It’s probably true that getting enough sleep does help you think better and your brain probably thinks for you while you are sleeping. Here’s an interesting article about sleep and how your brain is still working while you are dozing off.

Dozens of intriguing studies over the past several years show clearly
that your brain is active—very active—during sleep. (Reference 1-7) It’s busy doing something miraculous, something that we can’t even come close to explaining.

Basically, your brain goes on automatic pilot. Without your being aware of it, something inside your head comes alive and starts mulling over all the things you learned that day. It sorts through them, organizes them, considers them, calculates them, decides what’s important and what’s not.

via smart-kit