"Mathematicians have no friends, except mathematicians. They are usually fat, unmarried, aren't seeing anyone, and have wrinkles in their forehead from thinking so hard."
Sound familiar? How about this?
"[Mathematicians are usually] bald, overweight, unmarried men who wear beards and glasses and lead little or no social life."
Neither statement would come as a surprise if you were in the habit of asking school pupils to describe their image of what a typical mathematician is like. The two quotations are taken verbatim from the recently released report of a study of 476 12- to 13-year olds in the US, Britain, Finland, Germany, and Romania, reported in the Christian Science Monitor on 8 January. They are representative of a strongly negative stereotype of my profession widely held by young adolescents.
Now, a straightforward application of classical probability theory tells me that, among the thousands of readers of Devlin's Angle there probably is a fat, unmarried, forehead-wrinkled, friendless individual who can't get a date. I dare say my readership also includes the occasional bald, overweight, unmarried man with a beard and glasses who leads little or no social life. To such readers, let me, like many a commentator before me, say please don't blame the messenger. I'm not making this up, I'm simply reporting it. The question I want to ask is, "How representative is that picture of a mathematician?"
Having moved in mathematical circles for over thirty-five years now, my answer is an unequivocal "Not at all."
"So why worry?" you might say. "Does it matter that we don't all look like the tall, blond-haired, blue-eyed Matt Damon in the movie Good Will Hunting?" Of course it doesn't matter. Being a mathematician has nothing to do with physical appearance or an ability to get a date. (And, for the record, I personally don't have a problem with fat, unmarried, forehead-wrinkled, friendless individuals who can't get a date, nor do I mind if such people become mathematicians.)
The reason the report bothers me is that it may indicate a major reason why so few children elect to study mathematics (or allied fields like physics or computer science) at university, and hence go on to pursue a career as a mathematician or a mathematics teacher. As Susan Picker, a member of the research team that produced the report, observes, "For children, images tend to be gatekeepers, and kids who would prefer an active social life don't want to end up being lonely geeks."
Unfortunately, according to Professor John Berry of Plymouth University in England, who ran the study, "The image we got ... was a very negative one." "The average picture was of a scruffy person, probably with pens in his shirt pocket, holes in his clothes, and equations written on his arms." (Professor Barry also points out that the children interviewed almost invariably assumed math teachers were male.)
Picker adds that when she asked children to draw a mathematician, the result was predictable. "The children saw them as unprepossessing nerds."
With countries such as the United States and Britain currently facing a chronic shortage of students electing to study math and go on to become mathematics teachers, the report raises some significant questions. The first one being, "Where are these young children picking up this stereotype?" It's tempting to blame those familiar whipping boys: television and the movies. Except that mathematicians are almost never portrayed on either medium! As far as Hollywood and the television production companies are concerned, mathematicians simply don't merit any attention, positive or negative.
So maybe the problem has its origins closer to home. Perhaps we can see at least elements of the stereotype in reality. In a profession where, in the final analysis, truth is everything and appearance nothing, maybe many of us do pay little attention to our dress. But people in many other professions don't spend a fortune on clothes or hours in front of the mirror either. Likewise, few of us in any profession have the slim, youthful appearance of a movie star. So the children's' comments on clothing and corporal geometry must surely be a manifestation of something else. I wonder if that something else might be attitude. Perhaps some of us ---- actually, given the report's findings it would have to be many of us --- after years of struggle trying to get students to "see it", start to show signs of weariness and/or impatience.
For instance, according to the report, in Finland several children drew pictures of math teachers holding machineguns. One pupil wrote a caption: "If these sums are wrong, it's the end of you."
Does that tell us anything?
A few years ago, I was speaking at a conference for middle and high school mathematics teachers. In my presentation, I made the point that I thought it was important for those of us in the mathematics education business to convey the notion that mathematics can be fun --- that there is enjoyment to be had from working out a problem that at first seems impossible. The mathematician who spoke directly after me began by remarking that he did not think mathematics should be fun at all. Now, I knew --- and I confirmed it with him afterwards --- that his opening remark was intended to be amusing. After all, like me, this person was someone who loved mathematics and had devoted his life to it. Unfortunately, to both our surprise, a large section of the audience burst into loud and enthusiastic applause at his remark. Neither of us were in any doubt. These teachers believed down to their socks that mathematics should not be fun. Like long cross-country runs and cold showers, you did mathematics because it was good for you, and the pain and the misery was an essential part of it.
Well, we live in a free country, and every one of those individuals in my audience was entitled to his or her view of how mathematics should be taught. Whether or not society should employ them as teachers of our children is another matter. Particularly if, as the Plymouth study might suggest, the result is that the attitudes of a minority of teachers results in a negative stereotype that is applied to the majority.
These thoughts were brought to my mind when I attended the World Economics Forum meeting in Davos last month. After I gave my talk --- a brief survey of how mathematics can be applied in the modern world --- a significant number of members of the audience came up to me and started to recount their own very negative experiences of mathematics at school. Now, by the very nature of the annual Davos meeting, all of the attendants are there because they have been highly successful in their chosen arena and have reached positions of power and influence in society --- often considerable power and influence. The ones who attended my talk did not appear to have a genetic predisposition to hate mathematics. Indeed, many of them told me they found what I said fascinating --- as any mathematician knows mathematics is. And yet our profession, the mathematics educators, had sent these future leaders of society out into the world with a highly negative experience of the discipline.
As a profession, we debate endlessly what is the best way to teach mathematics. And that is all to the good. But what we teach and the methodology we adopt are surely not all there is to it. The attitude we convey is, at least in my view, also important. In fact, I think it is crucial. If the teacher does not convey enthusiasm and love for mathematics --- let alone if he or she does not even have that enthusiasm and love --- then no amount of curriculum development or good instructional technique is going to succeed.
My guess is that the negative stereotype of mathematics teachers that came out of the Plymouth study is simply a stereotypical representation in physical form of a psychological impression. Read what the children said not as a description of how their teachers actually looked but rather as a code for the way they came across in the classroom, and a very different picture emerges. One I feel we need to do something about.
I fear it is unlikely we can completely solve the problem of the highly negative image of mathematics and mathematicians until society decides to pay mathematics teachers more, and thereby attracts more qualified people into the profession. After all, it's hard for a teacher who does not him or herself feel comfortable with and have a love for mathematics to convey the subject in an exciting and engaging way. (I suspect that those "make 'em suffer" teachers at that conference I attended had little real love for the subject, and adopted the attitude that what they felt was good for them was darned well good for their pupils.) Well, even with increased funding and conditions for math teachers, it would take at least a generation to fill our schools with top notch math teachers who could really inspire their pupils. But those of us who are mathematicians in colleges, universities, or industry can do something now. We can provide young children with role models.
Another session at Davos was about the importance of good role models in many walks of life. (Incidentally, forget all those newspaper articles about the annual Davos meeting being simply an exclusive club where the world's elite get together once a year to plot the future of the world. There is much talk about ethics, about science, about education, and in general about trying to improve the world.) World leaders of all kinds spoke of the crucial influence role models had played in their lives. We can learn from them. It takes very little time or effort to visit a local school occasionally to tell the students what we do --- what mathematicians do. And in my experience, most teachers are delighted to have a "real, live, practicing mathematician" come into the classroom. The effect can be significant.
As Picker describes in the Plymouth report, after the research had been completed, she arranged for a group of children from the study to meet and talk with eight leading mathematicians. "After that, the drawings they did were quite different," she said. "They saw mathematicians as real people." Real people. Now there's a thought.
I think we need to work on our image. And I don't mean our wardrobe or our waistline.
Devlin's Angle is updated at the beginning of each month.