In and of itself, this might not seem like a particularly newsworthy achievement – as any Pi Day aficionado can tell you, there are people who have memorized more digits.  Perhaps what makes it newsworthy is the fact that the student is only twelve years old, or, more perversely, the fact that his accomplishment came in response to the challenge of his math teacher, who asked his students to memorize as many digits of pi as possible.  By far the most depressing part of the video is a brief clip that shows all the students in the classroom mindlessly rattling off successive digits of pi.  The lack of enthusiasm is almost palpable.

Now, I don’t want to come off as too much of a curmudgeon here.  I have no doubt that this student is stoked that he made it on to TV for an academic achievement, regardless of the actual merits of that achievement (at least the student is aware enough to remark that the information he’s memorized will probably never be put to use).  That’s fine – he has every right to be proud of himself for making it onto the local news.  What really gets my goat is the fact that this teacher thought it would be a good idea to make students memorize digits of pi.  I can think of few better ways to dampen a natural enthusiasm for mathematical learning than by asking students to memorize a series of digits that will have no practical value for any of them, ever.  It would be like having an English teacher ask students to memorize a random string of words which, taken collectively, didn’t teach the student anything about vocabulary or grammar.

Is there any benefit to this exercise?  According to the teacher, “The ability to memorize that much stuff has to help tremendously.”  Well, ok.  But aren’t there more important things to learn about in math class?  Is math class really the best venue to discover a talent like this?  I am fairly certain that students in Singapore aren’t spending class time and homework time memorizing digits of pi.  I’m sure this teacher has good intentions, but I fail to see much value in this apparently newsworthy event.  The mystique of the number pi, I suppose, never fails to attract attention.

If this exercise is what gets this sixth grader interested in math, then by all means he should memorize as many digits of pi as he can.  For the vast majority of students, however, such an exercise is probably beyond tedious.  I can only hope that this news story doesn’t inspire other teachers to compel other students to do the same thing.

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.

His opening is spot on: “I teach high school math.  I sell a product to a market that doesn’t want it, but is forced by law to buy it.”  He goes on to argue that the problem with math education, a problem exacerbated by most textbooks, is that it discourages what he terms patient problem solving.  Problems in textbooks rarely reflect the types of problems one encounters in real life: textbook problems usually supply you with just the right amount of information, and the question is frequently just a matter of plugging values into an appropriate formula.  More complicated questions are frequently presented in multiple parts, so that students rarely have to think long and hard about any one thing.  Instead, they are offered bite-sized pieces of a larger problem, any one of which is relatively simple.  Taken together, the net result may be the solution to an interesting problem, but by holding students’ hands like this along the way, they never develop a taste for solving difficult problems.

This hand holding, Meyer argues, trains students to become impatient when they encounter an actual problem.  If a question isn’t broken down into easily digestible pieces, any one of which can be solved by plugging and chugging into one of a short list of formulas, students are trained to throw up their hands.  In a world fraught with problems, however, this does a disservice not just to students who study mathematics, but all students.

The video is a little over 10 minutes, but if you have the time I’d encourage you to watch it.  Meyer talks about potential solutions to this failure of our educational system, and compares the current state of affairs to watching episodes of Two and a Half Men.  And despite the presence of a fraction in the title, the comparison is not favorable.

Enjoy!

(Hat tip to Patrick for sending me the link.)

Late last year, a study was published in Proceedings of the National Academy of Sciences which tried to pin down origins for the gender gap in mathematics education.  As I’ve discussed before, the gender gap in math education is shrinking, and has been shown to be less about biology and more about culture – in cultures where gender equality is weaker, the gender gap is stronger.  Nevertheless, even in American culture, the gender gap still persists, and this study by Sian Beilock and others has tried to figure out how, if the gender gap is culturally based, it comes about in young students.  The original study can be found here, while a discussion of the study that was featured in the news can be found here.

Professor Beilock and her colleagues tried to correlate young students’ math anxiety with the math anxiety of their teachers.  In particular, they looked at 1st and 2nd grade students, of whom a vast majority (over 90%) have teachers who are female.  The study assessed the math anxiety of the teachers and measured the math achievement of the students at the beginning and end of the year.  Here are the results, taken from the introduction to the paper:

There was no relation between a teacher’s math anxiety and her students’ math achievement at the beginning of the school year. By the school year’s end, however, the more anxious teachers were about math, the more likely girls (but not boys) were to endorse the commonly held stereotype that “boys are good at math, and girls are good at reading” and the lower these girls’ math achievement. Indeed, by the end of the school year, girls who endorsed this stereotype had significantly worse math achievement than girls who did not and than boys overall.

These findings make intuitive sense, and lend further support for the need to better our mathematics education at all levels, or at the very least require primary educators to study mathematics more seriously.  Teaching mathematics with confidence is not something that comes automatically, even for those who may have been good at math in their early years.

It’s interesting that boys weren’t more likely to endorse the view that boys are good at math and girls are good at reading if their teacher had math anxiety.  I’d be curious to see what the case is in a classroom led by a male teacher, both with and without math anxiety.  Given the dearth of male primary educators, however, this type of data may be harder to acquire.  In any event, the lesson here is clear: if you want your daughter to not fear math, it wouldn’t hurt to demand that her teachers not fear it either.  Or at the very least, demand that any math fear be exhibited only by male teachers.  That may be a cheaper solution.

I’d also be interested in knowing whether this trend can be reversed by a suitably competent teacher.  If a group of 2nd grade girls is taught math by a woman who is unqualified, but in 6th grade is taught by a woman who is exceptional, can this help undo the damage that the 2nd grade teacher has done?  I would hope so.

It's too bad Prezbo doesn't have lady parts.

Lockhart’s article lambasts the current state of mathematics education in this country. Some of his main points are the following:

• Mathematics is an art form, but unlike other art forms like music or painting, is not understood as such by the general population. As a result, students are not exposed to the beauty of mathematics, and are instead taught through drill and memorization, which effectively kills any natural curiosity the student may have.
• The most important part of mathematics lies not in the facts or theorems that students memorize, but in the arguments that show why these facts must be true. By stripping away the beauty and elegance that lies behind many of these arguments, students don’t develop an appreciation for (or a real ability to do) mathematics.
• The only class that does emphasize proof (high school geometry) sterilizes the process so much that all the beauty is drained from the arguments.
• Math education spends too much time trying to force artificial connections to the real world, rather than exposing the natural beauty that lies within mathematics. Most word problems don’t actually reflect any type of problem that one would find in the real world.

• Lockhart has no love for the endless drilling that goes on in current math classes (the type of drilling that continues all the way up through calculus). But to what extent are drills a necessary evil? If you want to become a concert pianist, you’d better practice your scales. Nobody will argue that drills are particularly taxing, but they do have their purpose in other arts – shouldn’t they in mathematics as well?
• Many are quick to point out the one major problem with comparing mathematics to other art forms: mathematics has wide applicability to other fields, whereas other art forms do not. Lockhart argues that even though this is the case, the essence of mathematics isn’t its practical consequences. This may reflect his own personal bias (after all, he was a researcher in analytic number theory), and while it’s a bias I share to a certain extent, I doubt that this is a universal belief among mathematicians in general.
• I often find that students feed into the current system of teaching the facts rather than the ideas, because the facts are easier to check on standardized tests. Most students want to know a technique for solving a problem, and couldn’t care less about why the technique works, where it came from, or most importantly, its limitations. In essence, I see a tremendous lack of curiosity. Much of this seems to stem from a desire to get a good grade (which may lead to a good job), rather than wanting to learn for learning’s sake. However, this is a problem that goes beyond mathematics – to what extent are the problems Lockhart address indicative of broader problems in education?

Give it a read – if nothing else, it will give you something to think about.