Issues in Educational Research, 5(1), 1995, 11-22.

The bell curve: Should intelligence be used as the pivotal explanatory concept of student achievement?

P. G. Cole
Edith Cowan University

This paper contains an analysis of Herrnstein and Murray's (1994) thesis on the relationship between IQ and scholastic attainment. The paper focuses on the theoretical framework proposed by Herrnstein and Murray in their book The Bell Curve and examines some of the key arguments contained in that volume. The educational implications of the theoretical framework are given particular attention. The genesis of the definition of intelligence used by the authors is scrutinised in some detail. The relationship between IQ and school attainment is discussed and some alternative interpretations of their data are proposed. It is suggested that the Herrnstein and Murray thesis contains a flawed conceptual analysis and that other interpretations of the data would lead to more cogent explanatory models.

Key terms: IQ controversy, Herrnstein, Murray, bell curve.

This paper contains an analysis of several of the main arguments contained in Herrnstein and Murray's (1994) thesis on the use of IQ measures in the explanation of scholastic attainment. Several of the key arguments proposed in the Herrnstein and Murray text have been selected for critical analysis. The educational implications of their judgements on the place of IQ in the explanation of school attainment are given particular attention. School attainment in this context refers to levels of achievement on Year 12 test results, high school completion rates, and university degree completion rates.

The procedures used by Herrnstein and Murray to explore the relationship between intelligence and attainment have received some attention by reviewers (Gould, 1995), but most have either ignored the issue or treated it in a cursory manner (see Jacoby & Glauberman (1995) for a collection of reviews). The present paper contains a section on the background to the debate about the controversy regarding IQ and attainment and related matters. The major thesis in Herrnstein and Murray's book is explicated. The relationship between IQ and attainment is then discussed, followed by an exposition of the importance of the general factor (g) in the overall debate. Finally, an alternative interpretation of the relationship of IQ to attainment is outlined.

The background of the study

The authors of The Bell Curve use the construct of intelligence to explain a major part of variability observed in school attainment. Herrnstein and Murray contend that the intelligence quotient is the critical attribute that explains why some children do well in school and others do not. The authors argue against the populist notion that environmental deprivation, family background or social class are primary causes of success and failure in schools. They oppose the more liberal interventionist view that society can do much to overcome the deleterious effects of low IQ, poverty and social disadvantage. Their thesis favours the politically conservative view that there is little that the state or individual teachers can do to offset the dominating influence of intelligence and inherited genetic advantage in the explanation of the wide range of attainment test scores reported on a typical cohort of students.

Not surprisingly, this contentious thesis has caused much controversy in the United States, particularly in political circles (Jacoby & Glauberman, 1995). The Bell Curve was on the New York best-seller list for many weeks. Scholars and critics have been either enthusiastic in their defence of the book, or vehement in their opposition (Jacoby & Glauberman, 1995). Most have been somewhat critical of the constituent arguments relating to the supposed importance of IQ in the explanation of social and academic efficiency (Kamin, 1995). Others have claimed the book has rekindled potentially harmful debate about the likely causes of different levels of mean IQ reported on many racial and ethnic groups (Dorfman, 1995). However, not all the critics have been opposed to Herrnstein and Murray's views. A significant proportion of commentators has been supportive of many of the conclusions stated in the book, particularly those critical of the so-called liberal views of the educational establishment. One renowned psychologist has given considerable support to the analytical methods and policy guidelines used by the authors (Bouchard, 1995).

Herrnstein is well known in the fields of psychology and social and political affairs. He was a professor of psychology at Harvard before his death in the early eighties. He made his reputation as an experimental psychologist in the area of decision making. His principal work was done in comparative psychology, mainly concerning himself with the behaviour of birds and rodents. He was also an expert in experimental methodology. Several commentators have stressed the fact that he had no credentials in the field of the genetic basis of behaviour and no reputable scientific papers on intelligence and its relationship to human affairs (Dorfman, 1995). However, he published papers of commentary on important social issues, such as the relationship between IQ and crime and related matters. Charles Murray is a political scientist. He holds a PhD in political science from the Massachusetts Institute of Technology. He has a post at the Bradley Enterprise Institute, an American research body devoted to the support of conservative views about social affairs. Murray has no expertise in genetics, social science or psychology. Both authors have been longtime supporters of the Jensen (1973) thesis that blacks are consistently inferior to whites on IQ measures and have adopted views in support of the possibility of genetic factors in this relationship.

Herrnstein and Murray's limited background in the academic field of intelligence testing and educational research did not preclude them from making extended comment about the structure of intelligence, the relationship of IQ to attainment and the likely origins of the low level of scholastic attainment of students in some schools. Both of the authors were also active in conservative political circles. This background must be taken into account in judging the validity of their arguments. It is important to be cognisant of their political agenda and its relationship to the kinds of analyses they used to promote their cause.

Major tenets in the Herrnstein and Murray thesis

The authors of The Bell Curve support the use of IQ measures in school settings to explain much of the variability in school attainment. Herrnstein and Murray argue that intelligence is a highly salient predictor of a wide range of variables used to measure efficiency on school-related tasks. This generalisation is said to apply even when other supposedly important factors like social class and home background are controlled. Herrnstein and Murray maintain that intelligence (they define it as a generic term for "smartness") is the pervasive characteristic that distinguishes students in schools and society and that this cognitive characteristic is essentially non-modifiable, or alterable only to a limited extent, by educational intervention. Herrnstein and Murray allege that IQ is the dominant factor that separates the social classes. The g factor inherent in such tests is said to have a strong genetic basis. It supposedly differentiates the civilised from the non-civilised and it is claimed to be a major factor in determining the differences among ethnic groups.

The authors claim that over recent years schools have become more discriminating of talent and they claim that it is now more probable that only the best and brightest students enter the elite universities. They claim that extremely intelligent students in such universities achieve at exceptionally high levels in the traditional subject disciplines compared with students in less prestigious universities. According to Herrnstein and Murray, students in the top universities will be the dominant leaders in the next generation of scientists, artists and scholars. In like fashion they argue that low ability students have meagre abilities for abstract problem-solving and that compensatory education is an unlikely remedy for their difficulties.

The nature of intelligence as measured in the NLSY survey and its relationship to attainment

Herrnstein and Murray chose to use results from one particular survey on adolescence and early adulthood as the basis for much of their analysis. The data on intelligence were derived from tests given as part of the National Longitudinal Survey of Youth (NLSY). The students tested were aged from 14 years to 23 years. The IQ test used was the AFQT (Armed Forces Qualification Test) and was claimed to be a measure of general mental ability. The AFQT is derived from a larger aptitude test, the ASVAB, the Armed Services Vocational Aptitude Battery. The AFQT is a set of pencil and paper tests given to groups of American adolescents, some in school and others in the work force. This intelligence test is not age-normed and the authors have controlled for this by ensuring that all analyses included in the study were corrected for age differences. The age factor was partialled out of all analyses and then the data were examined for relationships among other cognate variables. The AFQT provides scores on particular ability domains believed to be integral to the essence of what the authors define as intelligence.

Examination of the content of the AFQT reveals a multi-dimensional test. The authors of the report indicate that the "scoring version" of the test used in their particular survey relied on four subtests. These subtests were Word knowledge, Paragraph Comprehension, Arithmetic Reasoning and Mathematical Knowledge. Each of these tests depends to a large degree on the capacity to read the content of the individual items and follow the prescriptions indicated in the test instructions. Word knowledge tests require respondents to choose synonyms for given words from lists of possible answers. Paragraph comprehension requires the capacity to read passages of text and answer questions related to the content of the material presented to the individual. Arithmetic reasoning "has only word problems" (Herrnstein & Murray, p.582), whereas mathematical knowledge "applies the basic methods of algebra and geometry" (Herrnstein & Murray, p. 582). The four tests are concerned with different kinds of subject content. The first two tests are highly verbal in content and require the ability to read; the second two are tests of mathematics ability and require competence in the ability to read mathematics problems and apply relevant mathematical algorithms. Herrnstein and Murray offer no experimental studies to support their thesis on the relationship between IQ and attainment. Subjects of different ability levels were not randomly assigned to conditions and given the same subject curricula to learn. There were no controls on preliminary subject area knowledge in the several subject domains and no controls over student motivation. Instead, a logistic regression analysis methodology was used exclusively to determine that which can only be properly answered by experimental studies. A regression analysis of this kind is post hoc and offers nothing more than a set of possible interpretations of patterns of relationships among selected variables deemed important in the particular problem area.

Such IQ tests have poor validity if used to explain deficiencies in the school attainment of individual students. The major problem relates to the commonality of the items contained in the AFQT and the content of the attainment measures. Almost all of the content of the AFQT is similar to that contained in routine assignment work completed daily by most students in schools. The vocabulary knowledge and reading comprehension tests are of a kind typically used in English classes. One of the mathematics tests contained in the AFQT is a straightforward measure of problem solving in mathematics; the second test of mathematicss is a measure of algebra and geometry, subjects usually taught in high school. It is very likely that high ability students received more of this kind of content instruction than their low ability peers. Students streamed into high ability classes are typically given far more algebra and geometry than those of low ability.

In essence, Herrnstein and Murray use one kind of test, called an IQ test, to predict various measures school attainment, assessed by a composite of achievement test performance, school completion and related indices. However, examination of the content of both kinds of variable reveals that they contain much the same kinds of measures of efficiency. In particular, tests of IQ and measures of school achievement measure fundamental skills (e.g ,the ability to read) general knowledge (knowledge of the culture) and capacity to reason with the materials contained in the tests. There are no essential constituent differences between these two types of test worthy of serious consideration. Gould (1981) has reported similar kinds of problems in the very early work by Yerkes on the Army Alpha and Beta tests.

One further problem needs to be highlighted at this point. Underlying cognitive processes is a key issue. The AFQT is supposed to give a cognitively-based explanation for the performance on the achievement tests. However, performance on both the IQ test and achievement tests done in the final year of high school reflects much the same kinds of underlying knowledge and associated cognitive processes. It is absurd to suggest that different cognitive processes explain the performance of the same students who completed these two classes of tests, since as already noted, the content of the tests is very nearly the same. The only point that could be sustained by cogent argument is that more problem-solving items are usually included in IQ tests, but even this is not readily apparent from the description of the content of both categories of test.

Carroll's (1993) study is a worthy comparison in this context. He published a definitive study on the factor structure of a very comprehensive set of cognitive ability tests, much like those used in the NLSY survey. He derived a verbal or printed language comprehension (V) factor from tests that require the ability to read. Included in the tests used to measure this factor are "test types measuring general language development including various types of vocabulary tests and reading comprehension tests" (Carroll, p.157). He further extracted lexical knowledge (VL) as a vocabulary factor and concluded there was evidence that "vocabulary knowledge can be regarded as a separable component of language development" (p. 159). He also derived a reading comprehension (RC) factor separate from the other two factors already described. In the mathematics domain, factor solutions were found to be more complex. Carroll (1993) concluded that there is probably not a single entity called mathematical ability, rather that proficiency in this domain depends on the characteristics of the mathematics tasks. Mathematics demands a variety of abilities, some of which require high-order factors (e.g., general and crystallised intelligence), others low-order factors (e.g., one of which Carroll defines as numerical facility, N). Carroll makes the claim that to discuss factor abilities in mathematics it is necessary to relate the findings to the grade level being taught and the educational experiences of the individual student.

The factor analysis studies of Carroll (1993) give little support to the Herrnstein and Murray analysis. It is obvious that there is much in common in the measures of intelligence and the tests of achievement used as a basis for their analysis. Tests of word knowledge, paragraph comprehension, arithmetic reasoning and mathematical knowledge can be found in ability tests and achievement tests. Many would claim that criteria that differentiate ability and achievement tests can be determined (Carroll, 1993), but clearly the two different categories of tests used in The Bell Curve do not match such criteria.

In summary, the difficulties with the Herrnstein and Murray thesis are threefold. First, they fail to show experimental evidence to support their major proposal. That is, their analysis is based almost entirely on correlational and logistic regression analyses and not on experimental paradigms. Second, they fail to show that the model they propose has explanatory power. The model they use has limited utility and does not give account of many alternative background and motivational variables that have been shown to have causal relationships with school achievement. Last, and most importantly, near-identical states are included in the logic of their explanatory model (Smith, 1951). In other words, all that Herrnstein and Murray have done is demonstrate that students good at selected tests of mathematics and verbal problem solving found in IQ tests are good at other tests of mathematics and verbal problem solving that lead to higher or lower completion rates for selected educational credentials. They state the obvious in claiming that students who perform well on mathematics and problem solving will be good at completing course requirements for high school and university. The partialling out of selected background variables does nothing to correct the errors revealed in their empirical logic. Herrnstein and Murray's explanations do little to explicate the relationship between IQ, cognitive processes and school attainment.

The g factor

There is one feature of the Herrnstein and Murray argument that has yet to be analysed. The reference here is to the general factor (g) and its importance to their thesis. Their position in regard to this general ability concept will now be given closer examination.

The AFQT tests chosen by Herrnstein and Murray to measure intelligence were claimed to load heavily on the so-called g factor. They place strong emphasis on the relationship of these tests to the general ability factor. This general ability factor was said to account for 64% of the total variation in the ASVAB. They claim that the correlation between the selected four subtests selected for the AFQT and g are the highest in the correlation matrix reported for the various IQ and achievement tests. Herrnstein and Murray argue that since the four selected sub-tests of the AFQT are highly inter-correlated and since they all load substantially on the g factor, then the validity of the intelligence construct in this context is clearly evident. Similar arguments have been put by Humphreys (1979) in his justification of the g factor as the primary constituent of intelligence.

Other research in this contentious area demonstrates the validity of other perspectives (Fancher, 1985). Cooley and Lohnes (1976) suggested a somewhat different interpretation on data of this kind. Cooley and Lohnes also placed great store on the value of the general ability construct. They demonstrated in a number of analyses that various dimensions of school achievement and standard group-based IQ correlate highly. They showed that many achievement tests and intelligence tests assess a common entity and that this factor can be identified with the general factor. Further, their analysis revealed that there is considerable redundancy in the general factor derived from IQ tests and the general factor derived from achievement tests. Cooley and Lohnes claimed that the commonality is not such a conceptual problem as first appears. They stated that the fundamental aim of education is to increase the intellectual capacities of students and that this is normally achieved through acquisition of a wide knowledge base founded on the subject disciplines. They asserted that it is, therefore, not surprising that achievement tests and IQ tests can be shown to measure of the same substantive entity. It follows that the general factor for intelligence cannot be clearly distinguished from the general factor in the achievement domain.

Keeves (1972), in his well known study of Canberra school children, made a similar point and arrived at a similar conclusion. He demonstrated that group IQ tests correlate highly with other measures of achievement and that such intelligence tests can best be interpreted as tests of achievement, with a focus on the problem-solving capacity required in the traditional domains of reading, mathematics comprehension and general knowledge. The claim that group-based intelligence tests and achievement tests measure two orthogonal and structurally independent entities is therefore highly questionable. It makes no sense to say that achievement can be largely explained by a general factor of intelligence if these two entities are constituted of the same factor.

One further point needs emphasis. Every test of intelligence is, in part, a measure of an individual's willingness to participate in a formal test situation. It also measures a person's tolerance of the test's prescriptions and problem-solving idioms required for testing cognitive ability. Further, such IQ measures require that individuals show consistent endeavours to complete the relevant tasks. Motivation to do well in tests of this kind explains much of what is recorded as variability in intelligence and achievement. Individuals motivated to achievement goals over long periods are generally far better able to cope with problem-solving demands in that area than individuals with little motivation or commitment.

An alternative to Herrnstein and Murray's analysis of the relationship between predictor variables and achievement

If Herrnstein and Murray are so astray in their analysis, what kind of analysis would lead to a more viable explanation of these phenomena? What class of variables can we use to predict school achievement? How does IQ rank with other variables in the explanation of variability of student attainment? At least four kinds of variables deserve serious consideration in response to these questions. The first of these includes what has been called the IQ and cognitive processing variables. It has been already noted that when such variables are considered they must be essentially different in content and type from that used to measure school achievement. Many cognitive achievement measures are appropriate for this purpose, for example, memory for verbal and abstract material, apprehension of figural and verbal relationships, and language development measures. Carroll (1993) has given clear directions in regard to the kinds of cognitive tests that are unconfounded by achievement and knowledge background factors.

The second in this category includes prerequisite skills variables in the particular achievement domain. These refer to the knowledge and skills deemed to be necessary for higher level attainment in the particular subject area. Such knowledge and skills are often linked with the early stages in the sequence of learning objectives in the particular curricular area in question. The structure of knowledge in the subject area largely determines the sequence in which the elements of content are taught.

Prerequisite skills in a defined area of competence are usually highly effective predictors of achievement in the particular domain. Bloom (1976) demonstrated that if prerequisite achievement skills and IQ are entered into a path analysis aimed at predicting achievement, the best fit with the data is the link between prerequisite skills and achievement in the particular subject domain, after IQ has been partialled out of the pattern of possible relationships. However, if the prerequisite skills are partialled from the relationship between IQ and achievement, the partial correlation between IQ and achievement drops to near non-significant levels. Bloom suggests that prerequisite knowledge (which he calls a specific CEB in the context of his theory) is the critical predictive variable and that intelligence is a poor substitute for prerequisite knowledge in any such analysis.

Despite such evidence, the prerequisite skill-achievement relationship does not always fit with popular notions of an acceptable explanation. There is a natural reluctance to believe that what has been learned in the past in a particular domain is the key to an explanation of how well tasks in the same domain will be done in the future. Achinstein (1993) has made this point clear in his analysis. However, this need not be an intractable obstacle to sound explanation of relevant achievement measures. Consider the case of a knowledge prerequisite that is known to be a likely condition for competence on a higher-order task, such as a student's comprehension of a particular phenomenon. In such a case it would be acceptable to hypothesise that an adequate knowledge base is causally related to comprehension of the higher-order task. The prerequisite knowledge and the comprehension of such a phenomenon could be shown to contain elements that are non-identical in essential characteristics (Smith, 1951).

The third embraces the social background and environmental variables that are often correlated with achievement test scores. These have been extensively examined by many researchers (Cooley & Lohnes, 1976; Keeves, 1972; Husen & Tuijnman, 1991). Social background, teacher expertise, school climate, social class and other social background factors have been shown to predict school achievement. Herrnstein and Murray have ignored the substantive research in these areas. Instead they have focused on cognition, after partialling out some of the background variables. They give little attention to many of the variables that could confound their analysis.

The conclusions stated in The Bell Curve are based on a one-sided interpretation of data. In many cases IQ is affected by schooling and not the reverse. Husen and Tuijnman (1991) showed that schooling has a long-term effect on the level of intelligence. Using an approach not dissimilar to that adopted by Herrnstein and Murray, they showed that education increases a student's capacity to deal with the problem solving tasks typically found in intelligence tests. Research completed in developing countries (for a summary see Ceci, 1991) also suggests that many school and background variables have an extremely important role to play in the prediction of both IQ and achievement in such cultures. Keeves (1972) also examined background variables to determine the effects of such variables on achievement. Keeves' research indicated that prerequisite skills and knowledge of lower-grade subject matter are critical if prediction of higher-order competencies is the key objective. Bowles and Gintis (1976) showed that environmental and social structure variables are highly predictive of school results, income and employment, and that IQ is a relatively unimportant predictor when factors in the larger social structure are given due attention.

The fourth group includes motivation and other affect variables. Motivation to succeed in a task is a critical variable that always needs to be considered in this context. Much of the work on affect variables (including self-efficacy, self-esteem, perceptions of competence, willingness to set high goals for achievement) are important in this context. Particularly important here are the level and type of goal-directed behaviour. Students who set high standards for themselves on cognitive tasks and are motivated to achieve such goals invariably do better than students who set low goals and who are not motivated to succeed. There is not much doubt that such variables not only contribute to the prediction of levels of achievement states, but also explain a good deal of the variance in school achievement. The four groups of variables outlined here sometimes overlap with one another, both in inherent content and in causal linkages. In terms of inherent content, the difficulty is that it is often difficult to get a pure measure of these variables, since the measurement of any one of these variables leads indirectly the measure of another. For example, in measuring verbal fluency the researcher is also measuring a subject's willingness to participate in the test situation. Further, willingness to strive for high levels of achievement overlaps with task completion rates for tests of this kind. The overlap among such variables is often idiosyncratic: in some school systems one causal path will explain a relationship; in another school system other paths will lead to alternative explanations.

Such statistical interactions among these categories of variables is relatively common. The factors relate to one another in different ways depending on the particular level of other variables being considered in the context. At one time interval, there may be a significant correlation between IQ and achievement. At another time interval the effect may be transitory or attenuated to such a degree that it is not worthy of consideration in any statistical or probabilistic sense. Reports of the prevalence of such effects abound in the literature.

Herrnstein and Murray's analysis allows no such complications. Their model is driven by an uncomplicated political agenda that is biased toward predetermined solutions. They give little credence to the many studies completed in recent years that contradict their central thesis. The scope of their analysis is limited by its narrow theoretical base. The Bell Curve contains a host of conflicting and circular arguments and deserves the negative criticism it has received from the scientific community.


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Author: Peter Cole is professor of education (Psychological Foundations) at Edith Cowan University. His research field is special education. He has written chapters on intelligence and motivation and learning in the recent edition of Mathby, Gage and Berliner's Educational Psychology. He has recently finished a paper on the developmental theory of intellectual disabilities and another on regression effects in the interpretation of giftedness.

Please cite as: Cole, P. G. (1995). The bell curve: Should intelligence be used as the pivotal explanatory concept of student achievement? Issues In Educational Research, 5(1), 11-22.

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