# Dump Algebra

Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is **Andrew Hacker**, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book *Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It*, co-authored with **Claudia Dreifus**, convinced me that tenure is harmful. His latest broadside, “Is Algebra Necessary?”, in last Sunday’s *New York Times*, is as provocative.

He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right.

Support for Hacker’s view comes from the observations of engineer and senior executive **Robert Pearson** (published in his article “Why don’t most engineers use undergraduate mathematics in their professional work?”, *UME Trends*, October 1991). Based on his “fifty-four years of experience as a design engineer, as an engineering manager, as a member of management assigned to help alleviate engineer-shop design and manufacturing problems, as a product cost and reliability analyst, as a corporate executive, and as an undergraduate mathematics instructor,” he asks, “Why do 50 percent (probably closer to 70%) of engineering and science practitioners seldom, if ever, use mathematics above the elementary algebra/trigonometry level in their practice?” If algebra is the limit for most engineering and science professionals, why does a typical citizen need algebra?

As Hacker says, much more useful than algebra is quantitative literacy: being able to estimate, judge the reasonableness of numbers, and thereby detect bullshit. Our world offers plenty of practice.

My only disagreement with Hacker is small: whether, as he says, young people should learn to “do long division, whether they want to or not.” I teach mathematics and have written a mathematics textbook, but long division I haven’t used for at least three decades.

## jeff

Why don't we put the little bastards to work at age 13? They've learned all they're ever gonna use!

## Jose F.

"As Hacker says, much more useful than algebra is quantitative literacy: being able to estimate, judge the reasonableness of numbers, and thereby detect bullshit. Our world offers plenty of practice."

This sentence sums up the myopia of the "dump algebra" supporters. How will you teach basic ideas of statistics without algebra? If we are going to work on the hypothesis of removing the hardest hurdle to graduate to improve outcomes, then would not college level basic statistics be next on the chopping block as many students fail this course? In fact, the re-designing of algebra already exist in most colleges under the title of Finite Mathematics.

## Seminymous Coward

Algebra is necessary as conceptual training if nothing else. Manipulating abstract symbols is a vitally important reasoning skill.

The Cartesian coordinate graphing generally taught in the same class also extremely helpful in understanding virtually every kind of numeric value that changes with respect to an input, e.g. time. An obvious example is the exponential growth seen in compound interest and inflation, the understanding of which is a financial necessity.

## Bill Strickland

I'm not so hasty to dismiss what may be the only formal use of symbolic thought many people experience. My belief is that the differences between arithmetic and algebra constitute a different thinking skill that clarifies and improves thought. Parallel arguments can be made for constructing even one "proof" in geometry and some slight familiarity with a second spoken language. Never overtly using a formerly acquired skill doesn't mean traces of that skill, or of its acquisition, don't remain to influence thought in a positive way later on.

## Bruce

Sanjoy,

You may be a math teacher, but your logic skills are seriously flawed.

a) Quantitative literacy *is* very important, but why do you believe that teaching/learning quantitative literacy and algebra are mutually exclusive. In fact, I would argue that quantitative literacy almost certainly requires algebra. As a math teacher, you should know that one of the essential skills learned in algebra is taking real-world questions and correctly structuring a mathematical equation to model that question and answer it. Arithmetic doesn't get you anywhere except for solving arithmetic problems -- and there are relatively few of those in daily life beyond making change.

b) Pearson's observation that engineers rarely use skills beyond algebra, so typical citizens don't need algebra is another logical fallacy. Pearson should have asked if engineers rarely use skills beyond algebra why are engineers required to study so much higher level math. Engineers not using higher level math says nothing about typical citizens and their use/need for algebra.

Algebra is fundamental if you're going to intelligently analyze budgets, income projections, taxes, statistics, and almost anything else with numbers. Arithmetic is a necessary skill, but if you don't know how to express a problem mathematically, you're left with nothing to calculate.

Plus, Algebra is EXERCISE FOR THE BRAIN. You wouldn't want American children to have flabby waistlines and flabby frontal lobes. too!

And, EVERYONE CAN LEARN ALGEBRA with a decent teacher and a little diligence. Perhaps we need to focus on deficient math teachers (many of whom have teaching degrees but lack adequate math education themselves) and students who don't put in the same type of hard work in Algebra that they'd apply to getting past a challenge in their favorite videogame.

For the record, I taught middle and high school math for seven years and worked in the computer software industry before that.

## YX

Very good ideal, if this come true I would not need to worry about some kid fresh out of college to take my job twenty years later.

## Mario

In education, math in general and algebra in particular allow students to develop a structured method to solve quantitative and logic problems. Its value as a skill to know how to get the numeric value(s) of a quadratic equation or an integral is well behind.

## Eric M. Jones.

I am amazed that anyone thinks that what is taught in school needs to be "relevant". That's not the point of early education. Teaching how problems are solved is the point. Stopping the teaching of algebra is one step closer to the total destruction of the educational system (which, as it turn out, I'm in favor of bulldozing, but that's another subject.)

Next we'll go back to the Black English hubub...and who needs to larn spellin anywae?

## Jacob

I feel like this opens a huge can of worms. Sure, perhaps the average citizen doesn't need to understand algebra to succeed in life. However, the same can be said of almost every subject. You can do perfectly fine in life without a basic understanding of history, literature, music, art, etc. Like algebra, these were all required in my education. Should we stop teaching them as well?

Hacker argues that "it’s not easy to see why potential poets and philosophers face a lofty mathematics bar." If we accept that, why should aspiring engineers and scientists be forced to read Virginia Woolf?

I also think removing algebra from the list of required courses would have disastrous consequences for the future scientific community. It's no secret that American math education leaves something to be desired and that many math courses, especially at the high school level, involve little more than endless rote repetition. As a result, most students (my past self included) would skip algebra (and therefore all subsequent math education) if the opportunity presented itself. This will lead to large number of incoming undergraduates without algebra, including many who would have turned to the hard sciences.

There is no way an undergraduate who doesn't know algebra can complete a physics (or materials science or electrical engineering or chemical engineering or aerospace engineering) degree in four years, as currently structured. If the program were restructured, students interested in a graduate education would be woefully unprepared to compete with foreigners who could start learning complex material much earlier. American students already struggle to compete with foreign students at the graduate level, who in general work harder and have a stronger math background. Removing algebra would exacerbate this, obliterating any advantage the US currently holds in hard science academia.

## Ally

How can you teach quantitative literacy without algebra? Exponential and log functions, for example, are absolutely integral to understanding most of what happens in society and the world. If you don't know a bit of algebra, you can't even talk about these things meaningfully, let alone reason about them.

Moreover, the basic skill taught by algebra is abstraction, which is a fundamental building blocks of human thought. You might not use algebra per se, but in being exposed to it, you have developed a mental toolkit to abstract problems from their context and manipulate them logically.

Hacker argues that algebra should not be taught because many people find it challenging. By that logic, why teach people anything at school? Why not let them study only what they happen to find appealing or is directly useful for their future careers? One answer is that society is better off with citizens who understand their world and can make intelligent choices about it.

By all means, revolutionize the math curriculum. But removing algebra would be insanely stupid.

## Oliver

I have a friend, he is Chinese, and came to France to finish part of his studies (I'm French).

Today, he told me his whole family, in China, whole-heartedly supports the idea the American kids don't need to study Algebra. That will be less competition in the future, they say.

## hanmeng

So, how does one learn quantitative literacy? I rarely understand large figures about things like government expenditures because reporters rarely offer any context. (I'm afraid that's because they have a tendency to parrot what their sources tell them and don't bother to understand the context either.)

## Mike

This is typical hindsight and probably sampling bias too. You're asking people that ALREADY know algebra and likely have a grasp on even higher order mathematics as well. Those same individuals have likely integrated "algebra" into their problem solving schema and have never again thought about the skill sets that are derived from it.

This is evidenced further by the fact that he goes on to point to quantitative literacy skills, like estimation, as being more valuable. However, he does not explain how to get to those skills or how to use them in any meaningful fashion if you don't have the tools of basic algebra.

All of that said, if the idea is to move to a more holistic discussion of mathematics education wherein algebra and geometry are fit within a curriculum directed at practical application of those skills, then we should have that discussion. That's a different problem.

## Rrose Selavy

I am not an engineer, but apparently I use algebra more often than even they do. Algebra is the basis of problem-solving a variety of everyday problems that I encounter just by going through life, much less work. And it's not that hard to learn the basics.

## Joe J

I whole heartedly agree we should re examine what and why are teaching the classes/subjects we are in schools, you want them to be relevant and useful in future life and to expand the mind. Which I think is much of the problem in schools, too often the kids realise I'm never going to know or use this. Which is tooo often true.

That being said, I wouldn't put Algebra up at the first thing to be chopped. Forcing me to read Charles Dickens tops that list. Ugh.

I'd much rather them have a basic home economics and home finance course than half of the things that are currently taught. Balancing a check book, figuring out credit cards, mortgages.

And for those who say algebra isn't ever used? Take a second look at your income tax forms and try to write that mathematically, looks like algebra to me.

## vexorian

Let's all dump writing. How many people write books nowadays? If writing really important for the average citizen? Far more important in life is to be able to read an article and understand it. Thus we should teach kids only to read and never to write.

## Erik

You didn't use long division to write a mathematics textbook?

## Djyrn

I don't think Algebra should be dumped.

I do think that many people learn more algebra outside algebra than they do within it. This suggests to me that maybe it's not a matter of dumping algebra but de-emphasizing it as a stand alone subject and working with it across the maths curriculum.

## Jill

My husband is a software engineer and uses higher mathematics in his work on a daily basis. I use the basics at least once a week. Come on, even cooking requires basic algebra... and if you have any desire to have kids, you're going to have to brush up those long division skills for when about 2nd grade hits.

## Mark D.

Algebra is essential to successful modern day survival, because it is essential to basic financial literacy. If you can't easy calculate the cost/benefit of things like renting vs. buying, you're going to have a much harder time of life and are going to be taken for a ride by shady real estate agents, car dealers, investment brokers, employers, the taxman (if you don't know the tax tables and tax deferment strategy) etc.

In fact, I'd argue that much of the problems of late are exactly because of the lack of focus on fundamental things such as algebra - people are much more susceptible to outright B.S. because they don't have the skills to determine simple truth in numbers.