Math, to hear most people talk about it, particularly most students, is boring, irrelevant, difficult, pointless and just a great big waste of time. Maybe they’re right. When’s the last time you divided fractions? Or solved a quadratic equation?
No, they aren’t right. And if you want to know why I don’t think they’re right, just keep reading.
Why teach math?
OK, we need to know some basic arithmetic.
Even in this day and age, we need to know how to make change, tell time, and so on. But, let’s face it, very few adults ever need algebra, or trigonometry, let alone calculus or number theory.
Why teach math?
Well, to hear some people, math is supposed to teach you how to think. I duuno. I think I was thinking before high school….if anything, I did less thinking in high school than before or after. And, while I like to think that I do a little bit of thinking nowadays, outside of work (and some of my diaries here), I don’t use math much, probably no more than you. (At work, I use math quite a bit, I am a statistician).
Why teach math?
Why teach music? Why teach painting? After all, how often in adult life are most people called on to sing or paint?
We ought to teach math for the same reason we ought to teach painting and music. Because appreciating math, and doing math, is part of what makes us human; it’s part of what makes life more than a mere struggle to postpone death. We ought to teach math because math is beautiful, awe-inspiring, and, well, a whole lot of fun!
No, I’m not high on drugs. I really mean it. And if you ask any mathematician about why they do what they do, words like ‘beauty’ will come up.
The real question, then, is why we teach math so freakin’ BADLY! Why do the statements above strike many who do not do math as absurd? After all, I can’t paint or sing, but I think of them as beautiful and worthwhile.
We teach math not just badly in the way other things are taught badly (or well), but in ways that are almost guaranteed not to give the essence of the subject, and to turn people off the subject. For example:
What’s the most basic math? Maybe 1 + 1 = 2. This is a profound and amazing abstraction of the world. What does it mean? Two great mathematicians (Bertrand Russel and Alfred North Whitehead, in Principia Mathematica) spent an entire volume full of very dense math trying to figure out what this meant, and to prove it was true, and then Kurt Godel came along and said they got it wrong! In fact, he proved that they got it wrong.
We teach math as if ‘not getting it’ means you’re stupid. What’s one of the first things that confuses a lot of kids? Well, one thing is negative numbers. But it took the greatest mathematicians thousands of years to really figure out what these were.
And then, in adult conversation, we talk about math as if it is some sort of badge of honor to be bad at it.
No wonder (almost) no one likes the subject!
We ought to teach math as a voyage of discovery on some of the most beautiful seas man has ever sailed; then arithmetic becomes the equivalent of learning how to sail a boat, while math becomes the trip.
Since writing the above, I have begun to explore the works of Alfred Posamentier a math educator who seems to think the way I do (it’s nice to find one! The above was all ‘out of my head’ as, although I have a degree in education, I’ve never taught in a school). I’ve also run into the best math teachers I’ve ever seen, Bob and Ellen Kaplan, who run the Math Circle, in Boston. I will write an article about them soon.