A few weeks ago on NPR's popular afternoon program All Things Considered, Tom Magliozzi, who together with his brother Ray hosts the even more popular NPR program Car Talk, suggested that the teaching of algebra, geometry, and calculus in schools was a waste of time, and that we'd all be better off if pupils were taught more useful things. [You can hear the commentary by clicking here.]
Now, along with millions of other listeners who make Car Talk by far the most popular show on NPR, I am an avid fan of the Magliozzi brothers. If tomorrow morning my 1995 Buick Park Avenue with 75,000 miles on the clock developed a strange BRRR--CLICK--BRRR-CLICK--BRRR-CLICK sound, Tom and Ray, who go by the nom-de-radio Click and Clack, would be the first people I would turn to for help. When it comes to cars, they know their stuff.
But when it comes to mathematics, well, Tom, I've gotta tell you, you are so off base, it's scary. So scary, in fact, that when I heard your comments, I said to myself: "This is a smart guy -- heavens, he was a professor at MIT for many years. How come he thinks teaching mathematics serves no useful purpose?"
It didn't take me long to find out. Thanks to the World Wide Web -- an entirely mathematical invention by the way -- I was able to replay Tom's words again, and it was clear what was going on. The real culprit isn't Tom, it's the way mathematics so often gets taught in schools.
The event that prompted Tom's remarks was a back-to-school night at his son's high school. On the board in the math classroom Tom read the following statement:
Calculus is the set of techniques that allow us to determine the slope at any point on a curve and the area under that curve."
AGGGHHH. If I didn't know any better, that would have made me react the same way as Tom, although I'm not sure that Tom's phrase "Who gives a rat's patootie?" works as well in an English accent as it does in a Car Talk voice.
Having been a mathematician -- not a math teacher I should add -- for thirty years, I can think of dozens of things I might have written on the board to describe calculus.
For example: Calculus is a set of techniques that scientists and engineers use to describe accurately the way things move -- planets, space shuttles, ballistic missiles, electricity, radio waves, stock market prices, blood, the heart, the muscles of the body, and so on.
Or, and this one is designed specially for Tom: calculus is the set of techniques that enable automobile designers and manufacturers to design and build a modern automobile, with all its moving parts.
Or: calculus was the major intellectual discovery of the seventeenth century that made possible the scientific revolution and all of modern science, technology, and medicine.
Or, calculus is an absolutely indispensable tool for designing computers, radios, televisions, telephones, VCR machines, CD players, airplanes, artificial heart valves, CAT scan machines, the GPS positioning system, I could go on for ever.
Or: calculus is the language physicists use to understand the universe and the world we live in.
Or even simply, calculus is one of the greatest intellectual achievement of humankind.
But if you take one of our culture's most impressive and useful inventions, that quite literally changed the world, and reduce it to a trivial statement about finding slopes of curves, as Magliozzi's son's teacher did, then there's no wonder Tom reacted the way he did.
So we shouldn't blame Tom. He's simply the product of the education he received -- although I wonder who he mixed with during all those years on the faculty at MIT. And we shouldn't blame the hapless teacher who started this whole thing. It may well be that he or she is doing their best, given their education. Much of the blame lies in the way universities train future mathematics teachers.
Mathematics only exists because it is so useful. No part of the subject should ever be taught at school level without explaining why is was invented and what some of its uses are. Uses that directly affect everyone in the classroom.
According to Magliozzi, the purpose of education is, and I quote, to "help us to understand the world we live in." That, Tom, is precisely why some of our ancestors developed mathematics. Without mathematics, your weekly show would have to be called Horse Talk and you and your brother would have to be called Whinnie and Neigh -- except that without mathematics there wouldn't be any radio to do it on either, so you'd have to do it by standing in Harvard Square and yelling as loud as you could.
By the way, I still think Car Talk is one of the best programs on radio.
Devlin's Angle is updated at the beginning of each month.