Is Algebra Worthless?
Richard Cohen uses the anecdote of a girl who dropped out of high school because she couldn’t pass algebra as the basis for a column arguing that one can get by just fine without math.
I confess to be one of those people who hate math. I can do my basic arithmetic all right (although not percentages) but I flunked algebra (once), barely passed it the second time — the only proof I’ve ever seen of divine intervention — somehow passed geometry and resolved, with a grateful exhale of breath, that I would never go near math again. I let others go on to intermediate algebra and trigonometry while I busied myself learning how to type. In due course, this came to be the way I made my living. Typing: Best class I ever took.
Here’s the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know — never mind want to know — how many boys it will take to mow a lawn if one of them quits halfway and two more show up later — or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note — or reason even a little bit. If, say, the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.
University of Minnesota biology prof P.Z. Myers is furious.
Because Richard Cohen is ignorant of elementary mathematics, he can smugly tell a young lady to throw away any chance being a scientist, a technician, a teacher, an accountant; any possibility of contributing to science and technology, of even being able to grasp what she’s doing beyond pushing buttons. It’s Richard Cohen condescendingly telling someone, “You’re as stupid as I am; give up.” And everything he said is completely wrong.
Algebra is not about calculating the answer to basic word problems: it’s about symbolic reasoning, the ability to manipulate values by a set of logical rules. It’s basic stuff — I know many students struggle with it, but it’s a minimal foundation for understanding mathematics and everything in science. Even more plainly, it’s a basic requirement for getting into a good college. . . .
Quite true. Of course, the last begs the question. Perhaps it shouldn’t be a requirement for getting into a good college?
One could argue, as Cohen does tangentially, that people who lack the capacity to pass high school algebra are unlikely to contribute much to science and technology but might nonetheless go on to meaningful tasks, like journalism. (Of course, as Mark Tapscott and others will tell you, inumeracy is a decidedly bad trait in an aspiring journalist.)
This all gets back to an even more fundamental question: What is the purpose of higher education? Or, indeed, education, period? Is it mere training for a job? Or is it, as Myers would have it, something more?
[To] push a little bit, stretch our minds, challenge ourselves intellectually, learn something new every day. We ought to expect that our public schools would give kids the basic tools to go on and learn more — skills in reading and writing, a general knowledge of their history and culture, an introduction to the sciences, and yes, mathematics as a foundation. Algebra isn’t asking much. It’s knowledge that will get kids beyond a future of stocking shelves at WalMart or pecking out foolish screeds on a typewriter.
If a degree is merely a credential for employment, there’s not much argument for requiring algebra for those not aspiring to scientific and technical fields. Ditto literature and the arts for those who are not headed in that direction. Or foreign languages for those not intending to travel. If it is about broadening the mind–in a sense, an end into itself rather than merely a means–then all those things must be part of the curriculum.
English (or whatever written and spoken language predominates in a given society) and mathematics are the two essential languages of education. One is simply not educated without a solid foundation in both.
I have a BBA so I understand the importance of Algebra in the hard sciences. However, I would have been more than happy to have not been required to take so many literature courses. While I did enjoy my literature courses (because I tried to cherry-pick the ones that interested me the most),with a few exceptions, I have found little use for them, outside of a social context, in the real world.
I’m not sure how much I got out of my lit classes, either. I’m not one that remembers a lot of details of that type of thing, so I couldn’t quote any poems back to you that don’t involve Nantucket or the number of days that September hath.
I have certainly forgotten a lot of the math and science I learned, too, out of sheer atrophy.
Still, the hope is that being exposed and forced to grapple with these things improved my analytical ability and broadened my perspectives. Since I don’t have a James-Prime that did not have that training to compare myself to, it’s not something that’s easily falsifiable.
I am an engineer by training. So I understand the requirement of mathematics to understand reasoning and as a basis of characterizing the physical world on a sheet of paper. But I also understand the requirement for literature and language to round out the overall education, to understand history, human thought, etc. Knowledge can never be a bad thing.
Education is the opening of doors of opportunity by establishing sets of skills or basic understandings of how the world works.
If you ignore math or algebra you close a door that you may not be able to open again. That’s the importance of it, you keep your options open as well as open your mind to new ideas.
Math is something best learned in a linear fashion building skills upon other skills. If you decide to get back into it later in life it is much more difficult to restart the process and keep it going.
That is one of the most profoundly true statements I have ever read. Kudos to you James.
I tried to do this but found I had more luck cherry-picking the professors that actually made the material interesting.
So the next time you read a newspaper article, written by a journalist, regarding opinion polls, the economy, relative prices, the costs/value of some government action or anything involving mathematics, keep what Richard Cohen wrote in mind.
I’m sure that similar things could be set of virtually any academic discipline…that its not important and that you’ll never use it in the “real world.”
However, I think Myers is right…a college education is about more than simply learning the skills an average person will need in their daily lives. Ideally, primary and secondary school is where you would learn the basic skills of typing, reading, basic math, how to type, balance a checkbook.
Ideally, the university is where one goes to learn to “think”…and as difficult as math has always been for me, I agree with Dr. Myers that algebra, geometry, trigonometry, etal., are important not simply because they’ll help you plan how long it’ll take you to mow your yard, but rather because they train the mind to think and to solve problems logically and rationally. Of course, other disciplines – literature, history, political science, natural sciences, etc. – do so as well…
If he’s never used algebra hopefully he doesn’t drive.
I noticed that no one has commented that he is dependant upon a “Computer or Calculator” to do it all for him. Black Box technology, plug what you want in, and get an answer back, even if its wrong and you don’t know it, even if its off by a factor of 10, he’ll trust it.
He’ll trust whomever the maker of the Black box to get it right, if it’s Microsoft, TI, or Google.
What a dummy, and to think he has a column.
My son is not as gifted as I was in math, but he still put up with his HS’s courses in algebra, calculus, and trig, passing them all with decent grades.
In university, he decidedly not going down the maths/sciences route, which if is fine as his true talents lay elsewhere. But he was still smart enough to take a Statistics class to learn how to understand an increasingly important (and plotical) aspect of modern life.
Innumeracy is the bane of journalists–Google the term and go to the Amazon links, it’s an entire field of publication. Reporters cannot accurately report that which they do not understand. And numbers, as Cohen often demonstrates, are far beyond the majority. As a result, we all lose through misrepresentation of reality, intentional or not.
Cohen’s a jerk.
Judging by OTB’s commenters, biology would be a good requirement also.
I’m not always a big fan of Cohen’s. He takes a lot of cheap shots at Bush. But he’s on the money here. Numbers aren’t what matters. Faith is what matters. We had a number-based president recently. He left us with a recession and a big terrorist attack. Now we’ve got a faith-based president and the economy is strong and our nation is safe. That says all you need to do about the “importance” of numbers.
Some one has already said it, but I will go ahead and beat the dead horse.
As an engineer, when I look at headlines or articles in newspapers, I cringe at the complete ignorance of math or statistical reasoning, let alone probability risk assessment. ItÂ’s always the same:
if the problem is small i.e. 5000 people a year die of disease X, then they quote the number, (never mind that because of sample size the probability in any given year of dying maybe .000001%).
Reporting that special interest group K said that crime R occurs X times every Y seconds, even thought simple math would show that to be an impossibly large number.
Not understanding that cutting the RATE of growth, is not the same as cutting the funding.
Not understanding, that when an engineer says that chemical X could increase the mortality rate by one addition death over the next 20 years, he is not saying that someone will die because of chemical X.
That for most engineers, unless an idea violates a fundamental law of the universe, the idea is possible, hence, when a reporter asks “is it possible for this nuclear plant to meltdown?”, and the engineer responds “there is a one in 18.4 million chance per operating hour” the head line should not read “ENGINEER SAYS PLANT WILL MELTDOWN!!!!”
As for Cohen, IÂ’m exactly the opposite, I have spell check and grammar check, why learn anything as useless as English, hell 80% of the people I work with, English isnÂ’t even their primary language. WhatÂ’s more, I have the ability to check the black box calculator, question the answer, and ensure that the answer makes sense. Unless reporters have the mental tools to rationally question the results, they are just passing along and printing whatÂ’s given to them. That truly is work for a computer.
I think the important thing to take away from high school algebra is basic symbolic reasoning and a few basic algebraic tools. Additional algebraic tools are important for later mathematics and science but I suspect most people aren’t going to often use the quadratic formula or sines in their daily lives much.
I do worry that someone who can not pass algebra perhaps won’t be able to compute or estimate whether paying an extra $5000 for a hybrid vehicle makes financial sense if it gets 20% better mileage, gas stays around $2.50/gallon, they drive 12,000 miles a year, and they expect to keep the vehicle for 5 years.
When I went back to school at 30 after having spent 10 years raising my two sons, the first thing I realized was that in order to be a fully-thinking human being I needed to round myself out.
Therefore, instead of majoring in my strong area (literature, or the humanities) I loaded up on math, statistics, and economics courses.
What I gained was invaluable: an entirely different way of thinking and of looking at the world. And one which, Nancy Hopkins aside, tends not to be the default mode for many women.
I think Richard Cohen may have inadvertently shown us what is wrong with most of his columns. The man never learned more than one mode of thinking, and this severely limits both his objectivity and his ability to examine many of the issues of the day.
But cocooned in his smug little world as he is, he will probably never be able to see that.
And Leonidas, I think a nation needs both faith and reason. It is not one or the other that poses a problem, but an imbalance between the two.
My brother has a PhD in Mathematics. He’s undoubtedly a very smart guy, but I’ve never seen anyone so willing to utterly dismiss “inconvenient” facts, nor to focus on individual trees to the exclusion of the forest.
I work with numbers and at least in social science or decision-making, they aren’t meant to be used out of their proper context. One still has to apply a bit of critical judgment when working with statistics. I have no patience with people who want what I like to call a single “Golden Number” (usually an average, for Pete’s sake) that somehow explains everything. It doesn’t exist.
Leonidas wrote: “I’m not always a big fan of Cohen’s. He takes a lot of cheap shots at Bush. But he’s on the money here. Numbers aren’t what matters. Faith is what matters. We had a number-based president recently. He left us with a recession and a big terrorist attack. Now we’ve got a faith-based president and the economy is strong and our nation is safe. That says all you need to do about the “importance” of numbers.” Stuff’n nonsence. Oh, I’m sure that Cohen is critical of Bush (the President says and does so much that is just plain un-American that it’s a wonder he doesn’t have more critics). But while faith does indeed matter, institutions of higher learning cannot give this to you. Schools of higher learning exist to educate the mind. And even most seminaries require one to have graduated high school. While I’m no fan of math, and can probably be considered an innumerate, I believe it is an important aspect of a good education; I wish that I had focused more time and thought to it when I was in school.
As for the rest of your remarks. . . President Clinton may have left us with a recession (if he did, I wasn’t aware of it, and I never liked the man), but his presidency was left a recession by our current president’s father (remember all those massive layoffs that took place just as Clinton entered office?). Moreover, if one’s fruits are how one is known, then our current president only pretends to faith. His actions are certainly louder than his words. He prefers to seek loopholes in the law, concerning the torture of prisoners, rather than to be faithful to Christ and not mistreat his enemies. He actively seeks to discover who leeks information about his administration (information which is not critical to national security) with a view to firing and prosecuting them, rather than follow Christ in turning the other cheek and blessing those who curse him. (Examples could go on.) Oh, and the major terrorist attack that Clinton left us with? That happened on our current “faith-based” president’s watch! For the life of me, I can’t see how that can be blamed on Clinton any more than the release of the Iranian hostages, during the early days of President Reagan’s term, can be credited to President Carter.