probably don't even notice whether I try to say hi or not, and even if I do it's not going to change their day at all. Even if there is some awkward gesturing such as me going for a hug and them a hi-five, that will blow over quickly. So, what can be done to prevent unnecessary overthinking?
A short answer is: just say hi. The worst thing that could happen is that they don't say hi back. But, you tried to be friendly and perhaps the start of saying hello outside of the classroom will allow an advancement in the relationship: acquaintances to semi acquaintances. And who knows, maybe after a couple times of saying hello, you might make a friend.