Who needs advanced math?

I know, I know…you probably think I got the title of this post from Trophy Wives Don’t Need Advanced Physics, the famous book written by my colleague, Boris Korsunsky. But actually I got it from a column by Jane Karr in the New York Times.

Nevertheless, there is a definite connection, albeit an unintended one, as you’ll see.

Karr’s column comes from an interview with Andrew Hacker, political science professor at CUNY. Hacker teaches what might be a discrete math course (hard to tell) and is the author of a soon-to-be-published book called The Math Myth and Other STEM Delusions. I have it on reserve from the library, but I won’t review it until after I’ve actually read it (very restrained of me, isn’t it?). Hacker’s argument — which he has made before — is that most people should not take algebra, geometry, and calculus, because they don’t need the skills taught in those courses:

The number of people who use either in their jobs is tiny, at most 5 percent.

That may well be true. But it’s not really the point. There are three big reasons to take those courses in high school: they keep doors open (since teenagers don’t really know what they’re going to be doing later in life), they provide important skills in quantitative reasoning (which is exactly what Hacker currently teaches), and, if taught right, they further the ultimate goal of teaching math (see quote from James Tanton in the box below). Yes, of course other topics such as those in discrete math may well be more useful to most while at the same time providing those quantitative reasoning skills and furthering the goal of teaching math. So I really need to read Hacker’s forthcoming book. Even without that, however, I feel quite confident that he and Korsunsky aren’t at all on the same page.

A view similar to Hacker’s is expressed in a recent article in The Atlantic, “The Man Who Tried to Kill Math in America,” by A.K. Whitney;

Kilpatrick told his adoring crowds that “we have in the past taught algebra and geometry to too many, not too few.” … Kilpatrick believed that anything beyond arithmetic was useless to most of the population. He even worried that the instruction of complex math was harmful to everyday living.

William H. Kilpatrick is the subject of Whitney’s article. His views wouldn’t matter…except that he had a great deal of influence on education in the early 20th Century.

James Tanton: An Effective Approach to MathematicsAll of this is somewhat reminiscent of the Math Wars, except that that conflict is more usually about pedagogy than content. For a salutary up-to-date view on the Math Wars, we turn to James Tanton, who is always worth paying attention to. His description of his philosophy, quoted in the box on the right, is spot on — and far more to-the-point than any controversies about whether everyone should learn algebra. Anton is describing the important stuff, and we should take it all to heart.

In the context of the modern Math Wars, here are a few disconnected excerpts from his recent newsletter (just enough, I hope, to make you want to read the entire newsletter):

My fear is that over the past century we have a developed a society generally afraid of mathematics (with accompanied societal pride to publically not like mathematics). Consequently, parental attention to education is focused on K-7 mathematics. There is too much fear to comment on, or even look at, the state of mathematics education in grades 8 – 12…. The phrase “understanding trumps memorization” actually comes from my work in high-school mathematics, when discussing polynomial division and the like. At that level, I really do feel that understanding the mathematics of polynomials is far more valuable and productive than memorizing the mechanics of their algebra.

I sincerely worry about the lack of support of teachers caught in the middle of these math wars experience. They are parents and people too. And when a change in the curriculum comes along, they may well need help and support in making sense of it. The trouble is that they are often put in the spotlight right off the bat and their work, as they try to figure things out, is held up as exemplars of inanity and badness. I hope we can always be understanding and kind.

Is memorizing the quadratic formula the right thing to do too? Is memorizing the rules of trigonometry vital too? The proposition numbers of Euclid’s geometry theorems? All the log rules? Again, are we talking only computation and arithmetic facts?

As a professional mathematician I’ve never memorized the quadratic formula. I can derive it if you want me to. But in solving a quadratic, using the formula is usually an unenlightening way to work through the challenge: playing with my understanding of symmetry often leads to new insights and advances in thinking. The fact that I can recite the sine of 45 degrees is only because I’ve had to work with the value of this quantity multiple times, and now it is in my just my head. I will never memorize the log rules as they all just follow logically from the basic definition of logs. Once I’ve got that understanding, there is nothing for me to store in my head.


Categories: Life, Teaching & Learning