"So the universe is not quite as you thought it was. You'd better rearrange your beliefs, then. Because you certainly can't rearrange the universe." - Isaac Asimov
I have a few assignments in which I trust students when they tell me they did it. If they don’t, then they will struggle with later projects. I explain the rationale, but they are still confused that they don’t have to hand anything in.
STEM fields are related, but are fundamentally very different. Science explores nature as it exists. Technology and engineering control and apply natural phenomena. Math applies and explores patterns.