Arnold Kling  

Thoughts on Education

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In this essay, I pull together thoughts on education, based on my reaction to Charles Murray's recent op-eds.

He tends to treat IQ as if it were a measure of one's capacity to hold knowledge, like the volume of a container. According to Murray, a high-IQ jar can hold advanced physics. A low-IQ jar can only hold, say, 4th-grade mathematics.

The container metaphor implicit in Murray's essays could be misleading. Instead, IQ might be a measure of the speed with which someone can absorb knowledge, rather than a measure of how much they can absorb. A high-speed car will get to the destination faster, but a low-speed car will still get there, if given enough time.

If the jar metaphor is correct, any resources devoted to trying to teach calculus to an average-IQ student are wasted. However, if the car metaphor is correct, and it is really important to teach calculus to the average-IQ student, then we should be putting more resources into doing so.

The economic approach to education would be to maximize benefits minus costs.

UPDATE: See also Seth Roberts, who has a somewhat similar take on Murray.

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COMMENTS (17 to date)
james writes:

Calculus? Isn't that one of the least practical subjects?

jb writes:

Calculus was just an example, no?

In any case, I think you're both wrong. Because I've known plenty of people who are brilliant at, say, math or music or history, who are very bad at comprehending software programming, or even figuring out how to uninstall a software program. And vice-versa. In an area where you are "gifted", you learn quickly and you retain a lot. In other areas, not so much.

In my experience, if it takes you a long time to understand something, by the time you get to the end, a bunch of the stuff at the beginning has been pushed out of your brain. I've never seen anyone that takes a long time to learn something relatively "compact', and subsequently demonstrates mastery of that subject.

So, in my opinion, for an individual, learning speed and content retention are consistent, but only on a subject-by-subject basis

Bruce G Charlton writes:

I just thought this was an excellent TCS column, full of really good ideas. That's all...

Caliban Darklock writes:

I've always found it productive to think of the brain as a muscle and IQ as how much it can lift. Then you can just connect the dots.

If you don't have a lot of upper body strength, and can only bench-press 45 pounds, you can spend a few weeks working on that and rapidly increase your ability. Since your ability is low, it will increase quickly. But there is a maximum, imposed both by your own personal genetics and by physics itself. You are never going to bench a whole ton. Nobody is. You're probably never going to bench more than 600 no matter how hard you work, because only a tiny minority of people are capable of that. However, the more important limit is how hard you will work - most people will never bench more than 250, because they simply DO NOT CARE if they can bench more than 250. And, of course, if you stop working out... you lose your ability to lift heavy weights.

Same with your brain. Work your brain, you can think smart thoughts. Stop working it, you lose your ability to think those smart thoughts. You'll probably never be Einstein or Galileo or Descartes, because almost nobody is, but there's a lot of room between that and where most people stop.

And that's where the geeks and nerds hang out, in much the same way there's a core "freak" group at most gyms that hangs around benching three and four hundred. Nowhere near their limit, nowhere near legendary, but far above and beyond the average.

TGGP writes:

Setting aside economics, I am inclined to believe that Charles Murray understands IQ a whole lot better than you, Arnold.

Sam B. writes:

Setting aside economics, I am inclined to believe that Charles Murray understands IQ a whole lot better than you, Arnold.

And what makes you believe that? Murray has a PhD in political science. As far as I know, he is not an expert in psychometrics or genetics. What does he know about this variable (IQ) and its intersection with public policy that is beyond the grasp of Arnold or any other well qualified economist?

Tim Lundeen writes:

The metaphor I like is to athleticism (I think Jenson uses this in his book). If you measure how fast someone can run a 10-second dash, that speed is highly correlated with general athleticism. If you did multiple tests of athletic ability (speed, endurance, weight lifting, broad jump, high jump, etc), they would tend to be highly correlated and you could get a single measure of athleticism, call it "a".

In the general population, athleticism is the result of many individual factors, so should have normal distribution, just as IQ or g does.

Now people with higher "a" are better overall athletes than people with lower "a", and given any event and two randomly chosen people, you would win money over a series of trials by betting on the person with higher "a". But in any given event, other skills come into play. Someone with low "a" might be very good at a particular event, or someone with average "a" might be good at everything but not have any upper body strength and do very badly on that subtest, so their overall score is just average.

My guess is that if we did this, we would find that almost all baseball players would have very high "a", and we could say that you are exceedingly unlikely to be a pro baseball player with an "a" below 160 or 170.

In the same way, you are quite unlikely to be a Mathematics professor with an IQ below 160, and you are unlikely to win a Nobel prize in a hard science with an IQ below 140.

g is a statistical construct, the common factor across all intellectual endeavors. Someone with high g will tend to be superior in all intellectual endeavors, just as a good athlete will tend be superior in all athletic activities. But on individal events, specific talents or flaws come into play, and of course you can find examples of specific skills (memory, "deepness", speed, creativity, musical ability, etc) where someone's specific skills are not the same as their g factor.

IQ is highly correlated with g, but is not a direct measure.

One other thought along these lines. Research is showing that brain structure (neural density, mylination and signal propagation speed, brain metabolism) is correlated with g, in the same way that muscle composition, glucose metabolism, size, etc are correlated with athleticism.

Josh writes:


I agree with your metaphor for IQ more than Murray's. But even using the speed concept, I think Murray's "jar" concept emerges. The problem is adaptation. If all we're talking about is education in theory, then I agree that given enough time, each person could probably learn most anything. But if we think of a practical education, where learning opens doors to solving new problems, and where each new problem requires additional learning to solve, then I think for all practical purposes, a low IQ person WON'T ever learn what he needs. To use your car analogy, it's as if every time the fast car arrives at its destination, the destination moves a few miles further. The slow car may never arrive.

Steve Sailer writes:

To put examples to Tim's idea of a general factor of athleticism, in the Super Bowl we'll see Bears cornerback Ricky Manning defending against passes from Colts quarterback Peyton Manning. The way everybody in the NFL uses the term "athleticism," Ricky has more than Peyton -- the cornerback can run faster, jump higher, run more elusively, stop faster, etc. than the quarterback. But the quarterback has specific skills -- eye-hand coordination, arm strength, and mental abilities to comprehend the chaos of the field -- that make him a superstar. The athleticism factor glass is both half full and half empty.

The general factor of intelligence g is quite similar.

TBox writes:

I think both Tim Lundeen and Steve Sailor are missing Arnold point. Your description of how IQ correlates with some general ability is probably correct. But even if we take it as given, Murray's policy argument do not necessarily follow from it.

Your analogies all make sense in an academic discussion of the topic. When it comes to making policies, we have to go beyond a general measure of intelligence into specific skills. As Arnold and others pointed out, not all high-IQ can make programs or write a literary masterpiece or put forth an elegant mathematical proof. So IQ matters but only to a certain extent.

Dr. T writes:

IQ: Is it learning speed, learning capacity, or ablity to understand complex things.

It is all of the above and more.

People with higher IQs can learn tasks of average complexity faster. (Example: Learning the basics of using a word processor.) [The car metaphor.]

People with higher IQs usually can retain more knowledge of more subjects. [The jar metaphor.]

People with higher IQs can learn more complex subjects. A person with a 100 IQ is unlikely to master a complex subject (such as the physical chemistry of crystal lattices or the roles of cytokines in inflammation) even if he devotes five times as much effort as someone with a 130 IQ. [The high bar metaphor.]

Creativity (artistic and intellectual) is less important to measured IQ, but may be very important for some persons. Two people could have identical IQs in the verbal realm, but the one with greater creativity could become a critically acclaimed author while the other could be his editor.

Getting back to your reply to Charles Murray, I believe that you must combine the jar and car metaphors and add the "high bar" metaphor. Most persons with an IQ of 100 are capable of learning basic calculus. However, the effort required (of learners and teachers) to achieve that goal would be much greater than for persons of >125 IQ.

I agree that education should maximize (benefits - costs). The problem is objectively measuring the benefits of educational goals. I distrust the abilities of professional educators to assess benefits. I would be more likely to trust economists' assessments of educational benefits.

meep writes:

I have a post of my own on his third piece here:

I think it's unfortunate that Murray is attacking it from the point of view of IQ because everybody is focusing on that and want to go down the road of "multiple intelligences". However, it's undeniable that there are kids, for whatever reason, who can go much faster than others in key academic subjects, and that for some students there is a limit to how much abstract reasoning they can follow (though I bet this limit is much higher than Murray puts it at).

I think the third piece is most important in talking about what should be done with those who are intellectually gifted. The post I linked above deals with teaching wisdom to smart kids.

Chuckles writes:

Rather typical that any contrary examples can be filed away under "underachievement stories".

jaim klein writes:

(1) Is IQ absolute (a jar) or a function of time (velocity)? Now, Arnold, that is testable. And it has been tested so many times that the answer is blowing in the wind. Within the limits of a lifetime, IQ is a jar. Investing enormous effort, researchers succeeded in teaching chimps to use up to 20 - 25 words (push botton with the banana logo to get a banana), but no one ever passed a הבנת הנקרא text understanding test. Give Dr Murray some credit on the subject.
(2) Murray is carried away when says that normal kids should stay in high school till 18. What for? IQ stops improving at age 12 or 13 and then, all the knowledge required for an average job can be learnt in one year. No, I am exaggerating, most jobs can be acquired in a two week on the job training, as it is done: supermarket cashiers, forklift drivers, taxi drivers, computer assembly line worker, strawberry pickers, etc. Some 90% of the workforce make a living from those kind of jobs, so why torture them till age 18? Let them start working and earning a salary at 16 and make children when they are biologically programmed for so, age 16 to 22.
(3) Regarding good students like me, his advise is to get them out of the undemanding college edens and give them some really hard exams, so to beat into them some sense of humility. That is exactly how my parents and their fellow ancestors thought, so I spent years tortured by sadistic foreign-speaking teachers. As victim of Prof. Murray's clones, I state that the experience is not enjoyable, and I think is useless, as life (and if not life, the stock exchange) beats into oneone, hour by the hour, a sense of deep humility and the frustrating awareness of our human limitations. The life that expects young people is no rose garden, so let's life and not Prof Murray discipline them.

A-town writes:

I don’t agree with what Murray says about having a higher IQ is about how long you can remember doing calculus or any other subject. I do think that it takes a certain amount of time for you to understand and learn something for an exam but after that exam if you don’t continue to study the material it just goes away. Everyone has there different study habits and they way they learn, some students may only need a few hours as others may need a few days to understand something. I don’t think that it is about how much or how quickly you can understand something. Everyone can learn, I learn something new everyday but it is the drive that each person and the effort the put forth which makes them stand out when it comes to IQ.

gm writes:

I believe Howard Gardner's model of multiple intelligences matches the real world better. Murray is advancing other agendas.

Tracy W writes:

In my experience, if it takes you a long time to understand something, by the time you get to the end, a bunch of the stuff at the beginning has been pushed out of your brain. I've never seen anyone that takes a long time to learn something relatively "compact', and subsequently demonstrates mastery of that subject.

Well I have one example. Me. It took me a long time to learn how to drive a car (a manual one), and yet I eventually got to the point where I could do it as well as most other drivers on the road.

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