Is Algebra Necessary?

It's easy to recognize that the author's arguments could apply just as well to any academic subject: literature, history, you name it. ("We should just teach 'citizen reading', where students learn to read recipes and furniture assembly instructions.")

But the real surprise to me is his ignorance of actual college math curricula. He says, "Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art". I don't know about his college, but the math requirement where I teach can be met with courses such as "Math in Art and Nature" or "Liberal Arts Mathematics". It's not as if his suggestions there are novel! But here's the kicker: for both of those classes, proficiency in algebra is a prerequisite. It turns out that you can't really describe those topics that he likes without actually using some math.

On the other hand, I have come around to agree that statistics is more broadly useful than calculus. Here's a TED talk by one of my old math professors making that case: http://www.ted.com/talks/arthur_benjamin_s_formula_for_chang...

Recent example. A family member who is an artist asked me about submission rules to a guild competition (now, of all people, the artists are commonly believed to require algebra knowledge the least). The flyer indicated, "the photos/scans you submit must be 300dpi" (dots/pixels per inch). Which is perfectly confusing because even a 100x100 pixel thumbnail can be considered 300dpi if you set its width to 1/3 inches. When I tried to explain said family member that the guideline is confusing, that whoever wrote it probably failed their high-school algebra, he started to mistrust what I'm saying. Words can't explain how dumb the situation was: one idiot writes a guideline that can't be followed (or rather one that can be satisfied even by a still from a security camera), another takes what is written on blind faith and refuses to use logic to understand why the guideline is insufficient.

Now imagine dealing with people who never completed high-school algebra but who are trying to calculate dosage of a drug. According to a pharmacist I knew, a child died on his watch because of incorrect dosage.

This is an interesting read, but the author is also a political science professor. If this article had been by a mathematics educator, it might be a bit more persuasive.

I'd argue that algebra is fundamental - the excerpts taken involve the quadratic equation and other supposedly tedious tasks, while ignoring that these are foundations for higher level problem solving. In almost any field, somebody will ask at some point "how many X do I need for Y" - and it's usually not that clear.

I would almost posit that the author is trolling the NY Times, but today that's probably not the case. While math is hard for some students, it's an essential part of education for just about anybody that hopes to be a mildly functional member of society.

I was forced to read The Scarlett Letter in high school, and I have never once had to use that knowledge in my professional life.

I memorized dates for history exams in high school, and that knowledge has had no practical impact on my life whatsoever.

When introducing myself to (non-math/science) academics and telling them I was a (now former) physics professor, I can't tell you how often the first thing out of their mouth was something along the lines of "I was never very good at math" or "I never liked science." I frequently have had doctors tell me how much they hated physics as a pre-med student. That kind of pride in ignorance is quite rare in the opposite direction. The most broadly educated people I know are scientists.

[edit: typo fix]

Yes it is.

You can easily swap solving math problems for writing essays in that article and get the same conclusion. Also the whole article completely lacks any statistic basis. 42% of students didn't pass their bachelor exams and 57% students of one university (not saying which faculties were included in statistics) didn't pass algebra course (one math course only is mentioned). So what? How is that connected? What are the long term trends? What about other courses and other universities? Same applies for all the article - throw together random numbers that SEEM to be related (they may be, of course).

Very shallow and probably incorrect article.

This is a perfect example of how Betteridge's Law can fail. Yes, algebra is necessary. Very much so. It's basically the first time students are required to operate on a formal system, which requires strictness and analytical thinking. As another poster has pointed out, algebra is a gym for your brain. Also, algebra has tons and tons of applications. Anybody claiming they "never needed to solve for x" has completely missed the point of symbols. They have certainly solved for x but haven't realized it yet.

The article lists arguments which can be applied to about everything else you learn in secondary education. How comes nobody ever complains about learning literature, arts, music or whatever, but people seem to insist that they'll never need math in their jobs, when in fact, math has made their lives possible as they know it.

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"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"

Nothing else leads to that either. Political opinions and social analysis have zilch value in understanding the Universe we live in. Math does.

Hmm.. Algebra is not hard. Its actually pretty easy if you know what you're looking for. Heck, the professor even tells you the answers before every test. Just follow the steps.

That's the problem though. There are many steps to be learned. Things like "order of operations" and "FOIL" are necessary to get the correct answer. Its not that learning Algebra is hard, its the discipline that comes from the. Trouble is, most young people don't see the rewards in learning this discipline.

For example here's a few other disciplines that takes time but seems more rewarding to a young student (or anyone)

Swimming - can have more fun at the beach Martial Arts - self defense and confidence, and proof that you're a bad ass Learning a FPS - bragging rights, more fun online against friends and other gamers Guitar Lessons - sing your favorite songs, perform live, get lots of friends/admirers

Algebra - learn about long term goals and ... processes?

Kids are not into the "long term". They are into the short term. Thus, they are kids. Adults needs to show them why it is important to learn how to find "X". Unfortunately, most adults would rather stay far away from that stuff because they've had a hard time with it as a child as well. Its painful to them. Its easier to tell the child "because it is important" than explain why.

I personally think algebra is very cool. I like how things can workout just because you know a proven formula for solving that problem. But then again, that's why I (and other CS) make the big bucks. We do the things that no one else wants to deal with.

Using your brain is hard. Solving a tough equation is probably equivalent to running a mile. It can be done. It can be fun. Yet, you don't see many people with long slender bodies running around everywhere do we?

Everyone has their niche. Its really up to them to find it.

I find it challenging to believe that individuals incapable of basic, entry-level algebra are really qualified to attend a university in the first place.

Having many good friends in disciplines which will never require the use of any sort of mathematics, I can safely say that none of them have had trouble with high-school level algebra.

Portions of the article strike me as a depressing appeal to entitlement amongst the lowest common denominator of students to a university education.

True story. I was having trouble sleeping and I went to a big box home improvement store for some custom cut roller blinds. I measured the blinds to the nearest 1/8 inch so less light would leak around the edges. I grab the blinds and go to the blind cutting machine, which has an arm marked off like a ruler to 16ths of an inch, with the cutting blade held by a screw clamp. There are no detents or grooves to force discrete measurements, just a screw clamp, so this machine can do any length between its min and max length.

Well, the young woman who comes looks at the measurements I wrote down and looks at me and says, "The machine doesn't do fractions."

I was floored. She was lying to cover her innumeracy, because she didn't do fractions. If this is indicative of a trend, it's bad news for the future of the United States.

Making a subject mandatory is a great recipe for sucking all the life out of it, and mathematics is one of the best examples. Is algebra awesome? Absolutely. Does every member of our society need to be able to factor polynomials? ...not really, especially not at the expense of a child's natural love of learning.

See algebra as the gym for your brain. Although you might not need algebra, you will benefit from the exercises.

Understanding variables is a hallmark of the "formal operational" stage of development.[1] It's the same reason why we hear some people "just don't get" programming. Same reason why languages like LOGO avoid this construct.

If grasping Algebra is actually about attaining this developmental stage, we need to be approaching the problem on a more fundamental level. Kids will move through these stages at a different pace and if you're on the tail end of developmental pace you're going to fall through the cracks.

[1] http://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive_...

There was a recent discussion on reddit following some Khan Academy controversy, where some education people mentioned some research about the concept of slope.

It turns out that a significant number of people don't understand speed as a rate. They think of it as an intensity, as in volume of sound or brightness. (Those are flux, which are related to rate, though that's not how we perceive them.)

People like that are alien to me. I think it also explains why freeway drivers in Houston often have about 0.3 seconds of separation between cars.

Math literacy is valuable even for regular people.

Case in point - an innumerate relative of mine has been duped into selling "Nu-skin" products for virtually no money. Nu-skin gave her documents explicitly stating her odds - 99.5% of active nu-skin sellers make < $15k/year. But they also showed her videos of people who won won carribean cruises and made thousands/millions.

Guess which one she bought into?

A math literate person would recognize that her odds are better working at chipotle and reinvesting some of the proceeds in vegas.

> Mathematics, both pure and applied, is integral to our civilization, whether the realm is aesthetic or electronic. But for most adults, it is more feared or revered than understood.

This is very true, but lowering expectations is hardly a solution. Ignorance (in the form of oh-well-that's-the-class-smart-people-take) is no better than fear. Before we set the bar too low, let's keep pushing to make mathematics less intimidating, less foreign and easier to learn for everyone.

I agree that algebra in and of itself is not particularly useful. However, an in-depth understanding of statistics is vital to basic scientific literacy and most certainly "leads to more credible political opinions or social analysis. I've often wondered why high schools don't place a bigger emphasis on statistics, but I'm not sure if you can teach basic statistics without algebra (or calculus).

I think algebra is necessary, and calculus, and geometry, and trigonometry, and everything else I don't understand in the realm of mathematics.

But they're important in the context of real life.

So, yes, we should keep these classes, keep having kids go through algebra and calculus and geometry...

...But you shouldn't be bound by arbitrary rules. Algebra is important, but if you find "x" by doing something other than some arbitrary thing where you subtract both sides, etc., you shouldn't get an F in the class.

Same with calculus, geometry, everything. The importance is the thinking and the logic, and what real-life application you can take from your knowledge. Making hard rules for these math courses, for example, definitely hurts this and does some of the things this article claims.

But true, honest exploration in math and thinking about it is very important, and if it's free and done in an honest way there is no question about whether it's necessary or not.

Richard Feynman covered this better than I ever could: http://www.youtube.com/watch?v=5ZED4gITL28

It's hard for me to comprehend that someone could understand any subtle (or even not-so-subtle) distinctions or complex arguments without at least a basic understanding of algebra and statistics.

I could be wrong though. What about famous thinkers like Jefferson or Lincoln -- did they understand algebra and statistics at all?

It seems likely to me that algebra during school is a cause for dropout not because it's harder, but because it's more objective.

If someone doesn't know anything about history, you can pass them along, claiming that they wrote a few essays or something. It's fraud, and any expert can see it, but it's easy enough to ignore it if you try.

But with algebra you can't ignore failure. It's obvious. Even the most basic tests will reveal ignorance quickly.

I conjecture that those people who drop out "because of algebra" are not proficient in any subject.

I observe that the alternatives suggested are less objective and more "hands-on". What does it mean to learn about the consumer price index without learning basic algebra? The only explanation I can think of is that it offers more opportunity to ignore educational fraud.

How is this not an article from The Onion?

To the extent that algebra courses consist of solving # + x = # over and over again, I agree that they are mostly useless. In life, algebraic questions don't come at you in symbols and numbers, they come in words. And I would argue that these questions surround us! It's just a matter of people recognizing that they are there. Therefore, in my opinion, a good algebra course (which is essential!) focuses on problem solving. Necessarily, the course would involve some mindless equation solving to learn the framework of algebra.

I'm biased since I'm a software engineer, but I believe algebra is extremely valuable. I can't imagine not knowing it! If I were to revise math education I would balance the amount of time spent on geometry (1 year HS), trig (1 year HS) and calculus (1 year HS, 2.5 yrs undergrad) better with discrete math, linear algebra, probability and statistics. The current system seems to be disposed toward creating 50's NASA fodder and economists.

I rarely comment, but I feel compelled to add to this discussion.

Algebra, as it is taught today in the U.S., is not necessary, and is probably detrimental in many of the ways stated in the article. I can't speak for non-traditional schools, but public schools, with their focus on standardized testing, have effectively destroyed the original spirit behind teaching mathematics.

Mathematics, much like other academic topics (e.g. literary analysis), was taught not as a practical skill, but as a way to improve your abstract thinking and problem solving skills. As another commenter stated, Mathematics (along with most later academics) should be a gymnasium for your brain. I like this metaphor, because if you think about solo athletics, all students are not expected to achieve at a pre-defined level. Rather students are evaluated based on improvement in performance over time.

Sadly, mathematics in recent years has become less about abstract thinking and problem solving and more about rote memorization, computation, and application. I taught basic algebra to college students for a semester. One of my most interesting experiences was with the dreaded story problem. Most of the students were simply unable to apply math to solve a problem. They were all very good all computation, but when faced with a problem in a form they didn't recognize they instantly began flailing.

Standardized testing has turned math into the process of recognizing a form, plugging in the numbers, and computing. We're now starting to see the first generation of math teachers that are a product of standardized testing, and the results are frankly, frightening. I've spoken with younger math teachers who couldn't explain the practical importance of their subject. While they loved math, they couldn't tell me why they were teaching it, other than: "It's on the [standardized] test."

This is the kind of Algebra we don't need.

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Incidentally, the only way I avoided the shocking deficiencies of standard high school "math" was by fighting my way into an advanced program at the local University. It was there I was introduced to Euclidean geometry and really learned what math was all about. I think everyone should learn Geometry using the Euclidean method. I learned from a simplified book (Geometry, by Moise/Downs) which starts out with a few more postulates than Euclid did. I'd go as far to say that geometry (properly taught) will make you a better programmer/problem solver/thinker.

Yes it is and we need to train teachers to teach it better.

Yes.

I stopped reading the moment I encountered 'I say this as a writer and social scientist...'

Telling that students struggling with a subject is considered evidence of a problem with the subject. Couldn't be the teachers or the curriculum or the students.