If you are interested in mathematics or in education, I strongly recommend that you read A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form. It provides the most convincing argument I have heard to date about why math can be beautiful and creative on its own, separate from its applications to engineering, physics, and the “real world.” Furthermore, it elegantly describes how we systematically prevent students from seeing math’s beauty and creativity. It’s a nice short read. Here are a few snippets.
Embedded in the following excerpt is a good list of the principles underlying mathematics:
Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity–to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs–you deny them mathematics itself.
A few more harsh, yet valid, criticisms about secondary math education:
By removing the creative process and leaving only the [mathematical] results of that process, you virtually guarantee that no one will have any real engagement with the subject.
In practice, the curriculum is not even so much a sequence of topics, or ideas, as it is a sequence of notations.
And finally, a description of how many smart students react to the math curriculum in its current form:
We are losing so many potentially gifted mathematicians–creative, intelligent people who rightly reject what appears to be a meaningless and sterile subject. They are simply too smart to waste their time on such piffle.