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Followup - What Is the Value of Algebra?

AlgebraWay back in the early days of this blog, in only the third month of its existence, I wrote an entry, What Is the Value of Algebra?, in response to an op-ed in the Washington Post that suggested doing away with algebra requirements for high school. Now, Andrew Hacker is up to similar antics, writing an op-ed for the N.Y. Times, Is Algebra Necessary? (h/t to Pharyngula).

Here's how he starts out:

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I've found myself moving toward the strong view that we shouldn't.

Later on in the article, he had this to say:

The toll mathematics takes begins early. To our nation's shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I've talked with cite algebra as the major academic reason.

I already expressed my opinion pretty well in my previous blog entry, so I'll copy a part of it here:

...I think that our education should be well rounded. History and English are important, especially history in my opinion, so that people can put current events into their proper perspective, and learn from the past. But algebra is just as important. And it's not like it's asking a lot for people to learn algebra. It's basic, basic stuff. It's not like the requirement is for students to know calculus, or differential equations, or vectors, or imaginary numbers. Algebra is only one small step up from arithmetic. I use it everyday, and to compare it to English, algebra is as fundamental as being able to recognize nouns and verbs. If a high school diploma is supposed to have any merit for saying that a person has a fundamental skill set, and isn't just a piece of paper saying that a student showed up to class for 12 years, I don't think it's too much to ask students to understand algebra (and language, history & science, as well).

To add to that, we live in a representative democracy. Everybody's vote counts equally, and we all get a say in who represents us, and by extension, what public policy will be. How can you expect that system to work if not for a well educated citizenry, and how can you expect to have a well educated citizenry without the foundation of most of mathematics? I mean, how can you even begin to understand claims about scientific issues like global warming or vaccine effectiveness without a basic understanding of math?

Granted, there may be a problem with students having difficulty with math. But students also have difficulty with a lot of things. Just go read this Newsweek article, America the Ignorant, for a sampling of some of the ignorance of our nation. Here are just a few:

  • "21 percent of Americans believe there are real sorcerors, conjurers, and warlocks out there."
  • "Sixty-three percent of young Americans can't find Iraq on a map, despite the ongoing U.S involvement there."
  • "...more than a third of Americans of any age can't identify the continent that's home to the Amazon River, the world's largest."
  • "Only two out of five respondents, however, can correctly identify the executive, legislative, and judicial branches as the three wings of government."

The solution to all of these problems, including algebra, is not to reduce standards. Rather, it should be improving the education system so that students learn what they need to (there are societal problems that also need to be addressed, as discussed in a different op-ed from the N.Y. Times, Class Matters. Why Won't We Admit It?)

Further down, Hacker had an example:

What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It's true that mathematics requires mental exertion. But there's no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis.

That is a truly basic bit of algebra. It's not asking someone to develop the quadratic formula or Phythagorean theorem. It's something that I would hope every high school graduate could do. And even if a few lower caliber students slipped through the system without being able to complete that task, I fully expect that politicians and public intellectuals would be able to do it (or rather, I should say that I'd hope they could do it - my opinion of politicians isn't too high). It's like saying, 'there's no evidence that being able to write a sentence with proper grammar leads to more credible political opinions or social analysis.'

I just don't understand the anti-intellectualism so prevalent in certain sectors of our society right now. Granted, not everybody can be a rocket scientist or a brain surgeon, so we shouldn't set expectations unrealistically high, but we also shouldn't set the bar so low that a high school diploma becomes meaningless. Algebra really is the basis of most 'real' math, and an understanding of it should be expected of all well educated individuals.


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