A commenter on my previous post noted somewhat derisively about Gödel, Escher, Bach: “I wouldn’t say it has much to offer as far as understanding math.”
I think the commenter misinterpreted my reason for mentioning this book in my post. It’s not because GEB helps a reader understand math, but it inspires a love of all things mathematical and is a model for the value of wonder that drives so many mathematicians.
But the more I think about it, the more I realize that I do think that this inspiration belongs in the category of “helping to understand math.”
It’s true: if you don’t have a fundamental understanding of the structure of our number system that we call number sense, the patterns that recur throughout this system and a good grasp of logic then you’ll quickly get lost in GEB. But as an educator, I have come to believe that the love of math is one powerful precursor to understanding math.
It provides the confidence to take risks and make mistakes–the coin of the realm for professional mathematicians.
It flushes the face with blood and the brain with endorphins when a lush, generative problem arrives–the rush of trying and experimenting, the gambler’s craze.
When you’re seven years old and you don’t know what to do but you think you might have the answer, you’re trying different things and ready to stake your life (or your reputation among your peers) on your next best guess, you can’t hold back, you have to share your ideas with your peers and teachers, you have to try adding this to that and subtracting the other thing…when you are still thinking about it when you get on the school bus to go home and you tell your family about it, maybe even your dog…you are practicing for a life of building math power.
Love of math is not automaticity. It’s not conceptual understanding. But it’s the building block for those. If understanding spreads like a bacterium, love of math and fearlessness for trying are the agar in the Petri dish.
I believe math power snowballs, one way or the other. When you’ve got it, that lust for more leads to an increasing sense of mastery over the number system. When you don’t, each successive stage from algebra to trigonometry to calculus seems only increasingly foreign and inaccessible.
Finally, when I read that comment I could not help but think of gender bias and elementary math instruction. I don’t have any research to cite here (I’m hoping my new readers can help crowd-source or channel Carol Dweck), but I know from my experience, my mentors and Larry Summers’ public comments that girls are typically not treated as mathematically capable.
And the snow gathers as time goes by and children grow into adults. Not a single text inspiring the love of math from my last post and comments was written by a woman (they were written by John, Peter, Douglas, David, Roger, Leonard, Tobias, George, Rafael, Scott, Martin and another John, if you were wondering).
Imagine what would happen if every little girl entering kindergarten were welcomed with, “You’re just going to continue to grow to love math and the mysteries that will unfold before you!”
Now tell me–can the love of math lead to math understanding?