Chris, Yes, personally experiencing mathematical discovery is the key to learning what math really is, so a place must be made for it in schools. Paul Lockhart's book, _A Mathematician's Lament_, is essential reading on what mathematics education should be. Unfortunately, (as Paul is the first to admit) relatively few teachers below the college level actually are trained to think like a mathematician, so they are not capable of leading a class in an exploratory approach to mathematics. Those who can usually find other careers. It is a difficult problem for society to solve, but still it is part of our jobs as mathematicians to help work towards a public understanding of what mathematics is. George http://georgehart.com/ P.S. Someone who helped me and many of my generation think like a mathematician is Martin Gardner. So here is sculpture construction at Princeton in his honor: http://www.youtube.com/watch?v=PzYzCEgTitA On 11/15/2013 10:24 AM, Cris Moore wrote:
George, I agree with you that people are to quick to make math optional.
But what do you think of Baker's critique of the way the curriculum is structured? He gives the example of teaching kids about removable and unremovable singularities in rational functions --- a lot of terminology-heavy stuff that seems more suited to memorization and multiple-choice standardized tests than actual understanding.
My suggestion would be for some math to be mandatory, but for the curriculum to be designed around getting a sense of how mathematics and mathematical discovery actually works. For instance, I would give them a taste of combinatorics and abstract algebra, where there are interesting and accessible proofs --- the current focus on algebra and calculus is about calculation but hardly ever about proof. ...