January 16, 2007

Charles Murray on the Lake Wobegon Fallacy

From the WSJ: First in a three part series:

Half of all children are below average in intelligence, and teachers can do only so much for them.

... Some say that the public schools are so awful that there is huge room for improvement in academic performance just by improving education. There are two problems with that position. The first is that the numbers used to indict the public schools are missing a crucial component. For example, in the 2005 round of the National Assessment of Educational Progress (NAEP), 36% of all fourth-graders were below the NAEP's "basic achievement" score in reading. It sounds like a terrible record. But we know from the mathematics of the normal distribution that 36% of fourth-graders also have IQs lower than 95.

What IQ is necessary to give a child a reasonable chance to meet the NAEP's basic achievement score? Remarkably, it appears that no one has tried to answer that question. We only know for sure that if the bar for basic achievement is meaningfully defined, some substantial proportion of students will be unable to meet it no matter how well they are taught. As it happens, the NAEP's definition of basic achievement is said to be on the tough side. That substantial proportion of fourth-graders who cannot reasonably be expected to meet it could well be close to 36%.

The second problem with the argument that education can be vastly improved is the false assumption that educators already know how to educate everyone and that they just need to try harder--the assumption that prompted No Child Left Behind. We have never known how to educate everyone. The widely held image of a golden age of American education when teachers brooked no nonsense and all the children learned their three Rs is a myth. If we confine the discussion to children in the lower half of the intelligence distribution (education of the gifted is another story), the overall trend of the 20th century was one of slow, hard-won improvement.

We can do a better job of schooling, but not until we start talking honestly about differences in intelligence. Our schools and legislatures are constantly coming up with policies that are based on the Lake Wobegon Assumption, and the left half of the bell curve pays the price.

For example, in California, the state wants all students to have a shot at qualifying to attend the prestigious University of California campuses. So, public high schools are compensated based on how many students they have enrolled in rigorous UC-qualifying college preparatory courses (the "A-G" courses). So, it's common for 9th graders to be dumped into Algebra I even though they are still struggling with fractions, because the high schools get more money the more students they have in college prep courses, even though they are complete waste of time. Thus, in some schools, students can't start taking the remedial math courses they desperately need until tenth grade.

It should be mandatory for all principals, school district officials, and legislators to read The Bell Curve. Of course, the opposite is closer to the truth -- it's a career-damager to read it and talk about it.

My published articles are archived at iSteve.com -- Steve Sailer


Floccina said...

One of the big problems that I see with schools regarding intelligence is that school is more of a long test than an education. The basic principles of physics and chemistry are very simple, in accounting debits and credits are easy to learn, the basics of principles of most subjects that would be useful in life are simple but we load the sciences up with math and accounting with concepts far beyond debits and credits so that we can grade the students. Better to educate students on the things that they need to know in life and grade them some other way. Economist Richard Vedder (author of going broke by degree) has suggested that we need to separate testing and teaching this would make education better and cheaper.

Increasingly, you hire a tutor or go to a for profit school to teach you but if you need credentials you must slog away for a long period of time in not for profit school.

BTW Some people make a tragic mistake of going to a for profit school when they are in need of credentials. They get out hoping to find a job but no one respect their education. For obvious reasons for profit schools do not want to flunk anyone thus no credentials.

Here is for a separation of education and testing.

Floccina said...

BTW do you think that the tighter range of inteligence in Korea, China and Japan contribute to the Koreans, Chinese and Japanese being so hard working?

I had a friend from Korea who told me that children in Korea often leave for school at 7:00am and then after school go to tutoring and do not get home until 10:00pm. With a smaller IQ range hard work can pay off. On the other hand it would be useless for a child with a 90 IQ to study hard when plenty of 130 IQ students are around.

Hubert said...

Well the quality of education in Britain's state system could certainly be improved. Last year, girls of African background (ie. excluding Caribbeans) actually had better average exam results than white boys.

Tom said...

Bad analogy from Charles Murray:

It is not within his power to learn to follow an exposition written beyond a limited level of complexity, any more than it is within my power to follow a proof in the American Journal of Mathematics. In both cases, the problem is not that we have not been taught enough, but that we are not smart enough.

A majority of high IQ people can't follow a proof in a mathematical journal precisely because they have not been taught math at that level. Murray seems intelligent enough to be one of them.

People who say advanced math is all Greek to them are right; many of them would be able to learn Greek easily if they put their minds into it.

But of course, not all of them will want to do that. Underachievement in some fields may be a prerequisite for overachievement in others.

Steve Sailer said...

"A majority of high IQ people can't follow a proof in a mathematical journal precisely because they have not been taught math at that level. Murray seems intelligent enough to be one of them."

Murray has a Ph.D. in political science from MIT. He had all the opportunity to learn higher mathematics a man could have. If he says he can't learn cutting edge math, I'd believe him.

Steve Sailer said...

As floccina suggested above, there is a real conflict of interest in education involving testing. Some forms of testing work pretty well, such as the SAT because the CollegeBoard doesn't give a damn what you personally score. But, allowing states to test their own students, and then grade themselves, which determines how much federal money they get under the No Child Left Behind act is a conflict of interest so flagrant it had to be intentional.

meep said...

This is part of the problem with NCLB: how to deal with the definitely mentally deficient. My grandma taught middle school special education in SC for decades, and finally left after the standardized testing was also being applied to her students. I visited her classroom when I was in 1st grade, and most of my normal intelligence classmates read better than her students. My grandma could teach them some rudimentary reading, but overall logical comprehension was low. And these were the "teachable" bunch. I've got other relatives who have dealt with the "trainable" group, where the level of achievement is learning to tie shoes.

That said, Joanne Jacobs made a good point at her blog (and Murray mentions it in his own article): what exactly =can= the 1 s.d. below average IQ people achieve? Maybe not calculus, but basic algebra and reading Dickens might be in their grasp (for crying out loud, he was a bestseller in his day -- he's not all that hard to read. Think of Harry Potter now - not all the kids reading it are above average intelligence). Who knows? Maybe they can achieve the 8th grade level that the 11th grade NAEP measures. Yes, it will take them longer to get there, and yes, they're not college bound (or they shouldn't be). But that doesn't mean they can't be held to =some= standard.

I'm with floccina on the separation of the teachers and the testers. I'm also big on letting the smart people meet the standard and do what they want (more here: http://meep.livejournal.com/1469581.html). I have more than once run into a situation where the kids haven't been tested to a rigorous standard because the teachers didn't want the kids to feel bad about themselves, and it does them no good as they'll eventually run into the reality that they're not as good as they think.

Of course, the damage can be even worse when there's no hard-and-fast way to prove to some people they're just not as good as they think.

In any case, I'm waiting on my results from my last actuarial exam. Now =that's= some harsh reality. You should see the Actuarial Outpost after scores come out. Sheeee. In my career, you can lose your job for not passing a test; you can get bonuses and raises based on passing those tests. It's nice to be in a profession that can shake out some of the incompetents.

Tom said...


"Murray has a Ph.D. in political science from MIT. He had all the opportunity to learn higher mathematics a man could have."

As a graduate student in political science? No schedule conflicts at all?

Well, perhaps, but did he pursue the opportunity? It could be that he studied just enough statistics to write the Bell Curve, and God bless him for that. Which is the better use of his time, applying formulae or to re-deriving them?

I'm not saying Murray could understand *all* the proofs or even many proofs. But there should be some he could follow if he had the training and the desire for it.

Few people other than mathematicians themselves (and perhaps some physicists and economists) can readily understand math papers. Are you saying high-IQ people are limited to those, Steve?

Even if Murray's brain were truly inadequate, which I doubt, his analogy still wouldn't be convincing, especially to those who do not want to be convinced (of which I'm not one). There's simply an easier explanation (your favorite Occam's Razor right here). Why can't he understand a math journal? Because he's not a mathematician!

Anonymous said...

Here in Chicago they are paying substantial amounts of money to "Hispanic" parents to get their kids to come to school.What a waste!

Anonymous said...

Most mathematicians wouldn't be able to read the articles in that journal, if they're anything like I remember. Most math articles are written =horribly= and assume you know quite a few major results in the particular field being written about.


Anonymous said...

I have an undergraduate degree in math, and I couldn't understand a math journal. Mathematics (real mathmatics - i.e. not algebra or even calculus) is not easy to follow unless you're an absolute expert in the particular branch being considered. Those journals are written for and by PhD people. In fact, I've heard that even the professors only understand a few articles from the journal in their particular field. Anyway, I agree. Pushing so many people to go to college devalues college degrees economically (and intrinstically as unfortunately many subjects get "dumbed down" as a result of unqualified students lowering the standards). Although the sciences and mathematics haven't met this fate yet, they probably will. Currently, I really don't think it's fair to bright people who are interested in the Humanities to have to be bored by dumbed down stuff. I was initally a Philosphy major because I really liked it, but the work was so dumbed down that I switched majors (didn't have the time or money to do a double major). Anyhow, I knew a Philosophy degree wouldn't prove anything like it should... At least I still got to minor in it. It's a waste of time for lots of people to go to college plus those of us who are suited for it no longer stand out.