A class with a few students can be called "a small class" ? And a class with many students "a big/large class" ?
(Not a teacher)
To my ear, "a small class" and "a big class" fit best, and are what I use/hear normally. "A large class" would be fine too.
I don't really understand the need for 'small-size'. What else would the 'small' be referring to apart from the size?
I agree. One year we were lucky and there were only 17 students in my daughter's class. The teacher had a small class. This year, there are 27. It's a large class. No need for "size."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.