09 September 2012

Some Thoughts on Other Ways to Teach Math

I once had a math teacher who said she wished she had time to revise the math curriculum to teach it as an art. She never did have the time - but she managed to point out items of aesthetic interest whenever they popped up in the regular curriculum. Those of us in the class who considered ourselves sworn enemies of math appreciated this.

Betty Smith, who grew up to be a writer, had the idea to assign each number a personality, and thereafter looked at each equation as a story about a relationship.

As a history nut, I always wished we could learn math as history; that is, in chronological order. We learnt, say, the Pythagorean Theorum without knowing a thing about Pythagoras or how he developed it, and I found the lack of context frustrating. The story of the unfolding of math is a fascinating one. Fractions become ten times more interesting to the aspiring historian when you learn that the ancient Egyptians regarded solving fraction problems as a form of magic.

In high school, we heard about some mathematician - probably Buckminster Fuller - who characterized Euclidean geometry as suitable for stationary things but unsuited to human beings, who are constantly changing, and developed in its place a geometry based not on lines but on rays, which are in motion. At the time I was madly in love with philosophy, and took this idea and ran with it: Euclid's geometry was physical; this alternative geometry was humanistic; I spent one delightful bus ride trying to work out a "monotheistic geometry", which was probably the first and last time I ever thought about math voluntarily.

To teach math as an art, a prose, a history, or a philosophy, would be unfair to those who actually like math, and think mathematically. But I'm surprised I haven't heard of anyone experimenting with offering history of math, or math for those who wish everything were humanities instead, as a parallel course - covering the same material, but presenting it differently - in one of those monster high schools where there are six classrooms all studying the same math simultaneously. By then everyone has had a taste of normal math study -- and most have decided what they think of spending the next four years experiencing more of it.

I broached this idea to a math-teaching friend once. "You mean you would test them on the life of Pythagoras?" she asked, aghast. No, no -- the point would still be learning how to wield the theorem: how to think logically and use math. Only the presentation would differ.

Charlotte Mason omits certain advanced math from the curriculum altogether, save as an elective, on the theory that none but a mathematician will ever need it.

Other ideas: mash math together with physics; teach trig using Ayil Meshulash; work into the math curriculum some of the mathematical portions of Gemara; coordinate with equation-balancing in chemistry class instead of letting students puzzle out why what works in one field does not work in another.


  1. In college we learned English and History hand in hand... loved it. I agree, I think math would benefit from a similar set up.

    In other news... your link is up on the Portland Bloggers Master List! Thanks for adding your name and I hope you'll follow along with the blog and join us at future meet-ups!

    1. Thanks very much!
      In middle school I also learnt "Humanities" as a single multi-faceted subject, which I thought - still think - wonderfully sensible.