Learning Disabilities

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CHAPTER 12 Learning Disabilities

Students with learning disabilities constitute the majority of school-age individuals with disabilities; the number of students with learning disabilities increased from 1.2 million in 1979 to 1980 to 2.9 million in 2003 to 2004.¹ Learning disabilities are the most common childhood disabilities and often have lifelong consequences for health and occupational success.² The prevalence of learning disabilities varies, depending on how learning disabilities are defined and, in the United States, may range from about 4% to 20%.³ In the past, much of the emphasis in medical and psychological pediatric practice has been placed on diagnosis and assessment; indeed, the most controversial issue in the field of learning disabilities currently concerns diagnostic and definitional issues, even though prevention and intervention are equally if not more important clinical issues.

This chapter begins with a brief historical overview of learning disabilities, followed by a discussion of current issues in the definitions and diagnosis of learning disability. What is known about the cognitive correlates of the two most common learning disabilities, reading disability and math disability, is presented, along with a selected review of research on the neurobiology of learning disabilities. The next section is devoted to research on prevention and evidence-based intervention/treatment programs for reading disability and math disability. A brief review of long-term outcomes follows. The chapter closes with a discussion of clinical management of learning disabilities with reference to diagnosis and assessment, comorbid conditions, and prevention and interventions. For further reading on these topics, we suggest peer-reviewed papers and chapters on assessment and identification,⁴ prevention and intervention,⁵ the genetics of learning disabilities,⁶ and comorbid conditions associated with learning disabilities.⁷^–⁹

HISTORICAL OVERVIEW

Learning disabilities were defined in U.S. federal law with the Learning Disabilities Act in 1969 to address the needs of these children who were not previously well served by the education system.¹⁰ The Association for Children with Learning Disabilities, formed by parents and educators and led by the psychologist Samuel Kirk, advocated for recognition of learning disabilities and access to special education services. Lyon and associates⁵ proposed that, as with many other advancements in fields of medicine, psychology, education, and public policy, systematic scientific inquiry into learning disabilities followed from the identification of real-world problems experienced by children and from public advocacy on their behalf.

Despite the mobilizing influence on research of the recognition of learning disabilities, the scientific basis of learning disabilities has historical roots in the neurology of acquired language disorders studied in the 1800s. In these studies of aphasia, specific deficits in the comprehension and production of language in the context of otherwise spared cognitive function were noted in adults with acquired brain lesions. These observations proved important with regard to one of the central features of learning disabilities: namely, that learning difficulties could result in selective rather than general cognitive deficits.¹¹

In the late 1800s and early 1900s, cases of what today would be called reading disabilities were reported by neurologists who observed children and adults with no known brain injuries who could not read despite seemingly intact general cognitive abilities.¹² In the 1920s, Samuel Orton, a neurologist, proposed that in children who could not read, development of left hemisphere dominance for language functions was delayed or had failed. He was the first to address the heterogeneity of learning disabilities as disorders that could specifically affect reading, writing, speech, comprehension, or motor skills.¹¹ In collaboration with the linguist, Anne Gillingham, he devised intervention programs for children with reading difficulties, variants of which are still in use¹³ and undergoing evaluation as to their efficacy.⁵ Another important influence in the field of learning disabilities arose from studies in which investigators attempted to understand similarities in behavioral disorders such as hyperactivity in children with brain injuries and in children with no brain injury who had learning difficulties and normal intelligence. It was inferred that this latter group had minimal brain dysfunction.¹¹

Several notions were common to these early conceptualizations of learning disability: namely, that there is a neurobiological basis for the learning difficulty; that there can be selective deficits rather than global retardation; and that processes that help or interfere with learning could be identified and remedied through interventions. The field of learning disabilities continues to be influenced by these conceptualizations, as discussed in the next section.

DIAGNOSTIC AND DEFINITIONAL ISSUES

Many policymakers and school administrators are concerned about the increasing prevalence of learning disabilities, at least in part because special education is much more costly than general education: $12,000 versus $6500 per student.¹⁴ This is at least one reason why establishing acceptable criteria for learning disability identification has been the most controversial issue in the field of learning disability. At the heart of this controversy is the IQ-achievement discrepancy. Although not required by law, a severe discrepancy between achievement and intellectual ability is most frequently used for identification. It is easy to see how the IQ-achievement discrepancy grew out of the early observations that learning disabilities were deficits in specific skills in an otherwise cognitively intact individual. However, the IQ-achievement discrepancy is fraught with measurement and conceptual problems. After a review of current diagnostic guidelines, we describe these technical difficulties.

U.S. federal regulations governing special education refer to learning disabilities as disorders that can occur in one or more of the following: oral expression, listening comprehension, written expression, basic reading skill, reading comprehension, mathematics calculation, and mathematics reasoning. The federal definition of learning disabilities is notable for its emphasis on exclusionary factors in identification, including the idea of a discrepancy between IQ and achievement that is not caused by a sensory or motor handicap; by mental retardation; by emotional disturbance; or by social, cultural, and economic factors.^15,¹⁶ In Canada, education is under provincial, not federal, jurisdiction. However, provincial regulations governing special education are very similar to those in the United States. For example, the Ontario Ministry of Education defines learning disabilities with discrepancy and exclusionary criteria similar to those in the U.S. federal definition.¹⁷

The Diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM-IV),¹⁸ and the International Classification of Diseases, 10th edition,¹⁹ provide criteria for diagnosing specific and general learning disabilities. For example, in the DSM-IV, learning disorders are classified into four categories: Reading Disorder, Mathematics Disorder, Disorder of Written Expression, and Learning Disorder Not Otherwise Specified. In the DSM-IV, Learning Disorders are also defined in an exclusionary manner. For example, a reading disorder refers to a failure to achieve at expected levels for reading accuracy or reading comprehension and would be diagnosed (1) when reading achievement, measured by standardized tests of reading accuracy and/or comprehension, is substantially below what is expected on the basis of the individual’s age, intelligence, and appropriate educational experiences; (2) when this failure interferes with academic achievement or activities of daily living that require reading; or, (3) if a sensory impairment is present, the reading deficit is in excess of what is typically expected for that impairment.²⁰

Classification systems are fundamental in many areas of science and practice, and as such, scientific evaluation of their validity, reliability, and coverage is required in order for them to be useful.²¹ Such scientific evidence was unavailable at the time learning disabilities were categorized, and despite substantial subsequent research on the validity and reliability of learning disability classification, the definition of learning disabilities and their categorization have not changed much in practice. We discuss evidence pertaining to validity and reliability in learning disability classification with regard to (1) the use of the IQ-achievement discrepancy, (2) the heterogeneity of learning disabilities, and (3) exclusionary factors. Comprehensive reviews of this literature were provided by Lyon and associates¹¹ and by Fletcher and colleagues.²¹

IQ-Achievement Discrepancy

The traditional learning disability diagnosis—low achievement in one or more of the learning disability domains that is significantly discrepant from intelligence—is a classification hypothesis that requires validation. Validation studies, in which groups defined by the discrepancy formula are compared with groups defined according to poor academic achievement without reference to IQ, reveal the following: First, few cognitive or affective characteristics such as memory and phonological awareness differentiate poor readers with discrepancies from those without discrepancies.²² Second, the degree of discrepancy from IQ is not meaningfully related to the severity of the learning disability.²³ Third, the degree of discrepancy is predictive neither of rate of growth in reading over time nor the reading levels of children with or without IQ-achievement discrepancy over time.²⁴ Fourth, the degree of discrepancy is not predictive of whether or how well a child will respond to intervention,²⁵ nor does it inform instruction in important ways.²⁶ Fifth, differences in heritability estimates for children with and without the discrepancy, although significant, are typically small even in large samples.²⁷

In addition to problems with validity, other difficulties in the reliability of the discrepancy hypothesis concern measurement error of the intelligence and achievement tests, unreliability of difference or discrepancy scores, and use of arbitrary cutoff points to partition what is a normal distribution of skills, particularly in the absence of validation studies indicating what those clinical cutoff points should be.¹¹ If categorization based on IQ-achievement discrepancy is reliable, then the classification of children as having a learning disability by an IQ-achievement discrepancy should be stable over time. However, there is considerable instability in classification with actual or simulated data.^28,²⁹ In sum, evidence for the validity of the discrepancy hypothesis is weak, which raises questions about its use in assessment and identification of learning disabilities and in decision making with regard to special education services. Despite technical difficulties in traditional methods for learning disability identification, few experts disagree that the construct of learning disability is a legitimate one or that learning disabilities can have heterogeneous forms.

Heterogeneity of Learning Disabilities

Several types of learning disabilities are identified in classification systems, these types of learning disabilities frequently co-occur, and learning disabilities are often accompanied by other childhood disorders such as attention disorders and problems in social and emotional domains.^8,³⁰

How well do the classifications in federal law and the DSM-IV capture what is known about heterogeneity of learning disabilities? There is strong evidence for the existence of at least two types of reading disability—one in word reading and one in reading comprehension—and perhaps a third in reading fluency.²¹ When reading decoding accuracy and fluency are intact, the deficit in reading comprehension parallels that observed in listening comprehension,³¹ which suggests that disabilities in reading comprehension and listening comprehension may be indistinguishable. In a similar way, some evidence substantiates at least two forms of math disability, one in arithmetic calculations and another in word problems,³² but there is little evidence, at present, of a disability in math reasoning.¹¹ Evidence of a specific learning disability in written expression in the absence of other learning disabilities is also weak.²¹ In most cases, comorbidity (e.g., reading disability with math disability or reading disability with attention-deficit/hyperactivity disorder [ADHD]) is associated with greater impairment in academic domains than when disorders occur independently.²¹ In addition, there is some evidence that the nature of math disabilities and their cognitive characteristics differ in some ways, depending on whether there is a comorbid reading disability.³³

In sum, there is empirical support for some, but not all, of the learning disability classifications in federal law and in the DSM-IV. The issue of comorbidity in terms of symptom severity and overlap or differentiation in cognitive correlates is not addressed in current learning disability classification systems.

Exclusionary Criteria

The hypothesis that learning disability reflects “unexpected” low achievement—as opposed to low achievement as a result of emotional disturbance, social or economic disadvantage, cultural factors, or inadequate instruction—was not based on empirical validation of these factors. There is currently no evidence that children who suffer from emotional disorders such as depression or anxiety differ in any important way from children with learning disability without emotional disorders in terms of the causes of the learning disorder or their response to intervention.²¹

Environmental factors influence the developmental precursors important for learning how to read and perform math. Particularly striking are studies showing that children who are socially and economically disadvantaged have vocabularies half the size of those of nondisadvantaged children at school entry ³⁴; enter kindergarten knowing only one letter of the alphabet ³⁵; and begin school with less informal number and quantitative knowledge than do their middle-income peers.³⁶ However, provision of high-quality language and literacy instruction improves academic preparedness in children graduating from Head Start,³⁷ as do mathematical interventions with disadvantaged preschool-aged children.³⁸ Interventions based on phonological and alphabetical instruction also yield positive effects for older disadvantaged children.³⁹ In sum, socially and economically disadvantaged children develop in environments that may provide less than optimal support for the growth of cognitive skills that are important precursors for later academic skill learning, but they respond to high-quality interventions in similar ways as do their nondisadvantaged peers with learning disabilities. In view of these observations, the validity of exclusion on social and economic bases seems unwarranted.

At the time learning disabilities were defined, there was little consensus about what constituted adequate instruction. This knowledge base, at least for reading, is now substantive.^39,⁴⁰ The definition implies that the child’s response to adequate instruction should be assessed before the learning disability label is applied,²¹ and yet the adequacy of instruction is often assumed rather than measured.

One promising model for reconceptualizing learning disability is in terms of a failure to respond to validated intervention.⁴¹^–⁴³ Responsiveness to intervention (RTI) as an approach to identifying learning disability was first proposed in a 1982 National Research Council report.⁴⁴ Three criteria were suggested for judging the validity of a special education classification: (1) whether the quality of the general education program is such that adequate learning might be expected; (2) whether the special education is of sufficient value to improve student outcomes and thereby justify the classification; and (3) whether the assessment process used for identification is accurate and meaningful. When all three criteria are met, a special education classification is deemed valid. RTI links multiple short assessments over time to intervention and has been shown to have stronger validity and reliability than other identification models. Because identification of a learning disability under RTI is based on lack of response to high-quality instruction, intervention is attempted before the learning disability label is applied. This approach is quite different from all other models, in which diagnosis is applied before intervention.⁴⁵ However, for classification, there is still a need to be able to identify a child according to some criterion score, and this criterion score needs to be linked directly to functional outcome.⁴⁵

How Should Learning Disabilities Be Identified?

To summarize, several of the original criteria for identification of a learning disability and classification of learning disabilities have proved to be invalid or unreliable, although these research findings are only just beginning to have an influence on assessment and diagnosis. Furthermore, none of the current classification systems takes relations between learning disabilities or between learning disabilities and other developmental disorders into account. Despite the problems with current diagnostic and classification criteria, the reality is that many jurisdictions use discrepancy formulas and exclusionary criteria to determine who has a learning disability, and this has consequences for who receives special education services. Hybrid models that take into account both low achievement and response to instruction may better identify children who truly have “unexpected” low achievement despite exposure to high-quality instruction.²⁸ As an example, the current means of diagnosing a learning disability is typically based on a single formal assessment point, followed by treatment (the test-and-treat model), whereas the review just presented suggests that a better model would involve the use of high-quality intervention for low academic achievement (identified by teachers and/or parents and assessed by valid and reliable achievement tests), followed by assessment of response to intervention (the treat-and-test model⁴). It is important to note that the 2004 reauthorization of the Individuals with Disabilities Education Act provides the field of learning disabilities with RTI as an option to the IQ-achievement discrepancy for identifying learning disability. The implications of the critique of current assessment and identification systems and of changes to the Individuals with Disabilities Education Act for the practice of the developmental-behavioral pediatrician are addressed in the final section of this chapter.

CORE COGNITIVE CORRELATES AND NEUROBIOLOGICAL FACTORS

Reading Disability

WORD READING: ACCURACY AND FLUENCY

Core Cognitive Characteristics

Most children who receive special education services in the learning disability category are children with reading disabilities, and these disabilities have also received the most research attention in terms of developmental, cognitive, and neurobiological studies and interventions. Two core cognitive skills have been identified as being causally connected both to the ability to acquire word reading skills and to difficulties in learning how to read: phonological awareness and rapid retrieval of names for visual symbols, or rapid naming.

Although reading requires the decoding of print, it is actually the ability to gain awareness of the sound structure of language at the level of the phoneme, which is essential for learning how to read.⁴⁶ Unlike letters, which are discrete visual symbols, phonemes in syllables and words sound undifferentiated in normally paced speech. Phonological awareness is measured by tasks that tap the ability of the child to distinguish and manipulate language at the level of the phoneme, such as the abilities to listen to a word and to match sounds in words on the basis of phonemes, to segment words on the basis of phonemes, to blend sounds to form words, and to isolate phonemes in spoken words.⁴⁷ Longitudinal studies of the reading acquisition process show that phonological awareness at school entry is a potent and unique predictor of word reading ability well into the middle elementary grades.^48,⁴⁹

Phonological measures are also quite accurate for predicting which young children are at risk for reading failure,⁵⁰ and there is a wealth of research supporting the idea that deficits in phonological processing are at the core of word reading disabilities.⁵¹ Researchers who have attempted to identify reading disability subtypes have shown that almost all subtypes identified are characterized by deficits in phonological awareness.⁵² The use of interventions that address phonological awareness and word recognition are most effective for beginning readers considered to be at high risk for reading failure, and the severity of the deficit in phonological awareness is an important predictor of how easy or difficult it is to remediate reading.^53,⁵⁴

Longitudinal studies also show that the ability to rapidly access names for series of visual symbols such as numbers, objects, and, in particular, letters at school entry is predictive of word reading independently of phonological awareness, although these skills become less predictive past the early elementary grades.^48,⁵⁵ There is some evidence that performance on these rapid naming tasks is more strongly related to fluency and reading comprehension than is performance on phonological awareness tasks⁵⁶ (see Vukovic & Siegel⁵⁷ for an alternative view on rapid visual naming as a unique predictor of reading ability).

Subtyping studies show that some children with reading disability have a specific deficit in rapid naming that is not accompanied by deficits in phonological awareness.⁵² Lovett and colleagues^58,⁵⁹ demonstrated that children who have specific disabilities in reading rate have more circumscribed deficits in reading connected text, in spelling, and in some aspects of reading comprehension in comparison with children who have difficulty in phonological skills and word reading accuracy. Children who have deficits in both phonological awareness and rapid naming are reported to be more severely impaired in terms of their reading than are children with a deficit in only phonological awareness or rapid naming.^59,⁶⁰

The research literature on reading is replete with studies that relate reading skill to many other cognitive variables. The weakest of these predictors tends to be sensory and motor skills such as visual-perceptual processes and speech perception.⁵⁰ More contemporary studies of sensory processes and reading⁶¹^–⁶³ have been criticized on several grounds, including the criteria used to classify children as reading disabled, the insensitivity of these measures for identifying children with reading disabilities or subtypes of reading disability, and the failure of this research to explain how sensory deficits are related to learning how to read or to difficulties in learning how to read.^11,¹³ It remains to be seen whether newer proposals that combine theories of visual and auditory sensory processes to argue that reading disability reflects a general deficit in neuronal timing⁶² have validity.¹³

Between 15% and 40% of children identified as having a reading disability also have ADHD,^64,⁶⁵ and 25% to 40% of samples with children identified as having ADHD also have reading disability.^66,⁶⁷ Comorbid reading disability and ADHD leads to greater impairment in both reading-related and attention-related measures.⁶⁸ Results of a large-scale study of comorbid conditions⁹ suggest that children with reading disability alone and those with ADHD alone can be distinguished by different cognitive characteristics, which is consistent with previous findings.³⁰ Reading disability is strongly linked to deficits in phonological awareness, whereas ADHD is not.³⁰ However, children with reading disability only, those with ADHD only, and those with reading disability and ADHD had a common deficit in slow and variable processing speed.⁹ It remains to be seen whether this common cognitive deficit is replicated in other samples, whether it is related to shared genetic effects, and whether it has consequences for intervention.

Neurobiological Factors

Research on reading disability has revealed that (1) there are subtle differences in several brain structures between individuals with reading disability and those without reading disability; (2) the brains of individuals with reading disability show different patterns of brain activation than those of nonaffected individuals during tasks requiring reading; and (3) intensive evidence-based reading intervention “normalizes” these patterns of activation in the brains of children with reading disability or in those at risk for reading disability. Also, genetic studies have revealed that there is a susceptibility to inherit varying levels of word reading ability. These findings are reviewed as follows.

Structural imaging studies of differences in brain structure in individuals with and without reading disability have produced mixed results. Despite difficulties associated with structural magnetic resonance imaging (MRI) studies including the use of different imaging methods, methods of analysis, and so forth, the data generally support the notion that there are subtle differences between children with and without reading disability and these differences are most likely to be found in those left hemisphere regions that support language.^11,⁶⁹

In contrast to anatomical studies with MRI, functional neuroimaging studies have yielded reliable differences in patterns of activation during phonological and reading tasks in the brains of individuals with and without reading disability that indicate impaired processing and disrupted connectivity mostly in regions of the left hemisphere, including the inferior frontal gyrus, the middle and superior temporal gyrus, and the angular gyrus.⁷⁰ In studies of children using magnetic source imaging (MSI), Simos and colleagues⁷¹ demonstrated that children with and without reading disability did not differ in brain activation when listening to words but did differ when they read words. In children with no learning disability, occipital areas were activated, followed by ventral visual association cortices in both cerebral hemispheres and then particular areas in the left temporoparietal region (angular gyrus, Wernicke’s area, and superior temporal gyrus). When children with reading disability read words, the same time course of events was observed, but the temporoparietal areas of the right rather than the left hemisphere were activated. Such results suggest that it is not specific areas of brain that are “damaged” in reading disability but rather that the problem resides in the functional connectivity within the left hemisphere.⁷²

Perhaps the most interesting findings in the functional imaging literature concern the effects of intervention on these patterns of brain activation. Simos and colleagues ⁷³ provided 80 hours of intensive phonologically based reading instruction to children and youth with significant word reading disabilities. MSI before intervention revealed the same pattern discussed previously for reading pronounceable nonwords. After intervention, word reading improved significantly, and there was increased activation in left hemisphere circuits for each child, as well as some reduction in right hemisphere activity (Aylward et al⁷⁴ obtained similar findings with functional MRI and shorter intervention). Similar “normalization” of brain activation patterns have been found for young children considered at high risk for reading disability who responded to an early intervention program.⁷⁵

Reading problems have long been observed to run in families, and the risk for a reading disability in a child with a reading-disabled parent is eight times that in the general population.⁷⁶ Twin, family studies, and linkage studies all suggest that reading skill has a strong heritable component but that environmental influences are also significant.⁷⁷ Of importance is that heritability estimates for reading skill are quite high both in individuals with and in those without reading disability⁷⁸ and for several components of reading, including phonological and orthographic skills.⁷⁹ A review of linkage findings is beyond the scope of this chapter, as is new research on unique and shared genetic effects for reading disability and ADHD, as well as other childhood disorders.^6,^80,⁸¹

READING COMPREHENSION

Core Cognitive Characteristics

The cognitive characteristics of reading comprehension have been studied in both typically developing children and in children with difficulties in reading comprehension. However, less is known about the core processes involved in learning how to comprehend what is read than about learning how to read words.⁴⁰ It is clear that word reading and comprehension are dissociable in both typical and atypical development,^82,⁸³ although learning disabilities in both word reading and comprehension can be present simultaneously. Disabilities in word reading are easily identified before third grade, but disabilities in reading comprehension are more likely to be identified after third grade.⁸⁴ Leach and colleagues⁸⁴ showed that after third grade, of children identified with reading disability, about one third had specific word reading disability, one third had problems with both word reading and listening comprehension, and one third had problems with comprehension but not word reading. Some investigators have estimated rates of specific reading comprehension difficulties at between 5% and 10%.⁸⁵

Studies of children with reading comprehension disabilities, but no word reading disability, suggest that phonological skills are not deficient ⁸⁶ but difficulties with inference making, text integration, metacognitive skills, and verbal working memory are common.⁸⁷ In children with learning disabilities in word reading and comprehension, both phonological skills and these comprehension and memory skills may be deficient.⁸⁸ In some children, more basic language deficits in both vocabulary knowledge and understanding of syntax limit comprehension of both oral and written language.⁸⁹ Some researchers question whether children who read words well but have language comprehension problems actually have specific language impairment rather than reading comprehension disability per se. However, the majority of children with good word reading and poor comprehension do not meet the diagnostic criteria for specific language impairment.⁸⁶ Reading comprehension disabilities were reviewed by Lyon and associates¹¹ and Fletcher and colleagues.⁹⁰

In sum, phonological awareness is causally related to reading acquisition and reading disabilities, and successful reading interventions include phonological instructional components. The evidence for a separate deficit in the rapid verbal retrieval of visual symbols is more controversial, but it may characterize some subtypes of reading disability, particularly one that involves deficits in reading fluency. Evidence for deficits in basic sensory processes specifically related to the acquisition of word reading and to word reading disability is weak. Although reading comprehension difficulties can exist in the absence of word reading disability, they are probably synonymous with difficulties in listening comprehension. There is relatively little information on how comprehension skills develop or fail to develop; such information is needed in order to design valid assessment tools and identify core cognitive characteristics. In accordance with newer models of gene-brain-environment interactions, what is inherited is a susceptibility to competency in reading, which can be moderated by the environment (e.g., instruction), the product of which has a distinct neural signature. The neurobiology of disabilities in reading comprehension has received little study.

Math Disability

Math disabilities are as common as reading disabilities, and about half of all children with reading disability also have math disability.⁹¹ However, knowledge about the typical development of math skills, math disability, math interventions, and neurobiological factors related to math disability have not been as well studied as the same aspects of reading. One possibility for this imbalance is that reading disabilities have traditionally been considered to be of more cost to society in terms of both school achievement and general health and employment.⁹² However, human resource studies show that mathematical ability is as predictive of occupational success, productivity, and wages as is literacy.⁹³

CORE COGNITIVE CHARACTERISTICS

There is more uncertainty about the core cognitive processes related to math disability than about those for reading. This is compounded by the fact that, unlike reading, mathematics is composed of many different domains, including arithmetic, geometry, and algebra, each of which could have different developmental trajectories and cognitive correlates, different neural signatures, and different genetic associations. The most studied domain of mathematics is arithmetic, or computation.

The models and methods applied to the understanding of development of mathematical skills are the same models that are being applied to understand math disability, which reflects the beginning of a theoretical and methodological convergence in the field of math disabilities similar to that experienced earlier in the field of reading disabilities.^33,⁹⁴ The two most prominent theoretical positions about math disability arise from very different ways of explaining the origins of mathematical abilities.

One position ^95,⁹⁶ arises from the view that, in contrast to reading, which is a relatively recent human achievement, an ability to understand magnitude or quantities and compare numbers is an ability that human and even nonhuman animals are born with. Although there is debate over the interpretation of some of the infant research, very young infants are sensitive to differences in the numerical values of small sets.⁹⁷ Five-month-olds also appear sensitive to changes in very small set sizes involving adding and taking away.⁹⁸ Preschoolers can judge whether one set or number is bigger or smaller than another set or number.⁹⁹ Butterworth⁹⁵ suggested that this sensitivity to number is the infant’s “starter kit” for later mathematical development and that deficits in these very basic mathematical abilities that are not influenced by environment or schooling underlie math disability. Proponents of this view do not argue that this is the only source of children’s difficulty in mathematics. For example, mathematical tasks that require language, such as word problem solving, would be influenced by language skills.

The second view is that mathematical skills in different domains are built from other, more basic or general cognitive systems, such as the language system,¹⁰⁰ the visual-spatial system,¹⁰¹ and the central executive or attentional and working memory systems. Geary’s framework^33,¹⁰² is the most comprehensive example of this view. In this framework, the skills that are important for the development of mathematical competence are the same ones proposed to be deficient in the development of math disabilities. According to this view, difficulties in math could arise in the language system, the visual-spatial system, the central executive system that sustains attention and inhibits irrelevant information, or any combination of these general cognitive systems. At present, there is some preliminary evidence for the framework,¹⁰² but there is as yet no coherent body of literature that would allow researchers to fully test the model or that pits this model against another math disability model.

Despite these theoretical differences in the field of math development and math disability, consensus has begun to emerge from studies about the core math skills that are consistently deficient in children with math disability. Regardless of whether there is a comorbid reading disability or an acquired or congenital brain injury in childhood, children with math disability have difficulties in the accuracy and speed with which they can compute answers to single-digit problems.¹⁰³^–¹⁰⁵ This is often referred to as deficit in math fact retrieval. Before formal schooling, children learn to solve simple everyday problems through the use of counting strategies, such as adding two things to four things by counting 1, 2, 3, 4 and 5, 6 either on fingers or verbally. Practice with computing typically leads to a more developmentally sophisticated strategy in which the child counts up from the largest number (4, then 5, 6). Eventually, the child comes to associate the problem with the answer in memory such that he or she knows that 4 plus 2 is 6 (direct retrieval from memory). Accurate and fluent single-digit arithmetic is thought to be important for freeing cognitive resources during the learning and application of more complex procedures such as carrying and borrowing, and fluency in math fact retrieval is strongly related to accurate performance in multiple-digit arithmetic.¹⁰⁴ In view of the evidence of deficits in math fact retrieval in math disabilities, current research on the early identification of math disability is focusing on the developmental precursors of math fact retrieval.¹⁰⁶

As noted earlier, the combination of reading disability and math disability results in more severe symptoms in some areas of mathematics than does math disability alone. Young children with both reading disability and math disability make more counting errors when computing answers to single-digit problems than do children with only math disability,¹⁰⁷ and they also have greater deficits in word problem solving.^108,¹⁰⁹