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A Sufficient Mathematical Background

A couple of weeks ago, the Washington Post ran an op-ed written by G. V. Ramanathan, emeritus Professor in mathematics, statistics, and computer science, entitled “How much math do we really need?”  As the title suggests, Ramanathan uses his space in the paper to argue against the grain of conventional wisdom when it comes to mathematics education; his point is that American students are actually receiving too MUCH math, rather than not enough.  It’s an appealing thesis, especially for those looking for an excuse to embrace their own math phobia, but ultimately I find it to be less than responsible.

Consider, for example, the following passage:

How much math do you really need in everyday life? Ask yourself that — and also the next 10 people you meet, say, your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher.

Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as “Quantitative Reasoning” improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.

Those who do love math and science have been doing very well. Our graduate schools are the best in the world. This “nation at risk” has produced about 140 Nobel laureates since 1983 (about as many as before 1983).

Let’s address this passage point by point.  First, while it’s true that many people don’t use math in their everyday life, this is not a criticism that is unique to mathematics.  I’d contend that most people in the list he mentions don’t use U.S. history in their everyday life (except for perhaps the lawyer), nor would most of them use English literature or biology.  Does it therefore follow that none of these things should be taught in schools, either?  Ramanathan seems to be suggesting that the purpose of education is to impart only the skills that will be needed for the vast majority of the student population when it reaches adulthood.  This is fairly ridiculous, though, both because the range of human interest is so vast that what would comprise such a necessary intersection would seem to be not nearly deep enough (as he himself says, the math component could be learned in the “early years”), and also because it’s not entirely clear what skills children learn as students will turn out to be the most important to them in their future careers.  Perhaps Ramanathan is an advocate for having students focus on an area of interest earlier in their academic life, which might explain this position, but it’s never made clear if he believes this to be a sound alternative.

I'll concede that this guy probably doesn't need to know much math. I doubt whether the same can be said, though, for the people who create his games.

What’s more, students sometimes fail to realize how important mathematics is to their future career plans until they’ve already written themselves off as hopeless students of the subject.  By shutting academic doors prematurely, students are also shutting the doors to potential career opportunities.  The fact that so many students hate math I think speaks more to the way math is taught than the fact that it is taught at all.

And while we’re on the subject of career opportunities, in a time when job reports are at the forefront of the news, we should be encouraging students to go into technical fields, not telling them that since some of them might not use math, there should be less math in schools.  This seems to me to be a fairly nihilistic viewpoint, and in the interest of neutrality, I’d say the same thing about a professor in a different discipline advocating a similar platform.  As a graduate student in mathematics, I can’t remember the last time I directly applied knowledge I gained in a history class, an English class, or a chemistry class.  I do, however, see the value in my having taken such classes, even though my career path probably won’t benefit from that knowledge in any way.

This brings me to the next point: I don’t see why it’s at all obvious that mathematics has any less relevance to everyday life than literature, history, politics, or music.  The relevance of any of these disciplines to one’s everyday life depends highly on the life one is living, and while it may be true that on average mathematics appears less in popular discourse than these other subjects, it doesn’t follow that it is therefore less worth of study by a general population.  By way of analogy, just because news coverage may spend more time talking about Lindsey Lohan than the American presence in Afghanistan, does it follow that Lindsey Lohan is inherently worthier of investigation than the American presence in Afghanistan?  (Note that I don’t mean to equate Lindsey Lohan with literature, history, or music…politics, maybe.) The only unsubstantiated myth worse than the one that “courses such as ‘Quantitative Reasoning’ improve critical thinking” is the one that “[u]nlike literature, history, politics and music, math has little relevance to everyday life.”

Lohan's portrayal of a mathlete in Mean Girls, unfortunately, shatters my analogy.

Finally, let me address the final point in the quote.  Ramanathan remarks that American graduate schools in mathematics are the best in the world, but fails to mention what they lack: American graduate students.  The best in the world these schools may be, but that’s because the students are the best students in the world, not because they are Americans who have come up through the American education system.

Also, the statement that students who love math and science excel in it isn’t supported with any evidence, and it’s not at all clear that it’s true.  In fact, I’m sure there are a number of students in this country who enjoyed math but didn’t stick with it because they had an insufficient support system in their education.  It’s simply not true that a love of math is a universally good enough support system for a student who wants to study the discipline.  What good does it do to say “Among students who love a certain discipline, they will learn it well enough because they love it, and for everyone else, it’s not important anyway”?  If that is one’s philosophy, why have education at all?

The Nobel Laureate claim is also not completely relevant, since there is no Nobel prize in mathematics, and there are Nobel Laureates for disciplines that have nothing to do with mathematics.  If you want to measure a country’s math aptitude by big prizes (which itself seems like a rather dubious metric), a more natural thing to consider would be the Fields medal.  The difficulty here is that the sample size is smaller, but in the interest of comparison, here are some things worth noting: Since 1983, there have been 3 recipients of the Fields medal from America.  By contrast, from 1962-1982, the number of American Fields medalists was three times this number.  Moreover, in the last 20 years, only 2 Americans have won the fields medal, as compared to six French mathematicians and six Russian mathematicians.

The world is moving towards a state of more complexity, not less, and this will require a stronger mathematical background on the part of the world’s population.  Rather than burying our head in the sand, as Professor Ramanathan seems to be advocating, we should be seriously considering how mathematics can best be taught to a 21st century student body.  What good does it do to pander to a general population that already hates mathematics (due in no small part to the way they were taught, I’m sure)?

In the future, will the Washington Post print more insightful musings on the current state of math education in this country?  I certainly hope so.

  • Sandy

    I hope you sent this to the Washington Post as an op-ed!!

  • Cody L. Custis

    Ignoring the irony that my mighty mathematical skills provide the ability to get around the spam protection, I’m reminded of a conversation I once had with a student learning mathematics. He insisted that four and one-fourth were the same thing. I told him that they are different, and I’d be willing to give him one-fourth a dollar for four dollars. He refused to make the trade, but still wouldn’t conceed that they are different.

  • Mike Thayer

    I think the real point is: mathematics is _taught_ poorly. Or, perhaps, the mathematics _curriculum_ as used in the US is written poorly. Students spend year after year after year learning ever-more-esoteric mathematical techniques that the vast majority of them will NEVER use, which leads them to become more and more disengaged from the subject.

    In this world of high-stakes standardized testing, though, the question of “what to teach” is a big one.

    I speak as a math teacher at a good public high school in the Northeast, by the way. And I’ve been doing it long enough to recognize that the two “sides” in this debate are talking past each other. It is not, nor should it ever be, a question of “Math is useless – let’s not teach it” vs. “Students should learn as much math as possible, and be held to ever higher-and-higher standards”. The real question for math educators and/or mathophiles is – what math do we want the BULK of our students to know, how can we most effectively teach it to them, and how can we make students not dislike math so much? The students who will become engineers, physicists, mathematicians, actuaries, etc., etc., will take as much math as they can – they should be told that that is what they will need for their futures.

    But I have to confess, I have a very difficult time with the argument that ALL students need to know how to factor a quadratic, for Pete’s sake. And to compare learning how to factor with learning about literature or history is a foolish one – there is no analogy, in my opinion.

  • Dan L.

    Mike Thayer raises some interesting questions. I’m now retired, and I have to admit I’ve never needed to know how to factor a quadratic in ‘real life.’ Nevertheless, as you noted, that’s true for most of the details I learned in every discpline I was ‘forced’ to study as a child.

    However, executing my home-improvement projects (which I think would translate to the construction trades) has benefited from the higher-level math of algebra (e.g., equation solving such as finding the size of the missing piece when knowing the size of the whole) and geometry (e.g., appropriate angles for miter cuts). I suppose we could stimulate construction-services employment by constraining such information to trade schools to the detriment of the do-it-yourself industry.

    As someone with a math degree, I’m sure I’m biased, but my experience has been that those with math degrees also have strong English-language and analytical skills. This suggests to me that studying math is not only about mathematics but also about precision and problem-solving.

    Aren’t the humanities always presented as a means to a greater understanding of the human condition? Why isn’t math allowed to make such an abstract contribution?

  • Matt

    Thanks for the comments, all. Mike, I wholeheartedly agree with your points. There are many rich debates to be had here, and it’s unfortunate that this op ed doesn’t really appear interested in them.

    Dan, I agree with you that a solid mathematics education has helped me in other areas besides math. Regarding your question, I think part of it may have to do with the fact that mathematics has such wide applicability. Mathematics is frequently, it seems to me, viewed as a means to an end (how can we use math to study flight, or cancer, or physics); while these are all noble pursuits, the idea of math for math’s sake is not viewed in the same way. Perhaps it has something to do with the fact that math has a wide family of applications, unlike something like French Literature, so that math tends to be viewed more through the prism of what good it can do for us, rather than what makes it interesting in its own right (and therefore worthy of study for its own sake). I don’t think anything about the way math is currently taught will help to reverse this trend.

  • Rilian

    Why have school at all? That’s a good question. There is no legitimate answer.

  • Michael Laidlaw

    I’ve learned to view mathematics from a more ‘artistic’ viewpoint. Once I realized it was less about what I could solve and more about ‘learning something new’ I fell in love. Math allows me to view everything with a different lense. From this perspective, there is no limit to how much math we should learn.