WHenever i get into a new math class the first thing i hear is thhat i must always show my work. I generally dont like showing my  work so i may be a bit biased but what is wrong with not shwoing your work? I know teachers need proof that you actually did the work but what if you genuinely answered the question on the top of your head. Think about-  we dont use lines and sticks anymore to do addition or subtraction. In fact we dont even have to show work for that. Maybe teachers should start allowing us to algebraic equations in our heads as well so us humans can advance further and become smarter. Maybe one day we can solve a long calculus equation as easily as we can solve 2+2. So why are math teachers holding us back on this?

Because sometimes people make mistakes in their head, and showing the step-by-step process is like proofreading an essay. Sure, anyone can whip out a quality essay, but being careful and checking for errors along the way never hurt anyone.

My Algebra 2/Pre Cal teacher had the best policy to create a compromise. She said we didn't have to show our work, but she would give us "pity points" for each step-by-step process that was correct. You can do it in your head and on your own, but it's a zero if it's incorrect.