It is routine for a teacher to say "show your work". I don't recall ever seeing instructions that said "show your calculations". It wouldn't be wrong. It's a grammatically correct sentence and it makes sense in context. It's just not what people normally say.
Arguably "work" is more general than "calculations". "Work" could mean anything you do to figure out the answer to the problem. "Calculations" would normally be understood to mean arithmetic. If, for example, to solve an algebra problem I say that I expanded x(x+y) to x^2+xy, I wouldn't call that a "calculation", I'd call that an "algebraic manipulation". One could debate exactly what the word "calculation" means, but that's exactly why the teacher would be unlikely to use it in this context. It could be misleading or confusing.