Saturday, February 28, 2009

Thoughts on math curriculum

This article is written concerning the national Australian math curriculum, but I very much appreciate the author's perspective on how we think about math education:
What do I want from a national curriculum? I want a dodecahedron in every classroom, and beautiful diagrams to ponder. I want students to know why there are infinitely many prime numbers, and for them to realise no one knows about twin-primes. I want them to know what the golden mean is, and why it is irrational, and why we care. I want pattern and play and beauty. And I want the times tables.

Is teaching any of the above useful? It is exactly as useful as teaching Harry Potter and Shakespeare.

Ok - I actually think some of the most beautiful mathematics happens to also be very useful - in this regard, I don't totally agree with the author (Marty Ross). Understanding the structure of the primes and related ideas gives us many cryptographic tools, for example. Understanding the meaning of irrational or transcendental numbers lets us know when certain things are impossible - we won't waste our time searching for an algorithm to square the circle (using the traditional construction tools, that is). And that just scratches the surface.

But the analogy to popular and influential works - Harry Potter and Shakespeare - is something I think many educators and students don't recognize. It is obvious that the large majority of careers don't rely on a profound understanding of Shakespeare, and yet we feel that an education without such crucial literary components is incomplete. Why do so many people seem to consider the beauty and value of the world knowledge of math to be inferior? Some may argue that math lacks the cultural saturation of great works of art, and I would have to agree. And yet, math is everywhere, and not because we write stories about it, but because it describes the raw logic and flow of the world around us. To borrow a phrase from Robert Osserman, math is the poetry of the universe.