[mathking]

To the excellent suggestions here I will add two things. The first is to read. About different things. Fiction, non-fiction, whatever you want. Several posters have pointed out the importance of being able to identify and clearly state the question you are seeking to answer. Reading (and writing) are just as important as algebra skills when you are doing this. I taught for five years in a Paideia Critical Thinking Skills program with inner city middle school kids. Recently I was chatting with a couple of them who are now engineers and they both said that their middle school education, with weekly Socratic seminars, was excellent preparation for identifying and understanding problems, and it taught them how to defend their own ideas and listen to others' ideas with an open mind. At the heart of the seminar each week was reading some article or short literary piece.

The other piece of advice is to put yourself outside your comfort zone. Learning new stuff forces you to go back to the basics. Being able to walk a problem back to initial principles and assumptions is another important skill. The toughest class I have ever taken was music theory. While it was challenging, I learned a lot. Not only about music but about how to approach difficult problems and how to make sure that my understanding was correct.