I write pseudocode on paper before I implement anything, and it has helped me tremendously. In fact, I think programming on paper encourages nonlinear programming. You can DRAW! Use lines and arrows to code blocks. Sure, it might get messy, but doing it on paper gives you a better idea of how your algorithm should work. You make less mistakes because making a mistake is more costly (you have to erase/mark out the mistake), so you tend to be more careful.

When I got into professional programming compilers were a round trip to the machine room away. So one thing we did to save time was to 'desk check' our code. This usually meant a simple simulation using a piece of paper to hold the variables, crossing them out when they were overwritten. At some point I could do it for limited pieces of code by just simulating the code in my head.

Simulating code in your head goes a long way towards writing solid code, you'll be able to hold a model of the data and your code together and see whether it will work or not and fix bugs before your first compile.