August 11, 2006

Who hates algebra?

I started this entry Feb. 19, as I was packing stuff to head home from Atlanta, but it got stuck in "have more urgent things to do" land. But now, to comment on Richard Cohen's I hate math and am proud of it column, What is the value of algebra? Blog responses have included PZ Myers' pointed response. Essentially, Cohen refers to an L.A. Times story about those who drop out after failing algebra and says, "You will never need to know algebra. I have never once used it and never once even rued that I could not use it." I don't need to point out that maybe Cohen's failure to understand the value of algebra is rooted in his failure to understand algebra, or that there are gazillions (a technical term) of real-life situations which require at least a minimal understanding of abstract math: an investment's return, a lawsuit's settlement value, a country's life expectancy at birth, or the macroeconomic consequences of tax cuts. For dozens of situations, because large segments of the population don't understand algebra, those who do have to invent situation-specific explanations: "Pay off the highest-rate credit cards first." That's obvious to anyone who remembers algebra, but it needs to be taught explicitly as practical advice to those who don't. Those who don't, and who don't follow that advice, enrich credit-card companies unnecessarily. (Why is left as an exercise for the reader.)

Behind Cohen's bluster is a more serious question. What is the balance between raising graduation requirements and encouraging graduation? I have no doubts that algebra is a useful, good, noble, and beautiful subject: I was in Atlanta the weekend of Cohen's column because of a mathematical population model I can use to answer an important question about the history of American schooling. Understanding that model requires calculus. Yet the L.A. Times reporter is correct. Some percentage of students will drop out of school if they must pass algebra to graduate. Both algebra and graduation are in the best interests of students, and the two goals are in conflict.

What we face is essentially a question about raising expectations for the next generation when the skill of teachers is crucial to learning a subject. I'm not talking about high-school math teachers (though they're in short supply) but elementary-school teachers, many of whom have the same weaknesses in and fears of math as the rest of the adult population, including Richard Cohen. Unfortunately, young children are all too vulnerable to negative comments about math. We only discovered at the end of her first grade that my daughter's long-term substitute (long story about that) hated math and made clear that hatred to her charges. This was only one of many problems with this teacher, but it was the one that stuck with Kathryn, who decided firmly that she hated math. No wonder! The only reason why my wife and I agreed to have Kathryn in an advanced class in third grade was the promise that the teacher would work on Kathryn's attitude, which did improve. (She's currently in geometry in 9th grade, with no problems.)

For the die-hard anti-algebra crowd, here's one example of where algebra has a direct consequence for teaching arithmetic: Were you ever taught that multiplication is akin to stretching out a rubber band (to represent one of the numbers), and that one representation of division was the shrinking of the band? In many ways, that's a superior representation compared to the typical representation of multiplication as repeated addition: it shows division as a natural inverse of multiplication, and it can handle fractions easily. I have no idea whether this has ever been used (or what the comparative effectiveness would be), but I know where I got the idea: operations on the complex number plane in (you got it) algebra.

Or for teachers: isn't algebra helpful in understanding test scores and accountability statistics?

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Posted in Education policy on August 11, 2006 4:40 PM |