October 29, 2013

"Restriction of Range:" It's not just a statistical problem, it's a desirable lifestyle

From Quartz:
There’s one key difference between kids who excel at math and those who don’t 
By Miles Kimball and Noah Smith October 27, 2013 
Miles Kimball is an economics professor at the University of Michigan. He blogs about economics, politics and religion. 
Noah Smith is an assistant professor of finance at Stony Brook University. His blog is Noahpinion.

“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. 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.

How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:

Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input. 
On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B. 
The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind. 
The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage. 
Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

Sure. No doubt that's part of the story.

On the other hand, high school math students aren't restricted to just: 

1. "the well-prepared kids [who] get perfect scores"


A high school math student
2. "the unprepared kids [who] get only what they could figure out by winging it—maybe 80 or 85%, a solid B"

There are more levels of high school math students in heaven and hell than are dreamt of in your philosophy, Noah.

P.S. Robert VerBruggen correlates algebra grades and scores on the ASVAB military entrance exam here.


Luke Lea said...

Education Realist describes a piece of the problem here.

carol said...

What I used to hear was, I'm just not good at math. Now it's I just don't like math. A choice. Haha.

And just think, we're being ruled by a bunch of people educated at a time when colleges had dropped their general ed requirements - they didn't have to deal with math at all. Or science. No stats, no probability, definitely no calculus, or physics because you need math for that.

They're in charge.

Eric Rasmusen said...

How funny! After:

"On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B."

I thought they were going to say

"But gradually the unprepared kids catch up, because what really matters is not IQ or previous preparation, but what we teach them in the class, and it's easy enough that every child can do it if properly motivated."

But instead they conclude that the slow kids get discouraged. If so: what bad teachers they must be! (Probably because they say, "Hey, kids, this is easy! You all are smart enough that you should be getting A's--- there's no excuse for a B!")

David said...

"We've had enough."

All robots must be punched out exactly identically.

Left half of the Bell Curve? Right half of the Bell Curve? Functionally retarded? Independent course of study? We have never heard of such things.

Tony said...

Why did you have to put in that picture of that smokin' hot girl from the Zimmerman trial? How are we supposed to concentrate on the post?

Luke Lea said...

From The Spectator:

Teachers understand that many of the differences they see between children are influenced by genes as well as experiences. I say this with confidence because just a few years ago researchers from the UK-based Twins’ Early Development Study (TEDS) asked hundreds of primary school teachers exactly this question and more than 90 per cent said they believed that nature had at least as much impact as nurture on differences between pupils in how well they learn. What teachers see in the classroom is precisely what scientists see in the data. No controversy there.

And yet, when it is publicly acknowledged that children’s achievement in school is influenced by genes a tumbleweed moment often ensues. Putting genetics and education in the same sentence is a modern taboo.

Anonymous said...

OT: the irresistible force of anti-racism encounters the immovable object of public school teacher tenure


anony-mouse said...

Supposedly Michelangelo couldn't figure out why anyone couldn't be a great sculptor.

After all, all he did was to see the image in the marble and simply cut around it.

I actually believe that a lot of math aces (and aces in other subjects) can't understand why a lot of people can't do math.

You just look at the problem, follow the rules, and solve it.

ben tillman said...

The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.

Total bullshit. Below-average children aren't even aware of the concept of a "math person" and a "not a math person". This "not a math person" shtick is something used by women with three-digit IQs to explain their inability to avoid overdrawing their checking account.

Dookierope said...

Its fuzzy thinking like this that brings us no end to the liberal tinkering in everyones' lives and screwing things up for all. This article is a perfect example; basically it goes something like this:

I want to believe that all students who aren't honors 'A' students are capable of being 'A' students if they only worked a little harder (and I do mean a little. He assumes one of these kids will get a solid 'B' without studying).

Therefore, all students can be 'A' students and excel.

Education Realist said...

Steve, did you see Robert Verbruggen's piece correlating ASVAB scores and Algebra 2 grades? He put it together after we tweeted about this article. As you know, grades have their own problems, but as a big picture view, it's pretty compelling:


C. Van Carter said...

Smith is an odious toad.

Anonymous said...

on the other hand, if they do well for the unprepared b students then that is a good accomplishment.

Anonymous said...

but those kids are likely undiagnosed ADD sufferers anyway.

FredR said...

While we're hating on Noah Smith, I thought this post was particularly nasty and illogical: http://noahpinionblog.blogspot.com/2013/08/conservative-white-america-you-need-new.html

Billare said...

I prophylactically blocked Noah Smith on Twitter after reading maybe one or two of his blog posts, as the combination of the arrogance and his ignorance (on the stuff I know some about) even in the short span of a few minutes were so noxious I felt like my head would literally explode reading any more. In some sort of Emperor's New Clothes Syndrome, the econoblogger set somehow convinced themselves that this newly minted Ph. D. was "smart", but I've never read anything of his that suggests any kind of deep insight. And of course not that's not because I disagree w/ the POV; they anoint some very smart liberal wunderkinds but with him they seem to have laid the smelliest of eggs...

Personally, I wouldn't advise engaging with him. In the short span of one post, http://noahpinionblog.blogspot.com/2013/02/intelligence-boosts-for-everyone.html, he calls Hsu a racist, Razib a racist, without giving any indication that he understood Hsu's work in China or read GNXP in any depth. In another post, he criticizes g without even knowing the hierarchal model, and in general doesn't even try to engage with the oeuvre of the people he criticizes without using his not-for-long megaphone to blast them. He doesn't seem to realize he fits the liberal definition of crank by assaulting theories he isn't trained in outside of meaningful peer review.

Basically, he's a fool surfing his wave. I look forward to his downfall, because it's one thing if you're whip-smart but arrogant like Brad DeLong and some other people I follow, but it's another thing if you have no clue and are intemperate. One day he's going to charge in and attack some powerful researcher in his field in a technical area where there aren't taboos, who'll work to marginalize him to some ghetto where he'll never be read again.

I'm thinking someone who can stand the heat and has the rep should just offer to bet him and his uh, mentor, Kimball, on the success of their start-up. How confident are they in actually committing real numbers to the scheme, instead of writing op-eds?

stari_momak said...

Okay, I laughed at the picture and caption of Rachel Jeantel, but I felt bad about it. A little be unkind, Steve.

In general, the pictures/captions are a good addition.

Anonymous said...

The photo.

Looks like Sailer had no problem pushing a fat black girl onto the tracks to stop this PC train of thought by Noah.

Col. Reb Sez said...

In the Bell Curve, Charles Murray cites studies that say it is possible to increase IQ (a little bit, anyway)through intense educational effort. The problem is that no large group of people can be persuaded to undertake this herculean effort. So the authors of this piece are partly right. I'm not sure they would like to know they and Murray are on the same page.

Portlander said...

There was a link to an interesting twitter exchange by Ed Realist also at Robert Verbruggen's post.

ER observes Kimball & Smith are arguing we lie to kids to keep them motivated enough to work hard. The obvious rejoinder is, "alright Mr.'s Kimball & Smith, when do we stop lying to them?"

After they've taken the SAT and have miserable scores relative to the national sample? Or is that too soon, a college degree being so critical to lifetime earnings. So we admit them into college based on a curve (read: Affirmative Action).

Do we do it during college, when it becomes clear they can't keep up with the material? Well, that too is harsh, since by then they will have racked up a few thousand dollars in non-dischargeable student loans.

Apparently after Law School, when they can't pass the Bar exam, is OK.

Seems like a lot of complication and wasted effort though.

Whiskey said...

You probably CAN increase IQ. Radically. By radically altering DNA. IF that creates Parkinsons at age 35, or horrific cancers, or whatnot, darned if I know. But I'm sure its possible and the Chinese are already working on it with lots of human testing already (that's what prisoners and other people's kids are for in a socialist paradise!)

Cail Corishev said...

"We have both kinds of music: country and western."

That's hilarious. They know math teaching because they've taught both kinds of students: A students and B students! And the B students were just A students in disguise. Sounds like good work if you can get it.

Unlike these guys, I've tutored a failing (that's "F") student in math. I'm quite sure his problem wasn't lack of preparation.

Anonymous said...

"The photo.

Looks like Sailer had no problem pushing a fat black girl onto the tracks to stop this PC train of thought by Noah. "


Now we all need to lose our white empathy when it comes to the aliens, we will turn this whole world around in six months.


Anonymous said...

You should know that Terrence Tao does not have a very high opinion of IQ tests. There was a very interesting discussion about this on his blog after someone asked him if you have to have a high IQ test score to be a research mathematician. The resounding answer from Tao and his mathematical colleagues in this discussion-debate was no. Several of Tao's colleagues stated that they personally know elite mathematicians who had low IQ test scores.

One should be very carefull about the kinds of debates that one puts time and effort into.The IQ test score pyschometric debate is not really the fundamental issue for White Americans. The very rapid demographic shift is the fundamental isue. And the IQ test score psychometric debate is just completely irrelevant to this demographic issue unless you believe that White America couldn't thrive and prosper without the Asians...which of course they most definitely can.

If you want to know how dire the situation is:go the the Skyline Highway right now. Here is the demographics of the visitors:90 percent Asian...10 percent White.

Someone here stated that the only way to increase IQ test score is to change a persons DNA. OK, but so what? All that effort to genetically engineer DNA, and all you get is higher score on an IQ test? As if IQ test scores were some deep and profound measure of human intelligence? No matter how many high IQ test scoring Chinese that China genetically engineers, the Great Gorges Dam will still fail becaus of soil and mud buildup, and the Gobi desert will continue its expansion apace towards Bejing. China is doomed.

Bill Blizzard and his Men

Anonymous said...

Forget math and hard subjects. Any young person who wants to make double what a Ph.D. engineer makes needs to get on with a police department. Just look at one police department, CHP ( http://www.sacbee.com/statepay/ ), where sergeants can make over $300k. You can go through about a thousand pages of CHP salaries before you get under six figures (and these are technicians and typists). Or get a degree in business info syst and join the Air Force as an officer. You'll retire at 45 with a good pension and then you can make well into the six figures at EMC or one of the other government-contracting IT companies. You don't need a high IQ to make out like a bandit in this country at this time. I see a lot of Rachel Jeantel types who sign up with the Air Force as enlistees and get business degrees at some proprietary school, make a top salary in the military, retire with a generous pension, and then make six figures with a government contractor.

Bostonian said...

Stephen Hsu recently blogged about a new paper "Number sense in infancy predicts mathematical abilities in childhood". There is such a thing as innate math ability.

Pat Boyle said...

There is an element missing in these discussions of math ability. There doesn't seem to be the proper recognition that in many fields math ability pays better dividends than verbal ability.

Everyone in just about every job had a job interview with someone at some time. That means that they have been selected for their verbal ability. That means that in your group of recently hired junior executives everyone can talk. But half of them will immediately disqualify themselves from any kind of math problem or issue. If you rather just step forward and tackle those math oriented issues - two things happen. First everyone else is happy to let you deal with those kind of problems. And secondly you get an immediate reputation as a math whiz - whether it's deserved or not. That gets you recognition above your peers.

When I taught math I used to tell my students "It's not just getting ahead, it's getting ahead of the guy in the next cubicle".

Embracing math in the workplace is just a real good way to get ahead. Most of your rivals will not compete leaving the path open to you.


C. Van Carter said...

At his blog Smith is claiming individuals with 70 IQ's can do algebra.

Ray Sawhill said...

I realize that the big point here everyone wants to stress is that there really is such a thing as a math gift (and the absence of a math gift). I want to bring up a somewhat different thing I seldom see discussed in these parts: motivation. I don't know why it isn't discussed much. It's a real complicating factor too. Two examples:

1) Moi. I scored extremely well on math-aptitude tests but disliked math intensely and couldn't see any way anything above basic arithmetic was going to serve my life. So I bailed out on math as much as I possibly could and got mediocre grades in the classes I had to put with. I scored less well on language-aptitude tests, but since I enjoyed that side of things, I applied myself. Funnily enough, I've managed to do OK for myself in the language-and-arts part of the pro world.

2) Females. I've run into a lot of women have struck me as having terrific IQ-style horsepower, even math-style horsepower. But a lot of them just don't care to spend much time applying themselves to high-powered abstract reasoning. They'd rather tell stories, gossip, fuss with food and relationships ... They often don't do very well in higher math. But why should this bug anyone? They just aren't interested.

People who have some genuine math aptitude but who simply couldn't have less interest in the subject really do exist. And once you start discussing anything above basic arithmetic, these people are going to see less and less reason to take part. Math, and especially advanced math, is really hard -- why would anyone who isn't interested in it choose to devote a lot of care and energy to it? It's a recipe for misery.

Doesn't the division of labor exist for a reason? If you want a dress or a brochure designed for you on a pro level, you probably go to an expert. If the designer wants some difficult math explained or executed, why shouldn't she go to a math expert instead of having to crack it herself?

My solution: be sure schoolkids can do basic arithmetic. For all math above that level, make it optional/voluntary, etc.

Anonymous said...

Numbers matter!

This is all about parents stimulating their children’s mind with questions and praise at the earliest possible age.

Noah Smith said...

The example of the A and B student was just illustrative, not representative.

Even students at the 20th percentile of IQ can do high school math pretty well. I've taught them to do it many times. Dumb as a box of rocks, but a box of rocks can do algebra.

Of course, those kids often have other problems.

Bert said...

"While we're hating on Noah Smith, I thought this post was particularly nasty and illogical: http://noahpinionblog.blogspot.com/2013/08/conservative-white-america-you-need-new.html"

Oh lord, what a tossed-salad of leftist cliche thinking.

His thoughts on suburbs are particularly telling, because he doesn't actually deny what Stanley Kurtz is claiming.

Anonymous said...

Ray Sawhill

The IQ Test score is just so irrelevant to higher level math creativity. And this the whole point of the debate that took place on Field Medalist Terrence Tao's blog. Higher level math just doesn't resemble the types of problems that are fond on mathematics competitions. Higher level math creativity very much requires very deep understanding of mathematical concepts,structures,and themes.

I never believed that there was genuine deep scientific interest in IQ test score psychometrics. Lurking underneath it all was a partcular worldview regarding economic relations. You know resources are scarce..blah..blah...affirmative action.

Well here is my take on the whole thing.Imagaine if the 1965 Immigration Reform Act had not been passed,imagine if also all nonwhite immigration had not been shut down to 0,imagine if the US had an isolationiats post-World War 2 Foriegn Policy and a scaled down Military. There will be a lot more $$$$$$$ available for educational resources wouldn't there. OK, so Blacks scream about more $$$$ for education. To keep the social peace, $$$ is throw at black education. If they still fail..they still fail..and take it from there. This is a way more benign situation than the very explosive situation we have today in the US. Moreover, if there had been a complete shutdown of all nonwhite legal immigration post-WW2, a severe labor scarcity would have driven the real wage way up. There would be no credible case for affirmaive action in high wage economy post-1965.

It has always been my contention the Corporate Elites intense fear of a severe labor scarcity is the force driving post-1965 open borders scab labor immigration policy.

This is the context in which IQ testing should be understood. If there wasn't a post-1965 alternative source of labor in the form of both illegal and legal immigrants, there would be a greater commitment to develop home grown native talent, and it would be too costly to American Society to be tracking children with IQ tests and stamping an indelible mark on their heads as to what their inate scientific and mathematical apititude is.

Bill Blizzard and his Men

Mark Plus said...

Speaking of IQ and math competence, I would bet money that the government agencies which keep a low profile and require high IQ workers, like, say, the National Security Agency, have demographics like Silicon Valley's or NASA's in its prime. When you got to get results, or else, "diversity" considerations go by the wayside.

Education Realist said...

Even students at the 20th percentile of IQ can do high school math pretty well. I've taught them to do it many times. Dumb as a box of rocks, but a box of rocks can do algebra.

Love to see a cite for that. I don't think I've ever seen anyone prove that someone with an IQ of 90 can even attain basic proficiency in algebra.

And I'm absolutely certain you have not routinely taught algebra to people with an IQ of 90 or lower.

Well, I probably should say I'm reasonably certain. But I like to think that anyone whose ever worked with low ability people wouldn't make such moronic statements.

Anonymous said...

A kid with an iq of 90 does not know his multiplication tables thoroughly, has consistent dfficulty subtracting when borrowing is required, still uses fingers to add, etc....and THIS is in high school.

Anonymous said...

Why the negative focus on the picture? It's not a deliberately unkind drawing; it's the real thing, and an apt visual reminder that, contra ‘no child left behind’ prattle, not everyone is an A student, or an A student masquerading as a B student. Some students are D and F students, and no amount of prepping them for concepts they cannot comprehend, encouraging them to do things they are not capable of doing, and blaming their teachers for their inevitable failure will change that.

Cail Corishev said...

And I'm absolutely certain you have not routinely taught algebra to people with an IQ of 90 or lower.

Yeah, that's just silly. Does he think he's talking to NY Times readers here?

If you're able to teach algebra to a kid with a 90 IQ, that means either:

A) He napped through the IQ test, and his IQ is actually much higher than that, or;

B) he's some sort of math savant, so while his overall IQ is 90, his math-related scores are 100+ while other factors are 80 or lower.

But no, no one is routinely teaching algebra to 90-IQ high school kids and making it stick. No way. If anyone could do that, the Dept. of Ed. would be throwing money at him and he'd be too busy posing for the covers of national magazines to post blog comments about it.

ben tillman said...

Noah Smith,

I'd like to direct your attention to 18 USC § 1091 and ask you whether you think you have committed that crime by attempting to "drown" White Americans "demographically."


I. Renarde said...

I love it how the writer of that article says math genius is a myth, yet turns around and says that some people are "born with it." How can that be if it's a myth?

Oh, logic. It hurts.

Anonymous said...


Go take a look at the debate that took place on Field Medalist Terrence Tao's blog..."does one have to be a genius to do math"... four years ago. The point you raise was discussed-debated in great detail in the comment section.

Bill Blizzard and his Men