Sunday, March 23, 2008

Adam Smith overboard in Economist balloon debate

In an age where you need to be numerate to do almost anything else (from building bridges to conquering disease), governments anxiously compare their performance in mathematics with that of competitor nations. This month a new cry of alarm came from America, where a National Mathematics Advisory Panel, established by George Bush in 2006, reported that “without substantial and sustained changes” the country was doomed to “relinquish its leadership” in the world of numbers as the century wears on.

America has long masked its difficulty in educating enough mathematicians by importing lots of ready-made talent, especially from East Asia and the former Soviet Union. But the problems are real enough. As the panel noted, the share of American students doing degrees in maths or related areas fell from 32% in 1994-95 to 27% in 2003-04. And the share of maths-related doctorates at American universities that went to American citizens or residents fell over the past four decades from 80% of the total to less than 60%. The panel concluded that America's problems become apparent when students start to study algebra—for most, their first encounter with genuinely abstract thinking.

The Economist reports on scarcity in native mathematicians in the US.

The language used in this piece is somewhat odd. Try this on for size: 'America has long masked its difficulty in producing olive oil by importing it from Italy and Greece.' 'America has long masked its difficulty in producing Brie by importing it from France.' 'Britain has long masked its difficulty in producing wine by importing it from France, Germany, Italy, Spain, Portugal, Australia, New Zealand, Argentina, Chile and America.'

From an economic point of view, gearing up the American educational system to produce more capable mathematicians might be far more expensive than simply offering fast-track visas to mathematicians of proven ability who have had the bad luck to be born in countries with nasty political systems (I say 'nasty'; OK, 'nastiER'), underfunded universities, poor infrastructure, a scarcity of malls, fast-food outlets, first-class orchestras - WHATEVER it is that makes one place look less appealing than another to a mathematician of proven ability.

From a nationalistic point of view, um, isn't there something a bit fishy about this soul-searching? 'We're not producing enough second-generation, third-generation, fourth-generation, fifth-generation, n+1th-generation American mathematicians!!!!! We've had to fall back on first-generation Americans!!!!!!! The country is doomed!!!!!!!' If a State of Emergency has been declared because we are not producing enough Cherokee, Navajo, and other certifiably aboriginal American mathematicians, it has passed without comment by the Economist. Fact is, it's a country of immigrants. Today's Chinese math whiz, freed from the one-child-family rule, is tomorrow's parent of a gaggle of Chinese-Americans, some of whom may be math whizzes, all of whom will be American.

The real objection to America's poor showing in mathematical education is not a matter of economics, it's a matter of human rights. For reasons that are never entirely clear to me, religious beliefs, however loopy, are generally treated with respect even by those who don't share them. Mathematicians, however, are drawn to something that has no church and no tax-exemptions: a world outside this world of accidents, waiting to be discovered, a world of beauty, elegance and wit. Because of the strongly utilitarian bent of our educational system, because of the assumption that EVERYONE, regardless of aptitude or inclination, must achieve a certain level of competence, those drawn to mathematics are often forced to study it in a social group consisting primarily of contemporaries who regard it with unqualified loathing. We don't require Jews to study the Talmud in a class of bored, resentful Christians; we don't require Muslims to study the Qur'an in a class of bored, resentful Jews; we don't require Christians to study the Gospel in a class where they are outnumbered by Jews and Muslims 10 to 1. We do throw young mathematicans to the, ahem, unenlightened, with the result that too many end up unqualified to engage with those who should have been their peers.

A few years ago I gatecrashed a class on partial integration given by a Chinese lecturer at Columbia; the thing that stays with me is the wit he brought to the business of converting the seemingly unintegrable to something more tractable. If every American schoolchild could be taught by someone with his gifts we could count ourselves lucky.


nsiqueiros said...

I had a calculus teacher at university who was going through the grad program and she was required to do some student teaching. She basically looked like a blondhaired surfer chick or something. She'd come into class with flip-flops, hair in a ponytail, and sometimes even shirts that showed her midriff when she would right on the board. She was the best math teacher I've ever had. She made the subject so amazingly interesting and fun, or rather, she showed why the subject can be so amazingly interesting and fun. She would do proofs on the board that would just blow you away. Her enthusiasm towards math was totally contagious. I ended up specifically making sure she was my teacher for the following semester. I didn't want to be taught by anyone else but her. I did have a math teacher after her who was completely her opposite. He made things I already knew confusing. He should not be teaching math. Being a bad math teacher is definitely a crime in my book. They were both of foreign nationality by the way.

Lee said...

When talking about the US educational system, at least through high school, I don't know if you can compare the study of maths to that of religion - which, after all, is not basically permitted in school. Nevertheless, I do agree that, despite certain gifted programs, maths ought to be better taught, but then again, so should a lot of subjects - and areas of human endeavour that ought to be subjects!

Anatoly Vorobey said...


There's a brilliant essay on teaching math in schools, by a professional mathematician turned K-12 teacher: Lockhart's Lament (PDF), recently published in Keith Devlin's column.

I read it about a week ago and keep turning it over and over in my head since then. His is certainly an unusual take on the tired question, and if you haven't seen it, I think it's very much worth your time.

Mithridates said...

Lee: I'm not sure I understand your objection. I find the comparison clear and persuasive. Now, every comparison has its limits, beyond which it falls apart, but I don't think it's valid to say that the comparison is questionable b/c one discipline is permitted (in public grammar and high schools, is what you meant I think) and the other isn't. The idea that one is permitted and the other isn't really doesn't alter the validity of the comparison. Ithaca might have used a different example that had nothing to do with school curricula and I think it still would have worked. But she uses it here because the social machinery does not protect those who would like to be immersed in mathematics from being in courses with an overwhelming majority of students are either disinterested or even openly hostile to the whole discipline. They're a group whose rights are not protected in the same way that religious believers rights are protected. Coupled to this is the wrongheaded idea that absolutely everyone must achieve a certain level of competence in math. However, not everyone must achieve a certain competence in Talmudic studies and so forth. The religious have the right to worship and study among fellow believers, and even to kick out those who are hostile towards them or their beliefs (e.g. excommunication). I wish could have excommunicated lots of people from my high school sub-literature classes. But, anyway, not to speak for Ithaca, but if I'm right in understanding her comments in this way, then I agree; because I do think it's odd that we protect even the craziest religious groups in this way and not those who want to dedicate themselves to math or some other worthwhile subject (and--just for absolute clarity's sake--I'm NOT arguing that we should not protect the right to practice one's religion).