I don't check out the "Better Explained" website often enough!... they have a wonderful series of posts on mathematical thinking or intuition -- in fact, I think this series might make a GREAT pre-read BEFORE one tackles Keith Devlin's "Introduction To Mathematical Thinking" which I was extolling just a couple days back. There are currently 8 posts in the series, beginning here (there are links to all posts in the series at the end of each post):
The 7th post ("Finding Unity In the Math Wars") is actually a bit tangential, focusing on Khan Academy and the controversy surrounding it. However, this post is one of the best discussions I've seen on the whole Khan debate, and I would start with it, since it is such a hot topic in education today, and then go back and read the other posts. A fine series!