If you have an hour, it is worth spending it watching this lecture by George Pólya. Pólya was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University"
He makes some interesting points about teaching and learning. He said that teaching (and learning) is a process of helping students "discover things by themselves" and that all great scientific discoveries were conceived by "First guessing, then proving." His lecture takes a class of UCLA students through the "guess, discover, prove" cycle to solve a problem.
I like this for many reasons, but the one I wanted to focus on was the process of guessing, since this is often the hardest part of problem defintion and problem solution. The more technically specialized the person, the harder it is to get them to guess. Yet guessing is how the discovery process starts.
Watch Professor Pólya walk these students through the thought process to prove his point. Everything he describes fits perfectly with our observations of successful technology development teams - where guessing is the basis for rapid discovery.