The Bell Curve Tolls for Thee

We do not live in Lake Wobegon. In all areas of academic ability, half of the children are below average. This fact has implications for education and public policy, and yet it’s something most politicians and public intellectuals would rather not talk about. It amounts to educational romanticism. At its heart is a glib presumption that every child can be anything he or she wants to be if only the schools do their job properly. No one really believes it, but we approach education’s problems as if we did. We are phobic about saying out loud that children differ in their ability to learn the things schools teach. Not only do we hate to say it, we get angry with people who do. We insist that the emperor is wearing clothes, beautiful clothes, and that those who say otherwise are bad people.    

Just about every reader understands what below average means for some abilities. Either you know people who fit the bill or you fit it yourself. For example, about half of you are below average in bodily-kinesthetic ability. You were picked late when choosing teams for playground games. You were not good enough even to try out for the varsity.

You may think you also know what below average means for academic ability because you know you are better at some intellectual tasks than at others. But here you are probably mistaken. The fact that you are taking the time to read an essay on public policy means that you are probably well above average in academic ability and likely never had a close, long-term relationship with someone who was below average. Asked to describe the things that a person with average academic ability can do, you will probably describe a person who is actually above average. 

Therefore the first task is to understand what below average means when it comes to academic ability. The best way is to show an example of the kind test questions that people with below-average academic ability have trouble answering. Take the following one, for instance, from the National Assessment of Educational Progress (NAEP, pronounced “€œnape”€), the program used by the federal Department of Education since 1971 to track student accomplishment.

Example 1. There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year?
(A) 9 (B) 81 (C) 91 (D) 99 (E) 100

By eighth grade, it would seem that almost everyone should be able to handle a question like this. Children are taught to divide and to calculate percentages in elementary school. It is a problem based on a simple mathematical concept, using simple arithmetic, requiring a simple logical interpolation to get the right answer. It is an excellent example for starting to think about what below average means in mathematics”€”because 62 percent of eighth-graders got this item wrong. It does not represent an item that below-average students could not do, but one that many above-average students could not do. Actually, more than 62 percent did not know the answer, because some of them got the right answer by guessing”€”indeed, a better estimation of the proportion of students who did not know the answer is 77.5 percent.

The schools are the usual scapegoats for results like these. But how much can they be blamed that three-quarters of eighth-graders did not know the answer to that question? Ask those same children what 10 percent of 90 is, and you will find that many if not most of them learned enough multiplication and percentages to give you the answer. Ask them what 90 plus 9 is, and you will find that almost all of them can add those numbers. What they failed to do was put everything together”€”to realize that first they had to take 10 percent of 90, and then add the result to 90. This logical step does not lend itself to being taught in the same way that the rules for addition and multiplication can be taught.

Put yourself once again in the position of the teacher. How does one teach a child to make inferential leaps?

It is appropriate to blame the schools when it is reported that, for example, more than half of eighth-graders do not know who was president during World War II or that about two-thirds do not know why the Bill of Rights was added to the Constitution (real examples from NAEP). Lack of academic ability does not account for those astonishing percentages. Students with a wide range of academic ability can remember unadorned facts. But the example above is different. Part of the blame for the high percentages of wrong answers may be assigned to schools, but not nearly all of it. Many of the wrong answers reflect nothing more complicated than low academic ability.

Book Cover

Schools Have No Choice But to Leave Many Children Behind

In many areas, the educational system has realistic expectations and behaves sensibly. Children with below-average bodily-kinesthetic ability have to take PE with everybody else, but no one tries to make them into good athletes. Children with below average musical ability are usually exposed to music classes in elementary school, but they are allowed to drop out thereafter.

Only for linguistic and logical-mathematical ability are we told that we can expect everyone to do well. Neither politicians nor school boards will publicly accept the reality that I tried to illustrate with the questions from NAEP. Children in the lower half of the distribution are just not smart enough to read or calculate at a level of fluency that most of the rest of us take for granted.

Just not smart enough: It is a phrase that we all use in conversation, we all know what it means, and it has to be made available once again to discussions about educational policy. Some children are just not smart enough to succeed on a conventional academic track. Recognition of this truth does not mean callousness or indifference. It does not mean spending less effort on the education of some children than of others. But it does mean that we must jettison glib rhetoric that makes us feel good.

No more talk about leaving no child behind. No more accusations that to be realistic is “€œthe soft bigotry of low expectations.”€ No more celebrations of attempts to “€œchallenge”€ students without regard to their ability.

To get to that point”€”to accept that it is okay to think in terms of what a child may reasonably be expected to accomplish”€”I think it is appropriate to personalize the issue. Let us think about ourselves and what it is reasonable to expect of us. The proposition on the table is that our best educational experiences were ones in which adults insisted we could do better when in fact we could do better; our worst educational experiences were ones in which adults insisted we could do better when in fact we could not do better.

Take up the negative side of my proposition. Think of a time when you were a child and some smiling, well-meaning person in authority said “€œYou can do it if you try,”€ and you knew you couldn”€™t. I will go first. I was eight or nine years old, it was Little League, it was the last inning, the Bruins were behind, and I (usually a benchwarmer) was coming to bat. Inexplicably, the coach chose this moment to go up and down the bench assuring everyone that I, statistically the worst hitter not just on the Bruins but in my town’s entire Little League, would get a hit and win the game. More than half a century later, the memory of going up to the plate after that pep talk and (of course) striking out is seared into my psyche.

Now it’s your turn. Whatever painful experience comes to mind, it surely has something in common with mine. When your smiling, well-meaning person in authority said, “€œYou can do it if you try,”€ and you knew it was not true, the well-meaning person was not raising your self-esteem. Not getting you to find untapped resources within you.
He was humiliating you. Now imagine having substantial intellectual shortcomings.

* * *

There are three plausible ways to argue that I am wrong: The measure of academic ability is invalid. We can raise academic ability. The schools are so bad that low-ability students can learn a lot more even if their ability is unchanged. Let us take each of these in turn.

“€œThe measure of academic ability is invalid”€

The standard measure of academic ability is an IQ score. There are lots of things to argue about when the topic is IQ as a measure of intelligence, but that IQ scores are related to educational achievement is not one of them. The question here is not whether the thing-that-IQ-tests-measure is intelligence, but whether it is predictive of academic achievement. In practical terms, does knowing the IQ score of a first-grader tell you much about how well that child will do in school? That question is probably the most thoroughly explored topic in psychometrics (Psychological Abstracts already listed more than 11,000 citations of studies on the relationship of IQ scores to educational achievement as of a decade ago).

Briefly, the correlation coefficient of IQ test scores with achievement test scores is usually about +.5 to +.7 on its scale of _1 (a perfect inverse relationship) to +1 (a perfect positive relationship). That relationship is driven by the general mental factor g, which usually accounts for 80 to 90 percent of the predictable variance in scholastic performance. Furthermore, there is no known way to measure learning ability that captures qualities IQ scores do not. Psychometricians have attempted to measure learning ability independently of IQ, but when the data are analyzed it turns out that the measures of learning ability are so intertwined with the abilities measured by IQ tests that they serve no independent purpose.

IQ scores are not infallible. If an individual child has a low IQ score, it is appropriate to consider the possibility that the score is misleading. But continuing to insist that the child can do better if child and teachers try harder requires some sort of objective basis, not blind faith.

“€œWe Can Raise Academic Ability”€

Now we come to a sensitive topic, our capacity to change underlying academic ability”€”in terms of tests, our capacity to raise IQ scores. But sensitive as it is, I propose that the following sentence is as uncontroversially true, scientifically, as the truth that half of the children are below average:

The most we know how to do with outside interventions is to make children who are well below average a little less below average.

First, a few things that are not part of that truth. Environment plays a major role in the way that all of the abilities develop. Genes are not even close to being everything. Regarding IQ specifically, a total change in environment”€”adoption at birth provides the best evidence”€”can produce demonstrable increases in IQ scores. Living in persistent poverty and other kinds of severe socioeconomic disadvantage can depress scores.

This being said, we have no evidence at all that we know how to produce lasting increases in IQ scores after children reach school. All the data about the trajectory of IQ scores over the life span indicate that they stabilize around ages six to ten and typically remain unchanged until old age.

Most people who have tried to raise IQ have reasonably assumed that the best time to do it is in the preschool years. During the height of the optimism about the potential effects of social programs during the last half of the 1960s and throughout the 1970s, many aggressive attempts were made to raise IQ using intensive preschool interventions, not to mention the nationwide, federally funded Head Start.

Many of the programs were haphazardly or tendentiously evaluated, but enough good studies came out of this period to enable an academic group called the Consortium of Longitudinal Studies to conduct a comparative analysis of eleven of the best preschool interventions. The Consortium found that they produced an average short-term gain of about 17 percentile points relative to a control group. This gain fell off to about 7 percentile points after three years, a trivial change in any substantive sense. The Consortium’s bottom line was that “€œthe effect of early education on intelligence test scores was not permanent.”€ The relevant point of this study, and of those that have been conducted subsequently with similar results, is that everyone remained so far below average. Being at the 25th percentile is better than being at the 16th percentile, but it is a distinction without a difference for the life prospects of an individual.

“€œThe Schools Are So Bad That Even Low-Ability Students Can Learn a Lot
More Than They Learn Now”€

We arrive now at the heart of the educational romanticism that pervades American education. As I write, the nation is entering the seventh year of the No Child Left Behind Act (NCLB), predicated on the belief that all children can perform at grade level, and is in the fifth decade of massive federal programs in education predicated on the broader belief that the academic achievement of American students from disadvantaged families can be raised substantially.

One source of the romanticism is the belief that American schools are so bad that there’s lots of room for improvement for all students, including those in the lower half of the distribution. The brunt of the evidence from more than forty years of research says that belief is incorrect. The changes we can expect in academic achievement in the lower half of the ability distribution are marginal, no matter what educational reforms are introduced.

The Coleman Report

The Coleman Report, named after sociologist James Coleman who led the study, responded to a mandate in the 1964 Civil Rights Act to assess the effects of inequality of educational opportunity on student achievement. The magnitude of the effort remains unmatched by anything done since. The sample for the study included 645,000 students nationwide. Data were collected not only about the students”€™ personal school histories, but also about their parents”€™ socioeconomic backgrounds, their neighborhoods, the curricula and facilities of their schools, and the qualifications of the teachers within those schools.

Before Coleman began his work, everybody (including Coleman) thought that the study would document a relationship between the quality of schools and the academic achievement of the students in those schools. Any other result seemed impossible.

To everyone’s shock, the Coleman Report instead found that the quality of schools explains almost nothing about differences in academic achievement. Measures such as the credentials of the teachers, the curriculum, the extensiveness and newness of physical facilities, money spent per student”€”none of the things that people assumed were important in explaining educational achievement were important in fact. Family background was far and away the most important factor in determining student achievement.

The Coleman Report came under intense fire, but reanalyses of the Coleman data and the collection of new data over many years supported the core finding: The quality of public schools just doesn”€™t make much difference in student achievement.

No Child Left Behind

Once an educational romantic has explained away the Coleman Report and a library of evaluations that document the failure of educational innovations tried since then, he is faced with a final reality test, the results of No Child Left Behind. If ever an intervention were guaranteed to produce increases in test scores, it is NCLB. It raised the stakes for educating students in the lower half of the academic ability distribution to unprecedented levels, imposing severe penalties on schools that failed to meet progress goals that were set according to test scores. At the very least, the effects of teaching to the test, which is occurring nationwide, should produce increases in test scores even if the students are not learning more.

With regard to the math test, if we use the 2003 test as the baseline, just one year after NCLB began, the increases for students at the 25th percentile were a modest six points and four points for fourth-graders and eighth-graders respectively. There is no way to tell what happened to twelfth-graders in math”€”the 2005 test was too different from previous NAEP math tests to permit comparisons.

With reading scores, fourth-graders at the 25th percentile increased their mean score by three points between 2002 and 2007. The scores for eighth graders fell by two points. Twelfth-graders were last tested in 2005. Their scores had also fallen since 2002, by one point. Such small changes up or down are meaningless. The effective change for students at the 25th percentile was zero, as were the changes among students at the 10th, 50th, 75th, and 90th percentiles. Judging from NAEP, NCLB has done nothing to raise reading skills despite the enormous effort that has been expended.

There are many reasons to accept the reality of limits of educational reform and no empirical basis for thinking that great leaps forward are just around the corner. To continue to assert that major improvements are possible in the academic test performance of the lower half of the distribution through reform of the public schools is more than a triumph of hope over experience. It ignores experience altogether. It is educational romanticism.

Illusory Reasons for the Romanticism

Why then do so many people still believe the contrary? Why was NCLB passed with a large bipartisan majority in Congress and with broad public support? Why will this essay be greeted by all sorts of stories about teachers who took classes of failing students and had them reading Shakespeare in six months? There are many reasons for this, all of which look good at first glance but cannot withstand scrutiny.

The first illusory reason is that some inner-city schools in some of the nation’s largest cities are every bit as dreadful as people think. Accounts written by journalists, scholars, and teachers describe chaotic and sometimes violent classrooms, nonexistent standards, incompetent teachers, competent teachers who have given up, and lack of the most basic resources for teaching effectively, including textbooks. Rescuing children from such schools should be one of the top priorities of any educational reform, and doing so will produce improvements in their academic achievement.

But only a fraction of children attend such schools. Sixteen percent of all K”€“12 students go to schools located downtown in cities of 250,000 or larger.. Most of those schools are normal ones. What proportion of the 16 percent are going to the horrific schools? A quarter? A fifth? A tenth? There is no precise answer, but any plausible estimate leaves us with much less than 10 percent of all K”€“12 students going to the worst schools, and the right proportion could easily be around 2 or 3 percent. Rescuing all of those children is something we must try to do, but even complete success would only tweak the national numbers.

Another illusory reason for romanticism about what schools can do is the nostalgic view that many people hold of American public schools in the good old days, when teachers brooked no nonsense and everyone learned their three R’s. After all, just look at the McGuffey Readers that were standard textbooks in the nineteenth century, filled with difficult words and long literary selections. That’s what we expected everyone to be able to read then, right?

Wrong. American schools have never been able to teach everyone how to read, write, and do arithmetic. The myth that they could has arisen because schools a hundred years ago did not have to educate many of the least able. About half of all adults in 1900 had not reached the eighth grade. To put it another way, only a small portion of those toward the bottom of academic ability would have been around to take a NAEP examination if it had been administered to eighth-graders in 1900. Let today’s schools skim off the same part of the distribution, and they would show nearly 100 percent success in attaining NAEP’s standards of basic achievement in reading and math.

The final illusory reason for hope in the face of experience is the belief that private schools or variants such as charter schools can come to the rescue. I have long been an advocate of the privatization of American elementary and secondary education, but not because this would improve math and reading scores. Modest improvements in such scores, sometimes statistically significant, have been observed among students who get vouchers or go to charter schools and who would otherwise be consigned to the worst-of-the-worst schools in the inner city. But when the comparison is between a run-of-the-mill public school and a private school, math and reading test score differences have generally been minor or nonexistent. The real advantages of private or charter schools lie elsewhere”€”in the safe and orderly learning environments they offer their students (no “€œnerd harassment”€), and in curricula that typically provide more substance in subjects like history, geography, literature, and civics than the curriculum offered by the typical public school. But there is no reason to expect that private or charter schools produce substantially higher test scores in math and reading among low-ability students who would otherwise go to normal public schools.

* * *

No one wants to be education’s Grinch, especially when we are talking about children who have gotten the short end of the stick through no fault of their own. The impulse to romanticism is overwhelming. But it has led us to do things to children who are below average in academic ability that are not in their best interests. In assessing the state of American education, and what can be accomplished for the lower half of the distribution by any of the reforms proposed by either Left or Right, it is time to recognize that even the best schools under the best conditions cannot overcome the limits on achievement set by limits on academic ability.

This is not a counsel of despair. The implication is not to stop trying to help, but to stop doing harm. Educational romanticism has imposed immeasurable costs on children and their futures. It pursues unattainable egalitarian ideals of educational achievement (e.g., all children should perform at grade level) at the expense of attainable egalitarian ideals of personal dignity. We can do much better for children who are below average in academic ability, but only after we get a grip on reality.

Charles Murray is the author of two of the most widely debated and influential social policy books of the last three decades, Losing Ground: American Social Policy 1950″€“1980 and, with the late Richard J. Herrnstein, The Bell Curve: Intelligence and Class Structure in American Life. He is the W. H. Brady Scholar at the American Enterprise Institute in Washington, D.C.

This is an excerpt from Real Education: Four Simple Truths for Bringing America’s Schools Back to Reality by Charles Murray. Excerpted by permission of Crown Forum, a division of Random House, Inc. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.

A virtual copy of Real Education can be browsed here.



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