A New Formula ?

In the Metro section of yesterday’s Washington Post, there was an article, by Michael Alison Chandler, on “Algebra for All”.   The article discussed some of the approaches that are being tries to make math more accessible to a wider population of students.  As someone who has at one time or another taught math courses and tutored math students, I was naturally interested.  One objective of some of these efforts is to dispel the idea that only a few people can be good at math:

To counter the notion that mathematics ability is inscribed in DNA, school officials and corporate executives are waging a public relations campaign for the hearts and minds of the average math student. Their goal is to immerse more middle school students in algebra and toughen high school math requirements so graduates can compete for increasingly technical jobs. Their message: Advanced math is not only for rocket scientists.

Some of the tactics involve trying to make math more relevant or cool:  for example, Raytheon, the defense contractor, has sponsored appearances by pro athletes at schools to talk about the role of math in sports.

Celebrities also are trying to bring glamour to the quadratic formula. Danica McKellar, who played Winnie Cooper in the television series “The Wonder Years,” proved a mathematical theorem in college and has written two books, including “Math Doesn’t Suck,” to introduce math concepts to teenage girls through examples about cliques and shopping

I hope these efforts succeed, although I think that some of them are misdirected.  It seems to me that there are, broadly speaking, two obstacles to be overcome: cultural apathy toward math (and to some extent science), and the reality that learning math is hard work.

Although the use of mathematics is pervasive in the various tools and toys of our technological culture, the message the culture sends about the value of math is mixed at best:

To be sure, math apathy remains pervasive. “You don’t need math,” many students say. “I was never good at math, either,” adults reply.

I’ve never taken a survey, but I suspect that there are not many high-level people in business, politics, or the legal profession (just as examples) who would say, dismissively, “Oh, I never could understand any of that Shakespeare stuff”, or “Who needs Michelangelo, anyway?”.   At least, I don’t think they would express those sentiments in public, lest they be thought of as uncultured clods.  Culturally, though, being ignorant of math is perfectly acceptable.

I also suspect that part of the problem is related to some of the attempts to make math “fun”.  Now, I always enjoyed math and found it interesting, but I’m not sure I ever thought of it as fun.  (Ms. Chandler, the author of the Post article, has a post on her blog on this question.)   Learning math is work.  For what it’s worth, my friends that are really good in math — at the level that most people would call math whizzes — all say that it’s enjoyable but it takes work.

I think that the emerging understanding of our mental capabilities shows  there’s a good reason for this that is rooted in evolutionary biology.  (Much of this is discussed in Steven Pinker’s book How the Mind Works.)  Our brains are very good at solving some amazingly complicated problems: recognizing faces, understanding natural languages, and throwing a 90+ mph fastball to hit a catcher’s mitt.  But we can be bamboozled by simple problems in algebra, or probability.  I think that’s because learning to solve those problems is essentially learning to think in a different, more consciously-directed way.  It’s hard work, and it takes practice.  To put it another way, essentially every neurologically normal person learns to talk, walk, and recognize other people, and does it without requiring formal instruction.  On the other hand, I’m not aware of anyone who has spontaneously learned to solve differential equations.

In any case, it’s a fascinating area.  Just to end on a light-hearted note, you might be amused by a YouTube video of Tom Lehrer‘s song, “The New Math”, written about a previous “revolution” in math teaching.  (The audio is Lehrer’s original; the video part was added later by someone else.)