Miles and I have a new column out in Quartz, on how the fallacy of genetic determinism is killing Americans' math skills. Some excerpts:
“I’m just not a math person.”
We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.
Is math ability genetic? Sure, to some degree...[But for] high school math, inborn talent is just much less important than hard work, preparation, and self-confidence...
Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.”...We believe that this has to stop. Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz (here and here), that echo many of our views...
We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism. In the debate between “nature vs. nurture,” a critical third element—personal perseverance and effort—seems to have been sidelined. We want to bring it back, and we think that math is the best place to start.
Read the whole thing here!
Apostle Paul has written that our talents and gifts are remarkably different. Someone is born with melodious voice and they become successful singers if they capitalize on their natural endowments. No amount of preparation, hard work or confidence would turn Noah into a highly celebrated entertainer. It is true that talent can be wasted if not constantly watered and fertilized through hard work. But to suggest that hard work can make anyone a computational wizard committing no less fallacy than the advocates of inborn ability in math.
ReplyDeleteNo amount of preparation, hard work or confidence would turn Noah into a highly celebrated entertainer.
DeleteRight, because celebrated singers like Tom Waits are born with tuneful voices... Bullshit, he chainsmoked for hours a day for years to achieve that skill!
Anyway, If you read the article, you'd realize the superstar performer analogy is inappropriate. Maybe Noah can't become Povarotti through hard work alone, but there isn't much doubt that he could reach an ordinary level of proficiency in music that would allow him to participate in ordinary musical activities such as a church choir or garage band.
We have a lot of people in this country who function far, far below basic proficiency in math. People say 'you never use' algebra or trigonometry. This is primarily for the same reason that I don't use German or French: I don't have those skills in the first place. Trigonometry, on the other hand, i use all the time, because I learned it thoroughly by hard work, so I can easily recognize situations when it can be put to good use.
I never showed any 'natural ability' in Math until I got to Calculus, which came pretty easy. I would have never studied Calc if I had not struggled through all of the prerequisites, succeeding only because I was willing to put in more time than everybody else.
ArgosyJones,
DeleteI thought we were talking about average people and not social outliers like Tom Waits.
Apostle Paul has written that our talents and gifts are remarkably different.
DeleteAnd the opinion of a Bronze Age con-artist is relevant HOW?
conartist because because he spread the Word of one man for one woman? the man in the Information Age.
DeleteNo amount of preparation, hard work or confidence would turn Noah into a highly celebrated entertainer.
DeleteNow that's just false.
Redwood, I'm curious to hear when you think the Bronze Age was?
DeleteI'm just not a "letters" person.
ReplyDeleteConsidering that the average IQ among "certain groups of people" is in the 60s-70s, and IQ is the best measure we have at this point in time of one's logical cognitive abilities, I would say that, while locking a natural born genius in a dark closet from birth would concededly create an idiot, putting someone born of mid-60 IQ parents through the finest education and motivational program money can by would not create a math whiz.
ReplyDeleteAlso there is the fact that temperament is surely as affected by genetic determinism as is intelligence. Anyone who has any experience breeding dogs or horses can tell you that. (And yes, contrary to common (communist?) belief, the same principles of breed and heredity that apply to the animal kingdom also apply to humans.)
At the end of the day, no amount of sophistry on your or anyone else's part, or money on Mark Zuckerberg's part, is going to make the Newark public school student body perform on par with Taipei's. But of course, that won't stop you from arguing as such.
while locking a natural born genius in a dark closet from birth would concededly create an idiot, putting someone born of mid-60 IQ parents through the finest education and motivational program money can by would not create a math whiz
DeleteBut you don't need to be a math whiz to do algebra. Someone with an IQ of 70 can handle that, I bet. Do you have any evidence to the contrary?
Also there is the fact that temperament is surely as affected by genetic determinism as is intelligence.
Well that is a worry, of course.
At the end of the day, no amount of sophistry on your or anyone else's part, or money on Mark Zuckerberg's part, is going to make the Newark public school student body perform on par with Taipei's.
We don't need them to perform as well as Taipei's. Just better than they are performing now. And btw the gap between us and Taiwan is not as big as you might think, look at the #s.
Considering that the average IQ among "certain groups of people" is in the 60s-70s,
DeleteWhat group of people has that average IQ? The mentally disabled? Maybe they won't ever be geniuses, but I don't think that's a reason to deny them access to basic math education. Surely, they'd be more productive members of society with math education than without.
Thank you for putting "certain groups of people" in quotes. By application of logic, I deduce that you mean "certain races". As far as I know, there is no "race" of people whose average IQ is so low.
DeleteApproximately 95% of the world population have IQs between 70 and 130 (two sigmas or standard deviations from the "norm" of 100), and it is a demonstrated fact that an IQ of 100 in today's world is higher than an IQ of 100 from a hundred years ago (which means that as a population we're actually getting more cognitively capable). And as a teacher myself, I can demonstrate to you that students with IQs as low as 70 can go beyond the concrete world of basic arithmetic and grasp at least the basic abstract concepts in algebra. What students need most of all is time to study and practice, and motivation to do so. Without that, no matter their IQ, they will not do the work necessary to ingrain mathematical concepts into their mental frameworks.
"Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence."
ReplyDeleteThis paragraph is very well put, especially the last sentence, "For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence." Most people have the ability to do very well at the math, and mathematical/analytical thinking, necessary for the vast majority of college degreed occupations, and at least up to and including calculus.
There's also two big things about math success:
1) You briefly mention this – Math is unlike history, English, etc. in that even people who are extremely good at it often don't understand it right away (especially since it's often taught badly). It's like a puzzle; you think about it and figure it out. But a lot of people don't look at it that way, and as soon as they look at it and don't understand it they think there's something wrong with them, and don't like it. So you have to let them know this is often normal even for top math people; it's the nature of it. Of course, with history or social science a lot of people think they understand it right away, but don't really. But thinking they understand it right away makes them a lot less likely to dislike it, and not really try.
2) This huge; math really really builds on itself. Don't understand the first month's material, and it's often way way harder to understand the second. The solution, of course, and the ultra-efficient economists thing to do, is to not move on to the next material until you understand pretty well the current material. But traditional schools force students to keep moving on at the preset pace, and the tests for your class keep moving on, which can then be disaster after disaster. Letting students move at their own pace, and grading them at the end on quality and quantity covered (where there's no incentive to glaze ahead with terrible quality of understanding), is so so powerful for learning and competence, especially in math and science. And with a computer to give the lecture to each student, you don't have to have one uniform-speed lecture like in the past. One thing I really like about the Kahn Academy is that I heard Mr. Kahn in a TED really stressing the importance of this. By our house we have one of the best free K-12 charter schools in the country, and one of the best schools period, ALL (Accelerated Learning Laboratory). They're basically self-paced, but still with strong incentives to work hard.
Foreign languages are similar – systematic diligence gets you a long ways. A fair slice of the world's population is multilingual, though early language acquisition may be a bit different from adult learning. Roughly a billion people have learned to read Chinese, not all of them bright; ditto 100+ million readers of Japanese, which is if anything harder. There are lots of skilled trades as well (in the old days, banking?) where cumulative experience allowed otherwise ordinary people to do reasonably well. So this is hardly unique to math and language.
ReplyDeleteNote when I had kids in a local elementary school I was able to observe math and language acquisition in Japan. Lots of hours, relative to the US, but in small doses, and homework every night from the 1st day of 1st grade, but coordinated to be in 2 subjects, never 3 or 1. Very tightly structured from year to year, no disjuncture in elementary school from moving to texts that suddenly assumed material not covered before, and constant review. Plus a short summer break. Reputedly things detoriated when a few years later the school week went from 5-1/2 days to 5 days – that heightened the tension between festivals and other things that made school fun, and spending time on the 3 R's.
I'll try and not get too "mathy".
ReplyDeleteLearned skills and innate talent follow a distribution like just about every other concept in the natural world.
Sure, if you want to be the very best at something, you need some innate talent (genetic pre-disposition if you will). But you are never going to get there on innate talent alone. It takes years of hard work to develop those skills.
For the average joe, we might not have the innate talent, but there is nothing getting in the way of a more than proficient understanding of higher concepts. Sure, we might not publish papers on string theory or higher levels of economics, but there is nothing that should get in the way of understanding advanced statistics or similar. Other than our own perseverance ( or lack of it).
I worked pouring concrete summers as a student. It was grueling work that made you old long before your time. I got razzed for being a "college boy" by most of the workers, but I still recall one of the older workers told me to ignore them: "wish now I had paid attention in math class." I chose to focus on quantitative work not because I was particularly good at it--I tested much higher in verbal, reading, etc.--but for the same reason I chose concrete over lifeguarding. Because it was hard work, there was a better chance of landing a job and it paid a premium. I may be a hack, but I'm an employed hack.
ReplyDeleteOne issue, I believe, is form of instruction. The US abhors rote while other countries embrace it. In top Chinese schools, for example, they teach the math you need to know and you memorize it and then they test whether you've memorized it. The idea seems to be that any bright person can learn these equations and processes and that some, a relative few, can become really good at working these processes and some, another relative few, can become really good at understanding the inner workings. The US instead begins at the earliest age teaching understanding. As kids get older, they are expected to build understanding as though rote learning is inferior. The worst is the testing: while other countries test whether you have learned what you were taught, here we test whether you can take what you were taught and apply it in a different setting. No wonder kids get discouraged and fail.
ReplyDeleteFeynmann commented on this issue in his stories. He noted that overseas he wouldn't be asked creative questions even by grad students and realized that in the US students in college and grad school learned more creatively. That is a trade-off. Lose nearly everyone along the way to get a relative few who can work at a high level in upper levels. The alternative system is to get many more people up to a functioning level. It would seem a combination of systems would be best: more rote at lower levels, more creative understanding at higher.
This is backwards regarding K-12 education. Everyone teaches memorization of basic facts. In the United States we teach memorization of procedures as well, in China they teach for understanding. There is a classic book in math education by Liping Ma ( http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0415873843 ) that shows this clearly.
DeleteThe Teaching Gap describes a video study of math teaching in the United States, Japan, and Germany that was part of the Third International Mathematics and Science Study (TIMSS). What struck the team of researchers was that each country had a theme, or cultural approach to teaching. The image of teaching in Germany was “developing advanced procedures;” in Japan it was “structured problem solving;” in the United States it was “learning terms and practicing procedures.” One math educator on the team said that in Japan, the students engage in mathematics and the teacher mediates; in Germany, the teacher owns the mathematics and parcels it out to students, giving facts and explanations at the right time; in the United States, there is interaction between teacher and students, but he couldn’t find the mathematics. He didn’t see any real math in memorizing terms and procedures. (http://www.amazon.com/Teaching-Gap-Improving-Education-Classroom/dp/1439143137/ref=sr_1_1?s=books&ie=UTF8&qid=1382986503&sr=1-1&keywords=teaching+gap)
At the university level it is different because the majority of people of filtered out. Regarding inborn math ability, it is related to how we teach, because when we memorize what doesn't otherwise make sense, we think we aren't good at math even if we can get the right answer. But teach for understanding and that all changes. See Jo Boaler's book, or Keith Devlin's discussion of it at http://www.maa.org/external_archive/devlin/devlin_06_10.html
One of the factors receiving little attention in this discussion is the intent and quality of the teaching. In the sixties when I was in graduate school, the New Math was introduced in lower levels of schooling. The proponents were clear in their intent; out of all the grade school children being taught, a few would be able to conquer this and some might become "great mathematicians." It was never intended to teach the masses to understand percentages, of fractions, or anything that so many reporters get wrong in their stories. To this day, the kind of courses offered at most elementary, middle, and high schools, as well as at universities, still contain much of these new math concepts and are not well-structured to accomplish anything else. As a result, most people are incapable of understanding basic mathematics that is useful to them to understand their government, businesses, or even the arithmetic of sale prices at their local store.
ReplyDeleteI am a retired Mathematics Ph.D. who taught university math in the sixties and seventies before I got into economic consulting (which paid better).
It's an interesting pattern you guys describe in steps 1-4. Of course you know it is under-identified.... now if you could randomly assign parents to prepare their children for math classes, and still see the same effect you'd be onto something. :)
ReplyDeleteAny serious mathematician would say it's fallacious to claim that performance in high school math is unrelated to inborn math ability.
ReplyDeletePhysicist Steve Hsu has investigated this question empirically. It seems that there is a minimum SAT/IQ threshold below which being proficient at college level math is very unlikely. This threshold probably exists for high school level math as well, except that it's a lower one.
ReplyDeletehttp://infoproc.blogspot.com.br/2010/04/dating-mining-university.html
Just wanted to say thank you for the article. I have been teaching high school math at various levels for 11 years. I am SO tired of hearing parents say that their children aren't any good at math because they weren't either. Their children just give up. I always knew hard work was the key, so thank you for providing the research that backs that up!
ReplyDelete