In this particular problem, I simply noted "what I know" on one side, and "what I need" on the other, then, trying mechanically prove my goal from my hypothesis. Being able to "see my bricks" was the key part. On a screen, those bricks while exist, are separated by scrolling distance.
But in general, I never do drawing, but yes, definitely diagrams of some state machines for example. It's simply impossible to hold them in the head.