There was an interesting article in the New York Times this summer called “Is Algebra Necessary?“. The author is Andrew Hacker, an emeritus political science professor of political science at CUNY, who has co-authored a book entitled Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It.A provocative quote from the article is the following:
“Making mathematics mandatory prevents us from discovering and developing young talent. In the interests of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.”
One of the author’s points was that algebra is not used in day-to-day life as much as some other quantitative knowledge, like Statistical Science. He suggests, for example, that a useful topic to cover would be how the Consumer Price Index (CPI) is created and computed. Since I am a Professor of Statistics, people might think I would be all for this change of focus. I do kind of like the idea of educating future citizens about things like the CPI – it is after all based on a probability sampling— which is one of my main research areas. But I have some discomfort with the notion that we should only teach things that are applicable to daily life skills. Should we abandon Shakespeare?
I was delighted to find that Caroline Brettell thought the article was an interesting read too. In fact, she used it as a launching point for a discussion in the first ever SMU Interdisciplinary Institute luncheon discussion held on October 24. I attended the Interdisciplinary Institute luncheon discussion, along with several others, most of whom had an interest in math or math education. My reading of our luncheon discussion was that no participants completely agreed with the thesis of the article. Maybe that was expected because it was a self-selected group (NOT a probability sample, so not conclusions can be drawn about the university community!) Two ideas that surfaced were these:
(1) The problem is not algebra but the teaching of algebra. If only we could train teachers better, every child would be able to learn algebra and then it wouldn’t be a problem.
I am not so sure about this one. I have a child with learning difficulties and I tried every way possible to teach her mathematics (never mind algebra!) and there seemed to be something different about her brain that prevented the type of logic needed to make it click. So while I’m sure that better teaching would make algebra accessible to MORE people, I don’t think it would make it accessible to everyone.
(2) The level of education being discussed matters.
I think we were in general agreement that it seems like a bad idea to eliminate algebra for college educated people. If the criterion were that knowledge must be directly applicable, wouldn’t we be a trade school? But I feel a little conflicted about K-12. Maybe there are talented and non-college bound people who are discouraged by having to learn the abstractness of algebra but who could benefit from a course in “citizen’s data analysis”. But frankly, it is hard for me to see how to talk about things like the CPI, for example, without the language of algebra—just as a way of representing ideas. There is a famous introductory statistics text by some faculty at Berkeley (Statistics by Freedman, Pisani, and Purves) who attempted to write a book without formulas (we use it here in STAT 1301). Here is its definition of mean: “The average of a list of numbers equals their sum, divided by how many there are.” You should see their definition of standard deviation! Their book is still in print (since 1978), and we use it here in STAT 1301. However, there are few other texts that take this approach, and this may be because of its awkwardness, and maybe it really doesn’t help make things accessible.
One final thought that bothers me about eliminating the teaching of algebra for anyone is this. I think there is value in educating the general public about the existence of mathematical tools, and how they are used by scientists and social scientists, even if they themselves aren’t able to use them to solve problems. These tools start with algebra. I feel disturbed about the “my opinion is as good as your opinion” attitude that some people (and politicians) have about scientific questions like whether there are man-made contributions to climate change. If people are not even educated about the existence of mathematical modeling, it may be even more difficult to explain the nature of the scientific evidence. Maybe we need a math appreciation curriculum – modeled on the arts!