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Expectations for Students with Cognitive Disabilities: Is the Cup Half Empty or Half Full? Can the Cup Flow Over?

IQ and Disability: The Misunderstood Common Denominator

Despite their diversity of characteristics, the majority (58%) of students receiving special education services under IDEA share a common experience—most have been classified as having a learning disability or cognitive impairment (mental retardation) with the aid of an intelligence test. Despite many disputes over competing theoretical conceptualizations of intelligence and the utility of intelligence test scores, even the most ardent critics recognize that IQ tests "predict certain forms of achievement—especially school achievement—rather effectively" (Neisser, 1995, p. 96).

Despite a defensible rationale for their early development and continued deployment in the schools (Beirne-Smith, Ittenbach, & Patton, 1998), many people have developed inaccurate perceptions of the power of IQ test scores. Many laypersons, educators, policymakers, and other professionals have developed the inaccurate belief, often reinforced by court decisions (Reschly, 1988), that measured intelligence is a genetically determined, largely fixed, global, and enduring trait that explains most of a student's success (or failure) in school learning. Such a Sir Cyril Burt conceptualization of intelligence can doom a student to low expectations if his or her IQ score is significantly below the norm. This fixed entity view of intelligence, summarized in the belief in the predictive power of the single global IQ score, represents the mental jug or cup being "half-empty" or "filled to the brim" philosophy. According to this view, to expect more academic achievement than a person's estimated or measured IQ score is simply not possible.

A recent Education Week (2004) national survey (Count me in: Special Education in an Era of Standards) of 800 special and general education teachers suggests that most educators implicitly subscribe to the Burt IQ-potential philosophy. Eighty-four percent of surveyed teachers did not believe that students in special education should be expected to meet the same set of academic standards as students without disabilities. In addition, approximately 80% of the teachers felt that students with disabilities should not be included in the same state tests as students in general education, especially if the results are used for accountability purposes (Olson, 2004).

The surprising extent to which educators appear to hold alternative (and typically lower) standards and expectations for students with disabilities, although appropriate for many of these students, is troubling given the empirical reality of the predictive power of IQ test scores—scores that are often at the root of lowered expectations. Sir Cyril Burt's IQ-fixed potential legacy appears to be alive and well in America's schools (albeit not typically adopted maliciously or explicitly articulated).

Fortunately, decades of research on intelligence tests have repeatedly converged on a near unanimous consensus on the predictive accuracy of IQ test scores (Neisser, 1995). This consensus, which is explained next, indicates that it is time to "leave the Burt IQ-potential philosophy behind. "

Reality of the IQ-Achievement Relationship: Statistics Made Simple

In an era of standards-driven educational reform, educators and policymakers must recognize the truth about IQ test scores and the resulting disability categories that are based on a continuum of IQ test scores (e.g., mental retardation). The reality is simple. Given the best available theoretically and psychometrically sound, nationally standardized, individually administered intelligence test batteries, three statements hold true. Each of these can be explained in depth, and some of this explanation is provided in Table 1. For greater conciseness here, the statements that hold true are:

  • IQ test scores, under optimal test conditions, account for 40% to 50% of current expected achievement.
    • Thus, 50% to 60% of student achievement is related to variables "beyond intelligence."
  • For any given IQ test score, half of the students will obtain achievement scores at or below their IQ score. Conversely, and frequently not recognized, is that for any given IQ test score, half of the students will obtain achievement scores at or above their IQ score.

This last truism of intelligence test scores can be demonstrated via statistical equations or with real data. The second option is used here because it provides a more concrete explanation. The statistical explanation is provided in Table 1.

Table 1. Explanations of Statements about the IQ-Achievement Relationship

IQ test scores, under optimal test conditions, account for 40 % to 50 % of current expected achievement.

The typical range of reported concurrent IQ-achievement correlations is .40 to .70 (Reschly & Grimes, 1992), with the best batteries consistently displaying correlations from .60 to .70. Correlations of this magnitude are statistically significant and are among the strongest predictive relations reported across all fields of psychology. However, most laypersons, educators, policymakers, and other professionals, fail to recognize that the pragmatic "reality" of correlations is hidden from view. The critical "rubber-meets-the-road" IQ-achievement information lies in the amount of explained achievement variance, a value not directly apparent from a reported correlation. Rather, one simply needs to square a correlation (e.g., .70 2 = .49), multiply it by 100 (.49 x 100 = 49), and then tack a percentage symbol on the end (49 %). This value represents the amount of explained variance represented by a correlation. For example, an IQ-achievement correlation of .70 would indicate that "the amount of achievement variance accounted for by intelligence is approximately 49 %." A correlation of .60 accounts for approximately 40 % of achievement (.60 2 x 100 = 36 %).

50 % to 60 % of student achievement is related to variables "beyond intelligence."

It is beyond the scope of the current paper to review the extensive research on models of school learning that indicate that student intelligence and prior achievement are only two of a number of unique student characteristics (e.g., motivation, self-efficacy, social skills, self-regulatory learning strategies, etc.) that interact in a complex multivariate manner with quantity of instruction, quality of instruction, classroom climate, home environment, peer group, and exposure to mass media outside of school to produce academic learning (Neisser, 1995; Reynolds & Walberg, 1992; Walberg, Fraser & Welch, 1986). See McGrew, Johnson, Cosio and Evans, (2004) for a recent synthesis of essential non-cognitive academic facilitators (often collectively referred to as "conative" abilities) that explain additional portions of academic achievement above and beyond IQ.

For any given IQ test score, half of the students will obtain achievement scores at or below their IQ score. Conversely, and frequently not recognized, is that for any given IQ test score, half of the students will obtain achievement scores at or above their IQ score.

For statistically inclined readers, this truism of prediction is reflected in the Standard Error of the Estimate (SEest). Given IQ and achievement tests on a scale with an M = 100 and SD = 15, and an IQ-Ach correlation of r, SEest = 15 x SQRT (1-r 2). If r = .70 and SDach = 15, then SEest = 10.7. In real world terms, this means, that for any IQ score for this particular IQ test, the expected/predicted achievement (after accounting for regression to the mean effects) would be bracketed by + 10.7 points. That is, for any particular IQ score, 68 % of the population would be expected to show a range of 21.4 achievement standard score points (half above and half below the predicted achievement score). Stated differently, for any given IQ score, the predicted/expected achievement score would be bracketed with a "confidence of prediction band" of + 10.7 standard score points.

Figure 1 presents a scatter plot of the general IQ and Total Achievement (average across reading, math, and written language) scores for "real" norm subjects from the standardization of the Woodcock-Johnson Battery Third Edition (WJ III; Woodcock, McGrew & Mather, 2001). As can be seen in Figure 1, there is a strong linear relation between IQ and achievement, as evidenced by a strong correlation of .75. For illustrative purposes, subjects with IQs ranging between 70 and 80 are designated in Figure 1.

Figure 1. The Relationship Between General Intelligence and Total Achievement in a Nationally Representative Sample

This figure is a graph representing the relationship between general intelligence and total achievement in a national representative sample.  The x axis indicates general intellectual ability for individuals with IQs from seventy to eighty, as measured on the Woodcock-Johnson Battery Third Edition.  The scores on this axis range from forty to one hundred sixty in increments of ten.  The y axis indicates total achievement as measured on the Woodcock-Johnson Battery Third Edition.  Scores on this axis also range from forty to one hundred sixty in increments of ten.  The line on the graph runs from a starting point of approximately fifty on the x axis and forty five on the y axis to one hundred fifty on both axes, indicating a correlation of point seven five.  Points are scattered around the line, representing the amount of error.

The data presented in Figure 1 are based on unpublished analyses of the WJ III standardization by the first author of the current paper (McGrew, et al., 2004).

Figure 2, which is a rotated and "windowed" view of a select portion of the same data as are in Figure 1 (i.e., subjects with IQs from 70-80), clearly shows that even IQ tests that demonstrate some of the strongest correlations with achievement (r = .75) cannot be used to provide perfect estimates of predicted achievement for individual students. The range of total achievement scores displayed at the top of the Figure 2 illustrates that for subjects with IQs from 70-80, expected achievement scores range from a low of approximately 40 to a high of approximately 110. More importantly, the distribution of subjects (the data points) shows that half of the individuals with IQs between 70-80 achieve at or below IQ-predicted achievement, and the other half of these individuals score at or above IQ-predicted achievement.

Figure 2. Distribution of WJ III Total Achivement Scores for WJ III Norm Subjects with IQs 70-80   [D]

Figure 2 image of scatter plot graphic

The data presented in Figure 2 are based on unpublished analyses of the WJ III standardization by the first author of the current paper (McGrew, et al., 2004).

The data presented in Figures 1 and 2 suggest that the proper metaphor for the IQ-achievement prediction relationship is that the "cup can flow over." The carte blanch assumption that all students with disabilities should have an alternative set of educational standards and an assessment system is inconsistent with empirical data. Known IQ-achievement prediction research reinforces the position of Martha Thurlow, the director of the National Center on Educational Outcomes, who stated that "we have a range of students who have disabilities, so I would adamantly reject, as a blanket statement, that students with disabilities can't meet the same achievement targets—I would say that's not the case for the broad majority of students with disabilities" (Olson, 2004, p. 10).

The only time when IQ test scores could be used to make perfect predictions about expected achievement for individual students would be when the IQ-achievement test correlation approaches a perfect 1.0. No intelligence test will ever reach this level of prediction, with the reported range of correlations of .40 to .70+ most likely representing a ceiling on IQ-based prediction. This range of correlations refers to concurrent correlations, where IQ and achievement tests are typically administered during the same period in time. The correlations between IQ test scores and future achievement (e.g., one year later) are typically lower than concurrent correlations, which makes the prediction of AYP (annual yearly progress) based on IQ test score (or disability status as a crude intelligence proxy variable) even less precise.

The current reality is that despite being one of the flagship developments in all of psychology (Embretson, 1996; Neisser, 1995), intelligence tests are fallible predictors of academic achievement. IQ test scores (and associated IQ-based disability category labels) are adequate, but not nearly sufficient metrics, by which to make reasonably precise predictions about any particular individual student's future expected achievement progress. It simply cannot be done beyond a reasonable doubt.

The fallibility of IQ tests, coupled with the enduring presence of the ghost of Sir Cyril Burt's deterministic IQ-achievement educational philosophy, in the context of today's high-stakes educational accountability environment, raises the specter of many children with disabilities being denied the right to appropriate and demanding expectations. Stereotyping students with disabilities (often on the basis of disability label or test scores) as a group that should be excluded from general education standards and assessments is not supported by the best evidence from current science in the field of psychological and educational measurement. The potential soft bigotry of setting a priori IQ or disability label-based low academic expectations (for students with disabilities) needs to be recognized, understood, and minimized, if all children are not to be left behind.

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