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Make Us Do the Math

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Forgive Jen-Luc Piquant for being a bit rant-y, but today we are defending algebra. Again. We also defended algebra last night on the newly launched Huffington Post LIVE streaming network, along with a few other like-minded sorts. My high school algebra teacher is having a good laugh, because believe me, as a teenager, if I had read Andrew Hacker’s recent New York Times op-ed, advocating that schools ditch algebra, my kneejerk reaction would have been “Hell yeah!” And, like Hacker, I would have been so very wrong.

You probably heard about the controversy surrounding Hacker’s article; it was the op-ed that launched a thousand outraged blog posts. Cognitive scientist Daniel Willingham argued in the Washington Post that “The inability to cope with math is not the main reason that students drop out of high school.” Rob Knop asked why we’re not getting to the bottom of “why it becomes normal not to ‘get’ math,” and bemoans the willingness of students to “just do what’s necessary to get by without actually learning anything.” PZ Myers went for satire, questioning why we’re bothering to teach students antiquated skills like grammar and punctuation, when they’re all just texting nowadays anyway. Educating students is so much easier if you “strip out the difficult learning part.”

Mark Chu-Carroll trounced Hacker’s assertion that most students don’t need algebra in real life (so did Blake Stacey). And Melanie Tannenbaum of PsySociety weighed in with a thoughtful look at how algebra is taught, compared to what psychologists now know about how we learn: namely, “people are better able to remember events, facts and knowledge when it is integrated into people’s self-concepts,” and when “it’s situated within a social context.”

Even zombies need teh math. Credit: Jason Torchinsky.

You get the idea. What else would you expect from all those scientists? Well, I’m a former math phobe. I hated algebra, and avoided all advanced math and science until well into my 20s. But I’m standing in solidarity with the fusty old scientific establishment on this one.

There is, indeed, an important conversation to be had about education reform, and I heartily applaud any effort to address different learning styles and methodologies. If nothing else, Hacker’s misguided op-ed has fostered a discussion. And I agree that learning practical math like statistics and probabilities is dead useful for a good social citizen. I just think it should augment, not replace, the traditional curriculum.

Hacker tosses out a lot of statistics on students unable to pass algebra to support his “case,” but I don’t think anyone disagrees that this is a problem. I just can’t see how ditching algebra comprises a sensible solution. Hacker’s thinking seems to be that, because algebra is such a stumbling block for many students, we should throw up our hands and despair of ever teaching it to them. But do we really want to throw in the algebraic towel just because it’s, like, rilly hard?

This kind of experiment has already been done. We need only look to our Eastern neighbor, Japan, for a glimpse of the kind of future this could bring. Caltech string theorist Hirosi Ooguri minced no words when he reacted to Hacker’s article on Facebook:

This is extremely dangerous, and we should not just laugh at it. A similar argument led the Japanese Government to reduce elementary, junior high, and high school math education significantly during the 1990′s. In the past few years, the Government realized the mistake and is trying to reverse it. Unfortunately, a generation of children missed opportunities to get decent education in mathematics, and I am afraid that its negative effects will be felt for many years to come.” (Ooguri graciously granted permission to quote him).

He is referring to the yutori kyoiku (“room to grow”) educational policy that dramatically altered the elementary, junior high and high school curricula in Japan. It sounds great on paper: convinced that traditional rote memorization is insufficient in a 21st century world, Japanese students now were encouraged to develop individuality and initiative, and foster critical thinking and problem solving. The number of classroom hours was reduced, and so was the amount of required math. “Japanese had good basic study skills, so the idea was to add the more individualistic things that westerners have on top of that,” psychologist and author Hideki Wada told the Financial Times.

The results, as Ooguri says, were disastrous. According to the Mathematical Society of Japan, a recent study revealed that 1 in 4 Japanese college students can’t even explain what taking an average means. Of the five questions on the survey, only 1.2 percent answered them all correctly. Per an article in Asian Correspondent: “Students can still calculate the problems, but are not correctly answering proof questions. Educators say less time spent studying fundamental maths problems means students don’t understand why a problem is solved a certain way.”

Nor has it pleased employers. The Financial Times piece points out that Sumitomo Metal now offers remedial science classes for its factory near Osaka, and other companies have followed suit, because students “don’t know anything” when they graduate from college.

Granted, this a complicated issue, and certain Japanese educators maintain that the problem lies not in the ideology, but the execution, exacerbated by unique cultural factors. (This article by Ogi Naoki is an enlightening read.) But as we mull over how to address our own educational shortcomings, we might draw some lessons and guidance from our Eastern neighbors.

Maybe we can start by reaffirming the importance of learning for the sake of knowledge, in stark contrast to the commodification that has overtaken our educational system. No employer has ever asked me to analyze a Petrarchan sonnet, or expound on the intricacies of a Bach fugue, but I’m not sorry I have that knowledge, even if the latter meant suffering through the daily grind of musical scales on the piano as a child. The drudgery meant I might one day, in my teens, attempt Chopin. Granted, I didn’t become a professional musician; I didn’t ultimately have the chops. But my life is so much richer with Chopin in it.

I spent ten years training in jujitsu, yet I have yet to use my skills to defend myself from a real-world attack. So I guess those ten years were a waste, right? Wrong! The most important lessons I gleaned from martial arts had to do with learning to fail: getting my ass kicked and getting back up, again and again and again, until I mastered a given skill. Why wasn’t I willing to do the same for math?

All we’d end up teaching kids with Hacker’s strategy is avoidance. I was a master of avoidance. But learning to buckle down and do unpleasant things that don’t come easily to us prepares us for life. Consider this excellent response by Judy Bolton-Fasman, my fellow math-phobe, who learned geometry through the Khan Academy so she wouldn’t pass on her own math anxiety to her daughter:

To make it to the desk is the first of many small victories. Then it’s time to confront the equation that has to be solved, the Latin paragraph that has to be translated, the essay to say what you intend to communicate. These intellectual conundrums don’t simply loom large, they haunt one. You have to do this work because it matters. Hacker, on the other hand, reinforces the ultimate phobic behavior in education: avoidance.

There’s a lot to be said for confronting fear and anxiety head-on, and fighting through a wall rather than throwing up one’s hands in defeat.

Finally, there is a deeper, uglier under-current to Hacker’s article. What he’s really saying is that we should know our place in society, accept that we’re just not smart enough and don’t need to worry our pretty little heads anymore about anything that might interfere with our enjoyment of American Idol. It’s not like we were ever going to amount to much anyway, amirite? As journalist/science fan Jesse Emspak observed on Twitter: “The argument isn’t about math. It’s really about whether anyone but the privileged should be educated.”

A page from Al-Khwārizmī's al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala. John L. Esposito. The Oxford History of Islam. Public domain.

USC string theorist Nick Warner addressed this point in his own response to Hacker, eloquently articulating what is at stake:

Algebra is not just the language of mathematical elites, it is one of the cornerstones by which we have emerged from a peasant society, ruled by the small elites sometimes capable of abstract thought, to become a complex, vibrant democracy. Algebra has helped us to rise beyond the simple understanding of immediate, tangible experiences and frame questions and look for the essential data that will give us deeper understanding.

Only authoritarian and reactionary politicians benefit from a population for whom abstractions have no meaning. Such a population will be satisfied by sound bites and flag waving and will be placated by bread and circuses while their economy is subverted and their democracy implodes. Like mechanics problems in physics, the study of algebra, and the skills it develops, are not just critical to our long-term health individually but to our survival as a society.

This is a deeply personal issue for me. My father was the first member of his blue collar family to receive a college education, under the G.I. bill. Sure, he struggled at times to fill in the gaps in his background knowledge, but he persevered. He became a civil engineer, enabling him to give his children (including me) the kind of stable, middle-class upbringing he had lacked. And he made sure we got a college education, too, believing it to be the key to a better life.

Make no mistake: eliminating algebra for most students would end up disenfranchising them from any number of potential careers: physics, engineering, biology, chemistry, epidemiology, and psychology, as PZ points out. This matters because most of us have no idea what we want to do as a profession as teenagers. We have no idea what knowledge we’ll need. I didn’t even know science writing was an option. By the time we figure that out, more often than not, it’s too late to remedy our lack of background knowledge.

Educating Rita is a charming comedy from 1983, about a British hairdresser named Rita (Julie Walters) who decides she wants something more from life. Her husband thinks she just needs a baby; instead, Rita signs up for private tutoring lessons with an alcoholic English professor, Frank (Michael Caine), who is steeped in cynicism and self-loathing.

It doesn’t start off well; she simply doesn’t have the cultural background and supportive framework to even begin to grasp what is expected of her. Her idea of literature is Harold Robbins and Jackie Collins, and she struggles mightily with E.M. Forster. Her first essay assignment: “Suggest ways to deal with the staging difficulties in a production of Ibsen’s Peer Gynt.” Her cheeky response: “Do it on the radio.”

But Rita presses on. She experiences some nasty growing pains. And in the end, she passes the university exam with distinction. The first question she sees when she turns over the exam? “Suggest ways to deal with the staging difficulties in a production of Ibsen’s Peer Gynt.” She could have written “Do it on the radio.” Frank would have dearly relished such an act. And there was once a time when sarcasm was her only option. But because of Frank, “I had a choice. I did the exam.” What he gave her, apart from an education, was a choice.

When we take away fundamental subjects like algebra because most students “will never need it,” we are, in essence, taking away their choice, before they know enough to make an informed decision. We are limiting them before they’ve even begun. Life doesn’t end in high school or college. Some of us, like me and Judy Bolton-Fasman, take longer to appreciate the cultural richness and significance of math. But we get there eventually. And when our interest rekindles later in life, we’re very grateful for the math we did take. Yes, including algebra.

Dear educators: I get that you’re frustrated, that you are under tremendous pressure to accomplish more with fewer and fewer resources. I get that you are underpaid and unappreciated. No doubt it is demoralizing to stare out at all those apathetic, unmotivated faces week after week, and hear the kneejerk whinging about how awful it is, this subject you love so much.

But please don’t give up on us. Not yet. We need algebra, whether we realize it or not, regardless of whether we use it on the job or not. Help us appreciate that there is more to education than mere job training, and that “culture” doesn’t just encompass art, literature, music, history and philosophy; it also includes math and science. Don’t let us get away with doing just enough to get by, of being less than our best. Make us realize that just because something is hard, and doesn’t come easily, that’s no reason just to give up and stop trying. Some things are supposed to be hard, and those hard things are worth doing.

Make us do the math. Some day, we’ll thank you.

 

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. scicurious 9:00 am 08/14/2012

    Scicurious <3's this post!! I also was a total math phobe until I figured out I wanted to be in science. And then I was INCREDIBLY grateful that I had had to master Algebra. I now use it every single day.

    And there's also something else. I usually preferred English classes or music classes, sure, because those were easy for me. There was very little effort involved. I know I'd get A's without a challenge. But math, when I got an A in math I felt AWESOME because I really understood the accomplishment. And that's because it WAS hard and it DID require work. It's like Jujitsu, there's a lot to be learned and gained from the process of learning. It'd be very sad for all of us if we did give up on the difficult parts.

    Link to this
  2. 2. SpottedMarley 9:58 am 08/14/2012

    That excerpt by Nick Warner made my day. I feel that we are fighting the rising tide of idiocracy. There must be a drain plug we can yank.

    Link to this
  3. 3. fairlyme 10:07 am 08/14/2012

    The question of math (and science) acceptance for youth and among the masses is analogous to parents trying (sometimes in vain) to get their children to eat vegetables (especially the green ones). The initial reaction is “Nooooo I’m not gonna like it and you can’t make me.” If you’re a parent, you know the worst thing you can do is beat a kid over the head with it. The best thing you can do is continue to present it, in subtle ways, and eventually they’ll try it.

    I agree with all points pro-Math, however, we have to stop beating people over the head with it. This will cause more reaction and less acceptance.

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  4. 4. drskyskull 12:37 pm 08/14/2012

    My first encounter with algebra was in junior high, and I actually flunked a number of tests and finished the course with a very hard-fought “C”. Now, however, I’m a professor of theoretical physics and spend at least 50% of each day using algebra and higher math, and teach these subjects, as well!

    This to me highlights another weakness in giving students an “easy out” from algebra: how are we supposed to effectively separate those who “should” take algebra from those who should be excused? If I had been given the choice, I probably would have bailed out of algebra at that junior high level, and I almost certainly wouldn’t be a professor today. If we expect less of our students, we’ll get less — and many of our students will never live up to their potential.

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  5. 5. socorr 2:22 pm 08/14/2012

    There is a typo in the URL for Mark Chu-Carroll’s response.
    The correct URL is:

    http://scientopia.org/blogs/goodmath/2012/07/30/mathematical-illiteracy-in-the-nyt/

    The first “a” in mathematical was omitted.

    George

    Link to this
  6. 6. Jennifer Ouellette 2:49 pm 08/14/2012

    Thanks for the heads up. Link should be fixed now.

    Link to this
  7. 7. rge2001 4:08 pm 08/14/2012

    Couldn’t agree more. Every significant advance in human civilization can be traced, ultimately, to the advancement of science and technology. From wheels to steel to bridges to gunpowder to the transistor, science shapes how we live and what we can accomplish as a society. This is not annecdotal or wishful thinking as Hacker suggests, but a realistic assessment of where things stand. The ancient Egyptians did mathematics for the same reasons we do – it works to produce a better-engineered society and better-understood universe. To plunder a well-known phrase, the language of science is written in mathematics and to shirk the learning of that language is to turn our back on human ingenuity and potential. To those who are masters of subjects in which there are few, if any, right or wrong answers, mathematics must seem intimidating, but ask this: What possible advantage can there be in not expecting our children to strive and to learn, not those things that are easy, but those things that are hard?

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  8. 8. Evolouie 7:45 pm 08/14/2012

    “From wheels to steel to bridges to gunpowder to the transistor, science shapes how we live and what we can accomplish as a society”
    Seriously?
    The majority of people don’t invent wheels, or design bridges, invent gun powder or transistors.
    The Majority of people work in tech, labor or service jobs and they do not need anything close to even senior algebra let alone something more advanced.
    Get real people.
    We have computers now.
    I can assure you if you do a poll at the local pub or restaurant you will find a very small minority who use anything close to senior math in their daily job or life.
    I have been employed as a communications engineer in the telephone industry for 25 years and have yet to do one single math/algebra problem.
    If my boss actually caught me doing math/algebra rather than using my computer and appropriate and expensive programs, I hate to think what he would say.
    I wont waste my time or the companies money on doing the math/algebra when it can be done much more efficiently on a computer.

    Link to this
  9. 9. Jennifer Ouellette 7:52 pm 08/14/2012

    Maybe you should read the article again. Assuming you bothered the first time. You know, all those parts about it’s not just about what you need for your day job.

    Link to this
  10. 10. Evolouie 9:59 pm 08/14/2012

    I actually read the article back in July in the NYtimes Op-Ed.
    And I stand by my statement.
    The majority of the population will never see or need anything above first year high school math and algebra.
    Tell me does anyone submit their post via written word and snail mail? NO! Why? We have better ways of doing these things.
    The same with math and algebra.

    Link to this
  11. 11. Jennifer Ouellette 10:42 pm 08/14/2012

    Try reading the article above. It’s about more than just what you happen to find practically useful.

    Link to this
  12. 12. negablade 10:57 pm 08/14/2012

    “The majority of the population will never see or need anything above first year high school math and algebra.”

    Perhaps. But if the majority of the population never learn anything above first year high school math and algebra you can guarantee they will never need math above that level. If you don’t have the tools, you’ll find ways not to use them. You said you worked as a communications engineer and only used software to solve your problems. I can only conclude that your duties were routine. Someone else had invented the software tools for you, so the problems you encountered day to day must be well defined and understood. Since you didn’t need to invent your own tools it doesn’t surprise me that you didn’t need higher level math.

    But, not all problems have off-the-shelf solutions. Math and algebra are often important when you can’t rely on solutions other people provide.

    If you have a hammer you can drive in a nail. But if all you have is a screwdriver…you’re screwed.

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  13. 13. djamie 11:40 pm 08/14/2012

    I went to primary school in New Zealand in the 1970′s (that’s elementary school for you guys).It inculcated a deep fear of maths. I struggled throughout high school and my adult life. I was, and still am, a words guy.
    Recently I completed an MBA – full of statistics and algebra. For the first time in my life I appreciated the beauty and profound nature of numbers. We teach maths in the wrong way in high schools. We should start by appealing to kids interests. Do you aspire to be a CEO, drive that big car? Do you like fast aircraft, admire spaceships, listen to music on an iPod? Then you must understand maths – because it underlies and underpins all of these things. Steve Jobs said this century will belong to those who stand at the intersection of the sciences and the arts. I personally hope for a new generation of gifted teachers and educators who can explain this most fundamental and vital subject in compelling and relevant ways. In another life, I would have followed my dream and been an aerospace engineer. The thought of my children being told not to worry because its simply too hard and you’ll never really use it anyway make me want to weep.

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  14. 14. johannon 12:24 am 08/15/2012

    Link to Daniel Willingham’s response is also broken (seems like the random string at the end is different?), should be http://www.washingtonpost.com/blogs/answer-sheet/post/yes-algebra-is-necessary/2012/07/30/gJQAr6xMKX_blog.html

    and link to Rob Knop’s response is also broken (missing an ‘a’), should be
    http://scientopia.org/blogs/galacticinteractions/2012/07/29/when-andrew-hacker-asks-is-algebra-necessary-why-doesnt-he-just-ask-is-high-school-necessary/

    Link to this
  15. 15. Jennifer Ouellette 1:22 am 08/15/2012

    This is why it’s always better to copy and paste links rather than re-type. Will correct.

    Link to this
  16. 16. finstercat 9:23 am 08/15/2012

    A “communications engineer” who doesn’t need to do math? That explains a lot… It reminds me of the time a cashier gave me change for a $20 when I had given her a $10: She knew I’d given her $10 but had hit the $20 key as the amount tendered and, not realizing she’d entered the wrong NUMBER and in spite of my protestations to the contrary, insisted that she owed me the incorrect amount because the REGISTER SAID SO! She had not even the vaguest intimation of what my correct change should have been. Sad.

    Computers to the rescue? GIGO, and only if you have some understanding of the principles involved can you identify when the results (and, perhaps, input) are suspect.

    Link to this
  17. 17. socorr 9:13 pm 08/15/2012

    finstercat @16
    That explains a lot… It reminds me of the time a cashier gave me change for a $20 when I had given her a $10:

    To some extent, that seems like bad training. Most people who give change from registers, put the bill to be changed on top of the cash register drawer so that they can show what was tendered! But I did have a similar situation this evening, concerning how much beer I had consumed. She said three, I said four (I’m stupid that way). Each of the beers was $4.00, and I gave her a twenty. Because I was first charged for three and given her a twenty, and the original change was for that, as we worked out I should have been charged for four, she kept insisting that I should get $5.00 back in change. I said “Put $4.00 in the tip jar and $1.00 in the drawer.”

    What ended up with the “fifth dollar”, I have no idea. But this is an example about not being able to do trivial algebra and relying on the cash register.

    George

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  18. 18. ithaca 11:00 am 08/16/2012

    I think that this discussion mostly misses the point.

    A certain amount of math really is necessary to understand many technical subjects, and we certainly shouldn’t back away from requiring that level of understanding of every high school graduate. But the trigonometry used to calculate some diagonal in a building structure, say, or to understand whether a measure is statistically significant, is very different from the analysis that proves the theorems underlying these concepts and methods. A thousand people can (if properly trained) learn and apply these concepts for every one that can actually derive them from first principles.

    It’s proofs that are preventing the average person from enjoying the genuine empowerment that comes from being able to understand and apply arithmetic, statistical measures, physical trigonometry, and elementary analytic geometry (including enough algebra to cope with two-dimensional coordinate systems). A high school curriculum that taught those subjects using nothing but cookbook approaches to practical problems would give students a much more enjoyable educational experience and would satisfy the practical needs of just about everyone, including many if not most engineers and a fair number of scientists.

    The logical thinking benefits of math are real, but I believe that the entire benefit to logical thinking conferred by several years of math could be delivered in one well-taught semester of symbolic logic, and it would be more fun, too. Everyone who passed such a course would be better equipped to cope with real-world logic, and anyone who came out of it with a fondness for proofs could tackle the theoretical side of math. It would be great if the rather small minority actually suited for mathematical analysis could find themselves that efficiently.

    Jon

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  19. 19. mattdjorgensen 11:42 am 08/17/2012

    wow…GREAT article. as my daughter is just entering 2nd grade, i’ve been thinking a lot about her future education. i really dislike the idea that you either just ‘get’ math or you don’t. yeah, it can be hard. but does that mean we should just resign ourselves to never learning these concepts? thank you for your eloquent discussion of the benefits of engaging with something challenging.
    -matt jorgensen, madison, nj

    Link to this
  20. 20. Evolouie 3:41 pm 08/28/2012

    ” finstercat” You can not be serious?
    Do you always take a gallon measurewhen you go to the gas station?
    Do you always take your scale to the produce market?
    Do you always get a second opinion when the doc says you have a cold?
    Get real, advanced math is something few people will ever need or use.
    There are times you have to accept what the world throws at you.
    I do not measure the gas I purchase. I do not Weigh the produce I buy.
    I do not get a second opinion for a diagnosis of a cold.
    The reason is obvious, even if you can’t or wont see it.

    Link to this
  21. 21. Evolouie 3:52 pm 08/28/2012

    And as for the GIGO. It just doesn’t fly in the business world.
    If the math is off the software would not sell.
    I use many types of software all the time, and they work and save me many hours of my employers time and thus makes the company more profitable.
    Computers do work, always use them in place of pen and paper, use them when ever you can.

    Link to this

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