Here’s something you’ll never see in popular writing about musicians:
“Music. For most of us, the mere word conjures up memories of metronomes and endless scales, the student’s never-ending fear of playing a wrong note (or the right note at the wrong time), and the frowns of teachers from whom a curt ‘Good’ was the highest expression of praise. And yet there are some people who just can’t get enough of making music; they practice hour after hour, honing their skills and punishing their bodies, long after the stage of life when there are parents and teachers forcing them to do it. What strange quirk of character compels this behavior?”
As I said, nobody writes about musicians that way. And yet, when the subject is a mathematician, writers sometimes come up with passages like this:
“You and math – one of the greatest love/hate relationships of all time. What is it about the subject that excites us yet sends a chilling tingle down our spine at the same time? How can it be so precise, yet so fickle? We may never know the answers to these questions, but we do know that math is ubiquitous, though some of us may try to hide from it.”
This is from the introduction to a 2010 profile of mathematics editor Vickie Kearn, which I recently saw on the blog-site of Princeton University Press, where Ms. Kearn has worked as senior editor for many years. The intro continues in a similar vein. “While math may sometimes cause us to cry tears of despair, it has caused Vickie to cry tears of joy.”
This is an extreme example, I grant you (the author was an undergraduate intern). But the underlying approach is one I’ve seen other journalists use, though usually not so blatantly. I think I get what those journalists are trying to do: they’re reaching out to people who wouldn’t ordinarily read an article about math and saying “Hey, I’m not so different from you; you should really give my article a try.” But how far can one take this device before it becomes demeaning to the subject matter? It’s good for a writer to establish a bond with the reader. But how far can a writer go in distancing herself from her topic without snapping the thread connecting her to the topic in the reader’s mind?
A related gripe of mine is news editors who, when publishing an article about mathematics, feel they need to dispel the tension conjured up by the scent of math by sticking in a jokey headline like “It all adds up for math whiz” or “Math proves to be winning formula for local teen”. (If you’ve seen headlines like these, please submit them in the Comments!) Do these editors know something that I don’t about the cues that make a reader peruse one article rather than another? Is it the same thing that Stephen Hawking’s editors knew, when they told him (back when he was writing “A Brief History of Time”) that every equation included in his book would reduce his readership by a factor of two? I’d like to think that these editors are wrong about the world that they and I live in, but part of me is worried that they’re right — in part because I sometimes stop reading an essay or article when I hit a passage that calls for a little more thought than the part that came before.
I’m guessing that some of those journalists and editors are mathphobes, while others are not themselves mathphobes but are eager to keep their stories appealing to a wide range of readers, including mathphobes. But whatever their motive may be for reminding math-anxious readers of their math anxiety, I worry that the cumulative impact of these messages normalizes or even valorizes that anxiety. Part of what’s going on is a conflation of mathematics with arithmetic, combined with a fear of numbers. Numbers frighten many people, or leave them feeling cold. But what is accomplished when so many articles about math start by reminding readers of this?
Question: Is this sort of pandering to mathphobia an American phenomenon, or is it found in other countries? Somehow I don’t imagine French newspapers (for instance) adopting this sort of tactic.
The intern who wrote the passage I quoted strikes me as someone who fears math too much to be a good tour guide on a mathematical journey for non-mathematicians. Someone like me may not be the best tour guide either, since I don’t know first-hand what it’s like to be a non-mathematician intimidated by mathematics (though I do know what it’s like to be, for instance, a non-algebraic-geometer intimidated by algebraic geometry, which is a vaguely similar situation). Probably the best tour guides are people who have a dual perspective as insider and outsider. Who are your favorite converts-as-evangelists in the domain of mathematics? Let me know in the Comments!
Scott Kim (check out his website), an early reader of this essay, felt that I should go beyond pointing to the problem and include a corrective call to action. He suggests that the many “Don’t worry, I hate math too” messages being broadcast nowadays might profitably be counteracted by “You only think you hate math” messages. It’s an interesting tactic. He points out that there are all sorts of paramathematical activities, like Tetris and Sudoku, that huge numbers of people find riveting. and that the popularity of these pastimes suggests that there is something mathphilic in many people who don’t think of themselves as mathphiles. Jumping off of Scott’s suggestion, I wonder if anyone has suggested a Freudian framework in which mathphobes and “misomaths” are seen as people who have “displaced” onto mathematics their fear and hatred of unsympathetic teachers or mindless drill or procedures divorced from meaning and context, and whether the appropriate “therapy” is to help them figure out that it’s really something else they fear or hate. (Of course, this doesn’t necessarily get rid of the fear and hatred; it just turns it into something other than mathphobia/misomathy and thereby makes it someone else’s problem, ha ha.)
I’m not sure what sort of journalistic style the “You only think you hate math” stance would lead to, but I’m sure I’d like to see it!
Thanks to Sandi Gubin, Scott Kim, Keith Lynch, Joe Malkevitch, Hilarie Orman, and Evan Romer.
Next month, two essays: Introducing “Thirdsday”, and The Magic of Nine.
#1. Yes, this month’s essay is short and on the rough side. Thanks to an end-of-semester work crunch, I didn’t have time to develop the essay I’d originally planned to write. At the same time, I happened to read the profile of Vickie Kearn, which inspired these musings about math journalism as a substitute topic. To compensate for this month’s skimpy offering, in January you’ll get two Mathematical Enchantments for the price of one.
#2. Pre-reader Sandi Gubin raised the question “How prevalent is math anxiety?” Of course percentages vary because there’s no clear-cut definition of the condition. A good entry point into recent literature is the 2014 article “Mathematics Anxiety: What Have We Learned in 60 Years?” by Dowker, Sarkar, and Looi. Other pre-readers felt that, with the increased use of calculators in math education and the decreased emphasis on arithmetic procedures, number anxiety plays a diminishing role in math anxiety. They suggested that modern-day math anxiety is really several different ailments, distinguished by which particular course turned out to be a brick wall for the student in question. (Thus, Geometry Jitters needs to be distinguished from Algebra Angst and Calculus Conniptions.)
#3. Several early readers of this piece felt that I was wrong in thinking that math is treated any worse in the popular press than other arcane endeavors, and that areas seen as even “geekier” (such as science fiction) are portrayed with even more hostile distortion than math.
One reader pointed out the difference between subject matter stories and human interest stories, and said that writers of the latter often feel that the whole point of the story is the oddity of the subject: if they don’t make the person seem unusual, perhaps to the point of weirdness, then why should they write about that person at all?
It was also suggested that headline writers are nearly always encouraged to hook readers with some sort of wordplay, regardless of the topic.
#4. Several early readers of this piece felt that much more could have been said about similarities and differences between math education and music education, and the negative impact that they can have. If I’d assimilated these comments and come up with a synthesis of them, this would be a more interesting essay, but one that I don’t have time to write by my deadline.
#5. The reason the profile of Vickie Kearn came to my attention is that she recently announced her retirement from the Press. This came as a bit of a blow to me, since I was hoping to work with her someday in turning some of these essays into book-chapters. Hardly any of my Mathematical Enchantments pieces are “blogs” in the traditional sense; rather, they’re my way of testing out ideas, trying out ways of explaining those ideas, and more broadly, becoming a better expositor. My main disappointment with the process of blogging is how little feedback I get in the Comments section. Hopefully the very sketchiness of this month’s essay will encourage more people to respond than usual.
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I think the big difference for children/students practicing the piano or violin and practicing multiplying polynomials and factoring polynomials is that no matter how bad you sound when you play the piano or violin you can hear hints of tunes that give you satisfaction By comparison there is little MEANING (except possibly for the “mathematically inclined”) for skills involving the algebra of polynomials and many other topics in K-12 mathematics, and no marginal satisfaction (except perhaps pleasing your tiger Mom).
The reason I try to talk about applications, modeling, and contexts, in general education classes and courses for teachers that I have taught is that even if the students find what I show them unsatisfying they at least have the hints of the “tunes” of the way mathematics affects their lives (streaming video, cell phones, better weather forecasts, inventory maintenance, video games, snow plow routes, school choice, etc.)
The mathematics community to some extent is responsible for this problem in having moved from the NCTM Standards to the CCSS-M and now the 50 states reinterpreting the CCSS. These standards emphasize depth at the expense of breadth and systematically disregard many topics in discrete mathematics, which might better serve the needs of students in K-12. When students go on to college after high school the most typical mathematics the see is some version of “college algebra,” which attempts one more time to get them “proficient” with skills they have not learned in the past and in most cases they don’t need for the careers they wish to purse. No wonder we have many people phobic about mathematics in ways that are different from their “negative” encounters with music.
It often seems that K-12 curriculum has been chosen more for the convenience of those who go on in STEM fields by preparing them to take Calculus than to show them a broader range of topics that have no less chance of “hooking” the mathematically inclined to purse mathematics than what we teach now. Such topics include graph theory, modular arithmetic, mathematical models involving operations research and fairness questions, etc. In training future teachers, we should be especially sensitive to showing them more than the mathematics that leads to Calculus, and, and, thus, help to break the cycle of producing a surprisingly large section of the American populous that has had a negative reaction to the mathematics that they learn.
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I too made a comparison between math education and music education in a recent blog post (Understanding “Understanding” https://blog.mathed.page/2018/09/24/understanding-understanding/ ). My piano teacher friend was offended that his profession was used as a way to justify inane math drills. (“Before you can play a sonata, you need to play scales!”) When he teaches, the point is the music. What motivates students is the recital, not the scales. One does not come before the other. They are intertwined.
Alas, so much math teaching is not about the math. It is about obedience, memory, and speed. How quickly can you carry out steps you don’t understand or care about? The reason so many people fear math is not newspaper articles. It’s more the other way around: people write those things because so many people fear math. The causes of math anxiety are many, but almost all of them go back to bad teaching: separation of skills from understanding, boring drills, apparent pointlessness, sadistic time pressure, etc.
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I agree wth what Joseph implies above that the difference between math and music is that the latter provides a sort of immediate feedback that math generally lacks.
But with that said, I don’t think math holds a monopoly on negative attitudes… I have myself spent most of my life telling people that I have no artistic ability and ‘can’t even draw a straight line.’ Haven’t we all known folks too who said ‘I hate Western Civilization, it’s sooo boring’… math may be a particularly frequent example, but I think this self-deprecating tendency of people to point out their own weaknesses or dislikes (of things they know they ought like) is commonplace.
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(If you want more comments, one way to encourage them is to reply (quickly and in nontrivial depth) to the comments you get! Then your blog comments section can turn into a “lively discussion forum”, which feeds on itself. And even before that, readers can see that a comment will be “rewarded”. From my perusal of various blogs, I think this is one of the biggest distinguishers between the ones which succeed or fail in attracting comments.)
That’s a very interesting suggestion! I’ll give it a try. Thanks!
I suspect that a larger fraction of teachers of math (at pre-college level, and especially at pre-high-school level) don’t like math or are not good at it, than the analogous fraction of teachers of music. Maybe this is one cause of bad math teaching and high math-phobia.
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