Students frequently question the usefulness of algebra, and express various objections to "having" to take an algebra class. But do these objections stand up under scrutiny?

There was a time not so long ago when children in middle schools were assigned to "tracks" according to what "everybody knew" each child would "need". (This tracking was why middle schools were invented in the first place.) Educational "experts" presumed to know what the various children needed, based on culturally-based (but unjustified) presumptions. The educators then locked children into "appropriate" tracks, thereby locking many children out of college before they'd even begun high school.

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It might have been assumed, for instance, that Shaniqwa would be pregnant by the time she was fourteen, Jamal would be in prison, José would grow up to be a pool-boy, and Maria would be a maid. So these students would have been assigned to something like "consumer math": low-level math that was presumed to be "useful" for "that sort". Blonde, blue-eyed Tiffany might have been expected to marry well after a short and trivial "career", so she'd have been assigned to bookkeeping. Only Eustace James Whittington III would have had any chance of attending college, so only he would have been steered into the algebra class.

(By the way, did pictures pop into your head regarding the appearance of each of the above-named persons? If so, they popped up based on nothing more than just the statement of their names. This is a mild form of the kind of presumption I'm talking about.)

I would hate to see a return to the days when kids were assigned their roles in life, based on nothing more than the sound of their name, their gender, or the color of their skin, with non-WASP males being the only kids being allowed to reach their potential. And I can't understand why any student would *volunteer* today to put himself into the position that used to be *forced* on many women and minorities. Even if college isn't currently in your plans, please don't under-value yourself by classifying yourself as "that sort" by thinking that you could never use algebra. Don't diminish your future potential by denying to yourself any exposure to mathematics past grade-school arithmetic.

Did you ever notice that nobody asks why he "has" to take English Lit or phys-ed? But math and science are arguably much more crucial to the basis of a modern technological society than are *Moby Dick* or the rules to dodge-ball. So why do we generally only hear complaints about math and science? Perhaps because they're hard...? Because they require work and discipline...? Because they aren't always "easy"...?

Modern educationist philosophy in America seems to say that education has to be "fun" and "entertaining" to be justifiable. Today's students often absorb the ethic that, unless a thing is easy, they shouldn't have to bother. But most worthwhile things in life are going to require some effort. If you want that great job, that interesting career, that open-ended future, you're almost certainly going to need some mathematical skills. And algebra is the basis, the foundation, the tool-box, for those skills.

Think about why you go to the gym. Do you lift weights because it's "easy" or so you'll be prepared to lift weights "on the job" or "in real life"? Or do you do it to build strength so you can better deal with... whatever comes up? Why do people jog? Because it's "fun" to sweat and get shin-splints? Because they'll need to cover a half-marathon in the halls at work? Or do they do it because they want to be strong and healthy, able to face... whatever comes up?

Don't you want your brain to be strong, too? Don't you want to have trained your brain so as to be better able to face... whatever comes up?

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Let's be brutally honest here. The university didn't put a gun to your head and *make* you enroll. You decided you wanted their degree. You wanted their piece of paper.

Why? Probably so you could (eventually) get a better job. In order to get that job, you need at least some subset of the skills which are taught in algebra. You might be right that you'll never factor another quadratic in your entire life. But you want the university's piece of paper, so you're going to have to jump through the hoops required to get it. The algebra class is one of those hoops. If you don't want to jump through the hoop, that's fine; but you won't get the piece of paper. It's your choice.

A big difference between a student with an education and a worker with some training is the expectation that the student will have a deeper level of understanding, a broader base of knowledge, and a greater ability to build connections and learn new things.

Will you, to a certainty, need everything taught in algebra? No. Does this mean that you should drop out of school now, get a job, and get only the training which is specific to your position?

"I *can't* drop out!", you reply, "I can't get that job unless I have a college degree." Ah. So, to get the job you want, you need to demonstrate proficiency in basic job skills. To demonstrate that proficiency, you need a degree. To get the degree, you need algebra. In other words, you *do* need this stuff for your job.

It is often said (amongst math people, anyway) that one really only learns arithematic and pre-algebra in algebra, and one only really learns algebra and trigonometry in calculus. What we mean is that one gains a deeper understanding of the previous material once one has to use it in new contexts. So, even if you turn out to be right — even if you turn out, after a forty- or fifty-year work-life, never to have used algebra in the strictest sense — it's still a really good idea to have studied algebra before beginning that work-life. Why? Because everbody needs pre-algebra in "real life", in the sense of needing to be able to do basic arithematic, work with percentages, and understand negative numbers.

By taking algebra (that is, by going further than you might "need" to), you'll have made sure that you've got a stronger grasp of things like "miles per gallon", interest rates, and negative "growth" in your retirement account. You'll need to be able to work with the basic concepts in order to make intelligent decisions in the workplace. You don't want to be the guy whose job-security depends upon volunteer math tutors maybe getting around to doing your pre-algebra or basic-algebra tasks for you on online forums... where your boss could find it. (Yes, this really happens, in real life.)

Maybe. Maybe not.

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Consider the frequency with which "non-traditional" returning students have to take remedial math classes. The fact that they are taking algebra now, all these years past high school, strongly suggests that they haven't used algebra much in the years since they graduated. They got this far in life without algebra. But does that mean you shouldn't take algebra *now?*

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Consider the number of immigrants, struggling with learning English, who work very hard in mathematics. It's not because "well, Asians have a math gene, ya know" or other silly excuses. The fact that they're taking algebra now, only after they arrived, strongly suggests that they hadn't used algebra much in their life before coming over. They'd gotten this far in life without algebra. But does that mean you shouldn't take algebra *now?*

Middle-aged folks are going back to college after years at their jobs; this tells you that they have found out that they need more than only whatever math they'd previously been using in "real life". Many recent immigrants work very hard in mathematics after arriving; this tells you that they have found that, in order to succeed and make a positive contribution, they need more than only whatever math they'd previously learned. To move on, to move up, members of both groups have found that they need algebra in order to move on in today's society. Take the hint.

I have no idea. I don't know what degree you're pursuing; I don't know what your plans, hopes, or dreams are; I don't know what your future might hold.

But consider: You didn't learn your alphabet all those years ago because you knew you'd be reading *Moby Dick* this semester. In the same way, you don't take algebra now because you know that you'll be factoring quadratics in ten years. You should take math and science courses now for much the same reason you learned your letters back then: to lay the foundation for bigger and better things to come, and to open up new opportunities for future successes.

Nobody can say with assurance what skills will be needed twenty years from now. But what intelligent person would want to cut himself off from future opportunities or growth by refusing to expose himself to at least some of the knowledge which will be foundational for whatever is yet to come?

Even in the short term, you'll need some of the skills from algebra. If you're going to work with formulas in spreadsheets, you will need to be comfortable with variables and formulas. That's algebra. If you're going to be in meetings involving reports with tables, charts, and graphs, you'll need to be able to interpret these intelligently if you hope to hold your own in the discussions. That's algebra.

While jobs and their specific skill-sets may change over time, mathematics won't. Twenty years from now, two plus two will still be four, and quadratics will still be either factorable or prime. Whatever job you get will provide the job-specific training you need, but to get that job in the first place, you're going to need some background knowledge and skills. And to be able to keep up with progress, to keep on top of new skill-sets, to move up the ladder, to jump across into new and better career fields, you will need the flexibility of a broad foundation. That foundation includes mathematics.

The philosopher Santayana famously said that "[t]hose who cannot learn from history are doomed to repeat it". This doesn't mean that you'd better memorize all those names and dates, or else long-dead people will rise from their graves and repeat everything they'd done before. It means that you need to learn the patterns and lessons of history; you need to learn the cautionary tales to be gleaned from the (historical) mistakes of others, or else you may find yourself ignorantly making the same mistakes that those other people did. It is the lessons and the patterns which are important.

The lessons and patterns of mathematics are important, too. If all you take from algebra is a comfort with variables and formulas, an ability to interpret graphs and to think logically, and a willingness to use abstraction when you try to solve problems, then you have gained some incredibly useful life skills, skills that will open doors, give you options, and allow you to make your own informed choices.

The specific algorithms you might study are not as important as the general patterns, techniques, and lessons that you can learn. Don't short-change your future by opting out now.

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