Funnily enough, this goes away to some as you move along. Say I'm taking an exam and don't know how to do a proof. I pray and think that some equation is important, so I write it down with a little context. If I've done a great job up to that point, my professor will be more likely to think that I hit upon the key idea and give me 3/4 credit. If not, I'm probably more likely to just be marked wrong. You can also lose points for stylistic reasons if your professor is opinionated about them (-1 with "it is clear that" underlined and "don't write this ever again" in red ink :) ). Some professors will fail you if you get too technically correct with logical symbols everywhere instead of writing mathematical English. If you show too many steps you're wasting everyone's time; if you don't show enough or you don't seem confident you might get marked down. Etc