The Washington Post recently published an op-ed by mathematician G. V. Ramanathan. The subject? Mathematics education. It is a mix of good points and bad points. Let’s have a look.
Twenty-seven years have passed since the publication of the report “A Nation at Risk,” which warned of dire consequences if we did not reform our educational system. This report, not unlike the Sputnik scare of the 1950s, offered tremendous opportunities to universities and colleges to create and sell mathematics education programs.
Unfortunately, the marketing of math has become similar to the marketing of creams to whiten teeth, gels to grow hair and regimens to build a beautiful body.
There are three steps to this kind of aggressive marketing. The first is to convince people that white teeth, a full head of hair and a sculpted physique are essential to a good life. The second is to embarrass those who do not possess them. The third is to make people think that, since a good life is their right, they must buy these products.
So it is with math education. A lot of effort and money has been spent to make mathematics seem essential to everybody’s daily life. There are even calculus textbooks showing how to calculate — I am not making this up and in fact I taught from such a book — the rate at which the fluid level in a martini glass will go down, assuming, of course, that one sips differentiably. Elementary math books have to be stuffed with such contrived applications; otherwise they won’t be published.
The calculus book I used in college had a problem that involved a farmer dropping a bale of hay from an airplane to some cows waiting below. Someone in class objected that it seemed a rather implausible scenario. The professor (actually a graduate student) suggested it was likely that the problem was originally conceived during WWII, and involved dropping a bomb onto some helpless civilians. But feeling that to be in poor taste, the authors changed it to dropping a bale of hay.
Anyway, there is a lot of truth in what Ramanathan is saying here. Certainly an over reliance on asinine, contrived applications is a weakness of many modern textbooks. The notion that you might just explore patterns and try to discover abstract relationships for the sheer satisfaction of it is mostly disallowed. On the other hand, I think he might also be overreacting. I very much doubt, for example, that the problem about the martini glass was intended as part of a practical treatise on fluid dynamics. I suspect the author was just trying to present a standard calculus problem in an amusing way.
You can see attempts at embarrassing the public in popular books written by mathematicians bemoaning the innumeracy of common folk and how it is supposed to be costing billions; books about how mathematicians have a more clever way of reading the newspaper than the masses; and studies purportedly showing how much dumber our kids are than those in Europe and Asia.
This I don’t believe. That so many people seem to lack a basic number sense, not to mention a near total ignorance of basic probability and statistics, absolutely has practical consequences. Just to pick one of personal significance to me, I can’t tell you how many creationists I’ve seen bamboozle their audiences with slick-sounding mathematical arguments. A closely related problem is the ease with which statistics are manipulated by unscrupulous pundits to justify whatever conclusion they like.
As for those studies to which Ramanathan refers, I think they mostly show that our kids perform poorly in mathematics relative to kids in other countries. Not that they’re dumber. That is precisely the point, actually. Why do our kids perform poorly on math tests? If American kids were just dumber then we would have our answer. Since I assume no one is inclined to accept that answer, I’d say there’s something worth looking into here.
We need to ask two questions. First, how effective are these educational creams and gels? With generous government grants over the past 25 years, countless courses and conferences have been invented and books written on how to teach teachers to teach. But where is the evidence that these efforts have helped students? A 2008 review by the Education Department found that the nation is at “greater risk now” than it was in 1983, and the National Assessment of Educational Progress math scores for 17-year-olds have remained stagnant since the 1980s.
Now he’s back on track. Mathematicians tend to be unimpressed by specialists in mathematics education, for good reason. Mostly we are just lectured to stop lecturing, and also to use more group work (excuse me, “cooperative learning.”). Mostly my reaction is the same one my high school calculus teacher once gave to one of my classmates. After we had all done quite poorly on a test, my classmate asked, “Doesn’t it reflect badly on you as a teacher that we all did so poorly?” My teacher replied, “Nope. I taught it fine. It reflects badly on you as a learner.”
The second question is more fundamental: 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.
Yikes! Now we’re in crazyville. I might be willing to grant politics, and maybe even history (though it seems to me plenty of people manage to go their whole lives without thinking seriously about either one.) But how on earth are literature and music relevant to our daily lives? Who needs to read The Scarlet Letter, or The Grapes of Wrath, or The Great Gatsby, or any of the other novels we were forced to read in high school?
Ramanathan has far too narrow an understanding of what it means to use something in life. The fact is that virtually none of the topics you learn about in school is directly relevant to your daily activities. You learn about them in school precisely because you won’t learn about them anywhere else. There is more to life than getting through the day without doing something stupid.
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).
Somehow I really don’t think the authors of “A Nation at Risk” were concerned that America would no longer turn out ferociously talented people who will succeed in math and science regardless of what they learn in school.
As for the rest, there is no obligation to love math any more than grammar, composition, curfew or washing up after dinner. Why create a need to make it palatable to all and spend taxpayers’ money on pointless endeavors without demonstrable results or accountability?
We survived the “New Math” of the 1960s. We will probably survive this math evangelism as well — thanks to the irrelevance of pedagogical innovation.
The issue is not so much whether people love math, it is whether they reject it before developing any real sense of what it is. I also don’t care if any given student likes reading literature, learning history, or eating spinach. We make kids do those things because it is good for them, whether they appreciate it or not.
There are certainly difficult problems to solve in mathematics education. For example, I think everyone, math major or not, ought to be able to give a coherent description of what calculus is, and what sorts of problems it was invented to solve. But the things I want everyone to know bear little resemblance to what typically gets taught in calculus classes.
Many schools, my own included, offers a course to non majors meant to introduce students to a swath of higher mathematics that they would otherwise never see. Such things, I believe, are great in principle, though I don’t actually know how successful they are. Frankly, one of the biggest problems in math ed is simply large numbers of unmotivated students. People who are content to do minimal work and get by with C’s. The best teaching in the world will not overcome a student who is unwilling to work hard at a subject.
There is much to fret about. But Ramanathan has not manage to put his finger on any of the real problems.