I never really understood what showing your work meant in my schooling before college. I'd solve the problem through whatever I had memorized and would occasionally jot down the more complex parts like long division or large multiplications, at least until I was allowed to use a calculator. In high school we started getting to more complex things like algebra and inequalities and I was able to power through with intuition and a solid proficiency with my TI-83 and some Basic.

I don't know exactly what my teachers were doing but it all came to a screeching halt in college when I encountered severe gaps in my knowledge that made Calculus my hardest class. I had missed some very important lessons from earlier on that were huge hangups. It's hard to differentiate an equation if you aren't solid on how to factor the variables.