Kenneth A. Kavale, University of Iowa
Learning Disabilities Summit: Building a Foundation for the Future White Papers
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On April 6, 1963, Samuel A. Kirk told a parent advocacy group that "Recently, I have used the term 'learning disability' to describe a group of children who have disorders in development, in language, speech, reading, and associated communication skills needed for social interaction" (Kirk, 1975, p. 9). By 1968, "specific learning disability" (LD) became a federally designated category of special education (U.S. Office of Education, 1968). The formal definition offered at the time has not changed substantively and was reaffirmed in the 1997 reauthorization of the Individuals With Disabilities Education Act [IDEA] (Public Law 105-17) as follows:
The term "specific learning disability" means a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, which may manifest itself in imperfect ability to listen, think, speak, read, write, spell or do mathematical calculation. The term includes such conditions as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. Such term does not include a learning problem that is primarily the result of visual, hearing or motor disabilities, of mental retardation, of emotional disturbance, or of environmental, cultural, or economic disadvantage (IDEA Amendments of 1997, PL105-17, 11 Stat. 37 [20 USC 1401(26)]).
The federal definition does not stipulate procedural guidelines for LD identification. In fact, the definition is primarily exclusive, describing what LD is not rather than identifying what LD is. Consequently, operational definitions necessary for practice have usually considered factors that may not have been articulated in the formal definition. One such factor that originated in the Kirk (1962) LD definition was the notion of intra-individual differences, the possibility of subaverage functioning in only a few areas with average or above functioning in other areas. Gallagher (1966) termed these "developmental imbalances" that were represented by discrepancies in psychoeducational functioning. One of the first such discrepancies investigated was related to the cognitive abilities of students with LD. Using subtest scores from cognitive assessments like the Wechsler Intelligence Scale for Children (WISC), patterns of strengths and weaknesses were examined to determine whether the resulting scatter ("profile") differentiated students with LD from other average or low achieving populations.
The clinical use of scatter-analysis methods has precipitated debate about its relationship to the nature of LD (e.g., Miller, 1980; Wallbrown, Blaha, & Vance, 1980; Wallbrown, Vance, & Blaha, 1979). For example, hypotheses about uniqueness assume that the profile for samples of students with LD is characteristic of the entire LD population or that the LD subtest profile varies significantly from the average population. The empirical evidence, however, has not supported any assumptions about LD profile uniqueness (e.g., Dudley-Marling, Kaufman, & Tarver, 1981; Gutkin, 1979; Kaufman, 1981).
In a comprehensive quantitative synthesis, Kavale and Forness (1984) found no WISC profile for students with LD. For example, a discrepancy between Verbal IQ and Performance IQ (VIQ-PIQ) has been assumed to be a primary LD characteristic. The difference (PIQ > VIQ) was, on average, only 3 IQ points, which was well below the requisite 11 IQ points necessary for significance. In addition, although students with LD generally performed more poorly on Verbal subtests, no Verbal or Performance subtest score fell below the average level. Any measure of WISC inter-subtest variability ("scatter") was not significant and indicated no subtest strength or weakness that distinguished LD performance.
On the basis of hypotheses about cognitive performance, a number of different subtest score groupings have been proposed to reveal discrepant abilities. One method involves recategorizing subtest scores exemplified in the proposal by Bannatyne (1968) that included a Spatial, Conceptual and Sequential category, each based on three WISC subtests. An LD sample was presumed to show a Spatial > Conceptual > Sequential pattern, but, although exhibiting the required pattern, the magnitude of the score differences was well below required significance values. A second primary method was to seek a profile that either specifies particular subtest scores as high or low or identifies subtests where students with LD might score low. For example, Ackerman, Peters, and Dykman (1971) studied the ACID profile (low scores on the Arithmetic, Coding, Information, and Digit Span subtests) but, again, LD performance did not reach the required level of significant suppression. Similarly, WISC factor scores (e.g., Naglieri, 1981) and WISC patterns (e.g., Myklebust, Bannochie, & Killen, 1971) have also been investigated, but in no instance was discrepant LD performance at a level that could be termed significant.
The longstanding criticism (e.g., Bijou, 1942) of examining discrepancies in cognitive performance to identify LD appears justified. In summarizing the available research, Kavale and Forness (1984) concluded that "Regardless of the manner in which WISC subtests were grouped and regrouped, no recategorization, profile, pattern, or factor cluster emerged as a 'clinically' significant indicator of LD. In fact, when compared to average levels, the LD group was found to exhibit no significant deviations, and on average, revealed less variability than normal populations" (p. 150).
The failure to find significant cognitive (IQ) discrepancies in LD populations and the desire to reinforce notions about the academic achievement deficits associated with LD directed attention to the possibility of conceptualizing IQ-achievement discrepancies as a feature of LD. The IQ-achievement discrepancy notion was introduced by Bateman (1965) in a definition of LD that included the description of "an educationally significant discrepancy between estimated intellectual potential and actual level of performance related to basic disorders in the learning processes" (p. 220).
The idea of IQ-achievement discrepancy was introduced by Franzen (1920) in the "Accomplishment Quotient" (AQ). The AQ is the ratio of Educational Quotient (EQ) to Intelligence Quotient (IQ). The importance of IQ "lies in its diagnosis of power of adaptation, and it has a high correlation with maximum possible school progress" (p. 434) while the EQ "is the quotient resulting from the division of the age level reached on the test in question by the chronological age of the pupil" (p. 435). "[T]he ratio of EQ to IQ [the AQ] gives the percentage of what that child could do, that he has actually done" (p. 436).
In cases where the AQ is less than 90, there is potential "underachievement." A number of analyses appeared to show that, in general, AQs were typically less than unity (1.00) (e.g., McPhail, 1922; Pintner & Marshall, 1921; Ruch, 1923). The resulting discrepancy demonstrated by the "laggards" was often attributed to "laziness (i.e., lack of effort) and if pupils are pushed to the extreme limit of their ability, the correlation between their educational achievement and their intelligence is not only high but actually reaches unity" (Whipple, 1922, p. 600). In general, there was a belief that "bright" students were achieving less than expected, relative to ability, than were "dull" students whose lagging performance was presumed to indicate limited effort. Interestingly, with the 1920s view of intelligence as a fixed entity, IQ was regarded as an index of the upper limit for academic attainment which meant AQs really could not exceed unity. As suggested by Franzen (1920), "One's differences when EQ is subtracted from IQ are always positive when they are large enough to be significant and small enough to seem spurious when they are negative....It is safe, therefore, for practical use to assume that the optimum accomplishment is 1.00" (p. 436).
In reality, findings surrounding the AQ were unreliable because of a number of psychometric and statistical problems. In a comprehensive analysis, Toops and Symonds (1922) discussed a number of flaws with the AQ that were a presage of many later analyses of ability-achievement discrepancy. Many other critiques appeared; for example, J. C. Chapman (1923) pointed out the unreliability of using difference scores based on intelligence and achievement test scores. W. R. Wilson (1928) suggested that "Conclusions based on the use of the accomplishment quotient are misleading unless they take into account the reliability of the measures employed, the validity of the measures employed, and the part played by factors determining the intelligence quotient in school achievement under conditions of maximum maturation" (p. 10).
The major statistical criticism of AQ surrounded the operation of the "regression effect" (Crane, 1959; Cureton, 1937). The calculation of AQ assumed an almost perfect correlation between IQ and EQ, whereas the value is closer to 0.60. With less than perfect correlation between measures, scores well above average on one measure will be less superior on the second measure, and at the other end of the continuum, those scores well below average on the first measure will be less inferior on the second. Consequently, if AQ does not account for the effects of statistical regression, then there will be an overrepresentation of "bright" students and an underrepresentation of "dull" students. This result was demonstrated by Popenoe (1927) who found that "Instead of each pupil having an equal chance to get a favorable accomplishment quotient, it appears that out of almost five hundred pupils, in no case did an individual having a high intelligence quotient get a favorable accomplishment quotient, and that individuals having a low intelligence quotient obtained accomplishment quotients far above the average. So an AQ of 100 means an entirely different thing in a part of the range from what it does in another" (p. 45). The many difficulties with AQ led to the conclusion that "the administrative use of the accomplishment quotient is open to serious criticism" (p. 47) and foreshadowed many later issues about the use of ability-achievement discrepancy for LD classification.
The Bateman (1965) notion of discrepancy was not formally incorporated into the federal LD definition. In fact, there was no modification of the LD definition in the 1975 Education for All Handicapped Children Act (Public Law 94-142), indicating that an inherent vagueness and imprecision remained, as well as difficulties in using the definition in actual practice (Kavale & Forness, 2000). In an attempt to remedy the situation, the then Bureau of Education for the Handicapped issued regulations outlining procedures for LD identification. The U.S. Office of Education (USOE; 1976) regulations read as follows:
A specific learning disability may be found if a child has a severe discrepancy between achievement and intellectual ability in one or more of several areas: oral expression, written expression, listening comprehension or reading comprehension, basic reading skills, mathematics calculation, mathematics reasoning, or spelling. A "severe discrepancy" is defined to exist when achievement in one or more of the areas falls at or below 50% of the child's expected achievement level, when age and previous educational experiences are taken into consideration (p. 52405).
To assist the process, a formula to determine the presence of a severe discrepancy level (SDL) was proposed, but comments and testimonies about its usefulness were decidedly negative. For example, Lloyd, Sabatino, Miller, and Miller (1977) objected to the use of general intelligence measures and the negative effects of measurement error on accuracy, while Sulzbacher and Kenowitz (1977) objected to the standard 50% discrepancy across academic areas. In an empirical analysis of the SDL, Algozzine, Forgnone, Mercer, and Trifiletti (1979) cast doubt on the 50% discrepancy level "except for children whose measured intelligence falls exactly at 100" (p. 30). Danielson and Bauer (1978) reviewed the issues surrounding formula-based classification procedures and concluded by questioning whether "a technically adequate solution to the problem of LD identification exists" (p. 175).
By 1977, the SDL formula was dropped but not the concept of discrepancy as stipulated in regulations indicating the following:
A team may determine that a child has a specific learning disability if: (1) The child does not achieve commensurate with his or her age and ability in one or more of the areas listed in paragraph (2) of this section, when provided with learning experiences appropriate for the child's age and ability levels; and (2) The team finds that a child has a severe discrepancy between achievement and intellectual ability in one or more of the following areas: (i) oral expression, (ii) listening comprehension, (iii) written expression, (iv) basic reading skill, (v) reading comprehension, (vi) mathematics calculation, or (vii) mathematics reasoning. (USOE, 1977, p. 65083)
Thus, discrepancy was reinforced as the primary criterion for LD identification (see Chalfant & King, 1976) and, although not given precise specification in a particular formula, became over time almost the exclusive variable used for LD eligibility determination (Frankenberger & Fronzaglio, 1991; Mercer, Jordan, Allsopp, & Mercer, 1996).
QUANTIFYING DISCREPANCY: METHODS
With the idea that a severe discrepancy must be demonstrated, individual states were free to choose their own methodology, but wide variation in procedures introduced a substantial element of arbitrariness to LD identification (Divoky, 1974; Shepard, 1983). Nevertheless, an in numeris veritas [in numbers there is truth] mentally developed, and different means of quantifying the presence of a severe discrepancy were attempted even though "there is little reason to believe and much empirical reason to disbelieve the contention that some arbitrarily weighted function of two variables will properly define a construct" (Cronbach & Furby, 1970, p. 79). A significant question arose: Can two variables (ability and achievement) be combined to determine the presence or absence of a construct (LD)? The theoretical problems were exacerbated by practical difficulties surrounding the notion of prediction. As pointed out by Thorndike (1963), prediction is almost always imperfect because of (1) errors of measurement, (2) heterogeneity of the criterion (i.e., achievement), (3) limited scope of the predictors, and (4) impact of varied experiences upon the individual.
The simplest but least sophisticated discrepancy method examines grade level deviations where an expected grade level (EGL) score is compared to an actual grade level (AGL) score and the discrepancy is calculated from the EGL-AGL difference. For example, expected grade level might be based on chronological age (CA), and then discrepancy calculated in terms of "years behind" (CA - 5). The 5 represents the 6 years of informal activity before school entry, with one year subtracted because the real AGL is 1.0, not 0. When the difference is "significant" (usually 1 to 2 years below grade level), a discrepancy exists. The most fundamental problem is the lack of consideration for the level and degree of instruction received. In place of CA, mental age (MA) was substituted because of the presumed closer relationship between intellectual ability and school achievement (Harris, 1961). The search for increased accuracy led to formulas with additional factors and differential weighing of variables (Harris, 1971; Monroe, 1932). Although no formula proved entirely satisfactory, the grade level deviation method was at one time a relatively common procedure for LD identification in research studies (e.g., J. S. Chapman & Boersma, 1979; Gottesman, 1979; Selz & Reitan, 1979).
Funding for NRCLD is provided by the U.S. Department of Education, Office of Special
Education Programs. Award No. H324U010004. Opinions expressed herein are those of the National
Research Center on Learning Disabilities and do not necessarily represent the position of the U.S.
Department of Education.
© 2007 National Research Center on Learning Disabilities
Last Updated: November 19, 2007
Contact: nrcld@ku.edu