Classification of Learning Disabilities: An Evidence-Based Evaluation
Jack M. Fletcher, University of Texas; G. Reid Lyon, National Institutes of Health; Marcia Barnes, University of Toronto; Karla K. Stuebing, University of Texas; David J. Francis, University of Houston; Richard K. Olson, University of Colorado; Sally E. Shaywitz, Bennett A. Shaywitz, Yale University
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HETEROGENEITY HYPOTHESIS
In federal and non-federal definitions, LD is rarely conceptualized as a single disability, but instead is represented as a general category composed of disabilities in any one or a combination of several academic domains. In the 1968 federal definition, seven domains are specified: (1) listening; (2) speaking; (3) basic reading (decoding and word recognition); (4) reading comprehension; (5) arithmetic calculation; (6) mathematics reasoning; and (7) written expression. While the inclusion of these seven areas of disability in the federal classification ensures that the category of LD accounts for a wide range of learning difficulties, the practice implies that what may be highly variegated learning problems should be lumped together. Even today, many studies simply define groups of children as "learning disabled" despite considerable evidence that the correlates of LD in reading, math, and other achievement domains vary at multiple levels of analysis. In this section, we will ask how well these seven domains cover the range of LD and raise questions concerning what domains should be included in the federal definition.
Listening and Speaking
Disorders of listening and speaking are essentially oral language disorders. Such disabilities are incorporated in IDEA under the speech and language category, so the need for including them as types of LD category is not clear. As oral language disorders, they represent examples of difficulties with expressive and receptive language. What is the point of duplication, especially since disorders of listening and speaking are not formal areas of academic achievement? Difficulties in listening comprehension typically parallel problems with reading comprehension (Shankweiler et al., 1999; Stothard & Hulme, 1996). Children cannot understand written language any better than they can understand oral language. Any phonological, syntactic, or semantic problems that hinder oral language comprehension will also affect the ability to read written text or even to comprehend when someone reads them the text. While some children with LD have oral language disorders, the duplication is far from perfect (Tomblin & Zwang, 1999). The basis for including disorders of listening and speaking in the federal classification of LD is not clear and leads to conceptual confusion in classifying and defining oral language disorders in IDEA.
Reading Disabilities
The federal definition specifies two areas of reading difficulties, basic reading (word recognition) and reading comprehension. That difficulties with word recognition represent a specific form of LD in reading is well established (Shaywitz, 1996). Children can also be identified with comprehension difficulties that do not involve the word recognition module. Much more is known about the nature and causes of disabilities in word recognition, as less reading research has been devoted to studying how children understand what they read.
What are not addressed in the federal definition are difficulties that involve the automatization of word recognition skills and speed of reading connected text. These problems also occur in children with accurate word recognition skills. Unfortunately, less is known about fluency deficits in reading despite recent development of hypotheses suggesting that deficiencies in reading fluency represent a separate subgroup of RD (Wolf & Bowers, 1999; Wolf, Bowers, & Biddle, 2001). In the next section, we review evidence for subgroups with RD specific to word recognition, comprehension, and fluency.
Word recognition (dyslexia)
Word-level RD is synonymous with dyslexia, a form of LD that has been described during the 20th century as word blindness, visual agnosia for words, and specific reading disability (Doris, 1993). The evolution of the concept of dyslexia, and its link with word-level RD, provide an excellent example of how definitions of LD can move from exclusionary to inclusionary. As an example of an exclusionary definition, consider the 1968 World Federation of Neurology definition that was in part the basis for the epidemiological studies of Rutter and Yule (1975):
A disorder manifested by difficulties in learning to read despite conventional instruction, adequate intelligence, and socio-economic opportunity. It is dependent upon fundamental cognitive disabilities, which are frequently of constitutional origin. (Critchley, 1970, p. 11)
In contrast, consider the following definition of dyslexia formulated by a research committee of the International Dyslexia Society (Lyon, 1995; Shaywitz, 1996), which we have modified to be consistent with advances in research:
Dyslexia is one of several distinct learning disabilities. It is a specific language-based disorder characterized by difficulties in the development of accurate and fluent single word decoding skills, usually associated with insufficient phonological processing and rapid naming abilities. These difficulties in single word decoding are often unexpected in relation to age and other cognitive and academic abilities; they are not the result of generalized developmental disability or sensory impairment. Dyslexia is manifest by variable difficulty with different forms of language, often including, in addition to problems reading, a conspicuous problem with acquiring proficiency in writing and spelling. Reading comprehension problems are common, reflecting word decoding and fluency problems.
This definition identifies dyslexia as a word-level RD proximally caused by phonological processing problems. It is inclusionary because it clearly specifies that a child is dyslexic who has (a) problems decoding single words in isolation, and (b) difficulties with phonological processing. These constructs are easily measured. The difficulty, of course, is specifying the level of impairment that would be of sufficient severity to constitute a disability. The definition is directly linked to intervention and it is now well established that treatments emphasizing the development of word recognition skills improve reading achievement in these children (National Reading Panel, 2000; Swanson, 1999). It reflects the developmental origins of dyslexia, so that prior to the expected onset of word recognition skills, interventions addressing the development of phonological processing skills should prevent word recognition difficulties. There is considerable research support for this expectation (National Reading Panel, 2000; Snow, Burns, & Griffin, 1998). The definition clearly permits the identification of children who are at risk for dyslexia and also permits identification of children who do not respond to preventative interventions and who may need different forms of remediation. No mention is made of discrepancy and IQ tests are not required for identification. It stipulates that dyslexia is differentiated from mental deficiency and sensory disorders, but criteria for these differentiations would be included in the identification of these disorders in an overall classification of low achievement. No distinctions or stipulations concerning cause or etiology are made, including constitutional factors, and exclusions are not identified.
The definition reflects a view of dyslexia that is different from those found in the media, where dyslexia is viewed as a rare, exotic disorder characterized by unusual perceptual characteristics (e.g., seeing words and letters backwards). Dyslexia as defined here is the most common form of LD and has its origins in the language system (Shaywitz, 1996; Vellutino, 1979). Lerner (1989) reported that 80% of all children served in special education programs have problems with reading, while Kavale and Reese (1992) found that 90% of children in Iowa with the LD label had reading difficulties. Most children who have reading problems have difficulty with word-level skills. It may not be the only problem that these children experience, but it is the problem that makes them poor readers. Most children served in special education programs as LD likely have word-level reading problems as part of their disability (Lyon, 1995).
Dyslexia as defined above is a disorder that is not associated with specific qualitative characteristics, but occurs on a continuum of normal development. Thus, dyslexia is the lower portion of this continuum (Shaywitz et al., 1992). A critical issue is where on the continuum sufficient severity of reading difficulty occurs that would lead to a designation of RD. This issue has not been adequately researched, but should be tied in some way to response to interventions of different kinds of intensity, not an arbitrary designation (e.g., 20th percentile) that the examples in Figures 4-6 show to be unreliable.
People with dyslexia often have other academic problems and also seem to have problems that are in the social and behavioral realm. This is not a problem with the definition, but with the classification of LD. The key is to have a classification that signals when a child has a form of LD, and which recognizes that they may have other academic and behavioral difficulties. Many children with this form of RD have problems with spelling, writing, reading comprehension, and math (Lyon, 1996). The spelling, writing, and reading comprehension problems can be explained on the basis of the disruption of phonological processing and word recognition skills. Spelling is closely tied to phonological processes; a person with poor word recognition skills cannot identify or spell words accurately because of poor understanding of the relationship of print and speech: the alphabetic principle. They will have reading comprehension problems because they can not process the text. When math is also impaired, the child typically has other problems involving oral language and working memory (Swanson & Siegel, in press). As we discuss below, reading comprehension and math problems in the absence of word recognition difficulties can also occur, which must be accounted for in our classification--not our definition of dyslexia.
Disorders like attention deficit hyperactivity disorder (ADHD) represent a different classification issue. While ADHD commonly co-occurs with dyslexia (Shaywitz, Fletcher, & Shaywitz, 1997), what is important is that the child with both dyslexia and ADHD looks dyslexic when their reading and language skills are examined and looks ADHD when their behavior is examined (Shaywitz et al., 1995). However, dyslexia is a problem with cognitive development; ADHD is a behavioral disorder with cognitive consequences (Barkley, 1997). Thus, the child has more than one disability, although children with both dyslexia and ADHD have more severe reading (and other cognitive) problems than children who have only dyslexia or ADHD. The treatment implication is that both disorders need to be addressed and that interventions addressing only one disorder may be less effective (Fletcher, Foorman, Shaywitz, & Shaywitz, 1999). ADHD is not a part of our classification of LD, as the primary defining characteristics do not reflect academic achievement.
Altogether, word-level RD is the best researched type of LD and the difference between the 1968 exclusionary definition and the modified 1994 inclusionary definition represent what we believe is a model for other forms of LD. As we see in the next sections, much progress needs to be made in other forms of LD, though we could formulate reasonable inclusionary definitions of most of these forms.
Reading comprehension disability
There is good evidence for disabilities in reading comprehension in cases where reading decoding is age-appropriate but reading comprehension lags. Estimates of the incidence range from 5% to 10% depending on the exclusionary criteria used to define the groups (e.g., Cornoldi, DeBeni, & Pazzaglia, 1996 vs. Stothard & Hulme, 1996). These estimates have not been studied in relation to age, but it is likely that specific reading comprehension problems are more apparent in older children and emerge after the initial stage of learning to read. Some may have a history of word recognition difficulties that have been remediated.
Studies on specific reading comprehension disability commonly have compared children with good word recognition accompanied by good reading comprehension skills with those who have good development of word recognition skills but poor development of reading comprehension (Nation & Snowling, 1998; Oakhill, Yuill, & Parkin, 1986; Stothard & Hulme, 1996). This is in contrast to studies that have investigated reading comprehension problems in groups that contain a large number of poor word decoders (e.g., Perfetti, 1985; Shankweiler et al., 1999), in which the sources of reading comprehension problems are difficult to address separately from the influences of difficulties in word decoding. Proficient reading comprehension presumes fluent decoding, so studies of reading comprehension must separately identify those weak in comprehension, but fluent in decoding.
IQ and the definition of reading comprehension disability. Research in the area of reading comprehension disabilities does not follow the classification guidelines that are embedded in the federal definition of LD. Most studies of children's comprehension difficulties have not attempted to relate general intellectual ability to reading comprehension. Not surprisingly, there are few studies that use IQ-achievement discrepancies to define groups of poor comprehenders. The discrepancy formula that is most often used in studies of reading comprehension disability is that between good basic reading achievement and poorer scores on standardized tests of reading comprehension, without reference to IQ. Such approaches have not been fruitful, though most of the research is on children who also have word-level RD (Fletcher et al., 1998). One study that used an IQ-achievement discrepancy model to classify poor comprehenders found that children with average intelligence and average word reading skills but poor reading comprehension had difficulties in listening comprehension, in working memory, and in metacognitive aspects of comprehension (Cornoldi et al., 1996). A survey of individual cases showed that children with reading comprehension disability were heterogeneous with respect to the specific pattern of cognitive deficits that they displayed in these skills.
In some studies of reading comprehension disability, IQ has actually been used as an outcome measure rather than as an exclusionary criterion for group membership. For example, children with specific reading comprehension disability have been found to have similar phonological skills and nonverbal intelligence as children with no comprehension disability, but lower verbal IQs (e.g., Stothard & Hulme, 1996). Such findings have been interpreted by some as providing evidence that general verbal cognitive deficits underlie the reading comprehension disability of good decoders/poor comprehenders. In a recent study of normally developing readers, however, verbal intelligence was found to account for only modest variation in reading comprehension performance (Oakhill, Cain & Bryant, in press; also see Badian, 1999). After accounting for verbal intellectual skills, significant variance in comprehension was predicted by text integration skills, metacognitive monitoring, and working memory with stability in these relationships over a 1-year period. Interestingly, these are the same skills that Cornoldi et al. (1996) found best characterized their group of poor comprehenders with IQs that were discrepant from reading comprehension achievement.
What does it mean to say that children with comprehension problems have lower verbal IQ? A simple assumption of a unidirectional relationship between intelligence and comprehension, such that higher verbal intelligence somehow paves the way for the development of good reading comprehension, is probably incorrect for two reasons. First, there is some evidence that the relationship between reading comprehension and intelligence may be bidirectional (Francis, Fletcher et al., 1996). Consider, for example, that reading experience may facilitate growth of verbal and even nonverbal intellectual skills (Stanovich, 1993). Second, tests of verbal intelligence measure vocabulary and verbal reasoning, and these are some of the same skills that are measured by tests of reading comprehension. A moderately strong relationship between verbal intelligence and reading comprehension, then, is not unexpected and is relatively uninformative. Furthermore, given that there are important aspects of comprehension that IQ tests do not capture, verbal IQ cannot be used as a proxy for reading comprehension disability.
Core deficits in reading comprehension disability. Most of the research on specific reading comprehension disability has focused on determining the core deficits that underlie the disability. These studies have generally taken three forms. One is to compare children who are good decoders but poor comprehenders to good decoders-good comprehenders, matched for age. More recent studies use reading level match designs in which the cognitive processes of good decoders-poor comprehenders are compared to those of younger children matched for reading comprehension level to the older disabled children. Finally, studies of remediation have asked whether training in skills hypothesized to contribute to the reading comprehension deficit actually improves reading comprehension. The findings from the three methods are largely consistent and are summarized below.
Some studies have shown that children who are good decoders-poor comprehenders may have more basic deficits in vocabulary and understanding of syntax that would impair reading comprehension (Stothard & Hulme, 1992, 1996). Other studies have shown that even when vocabulary and syntax are not deficient, deficits in reading comprehension still arise (Cain, Oakhill, & Bryant, 2000; Nation & Snowling, 1998). The results from these studies are consistent with findings discussed previously (IQ-achievement discrepancy group in Cornoldi et al., 1996, and normally-developing readers in Oakhill, Cain, & Bryant, in press). These deficits involve inferencing and text integration, metacognitive skills related to comprehension, and working memory. In contrast, phonological skills, short-term memory, and verbatim recall of text are typically not deficient (reviewed in Oakhill, 1993; Cain & Oakhill, 1999; Cataldo & Cornoldi, 1998; Nation, Adams, Bowyer-Crane, & Snowling, 1999; Oakhill, 1993; but see Stothard & Hulme, 1992).
More recent studies in this area have begun to question how poor comprehension early in a child's reading history may influence not only later reading comprehension, but also continued development of word decoding skills. Although decoding and comprehension disabilities have been shown to be dissociable, children who are good decoders but poor comprehenders may begin to fall behind in their decoding skills in the later school grades (Oakhill, Cain, & Bryant, in press). To the extent that these individuals are not very good at using reading as a means to an end, they may come to read less, and so truncate their exposure to less common words (Cunningham & Stanovich, 1999). Alternatively, their poor ability to use semantic cues (a component of comprehension) to decode less frequent words may constrain higher levels of lexical development (Nation & Snowling, 1998).
Findings similar to those discussed for children with reading comprehension disability have also been found in studies of children with brain injury. For example, Barnes and Dennis (1992, 1996) have evaluated the discourse and reading comprehension skills of children with spina bifida and hydrocephalus. These children are often characterized by intact word recognition skills, but deficient reading comprehension (and math) abilities. Using a variety of tasks, Barnes and Dennis have demonstrated that children with this form of brain injury have difficulty making inferences and problems assimilating nonliteral information from text, and that these difficulties in the reading domain parallel problems that the children have in oral discourse comprehension and production. Table 1 summarizes the characteristics of reading ability in children with spina bifida and hydrocephalus, children with word recognition difficulties and poor comprehension, and non-brain injured children who have intact word recognition skills but poor reading comprehension.
Table 1. Academic subgroups of LD
- Reading Disability--Word Level
- Reading Disability--Comprehension
- Reading Disability--Fluency (?)
- Math Disability
- Reading Disability and Math Disability
- Written Expression--Spelling, text, handwriting (?)
The comprehension-related deficits outlined in Table 1 have been replicated across studies that have used different criteria for group membership, including brain injury. Questions remain regarding whether metacognitive, inferential, and working memory processes are primary causes or consequences of the comprehension deficit and whether difficulties in these skills reflect deficits in more basic reading comprehension processes (Nation & Snowling, 1998; Nation et al., 1999; Perfetti, Marron, & Folz, 1996). Given that reading comprehension may be a more multidetermined process than reading decoding, it is not unexpected that advances in knowledge in this area have lagged behind word-level RD.
Given that it is a multifaceted process, the assessment of reading comprehension is a major problem. In contrast to tests of word recognition accuracy in which there is a relatively transparent relationship between the content of the tests and performance requirements for word reading, there is more controversy about what reading comprehension tests measure. Standardized reading comprehension tests differ from everyday reading contexts along several potentially important dimensions such as passage length, immediate versus delayed recall, and learning and performance requirements (Sternberg, 1991). Reading comprehension tests, like other tests of complex cognitive functions, may be limited both by a lack of ecological validity and by the absence of a model of the reading comprehension process that would guide test construction. Thus, it is not surprising that there is less consensus on how to define reading comprehension disability and how to best advance understanding of the reading comprehension process in terms of both its normal and disordered development.
Reading fluency
More controversial is the question of whether there is a specific subgroup of reading impairment that is characterized specifically by difficulties in reading fluency. Wolf and Bowers (1999, Wolf et al., 2001) have argued for a "rate deficit" group that does not have problems in the phonological domain, but often has difficulties with comprehension because of a more general difficulty rapidly processing information. The subtyping study of Morris et al. (1998) did find evidence for a rate deficit subtype that was not phonologically impaired, but which showed difficulty on any task that required speeded processing, including rapid automatized naming and tasks as mundane as canceling target letters as fast as possible from an array of letters. This subtype also had difficulties with reading fluency and comprehension, but not word recognition.
Studies of ADHD show that reading fluency problems are common in these children with ADHD and that these difficulties are related to their performance on measures of rapid automatized naming (Tannock, Martinussen, & Frijters, 2000). Some argue that these difficulties reflect common underlying brain-based problems with timing or rapid processing that occur across all forms of reading disability, but more research needs to be completed (Waber, Wolff, Forbes, & Weiler, in press).
Studies of children with brain injury also provide evidence that the accuracy and speed of word recognition can and should be differentiated. Barnes, Dennis, and Wilkinson (1999) matched children with traumatic brain injury on their word decoding accuracy. Comparisons of reading rate and naming speed showed that fluency was worse in children with traumatic brain injury, paralleling observations with non-brain injured children with rate deficits (Waber et al., in press; Wolf et al., 2001). Fluency was related to reading comprehension scores in both populations (Barnes et al., 1999; Morris et al., 1998).
This discussion of rate deficits represents an excellent example of how classifications and definitions must evolve in supporting the provision of services for children with academic deficits. Although there may be insufficient evidence to establish a form of RD that involves only fluency deficits, the possibility is under active investigation. If evidence continues to accumulate for a fluency disorder, the classification must be changed and definitions of reading disability expanded to incorporate these types of problems.
It is also apparent that a single definition will not work for these three putative forms of reading disability. It is already possible to specify the attributes of each disability. These attributes can be measured at the level of the academic skill as well as its associated correlates. As we will discuss below, it may be possible to measure these attributes and form inclusionary definitions that lead to specific procedures for identification and have important implications for intervention.
Math Disabilities
The federal definition of LD specifies disorders of math calculations and reasoning. Disabilities in math have been studied for as long but not as extensively as RD. Nonetheless, there is a burgeoning research base, particularly on children who have computational difficulties. There is clear evidence for a specific subgroup of children with LD in math calculations; whether there is also a subgroup that has impairment in math concepts is unclear and hardly studied. It is even possible that there are other subgroups of MD that have yet to be determined. Consider that the skills that fall under the heading of mathematics are broad and varied and it is unclear whether learning in one domain of mathematics is related to learning in another domain (Geary, 1994). Unlike reading, in which development produces changes in quantity and quality of decoding and comprehension, the development of mathematical competencies involves learning new categories of skills such as geometry and calculus (LeFevre, 2000). These new skills depend to some extent on previously learned math knowledge, but these areas of math also represent significant departures from prior learning.
As in the reading area, studies of adults with brain lesions show that fairly specific math skills can be either preserved or lost depending on the damage to the brain (Dehaene, 1999). Whether the development of math skills across different domains can be similarly fractionated is an open question. In normal development, for example, the acquisition of basic arithmetic skills may facilitate the acquisition of more advanced math skills across a number of math domains (Geary, Fan, & Bow-Thomas, 1992). Because of insufficient knowledge about development of some areas of math, the cognitive skills that lead to competence in those areas, and the potential importance of computation in facilitating these other areas of mathematical development, this section will deal primarily with evidence for LD in basic arithmetic calculation.
Computational abilities and disabilities
There is a rich literature on the acquisition of skills such as counting, basic understanding of quantity, and use of strategies that are important to the development of early computation ability (e.g., Ashcraft, 1992; Bisanz, Morrison, & Dunn 1995; Gelman & Gallistel, 1978; Nunes & Bryant, 1996; Rourke, 1993; Siegler & Shrager, 1984). This work was not motivated by a need to understand disordered development of computational skills, but to understand cognitive development through mathematical cognition and to understand the development of the math system itself. In the past decade, some math researchers have used the theories and methods of mathematical cognition and developmental psychology to study the emergence and development of MD. Until recently, this work largely proceeded without respect to the specificity of the disability, that is, whether RD and MD were comorbid or specific (e.g., Geary, Bow-Thomas, & Yao, 1992; Geary, Brown, & Samaranayake, 1991; Jordan, Levine, & Huttenlocher, 1995).
In contrast, studies of children with LD, including those involving math computations, have indeed been concerned with describing differences between groups of children with either specific RD or MD and both RD and MD (e.g., Ackerman & Dykman, 1995; Fletcher, 1985; Morrison & Siegel, 1991; Rourke, 1993; Swanson & Siegel, in press; White, Moffitt, & Silva, 1992). Children with specific MD appear much less frequently than children who have both RD and MD, and precise estimates are not available (Rourke, 1993). The existence of such children is clearly established in many studies where children are defined as having word recognition difficulties, both word recognition and math computation difficulties, and only math computation difficulties. The latter children do not have problems with language of the sort experienced by children with word-level RD. They typically have difficulty with different forms of nonverbal processing and concept formation (Rourke, 1993). To summarize, these studies have found cognitive deficits in marker skills such as verbal and visual working memory and visual-spatial skill that differentially characterize the different subgroups of children with LD (see Figures 2 and 3). Although these studies reveal the importance of considering the specificity and comorbidity of learning disabilities, they do not permit an analysis of the mechanisms by which the cognitive marker skills influence math learning. Furthermore, such subtyping studies were interested in the issue of LD in math versus reading rather than in understanding the basic math processes that contribute to scores on math achievement tests (Ginsburg, Klein, & Starkey, 1998).
A recent development in the research on MD has been the attempt to combine research strategies from the fields of cognitive development, mathematical cognition, and LD (e.g., Geary, Hoard, & Hamson, 1999; Jordan & Hanich, 2000). These studies: (1) follow children longitudinally from the beginning of their school careers to understand how MD plays out over time in terms of issues such as stability and comorbidity; (2) measure the development of early, informal arithmetic skills such as counting and problem-solving strategies for computing numbers that may be related to the later development of school-based or formal mathematical competence (Ginsburg et al., 1998); (3) relate cognitive marker skills or cognitive competencies that are purported to support the development of math to the acquisition of specific components of the math system such as knowledge of counting principles (Geary et al., 1999); and (4) analyze components of the developing math system and their supporting cognitive competencies with respect to whether the MD is specific or comorbid with RD. In some ways this new research strategy parallels earlier longitudinal studies of reading acquisition in typically achieving children and those with reading problems. As these studies proved critical to our understanding of RD at multiple levels, the current studies may similarly begin to reveal the explanatory status of hypothesized core number-related skills and supporting cognitive competencies with respect to the classification and prediction of MD.
What are the core number-related skills and supporting cognitive skills that have been hypothesized to account for difficulties with mathematics calculations? Disability in math computation may arise from problems in learning, representing, and retrieving math facts from semantic memory and/or from difficulties in the acquisition and use of developmentally-mature problem-solving strategies or procedures to perform mental or written calculations (Geary, 1993). Whether difficulties in the spatial representation and manipulation of number information constitute a third source of MD in children with and without frank brain injury (e.g., Geary, 1993) is unclear and not well studied (Barnes et al., in press).
Comorbid reading and math disability
It has been suggested that the core deficit of children with both RD and MD might be difficulty in retrieving math facts from long-term or semantic memory (Geary, 1993). In its more general form (i.e., not just involving math fact retrieval, but also retrieval of lexical information), this memory-based deficit may also be related to some of the features of reading disability (Geary et al., 1999). Longitudinal research and treatment studies suggest that this type of computation deficit may not improve much with age or remediation (Geary et al., 1991; Goldman, Pellegrino, & Mertz, 1988). In terms of supporting cognitive skills, these types of math disabilities are hypothesized to relate to working memory and also to long-term memory access (Geary, 1993; Geary et al., 1999; McLean & Hitch, 1999; Swanson & Siegel, in press).
In studies of older children there is some support for the hypothesis that co-occurring RD and MD may share a common underlying deficit in retrieval from long-term or semantic memory: Children who are slow readers make more errors in retrieving math facts from memory than children who are neither RD nor MD and more than children who have MD, but not RD (Rasanen & Ahonen, 1995). Younger children with both RD and MD difficulties have poor counting knowledge. They treat counting as a rote activity, rather than having a solid understanding of the principles of counting, and these children also have difficulty on working memory tasks and on tests tapping retrieval of verbal semantic information from long-term memory (Geary et al., 1999). Other studies suggest that children who are impaired in both reading and math computations typically show more severe and pervasive disturbances of oral language than children who are only impaired in word recognition. Their difficulties reflect problems learning, retaining, and retrieving math facts, which are essential to precise calculation; these problems lead to pervasive difficulties with math. Thus, Jordan and Hanich (2000) found that children with both reading and mathematics difficulties showed problems in multiple domains of mathematical thinking. Working memory is generally more severely impaired in children with both RD and MD than in either alone (Swanson & Siegel, in press).
Specific math disability
The error-prone use of developmentally immature procedures and strategies in simple arithmetic, and perhaps in written arithmetic, may underlie the form of MD that is not related to RD (Geary, 1993). Data on the validity of this source of MD is less strong at the present time than data on memory-based deficits in math fact retrieval. At a younger age, these children may also have problems in counting and often make errors in the application of algorithms. Written problems involving carrying and borrowing are difficult, as is the learning of algorithms necessary to complete complex multiplication and division. There are no studies of which we are aware that link developmentally-immature and error-prone counting strategies in solving simple arithmetic problems in early childhood to later use of developmentally-immature procedures in solving more complex multidigit written arithmetic problems.
To return to our example of children with spina bifida and hydrocephalus who have profound difficulties with math, Barnes et al. (in press) showed that good readers with this form of brain injury made more procedural errors than age-matched controls, but similar numbers of math fact retrieval and visual-spatial errors. Furthermore, their procedural errors were similar to those of younger children who were matched in math ability with these older brain-injured children. In other words, the good readers with hydrocephalus made errors in written computation that were developmentally immature for their age, but not different in kind from younger children with no MD. These data are consistent with the hypothesis that children who are good readers but who are poor at math can have a procedural deficit that involves the application of developmentally immature algorithms for solving written computations.
Figure 7. Profiles of cognitive performance by children with only reading disability (RD), only math disability (MD), both RD and MD (RD-MD), attention-deficit hyperactivity disorder (ADHD) with no RD or MD, and no LD (NL). The profiles show differences in shape and level of performance suggesting that the groups are different with distinct patterns associated with RD, MD, and ADHD as well as areas of overlap suggesting comorbidity of RD, MD, and ADHD. The NL group is clearly different from all three groups with LD in shape and elevation.
Comparison of specific MD, RD, and RD-MD
Children with word-level RD, computational MD and no RD, and both RD and MD can be differentiated. Figure 7 compares these groups with a contrast group of children who only have problems with behavior, meeting diagnostic criteria for ADHD but with no evidence of LD. The contrast with ADHD is important as some of the hypothesized cognitive correlates of specific MD are also apparent in studies of children with ADHD (Barkley, 1997), though such studies rarely address the issue of comorbidity. A group with no LD (NL) is also included.
These groups are compared on variables that have been related to ADHD (attention, paired associate learning), both ADHD and MD (problem solving, concept formation), and RD (phonological awareness, rapid naming, and vocabulary). Figure 7 demonstrates the pervasive problems experienced by children who have specific or comorbid RD on measures of phonological awareness. In addition, whereas children with MD had the most significant difficulties with concept formation, children with RD and MD, ADHD without LD, and only MD share in common difficulties on a problem solving measure. Finally, it is clear that children with both RD and MD are the most pervasively impaired, whereas children with no LD and only ADHD show much stronger performance in areas that involve language, working memory, and visual-motor integration. The group with only ADHD has problems with sustained attention (continuous performance test) and procedural learning, the latter representing strength in the group with only RD.
If Table 7 broke the three LD groups out by IQ-discrepancy/low achieving or by presence/absence of ADHD, the effect would be only on the level of the profiles, not the patterns. As the RD-MD example demonstrates, whenever a child has a disability in more than one area, their overall performance is lower. While IQ may also be lower, it is knowing that the child is disabled in more than one domain (including ADHD) that is critical. Thus, assessment of the academic (and behavioral) domains, and cognitive correlates, are the keys to understanding the disability--not level of IQ.
The differences in results across studies of LD and ADHD may well reflect variations in whether these domains are assessed. For example, children with only ADHD have small cognitive impairments relative to any child with LD. A study that combined children with only ADHD and both ADHD and RD-MD would show more significant cognitive impairments that may be attributed to ADHD if the comorbidity is not addressed. It is not surprising that studies of children defined as LD without specification of the academic domains that are impaired have not contributed much to research or practice.
What is particularly intriguing about the differences in the three LD subgroups (RD, MD, and RD-MD) comes from the possibility that the neural correlates are different. Functional imaging studies of children with RD and RD-MD reliably demonstrate aberrant activations involving the left temporoparietal areas (see Constitutional Factors below). Although there are presently no functional neuroimaging studies of children with math difficulties, studies of how math is represented in normal adults show that there are different neural correlates of precise calculation versus estimation (Dehaene, Spelke, Pinel, Stanescu, & Tsiukin, 1999). Precise estimation involves the inferior prefrontal cortex in the left hemisphere, as well as the left angular gyrus. These areas overlap substantially with those that mediate language functions. In contrast, estimation tasks showed bilateral activation in the inferior parietal lobes, which represent areas that overlap with spatial cognition. As many children with specific MD have been found to also have spatial cognition difficulties, this overlap in neural representation of estimation and spatial cognition may help explain why the spatial processing difficulties do not seem to bear a strong relationship to math abilities in these children, but are often as profound as the math difficulties themselves. Any cognitive task sensitive to how these areas of the brain function will be deficient in children with specific RD, but this does not mean that the cognitive deficits themselves are tightly linked.
Altogether, there is burgeoning evidence for the existence of a group defined by difficulty in learning and retrieving math facts from memory (RD-MD), and some evidence for the existence of a group that has difficulty learning math calculations because of procedural difficulties (MD only). There is little evidence for a separate subgroup with impairment in math concepts, but this possibility has not really been studied. In a sense, all children with disabilities in math probably have difficulty at some level with math concepts broadly conceived. The meaningfulness of this putative category of LD--math concepts disability-- is not clear.
Written Expression
There is also research on disorders that involve written expression (Berninger & Graham, 1998; Graham & Harris, 2000). This is clearly an area of difficulty for many children. In some students, writing difficulties reflect an inability to spell, most closely associated with difficulties in word recognition skills (Rourke, 1993). Even some children with specific MD can have difficulty with handwriting, often because they commonly have impairments in their motor development. Their spelling errors, interestingly, are typically phonetically constrained, in contrast to children who have word recognition difficulties (Rourke, 1993). Once these two difficulties (spelling and motor skills) are taken into account, is there a subgroup of children whose difficulties are restricted to written expression? Here the classification research that is necessary to evaluate this hypothesis has not been completed, but there is some evidence for this possibility. In particular, some children have specific problems with handwriting and respond to prevention interventions (Graham, Harris, & Fink, 2000). Future research should target this possible subgroup in an effort to flush out the heterogeneity hypothesis.
Conclusions: Heterogeneity
There is support for the heterogeneity classification hypothesis. It is clear that there are at least two types of RD (word recognition, comprehension) and probably a third (reading fluency). In addition, there is evidence for a form of specific MD involving calculations. Children with both RD and MD have problems associated with either domain alone, reflecting more pervasive disruptions of language and working memory (Rourke, 1993; Swanson & Siegel, in press). This type of LD should be differentiated from specific RD and specific MD. Research is weakest for disorders of written expression.
Children with disorders in listening and speaking can be differentiated from children who have problems with reading and math. Although there is overlap, only about 50% of those who develop specific language disorders also develop reading and math disorders (Tomblin & Zhang, 1999). When a child with a speech and language disorder develops a reading or math problem, it is for the same reasons that a child with a reading and math problem and no disorder of oral language develops these difficulties. To illustrate in the area of word recognition skills, it is because the child does not develop adequate phonological awareness skills, has problems with rapid naming, and has deficient vocabulary and oral language comprehension skills. There is little evidence for meaningful dissociations of listening and reading comprehension when word recognition skills are adequate. Research in reading comprehension disabilities has largely proceeded from the assumption that the comprehension disability occurs in both reading and listening (with many researchers using oral language tasks to measure components of comprehension), and the data have amply demonstrated that when reading decoding and reading fluency are intact, the comprehension deficit is similar in written and oral language (e.g., Stothard & Hulme, 1992). Thus, many children who have specific problems with reading comprehension have parallel difficulties in listening, i.e., understanding oral language.
Why disorders of listening and speaking are included in the LD category is unclear, as there is a separate category for speech and language disorders and disorders of listening and speaking are not specific academic skills disorders. Dropping them from the LD category would increase the conceptual clarity of the LD category.
Table 2 provides a hypothetical classification of types of LD. Although the evidence for each of these types varies and there is undoubtedly overlap, there is support for each of these six types. Each of the academic domains representing the disorders can be measured and something is known about the cognitive correlates of each domain, except possibly for written expression. As such, a single definition for all these forms of LD seems less useful than a set of inclusionary definitions that specific the domain and its associated cognitive correlates. Such an approach would be more directly related to intervention and would facilitate communication.
Table 2. Comprehension in poor comprehenders with and without known brain pathology (Barnes & Dennis, 1996)
