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.
Earlier this month, Wired published an article written by Daniel Roth, enticingly titled “Making Geeks Cool Could Reform Education.” It serves as an interesting counterpoint to the commonly used argument that the best way to reform education is to better integrate it with the most current technology, so that going to school feels less like going to school and more like playing video games (family friendly ones, of course).
Sorry, Typing of the Dead, but you’re a little too creepy.
The essay in Wired takes a slightly different approach – it profiles schools that have successfully channeled the inner geeks of their students, the argument being that the geek subculture rewards intelligence with popularity. To do this, schools must make learning seem cool. This is a feat which is easier said than done, because, as we all know, there’s no better way to convince a teenager that something is uncool than to repeatedly say how cool it is.
One way in which the schools were able to motivate students to embrace their inner geek was to surround them with older people – teachers, parents, and working professionals. One school in particular forces students to present their work to groups of outsiders. The effect here is to downplay the importance of youth culture: if students can see what their education can do for them down the road, they’re more willing to value it in the present.
Other schools have taken different measures, but the goal of curbing a focus on youth is the same. For example, at Roxbury Prep, Roth tells us that “Kids eat lunch in the classroom, they’re not allowed to talk in the halls, and they’re disciplined for using the word nerd.” Certainly social time with peers is important, but this added emphasis on academic performance appears to be paying off, because students in these schools value learning for its own sake, and are rewarded for their efforts not just by their teachers, but by their peer group as well.
Applied to mathematics, this philosophy could have a significant impact. After all, many students will tell you they hate math because they don’t see the value in it. But if students were able to interact with people who used mathematics in their everyday lives (aside from their classmates and their math teacher), one hopes they would be motivated to learn the material. Or, even better, even for students who don’t plan to make a career out of mathematics, in a culture where learning is perceived as cool, one would hope that students would take advanced mathematics just to get a taste for what it’s like.
If only…at least a man can dream. Perhaps one day we really will see the triumph of Geek Chic at all levels of education. Certainly, this is a good sign (thanks Michelle). Once we see some modern pocket protectors, I think we’ll have reached the tipping point.
Let me begin by saying that, in response to the question Why is 9/09/09 so special?, my response is simple: it’s not.
In fact, I would argue that 09/08/09 is much more interesting. This claim has nothing to do with numerology, and everything to do with President Obama’s speech to the youth of America on the value of education. The speech made very clear the importance of taking education seriously, and hopefully convinced students that a good education benefits not only themselves, but also society at large. In case you missed the speech, the transcript can be found here.
Although the speech was about education in general, mathematics got a little bit of love too. Here’s one such example:
What you make of your education will decide nothing less than the future of this country. What you’re learning in school today will determine whether we as a nation can meet our greatest challenges in the future.
You’ll need the knowledge and problem-solving skills you learn in science and math to cure diseases like cancer and AIDS, and to develop new energy technologies and protect our environment. You’ll need the insights and critical thinking skills you gain in history and social studies to fight poverty and homelessness, crime and discrimination, and make our nation more fair and more free. You’ll need the creativity and ingenuity you develop in all your classes to build new companies that will create new jobs and boost our economy.
What a bunch of socialist propaganda. Even so, I’m glad the President decided to emphasize the importance of education today, and I hope that students were able to take something away from it.
As an addendum to this theme, I’d like to point out that while mathematics is an essential tool for fighting disease or curbing global warming, there is perhaps a more immediate benefit to studying math that was not highlighted in today’s speech; a benefit that appeals more to our self-interest than a sense of duty, but with the end result still being a knowledge of mathematics. That benefit, of course, is the almighty dollar.
Last month, the Free Exchange blog over at the Economist highlighted a paper by Joshua Goodman that analyzed the returns on learning math in high school. For some reason Mr. Goodman’s website seems to be down, so the link to the paper is broken, but you can also find the paper here.
What were his findings? While earlier authors had found that each year of schooling is correlated with an eventual earnings increase of 10-15%, Mr. Goodman found that a significant amount of this increase can be attributed to coursework in mathematics (results which were strongest for low-income black males).
Of course, we all know that correlation does not imply causation, so it’s a little disingenuous to say that if you take more math classes in high school, you’ll get more money as an adult (and certainly for those of us in graduate school, it’s easy to imagine that the opposite is true). However, as pointed out on the Economist’s blog:
One reason why people who learn more mathematics earn more is because doing maths makes you smarter and more productive. According to Clancy Blair, a professor of psychology at NYU, the act of performing mathematical calculations improves reasoning, problem-solving skills, behaviour, and the ability to self-regulate. These skills are associated with the pre-frontal cortex part of the brain, which continues to develop into your early 30s.
So, while math may not make you richer, it will probably make you smarter – and this in turn can (hopefully) help you live a more comfortable lifestyle.
Then again, how could a lifestyle involving mathematics not be comfortable?
I recently had the pleasure of stumbling across Paul Lockhart’s essay, A Mathematician’s Lament. Lockhart, a former research mathematician in analytic number theory who received his Ph.D. from Columbia in 1990, decided to leave academia in 2000 in order to concentrate on K-12 math education, which he hass been doing at Saint Ann’s School in Brooklyn.
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.
There’s much more, of course, but the article itself does a much better job of expanding on these points than I could. Lockhart takes an extreme position, to be sure, but in so doing he exposes much of what is horribly broken with our current system.
More than anything else I’ve posted, I recommend you read the article and percolate on it. Lockhart originally wrote this around 2002, but it wasn’t published until last year – since then it’s made the rounds in academic circles, I’m sure, but I hadn’t heard of it until it was posted on Slashdot earlier this summer. This is all well and good, but for most people with technical backgrounds, Lockhart is preaching to the choir. Since this blog caters to a more general audience, I would particularly encourage those who don’t work in the sciences to read through what Lockhart says – much of it will resonate with you, especially if you hated math as a student.
Lockhart certainly offers plenty for debate. Here are some questions I have after reading the article:
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.
A friend recently shared with me the following video from TED (see below). In it, mathematician (or, in this case, mathemagician) Arthur Benjamin gives a brief argument for eliminating calculus as the top of the “mathematical pyramid” in high school education, and replacing it probability and statistics. The main reason for this shift is that unless you are planning to have a career in a technical field, it’s unlikely you’ll find a use for calculus in your everyday life, but an understanding of statistics can benefit you no matter what you do. For example, it can help you to build an intuition about day to day decision making when risk and uncertainty are involved. Here’s the video (it’s short, only a couple of minutes):
A noble goal, to be sure, and it’s certainly a solution that wouldn’t cost a whole lot. There is an argument to be made for such a change lurking in here somewhere, but coming in at under 3 minutes, Benjamin’s argument barely scratches the surface. In no particular order, here are some of the problems I have with his proposal:
1) Arguing that students shouldn’t learn calculus because they may not use it in their everyday life is specious. By this reasoning, I should never have taken any courses in history, biology, or chemistry. The purpose of high school education in this country seems to be not only determining what educational avenues students want to pursue further, but also what avenues they don’t want to pursue. If you want to argue that students should only be learning things that they can apply to their everyday lives, then you are arguing for a much more sweeping reform of education.
I do acknowledge that there is an opportunity cost at work when we spend a year teaching a student calculus rather than statistics, and certainly the average student will find more use later in life for the latter. But there’s also an opportunity cost at work when we spend a year teaching a student statistics rather than calculus, especially for students who aren’t sure in what direction their academic future will head. If anything, this seems to be an argument for offering both statistics and calculus for students, rather than forcing them into one option or the other.
2) About 2/3rds of the way through the talk, Benjamin asserts that “if our students, if our high school students, if all of the American citizens knew about probability and statistics, we wouldn’t be in the economic mess we’re in today.” This is met with some cheers from the audience, but is it actually true?
The answer depends on your definition of “knowing” probability and statistics. I agree that having some knowledge of statistics is a good thing for the population at large, and there are no doubt many fundamental principles that could be taught at a high school level – for example, the idea that correlation does not imply causation, or the ways in which one can manipulate data or graphs of data. These topics, among others, are discussed in the book How to Lie with Statistics, which would be a great required reading book for any teacher trying to impart intuition and a healthy dose of skepticism onto his or her students, and is written for a general audience.
However, even if everyone in America had this basic level of knowledge, it’s not at all clear that this would have somehow saved us from economic catastrophe. If you work in finance, odds are pretty good that you already have a knowledge of statistics that goes beyond a high school level, but this didn’t stop the economy from tanking.
Nassim Nicholas Taleb wrote an excellent article last year on the limits of statistics, which is well worth a read if you can spare the time. One of the arguments he makes is that part of the reason the financial models caused such an economic implosion was that these models are necessarily unable to predict black swan events, which can have a tremendously negative impact, but are also tremendously rare. In fact, he argues that statistics is actually quite poor at trying to predict what will happen in extremely complex systems where rare extreme events can have a profound effect on the system.
However, this is not what one learns in a high school or even undergraduate class on statistics. Most problems at this level involve simple systems (games of chance, for example). In other words, studying statistics at a low level does not expose one to the subtleties and limitations of the subject – in particular, I don’t think it’s feasible to say that if every high school graduate had taken a course in statistics, somehow we would have prevented the current economic catastrpohe. To do so would have required a much deeper understanding of statistics among those applying the financial models than can be supplied at the high school level.
This brings me to my third point…
3) To have a good understanding of statistics, one must already have a working knowledge of calculus. There is a limit to the amount of depth a probability or statistics course can explore when calculus is not a prerequisite, and because of this many results (such as the Central Limit Theorem) are stated without proof. This is fine if you are simply trying to expose students to some of the standard tools in the subject, but if you can’t go deeper, there really is a limit to the level of understanding a student can achieve.
I agree that there is a great deal of value in teaching statistics to high school students, even at the level of pre-calculus. One can still impart a significant amount of intuition at this level. However, for students who plan to use statistics in any significant capacity, it’s important that they develop a working knowledge of calculus as well.
If you’re not planning on going into a technical field, certainly you’ll get more value out of a basic statistics class than you will a calculus class. But students who dislike math in general will probably still dislike statistics, even though there’s more to like for someone who’s not interested in math than there is in a calculus course.
This, in turn, brings me to my next point…
4) In the larger debate over the failings of math education in America, the choice of whether to teach statistics or calculus in secondary school misses the point entirely. By the time students reach the later years of their high school career, most already have a pretty well developed sense of their relationship to mathematics – either they had good teachers and enjoyed the subject, or through a series of misfortunes which may have been out of the student’s control, they feel like math is a subject they will never understand, and will struggle with until they have the freedom to not take a math class, and are finally free from its iron grip.
Sadly, the problems with math education in this country run much deeper, and swapping out calculus for stats at higher levels won’t alleviate the fundamental problems students have with mathematics. When I grade papers in a calculus class, students make just as many (if not more) algebra mistakes as they do calculus mistakes. In other words, many students leave the year without having mastered the math concepts presented to them during that year. Compound this over several years, and it doesn’t matter if you give them a calculus book or a statistics book – they will have trouble because they haven’t mastered the prerequisites.
Certainly one can argue that there are fewer prerequisites in a statistics class, but prerequisites are still present, and algebra is certainly one of them. If a student has a poor understanding of algebra, it’s reasonable to assume he will have significant gaps in his understanding of statistics, and if the goal is to give students an intuition for randomness and understanding data that can help them in their everyday lives, gaps in statistical understanding are significant problems. Therefore, achieving this goal isn’t as simple as making sure every high school senior has taken a statistics class – we really need to insist that every student first has a working knowledge of algebra. This is a problem we have already, and is not resolved by Benjamin’s proposal.
5) This is a small point, but important. What really bothers me about this talk is when Benjamin makes the statement that, “If [probability and statistics] is taught properly, it can be a lot of fun!” Well, yes, but this is true of any subject. Implicit here seems to be the idea that calculus cannot be fun, even if taught well. I’m sure this isn’t Benjamin’s intention, but it’s easy to misinterpret, especially if you are someone who has never taken a calculus class, or has fallen victim to the commonly held opinion that calculus is some kind of black magic whose secrets only a chosen few can hope to unravel.
The truth (and one that Benjamin knows) is that any math class can be fun if taught properly. A more accurate statement might be “it’s easier to make probability and statistics fun for students,” because of the vast applicability to everyday life, from games of chance to calculating the probability that someone in a family is colorblind. But to suggest that statistics is inherently more fun for students than calculus does a disservice to all the great teachers of calculus. Either class can be fun and valuable if taught well, or traumatizing if taught poorly.
Mr. Prezbo, using probability to make math fun. No doubt he could work this magic on other math subjects as well.
I understand what Benjamin is saying, and I also understand its appeal. The argument works well as a 3 minute sound clip, but upon further reflection, there are some significant questions that need to be addressed. There are many problems with math education in this country, and I’m not sure which, if any, are solved by this proposal.
From my own experience, no students in my high school were forced to take either calculus or statistics, although both courses were offered. Preparing students exclusively for either one or the other will of course do a disservice to some, so perhaps putting both on the table is the best compromise, although this becomes a problem for schools with limited resources. I am confident, however, that simply putting statistics on the pedestal currently occupied by calculus doesn’t do a whole lot in terms of fixing everything that’s broken.
Here’s an interesting article about Tom Farber, a high school Calculus teacher from San Diego who is fighting tough economic times and cutbacks in education spending in a rather novel way – he’s selling ad space on math tests.
The goal here certainly doesn’t seem to be the development of a second income. Many teachers report having to spend money out of their own pockets for school supplies – in this case, Mr. Farber is using the money to help cover the copying costs associated with making tests and practice exams to help students prepare for the APs. His intentions certainly seem benevolent, but are his actions as innocent?
It seems like the advertising is fairly non-intrusive. There are no graphics, and the ads run on the bottom of the page. The fact that a good chunk of the ad space was bought by parents who wanted to run supportive messages certainly makes this easier to swallow as well.
The article suggests that the main criticism with Mr. Farber’s plan is that it is a slippery slope: if he’s successful in using advertising to supplement a dwindling state budget, couldn’t the state then begin expecting advertising revenue to be used as a way to make ends meet? An important question, to be sure, but given that this seems to be an isolated incident, I think there are perhaps some more pressing questions that this raises.
Some that initially come to mind: how intrusive is too intrusive? Should advertisers be able to sponsor specific problems? It’s unlikely parents would be enthusiastic about McDonalds sponsoring their third grader’s test (If you have 4 boxes of 6 piece McNuggets, how many McNuggets do you have?), but what about advertisers which are less morally questionable? Should Scholastic books be able to sponsor individual problems?
Is this the future of math education?
The fact that all of Mr. Farber’s advertising came from parents and local businessness certainly makes this endeavor seem more innocuous than it would if his tests were being sponsored by Starbuck’s or Burger King. But is it really more ok to advertise on a test if you restrict to local businesses? Should local businesses be able to sponsor individual problems? Is it ethical for the local comic book store to sponsor a word problem that asks students to investigate how much money the store needs to make in a month to avoid closing? Is it more or less ethical to do this if the numbers are accurate?
These questions may seem a bit esoteric, but with all the buzz about the economic crisis, and California’s economic crisis in particuclar, these questions may become more important if teachers are pushed to look for creative solutions to patch up budget shortfalls. That is, if all the teachers don’t get fired first.
On the other hand, I guess you could look at it this way: people have been using math in their advertising for years, and math hasn’t been able to reap the benefits. Maybe now it’s time to start turning the tables.
Leave it to Nike to make math seem even more confusing.
Even though we’d like to accuse our math teachers of being more or less incompetent, there is at least one indication that math education in this country is making some progress. In particular, the results of the Trends in International Mathematics and Science Study shows American students have gained 11 points over their average performance in 1995. A comparison of US scores, along with an article describing the findings, can be read here.
With an international average of 500, American 4th and 8th grade students scored a respectable 529, on par with the Netherlands, Lithuania, Germany, and Denmark. As might be expected, however, we’ve still got a significant way to go when it comes to competing with other countries. Hong Kong made the top of the list, with a score of 607.
Of course, this data by itself doesn’t do much to explain what factors may be driving our improvement. One suggestion is that we are simply aiming higher. The article linked above ends with the following:
The congressionally appointed National Math Panel recently called for sweeping changes in how schools teach math, pushing for a greater emphasis on algebra and higher-order problem solving. [Brookings Institution researcher Tom Loveless], a member of the panel, says the changes would go a long way toward improving our international ranking. “We’re making progress, but we’re several decades from being first in the world,” he says.
Maybe, then, the problem isn’t that we’re not making progress – it’s that we’re just not making progress fast enough. The question then becomes: how can we identify what’s working, and crank it up so that we can get our kids to a competitive level on an international stage as quickly as possible?
It’s a heavy question, indeed. I’d encourage you to ruminate on it. Perhaps some School House Rock will help to inspire you.
It looks like middle school math teachers can’t catch a break. According to a recent study, a significant percentage of math teachers in grades 5-8 do not have a degree or a certification in math. Sadly, the numbers are even worse for schools in low income areas. While it’s certainly true that you don’t need a math degree to teach middle school math effectively, the data does suggest that there is a significant bloc of underqualified math teachers trying to impart essential knowledge to these young students.
Of course, I doubt this is all the teachers’ fault – elementary and middle school teachers are a rare commodity in this country, and kids need someone to teach them math. An understaffed school will do what it takes to make sure there’s somebody at the front of the classroom. And I certainly don’t envy those teachers out there who may not feel so confident in their math ability, but are nevertheless trying to impart all that mathematical know-how because nobody else will.
One thing that is a little confusing is that when this story made the news rounds, most headlines made a statement like: Teachers are only one chapter ahead of their students. The press release for the study, however, makes no such claims – instead, the main point seems to be simply that there are too many teachers without a major or a certificate in the subject they are teaching. This, of course, is an issue that needs to be addressed, but it doesn’t seem to be nearly as dramatic as the headlines would claim. If you’ve taught 6th grade math for five years, even without a certificate or a major, chances are you certainly know the material well enough that you aren’t only one chapter ahead, even if you are a lousy teacher. Similarly, some people have a natural talent for teaching, and can become good math teachers even without much of a mathematical background – just ask The Wire’s Roland Pryzbylewski.
Math teachers in action. You can tell Pryzbylewski means business.
Bottom line: we need more qualified teachers, no doubt. In a perfect world we wouldn’t have to worry about underqualified teachers, because the hiring pool would be large enough to fill schools with the right people. But in the meantime, blaming the teacher for being unqualified fails to get at the heart of our education problems, and so headlines like “Your kid’s teacher is only one chapter ahead!” tend to favor shock value over constructive discussion of the study involved or the problems we face.
Earlier this month, the New York Times ran an article about the dearth of U.S. students with strong skills in mathematics. While this is not quite a revelation, it is made more timely by the recent release of a study that looked at data from Putnam exams, International Mathematical Olympiads, and data from other programs meant to nurture younger students in mathematics.
This type of data is more powerful than looking at SAT scores, for instance, because exams administered in a mathematics competition are notoriously difficult. There are thousands of students who will score an 800 on the math section of the SAT, and so this test offers no way to distinguish between them. Looking at this other data, however, allows us to gain a much deeper insight into the abilities of students in the U.S. with an aptitude for mathematics.
The data suggests a couple of things. First, contrary to the Gender Gap theory I have discussed before, there are many women who perform extremely well on these exams. While the data can’t support or refute the Gender Gap theory conclusively, it does show that indeed there do exist women who are good at math.
The second conclusion, which is somewhat broader, is that a majority of students in the US who excel in these exams are either foreign (for example, the Putnam exam can be taken by any undergraduate in the US or Canada, not just citizens), or are children of immigrant parents.
The combination of these two points is highlighted in the breakdown by country of the women who compete in these types of competitions. The article informs us that, regarding the makeup of the teams sent to the International Mathematics Olympiads,
All members of the United States team were boys until 1998, when 16-year-old Melanie Wood, a cheerleader, student newspaper editor and math whiz from a private school in Indianapolis, made the team. She won a silver medal, missing the gold by a single point. Since then, two female high school students, Alison Miller, from upstate New York, and Sherry Gong, whose parents emigrated to the United States from China, have made the United States team (they both won gold).
By comparison, relatively small Bulgaria has sent 21 girls to the competition since 1959 (six since 1988), according to the study, and since 1974 the highly ranked Bulgarian, East German/German and Soviet Union/Russian IMO teams have included 9, 10 and 13 girls respectively.
The data is troubling because not only does it show that Americans are getting trounced on the international stage, but it shows that when we do excel, it’s often because of imported values from the countries that are trouncing us in the first place.
This leads to an important question: Is American culture to blame? Why do our students simply not perform as well?
Indeed, most people interviewed seem to think that culture is, if not the primary cause, certainly a guilty party. Simply put, mathematics is held in a much higher regard in other countries. Consider this explanation of the perception of mathematics in China:
Dr. Feng says that in China math is regarded as an essential skill that everyone should try to develop at some level. Parents in China, he said, view math as parents in the United States do baseball, hockey and soccer.
“Here everybody plays baseball,” Dr. Feng said. “Everybody throws a few balls, regardless of whether you’re good at it, or not. If you don’t play well, it’s O.K. Everybody gives you a few claps. But people don’t treat math that way.”
If we want to tackle this problem, looking for solutions from the cultural side shouldn’t hurt. There are many negative perceptions that keep math out of the cultural consciousness, not least of which is the idea that somehow mathematics is meant to be tedious, difficult to understand, and without application. If other countries can highly value mathematics, see the use for it, and believe that anyone can achieve a certain level of mathematical sophistication with due diligence, surely America can as well.
Of course, getting our culture to that point will require serious work. However, certainly there must be some baby steps that will help us along the way. With that in mind, here are some suggestions that may help bring U.S. culture and mathematics into a more harmonious relationship.
1. Get a mathematician on the Wheaties box.
The analogy between math and sport is certainly a rich one. Both require hard work and discipline in order to excel. Both should be included in any child’s education. And both attract people to their summer camps.
At the same time, there is quite a wide cultural divide that is perceived between these two groups. Athletes are put on pedestals (literal and metaphorical), and their toned physiques are heralded as the pinnacle of human achievement. They are also widely regarded for their dedication, their determination, and nobody questions their hygiene. Sadly, the same cannot be said for mathematicians.
To combat this inequality, why shouldn’t it be the case that top performers from both fields should be able to have their face on a Wheaties box? Certainly breakfast is the most important meal of the day for both athletes and mathletes – we should emphasize this point by highlighting the achievements of mathematicians on the orange box we all know and love.
That’s a nice throwing arm you’ve got there, Josh Beckett. But how’s your multivariable calculus?
2. Put a mathematician on The Simpsons.
Sure, The Simpsons doesn’t hold quite the cultural sway that it used to, but its longevity shows that it has carved out an enduring place for itself in our culture. It is still quite popular, and has its share of devotees, and for this reason many people still pay attention to what it has to say, even if it may have been eclipsed by other series (animated or otherwise) in recent years. In this respect, it is a bit like the Hillary Clinton of prime time television.
Therefore, it stands to reason that having a mathematician lend their voice to an episode of The Simpsons, if handled in the right way, certainly couldn’t hurt to flip the cultural perception of mathematics on its head. The Simpsons has featured hundreds of guest stars: celebrities, heads of state, authors, athletes … the list goes on. Moreover, a move to bring in a mathematician would not be entirely unprecedented – Stephen Hawking has made not one, but two guest appearances on the show, and although he is a physicist rather than a mathematician, it would not be such a huge leap to move from a guest star of the former occupation to a guest star of the latter.
Of course, we could give the show the benefit of the doubt, and assume that despite their best efforts, producers have been unable to find mathematicians who would be willing or able to participate. Should this be the case, I am willing to humbly submit myself for such duties. I believe I am able to shoulder the tremendous responsibility that such an opportunity would entail.
Stephen Hawking: Bringing theoretical physics to the forefront of pop culture since 1999.
3. Endorsements.
How do athletes and celebrities become cultural icons? Certainly their abilities take them far, but would Tiger Woods be as well known without his lucrative contract with Nike? Would Michael Jordan have been as successful without his deals with McDonalds, Coca-Cola, Hanes, and most importantly, Ball Park Franks? Would Gary Coleman be where he is today without Cash Call? I think not.
Given all of this success, there’s no reason why academics shouldn’t be able to dip into the same pot. You just got tenure at a major university? Well congratulations, here’s a contract with Gatorade. Solve the twin prime conjecture? Then you get to sport the 2009 Saturn Astra!
Of course, it’s a slippery slope to begin mixing economic incentives with academic achievements. But it certainly would help propel academics, and mathematicians in particular, into the spotlight.
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Ok, so I’m (mostly) kidding about the above suggestions. But this disparity between our cultural views of mathematics compared to the views of other countries really is troubling, especially as we look towards a future that demands more and more technical sophistication from its populace. Bringing mathematics out of the cultural doghouse requires more transparency on our part, so that people can see why mathematics is important, and it also requires a better educational foundation, so that students see math as something beautiful and widely applicable, rather than some draconian set of rules, the knowledge of which was rendered obsolete with the creation of the calculator.
With the right resources, we can turn this perception around. Until then, be on the lookout for any chance to defy the stereotype that math isn’t worth knowing. Every little bit helps, and every little bit will be needed.
As a footnote, those of you who read the NYT article will notice that it mentions a particularly hard problem from the 1996 IMO exam. So difficult was this question that only 6 students out of a pool of hundreds were able to completely answer it. If you’re looking for a good way to spend an afternoon, here is the problem in question (if nothing else, you can learn a new word by reading it):
Let ABCDEF be a convex hexagon such that AB is parallel to ED, BC is parallel to FE and CD is parallel to AF.
Let RA, RC and RE denote the circumradii of triangles FAB, BCD and DEF respectively.
Let p denote the perimeter of the hexagon. Prove that
As you may recall, my first post briefly discussed the California Board of Education’s mandate that every 8th grader in the state must take Algebra. My purpose here is not to discuss the ruling further, but rather to point out the response article published last month in the San Francisco Chronicle.
The article is well-researched and thoroughly written. Not only does it feature discussion of the pros and cons of such a mandate from a wide range of interviewees, but it also tries to address the question of why Algebra, and mathematics in general, is perceived so terribly by American kids and adults alike. It also attempts to paint a picture of what Algebra actually is, for those of us who fell by the wayside of mathematics long ago.
The current state of mathematics education is given quite a scathing review by the people mentioned in the article who actually know their mathematics. The harshest critic is former UC Santa Cruz mathematician Paul Lockhart, who wrote the following in a 2002 essay:
If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done … I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.
What is it about contemporary mathematics education that is so broken? There are three factors discussed in the article, and all of them are spot on: the failure of our curriculum to make math seem relevant, the educational system’s focus on testing, and the lack of qualified teachers.
Even though it is 2008, and technology surrounds us, many students have trouble seeing how math will help them later in life. Given the exponential growth in technological industries, not to mention reliance on data and statistics that is prevalent throughout the social sciences and other careers such as medicine, it is unlikely that this lack of foresight is due to the dwindling relevance of mathematics. If kids don’t see why math is useful, it’s because we’re not doing a good job showing them.
The article gives some examples of how math is used in unlikely places – from parking cops to delivery trucks to iPods. The main argument behind these examples is “Hey! Algebra is relevant – look at all this cool stuff that uses it!” On one hand, this may seem a bit deceptive. After all, saying that all you need is some Algebra to understand the machinery behind an iPod is a bit like saying that all you need to become a French pastry chef is knowledge of how an oven works – both make oversimplifications of the knowledge required. But on the other hand, algebra is a vital piece of foundation you will need in order to understand many modern technologies, even if a complete understanding requires a much deeper understanding of mathematics. It may be difficult to explain all the intricacies of how a circuit board works to a fourth grader, but saying something is better than nothing – especially when that fourth grader believes that studying math is essentially pointless.
“Math? My iPod taught me everything I need to know!”
The aforementioned Professor Lockhart advocates a less rigid approach to mathematics education, one in which the students can more freely explore mathematical ideas. Perhaps the reasoning here is to help guide the student down the same path of discovery that first led to the concept being taught. This is indeed a good way to teach mathematics, because it intertwines the concept with our own intuition, so that rather than seeming abstract and separate from reality, mathematics is seen as a way of interpreting the world in a rigorous, but natural way.
Unfortunately, such a pedagogical approach does not blend well with that pillar of American education: standardized testing. When teachers are forced to teach to a test, the motivation for studying mathematics is no longer to achieve a deeper and richer understanding of the world, it’s to fill in bubbles with a No. 2 pencil quickly and with minimal error. This brings up a slew of other issues: for example, how can we be sure that the tests are actually testing the mathematical knowledge we want the students to acquire? The article gives some examples of test questions at the end, but all of them can be solved by simply checking the given answers. While not an efficient test taking strategy for every question, it can certainly be used often enough to give the impression of mathematical competency.
Finally, the article pointed to a somewhat startling result: about a third of middle school Algebra I teachers do not have a math credential, and given the algebra mandate, that number is only expected to go up. Of course, there are probably good algebra teachers around who may not have a math credential, but at the same time, there are many math teachers in this country who are underqualified. Sadly, Jaime Escalante is but one man, and can only reach so many kids.
Given all this, the state of math education in this country may seem dismal. Perhaps it is. Will anything be done about it? I sure don’t know. But I am curious to see what effect, if any, this mandate will have. If nothing else, it should make for some interesting discussion.
