Andrew Gellman posts a link on his blog to a great talk by Dick De Veaux about teaching Statistics, making the point that unlike math and music, but like literature, doing stats requires life experience.
Like a lot of math/science geeks, I went through a phase of my undergrad where I was caught up in the beauty and elegance of “pure” math. Now, though, I find statistics much more interesting. Not that I read myself to sleep with stats textbooks, and the more esoteric it gets the less interesting I find it, but I do find myself more and more looking at the world using the tools of statistics (and its dark cousin, economics). Pure math, like programming, creates a perfect, orderly universe that can be mechanically understood, but statistics gives us tools to make sense of a messy, anarchic universe without taming it. But in order to use stats, you have to first pay attention to its world and try to understand it. And then stats will show you how wrong you are.