Charles Murray posted three articles this week on Education and Intelligence, a series that generated some conversation around the net:
- Intelligence in the Classroom:
Our ability to improve the academic accomplishment of students in the lower half of the distribution of intelligence is severely limited. It is a matter of ceilings. Suppose a girl in the 99th percentile of intelligence, corresponding to an IQ of 135, is getting a C in English. She is underachieving, and someone who sets out to raise her performance might be able to get a spectacular result. Now suppose the boy sitting behind her is getting a D, but his IQ is a bit below 100, at the 49th percentile.
We can hope to raise his grade. But teaching him more vocabulary words or drilling him on the parts of speech will not open up new vistas for him. 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. - What’s Wrong with Vocational School?
Begin with those barely into the top half, those with average intelligence. To have an IQ of 100 means that a tough high-school course pushes you about as far as your academic talents will take you. If you are average in math ability, you may struggle with algebra and probably fail a calculus course. If you are average in verbal skills, you often misinterpret complex text and make errors in logic.
These are not devastating shortcomings. You are smart enough to engage in any of hundreds of occupations. You can acquire more knowledge if it is presented in a format commensurate with your intellectual skills. But a genuine college education in the arts and sciences begins where your skills leave off.
In engineering and most of the natural sciences, the demarcation between high-school material and college-level material is brutally obvious. If you cannot handle the math, you cannot pass the courses. In the humanities and social sciences, the demarcation is fuzzier. It is possible for someone with an IQ of 100 to sit in the lectures of Economics 1, read the textbook, and write answers in an examination book. But students who cannot follow complex arguments accurately are not really learning economics. They are taking away a mishmash of half-understood information and outright misunderstandings that probably leave them under the illusion that they know something they do not. (A depressing research literature documents one’s inability to recognize one’s own incompetence.) Traditionally and properly understood, a four-year college education teaches advanced analytic skills and information at a level that exceeds the intellectual capacity of most people. - Aztecs vs. Greeks:
How assiduously does our federal government work to see that this precious raw material is properly developed? In 2006, the Department of Education spent about $84 billion. The only program to improve the education of the gifted got $9.6 million, one-hundredth of 1% of expenditures. In the 2007 budget, President Bush zeroed it out.
But never mind. A large proportion of gifted children are born to parents who value their children’s talent and do their best to see that it is realized. Most gifted children without such parents are recognized by someone somewhere along the educational line and pointed toward college. No evidence indicates that the nation has many children with IQs above 120 who are not given an opportunity for higher education. The university system has also become efficient in shipping large numbers of the most talented high-school graduates to the most prestigious schools. The allocation of this human capital can be criticized–it would probably be better for the nation if more of the gifted went into the sciences and fewer into the law. But if the issue is amount of education, then the nation is doing fine with its next generation of gifted children. The problem with the education of the gifted involves not their professional training, but their training as citizens.
We live in an age when it is unfashionable to talk about the special responsibility of being gifted, because to do so acknowledges inequality of ability, which is elitist, and inequality of responsibilities, which is also elitist. And so children who know they are smarter than the other kids tend, in a most human reaction, to think of themselves as superior to them. Because giftedness is not to be talked about, no one tells high-IQ children explicitly, forcefully and repeatedly that their intellectual talent is a gift. That they are not superior human beings, but lucky ones. That the gift brings with it obligations to be worthy of it. That among those obligations, the most important and most difficult is to aim not just at academic accomplishment, but at wisdom.
Joanne has notes [more], along with Nicholas Lehmann, who comments on Murray’s The Bell Curve: Intelligence and Class Structure in American Life. Technorati search. Clusty Search on Charles Murray. Brad DeLong posts his thoughts as well.
These articles really do justify a response. I’m just going to comment on the first part, I’ve not read much of his other comments, but right now, it is sufficient just to look and his first statements because they quickly assess his intelligence (which I believe should be numbered below 0).
Charles Murray is writing his opinion for the Wall Street Journal, it seems, but I don’t know what his relationship is to this organization, and what his support is at the “paper”. If anyone knows, please tell me.
First conclusion. I don’t know if Murray is above or below average at the WSJ but I am absolutely certain he is INCOMPETENT (though perhaps no more or less than other WSJ opinion makers, and the people who believe them).
I’ll pull two critical quotes from his introduction and briefly comment on them. That should remove any doubt you have that my assessment of him is true. Later, in further posts, as I have time, I’ll look of some of his other asinine comments.
First, the two quotes.
“Half of all children are below average, and teachers can do only so much for them. ”
“Today’s simple truth: Half of all children are below average in intelligence. We do not live in Lake Wobegon.”
The answer to these obvious statements? He’s almost exactly telling the truth, but a little off depending. But he’s incompetent (an absolute statement of his intelligence), because he believes statements make some important point.
You can quote any and all the statements below and be absolutely certain you will be tellng the truth.
1) About half the medical doctors in the U.S. are below average
2) About half the MIT graduations are below average.
3) About half the teachers teaching in Madison schools are below average.
4) About half of the principals of Madison schools are below average.
5) About half of Wisconsin public schools spend above the average cost per student.
6) About half the top 1% of all graduating seniors from Madison Public schools are below average.
7) Everybody is below average on some measure.
8) Everybody is above average on some measure.
Murray and people like him don’t know (and more likely, don’t care to know) this so-simple-any-child-can-and-understand fact.
Average is a property of a sample of people or things based on some measure or assessment.
Average is most often calculated as the sum of all the scores in the sample divided by the number of scores. This more accurately called the sample MEAN.
The MEDIAN of a sample is that value which exactly divides (partitions) the sample into two equal subsample sizes.
For any of these statistical values to make sense the test or assessment must spread the scores. That is, if you ask all graduating seniors what 1+1 is, all will say 2. This is a lousy test for discriminating between seniors, so all bets are off on the meaningfulness of the sample MEAN or MEDIAN.
(To complicate matters somewhat, the word “average” in educational contexts is sometimes used as a shorthand for the sample MEDIAN, rather than the sample MEAN. So, if you bother to read the literature, you need to isolate what “average” means in that context.
For example — I believe I read this somewhere on the ACT test site — the “average” ACT score is set to 20, which is the standardize score for the MEDIAN of the “raw” scores for that year.
By the way, do you see the other implication — if my memory is correct? If your son got a 24 on the ACT in 2000, and your daughter got a 24 on exactly the same test in 2006, it doesn’t mean they “scored” the same, because the sample of students in 2000 was different than the sample of students in 2006).
Now, the sample MEAN will partition the sample into equal sized subsamples, if the sample is exactly spread into a bell curve (the Gaussian distribution or Normal curve). Otherwise, the MEAN (or average) will be higher or lower than the MEDIAN. That is why each of my absolute truths begin with the word “about”. In practice, this means that the MEAN (average) will almost NEVER exactly split a sample of scores into 2 equal partitions (be the same as the MEDIAN), because a sample will almost never exactly fit a bell curve.
In fact, if the distribution of scores made by the test creates a highly SKEWed set of scores (that is, the distribution of scores has a big “hump” on one side, and a long tail on the other — plotting the scores as a frequency distribution), then the sample MEAN will not even come close to partitioning the sample of scores at about 50% on one side of the average and 50% on the other).
The key points you need to know: 1) what is being measured, 2) how valid and reliable the test is, 3) how well the test distributes the set of scores, 4 what the sample we’re talking about is, and 5) what the statistic being used is?
Let’s illustrate Murray’s asininity a little further.
Say, sample is all Madison children under the age of 5, the test is 10 questions of the form: 1+1=, 1+2=, ….
The policy decision from the results of this test will be, for those children who are at the lowest 25% on this test, we will label them unintelligent (stupid) and that we all agree that we will not waste taxpayer resources educating them. It is clear, of course that their IQ’s are too low to bother with them. We also might want to consider forbidding them to have offspring because we want to ensure the human race gets smarter and not dumber.
I have little doubt that Murray would agree to most of these policy decisions because it’s consistent with his knowledge and logic.
However, I would hope most readers would object to this test as unmeaningful, because, as you would argue, you can’t draw any of these conclusions because, for example, newborns and most kids below 3 will never get any answers correct. They’ve never had the opportunity to learn this material. It’s not a fair test.
This same assessment applies to all discussions regarding intelligence, capacity to learn, and predictions of success. Where there is little opportunity to learn whatever is being assessed, no measure is valid and fair.
But, an assessment that is fair and accurate with absolute certainty is that if a person who has a high school diploma, and is likely to be college educated (even from an Ivy League school (they’ll take anyone with money and connections) and makes a lot of money and writes columns for the Wall Street Journal) and makes the statements that Murray has made and those who equally believe what he says, then, it is proof beyond all reasonable doubt that he is INCOMPETENT. He and others like him have had the opportunity and formal education to know these basic quite critical ideas, and they were unable and unwilling.
It’s just 1+1=2.
QED.
Mea Culpa! I didn’t pay attention to the last statement, but this gives me another opportunity.
“Mr. Murray is the W.H. Brady Scholar at the American Enterprise Institute.”
Just wonderful.
This shows the importance of knowing the sample over which statistics and labels are applied.
Mr. Murray is a SCHOLAR! at American Enterprise Institute. So, by AEI’s own admission, he’s the cream of the intellectual crop that AEI has to offer. That must mean that the other employees at AEI are even dumber than he is.
As I said, “average” is all about the sample your comparing within; and so is the word “scholar”.