Monday, February 20, 2006

What Is The Value of Algebra?

This article, with the same title, has caused quite a stir on an education emaillist of which I'm a member. I mean, just who does this guy think he is, denigrating algebra so?

I'm inclined to take a less emotional, more logical look at the article and conclude the author's an idiot.

He makes plenty of mistakes in his article. "I hated algebra, so you can, too." "I barely got through algebra when I was in school, so it must be a worthless subject." "I don't need algebra, so you won't either." And my favorite, "The best algebra student in class couldn't find the Sahara Desert on a map."

Yep, those arguments pretty much prove the lack of value of knowing algebra.

The knee-jerk reaction to an article like this is to start finding all the ways algebra is useful in the world--cell-phone calling plans are the current rage for such illumination. This, however, is the wrong tack to take. While practical application has a value of its own, so does knowledge for its own sake as an opener of the mind. A well-rounded, liberally-educated person needs to be able to do more than just write, more than just calculate, more than just know geography. A well-rounded person needs to know all of the above. And can we not accomplish that minimum after 13 years of school (14, if Reiner's pre-school initiatives passes)?

Mr. Cohen, in his disgust for an entire academic field, wants to close doors for students before those students even get to those doors. How many times must we hear--by the same people who don't think students should be taught algebra--about how all our low-skill jobs are being sent overseas? Or how many times do those who denigrate algebra refer to it as "college track" or "higher" math, notwithstanding the fact that it's taught to 13-year-olds all over the world? The motives of people who do this remind me of the motives of the Planned Parenthood crowd--it's not that we want to give you options (for an abortion, or not to take algebra), what we really want is for you to do it our way (have an abortion, or not take algebra).

I also don't accept the false dichotomy of knowing math on the one hand, and being able to do anything but math on the other. Knowledge of math and knowledge of ____ (fill in the blank with your favorite topic) are not mutually exclusive. I'm glad Mr. Cohen has found a way to support himself despite his lack of math knowledge. However, I assert he has succeeded in spite of his lack of math knowledge, not because of it.

I don't know if Mr. Cohen has a college degree or not. If he does, and he never took a math class above high school geometry, then I'm disappointed. A college degree should be an indication of a well-rounded education, and here in California the minimum math required to get into a 4-year state school is Algebra 2. Can't pass that course? You shouldn't have a college degree. I've said that here before.

If you want to dance, go to Juilliard. If you want to be an artist, go to the Academy of Arts in San Francisco. If you want to get a college degree, you should have a well-rounded education. In fact, the liberal arts originally included math courses, but what did those Renaissance people know, anyway? I assert that high school Algebra II is not sufficient for a college graduate. But that's just an opinion.

Want to be a reporter but don't know math (and how dangerous would that be, anyway?), start in the mailroom and work your way up through the ranks.

I addressed the algebra graduation requirement in this post. The following comment from that post is, I think, the best rebuttal to Mr. Cohen's rant:

Finally, I should hope that we are aiming a little higher in our school systems than teaching students how to survive.



Robert said...

The thing is, Mr. Cohen's thesis is actually correct: A person does not NEED to know algebra. One can design an entire life around avoiding algebra, and succeed at doing so. It's easy -- simply tell yourself that any career or life activity that involves algebra is off limits to you. Tell yourself that you can never become a doctor or nurse, engineer, banker, or scientist; nor will you ever be able to help your kids with their homework in case THEY want to become one of these things and take algebra.

In that sense, nobody NEEDS to know literature, nobody NEEDS to know science, nobody NEEDS to know civics, etc. etc. etc. But does this serve the best interests of students? Well, you know what I think, because that's my comment quoted at the end of Darren's article. :)

Robert said...

By the way, I wrote a pretty lengthy article about this over at my place:

Nick Lopez said...

I'm going to have to agree with Robert here--it is possible (and, I'm sure, relatively easy to do) to have a life that involves zero algebraic issues. It is not the ideal life(nor is it anywhere near the ideal) but it is still possible.

That said, I am baffled as to why anyone would want to go about living without that knowledge. If, as Robert said, you make a choice not to become a doctor, nurse, engineer, etc., why on Earth would you even consider it?

Anonymous said...

I read Richard Cohen's article on the non-essential nature of high school algebra with a sense of dismay, but also recognition. Dismay, because he seemed to lack any appreciation or understanding for why so many have found value in algebra and other endeavors involving abstract thought. But also recognition that in fact many people do seem to manage just fine without any mathematical skills whatsoever. For those of us who value, enjoyed, and continue to use algebra in our professional lives (I'm an engineer, so no need to convince me) algebra class was a wonderful refuge. The only downside was having to listen to the teacher try, for the umteeth time, to explain the basics to those folks who just don't get it.

My own mother was one of those folks who somehow just didn't get it. Last year I was describing to her my own efforts to coach my son through high school calculus. She asked me if I really use this stuff on a day-to-day basis. My answer was that in fact I don't use it every day, but that didn't make it inessential. The foundations of my profession can't be understood without algebra and calculus, and you can't read the professional literature, or make even trivial extensions to basic theory, without a good mathematical grounding. Plus it's interesting, but that's where the nonbelievers will never go.

What I can't help wonder is whether it's worth the effort to force all those unwilling students into algebra. I suspect that many of them aren't bluffing when they way they just don't get it. In some cases I think they are experiencing the terror of being asked, for the first time, to actually think for themselves. But in other cases I suspect that they really can't understand the material, and no amount of explaining will help. This is a case where, I also suspect, you run up against the limits of what teaching can do. Algebra, perhaps more than most other high school subject, ultimately depends on the "aha" phenonomen, where a light bulb goes on in the student's head and they really get what it is you've been trying to explain. Without that "aha" they really are left in the dark, and no amount of explaining can light the non-existent bulb in their heads. Robert Heinlein suggested not to "try to teach a pig to sing. It wastes your time and annoys the pig." My feeling, elitest though it may be, is that everyone would be better off if the kids who don't want to be in algebra aren't there."

I think this is the point Richard Cohen was trying to make. We could have done without his clumsy aspersions on the entire field of mathematics, but on the other hand we can't really expect much else from the pigs. What I haven't seen, in all this blog or the others, is a good explantion why those kids who don't and can't get algebra need to kept in high school.

Darren said...

I'll save the question of whether or not those kids should still be in high school for the people to decide through their elected legislature.

What I don't accept, Anonymous, is that so many kids *can't* do algebra. They do it in other countries, and I don't accept that our bell curve has a mean far to the left of those in the developed countries of Asia and Europe.

Why don't our kids perform? We all know the answer, it's just not popular to keep pointing it out.

1. Poor elementary instruction
2. A culture in which it's considered ok not to know much math--but do you ever hear anyone brag about not being able to read?
3. A society that doesn't value hard work in education anymore
4. A refusal by so many teachers to "teach to the standards" because those teachers think they know what's best for their students

Easy to identify, hard to solve.

Terry said...

I call myself Terry. Sorry that I was identified as Anonymous for that last post.

I'll certainly accept that with better elementary instruction, cultural support for mathematical ability, societal value for hard work by students, and acceptance by teachers of the need for standards in education, more students will succeed in algebra than do otherwise. This has all been proven by private schools may times, and even by some public schools. At academically oriented schools the peer pressure works in favor of high achievement, and parents who want their kids to succeed in school, including algebra class, don't need to do much beyond getting their kids into the right school and providing a supportive atmosphere at home. Outside of private schools you mostly have to take what the government is offering. It may or may not be clear to Darren what needs to be done to promote widespread adoption of his prescriptions, but I have no idea how to make it happen. I just know that my kids are going to go to schools where all his points are second nature.

But that doesn't really answer Richard Cohen's question ("What is the value of algebra?"), or the many rejoinders to his piece. The particular case of Gabriela cries out for intervention by school adminstration. How can anyone try, and fail, to pass a required class even twice without special action being taken, much less a half dozen times? And if it was taken, why wasn't the special action effective? Not knowing the details of her case, I can only assume that she, and perhaps Richard, do represent cases of people who "don't and can't" benefit from algebra class.

I'm fine with requiring everyone to show a basic proficiency with arithmetic. Pretty much everyone has to handle money, and you can't do that competently without arithmetic, and society benefits when people are generally competent in handling their money. Richard never said arithmetic wasn't necessary, so much of the venom directed his way (by bloggers with examples of the value of arithmetic) seems off the mark. I just wish someone could make an argument in favor of widespread education in math that goes beyond "it's required for college" or "it's practical", the latter being true for some but manifestly untrue for others.

Darren said...

I could argue that the societal consequences of innumeracy are exactly those that John Allen Paulos posited in his book, Innumeracy :-)

But why do you reserve this "show me why it's necessary" requirement only for math? Why do we need to learn science, history, literature, or just about anything else we learn in school?

Yes, Gabriella's case cries out for school and/or district intervention, and if she didn't get that, *that* should be her grievance. However, she's still not qualified to receive a diploma under the rules. What would be the point of giving her a diploma when she can't do 8th grade work?

wshaw said...

Darren is a perfect example of an idiot calling someone else an idiot. Obviously he is a Liberal. I say this because his attitude seems to be “If you don’t agree with me you are an idiot.” It would be my guess that Darren is a college or university ( probably algebra) at one of the more liberal schools.

With Darrens logic, a person no matter what a genius they are in their field if they should not be allowed to get a degree. There are many fields of study that should require algebra. I also think there are many fields of study that should not. I love algebra and it comes easy to me, but to some people it does not. This fact should not make these people second class citizens and restrict them from getting a degree in a field of study where algebra will not be used in their occupation.

I currently know a girl that is studying psychology and has a 4.0 in her field of study. But because she can not seem to “get it” in algebra despite her great effort will not get
her degree. In my opinion this is a loss to society.

Darren said...

wshaw, if you're going to call me an idiot, please do so with some coherence so I can figure out what the hell you're talking about. You can't even communicate clearly in text.

I'm not a liberal--please note the title of the blog. And I'm a high school math teacher, not a professor.

And you're right, a college degree should indicate some certain level of well-roundedness--what used to be called a liberal education. Algebra 2 is a minimum for that, in my opinion. Call me names if you don't like that, but that's how I see it. As for your friend who is supposedly studying psychology--this story doesn't make sense. I'm assuming this person, if this person even exists in the real world, is getting at least a bachelor's degree in psychology. And this person is also taking "algebra" in a university? Huh? I know a person who double-majored in English and psychology and, while not a math person at all, was still required to do some pretty intense statistical work in his psych classes. If you're studying a science, I don't see how you can get around math.

And if you treat a college degree as nothing more than a ticket to punch to a career, you devalue a degree. I want it to mean "educated", not merely "ready for work". Like I said, if you want to work in a field but can't do college work, find a job in the field that doesn't require college work. Sounds pretty simple to me.

You might read this post, too:

And next time you come here, please be a bit more civil.