sld math problem solving

What is a specific mathematics disability?

By Sheldon H. Horowitz, EdD

Q. What is a specific mathematics disability?

A. You may hear the terms specific math disability , specific learning disability in math , or dyscalculia . These terms all refer to a type of disorder that significantly impacts a person’s ability to learn and perform in math.

There is no single profile of this disability. The signs of dyscalculia will vary from person to person. And they will affect people differently at different times in their lives.

Some people with dyscalculia have no trouble memorizing basic math facts. It’s performing calculations and solving problems that cause trouble. Others struggle with calculation and basic math operations like multiplication and division. But they can grasp the big concepts and easily understand how a problem can be solved.

Disabilities in math are often missed in the early years because kids are learning many basic skills through memorization. Young kids with dyslexia can often memorize their ABCs. But they might not understand the complex relationship between letters and sounds. Similarly, kids with dyscalculia may be able to memorize and recite their 1-2-3s. But they may not be building the number sense that is essential to future math learning.

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Strategies and Interventions to Support Students with Mathematics Disabilities

This tool gives practitioners insight into helping students with disabilities learn math. 

This InfoSheet provides an overview of strategies and resources to support students with, or at-risk for, mathematics learning disabilities. The resource explores instructional strategies for teachers and learning strategies for students for mathematical problem-solving, vocabulary development, algebraic concepts, and metacognitive skills. Detailed examples are provided. The resource also includes a list of suggested websites with a summary of the resources found there and how they can be used to teach a variety of mathematical concepts across levels.

This InfoSheet includes many features which would be helpful in linking research to practice. It provides an overview of strategies and resources to support students with, or at-risk for mathematics learning disabilities. This strategy training helps students with math learning disabilities understand concepts and procedures. 

This resource provides many instructional strategies and other teaching resources that could be used in working directly with adult students to help them find their strengths and challenges.  It could also be used to develop a learner’s individual education plan (IEP) or instructional plan.

In addition to the instructional strategies, the resource also describes the learning strategy that learners will utilize in order to use their strengths to overcome learning challenges. This resource includes different examples of learning strategies (e.g. acronyms) that can be taught to learners so that they can be successful in math.

This resource might be particularly helpful for new adult educators as a pre-reading assignment. It also lends itself as a topic for a Study Circle.

This site includes links to information created by other public and private organizations. These links are provided for the user’s convenience. The U.S. Department of Education does not control or guarantee the accuracy, relevance, timeliness, or completeness of this non-ED information. The inclusion of these links is not intended to reflect their importance, nor is it intended to endorse views expressed, or products or services offered, on these non-ED sites.

Please note that privacy policies on non-ED sites may differ from ED’s privacy policy. When you visit lincs.ed.gov, no personal information is collected unless you choose to provide that information to us. We do not give, share, sell, or transfer any personal information to a third party. We recommend that you read the privacy policy of non-ED websites that you visit. We invite you to read our privacy policy.

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Specific Learning Disorder With Impairment in Mathematics

Specific Learning Disorder (SLD) with Impairment in Mathematics

SLD with impairment in mathematics includes possible deficits in:

• Number sense
• Memorization of arithmetic facts
• Accurate or fluent calculation
• Accurate math reasoning

Warning Signs and Symptoms

An SLD with impairment in mathematics, like all specific learning disorders, impacts upon all aspects of an individual’s life. SLDs are present in all ethnic and language groups, and may disrupt a child’s home life, education, behaviour, and social life. At home, children with a SLD with impairment in mathematics face many of the same difficulties they do in school. Trouble calculating impairs simple tasks like going to the store, organizational difficulties when assigned tasks to be performed at particular times difficulties managing home-work or organizing schedules may impact negatively upon home life. At school, they have trouble completing math or science class work and assignments, and may often miss valuable information due to inability to process logical problems and formulae.

An assessment is a necessary step before decisions can be made about accommodation and eligibility for services. The diagnosis of an SLD with impairment in mathematics, as with all SLDs, is conducted by a qualified assessor who is registered in the province to complete assessments. The diagnostic criteria for SLD are described in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition Revised (DSM-V).  If you suspect you or your child may have a SLD please contact the office to speak about assessment options.

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Understanding, Educating, and Supporting Children with Specific Learning Disabilities: 50 Years of Science and Practice

Elena l. grigorenko.

1 University of Houston, Houston, USA

2 Baylor College of Medicine, Houston, USA

Donald Compton

3 Florida State University, Tallahassee, USA

4 Vanderbilt University, Nashville, USA

Richard Wagner

Erik willcutt.

5 University of Colorado Boulder, Boulder, USA

Jack M. Fletcher

Specific learning disabilities (SLD) are highly relevant to the science and practice of psychology, both historically and currently, exemplifying the integration of interdisciplinary approaches to human conditions. They can be manifested as primary conditions—as difficulties in acquiring specific academic skills—or as secondary conditions, comorbid to other developmental disorders such as Attention Deficit Hyperactivity Disorder. In this synthesis of historical and contemporary trends in research and practice, we mark the 50th anniversary of the recognition of SLD as a disability in the US. Specifically, we address the manifestations, occurrence, identification, comorbidity, etiology, and treatment of SLD, emphasizing the integration of information from the interdisciplinary fields of psychology, education, psychiatry, genetics, and cognitive neuroscience. SLD, exemplified here by Specific Word Reading, Reading Comprehension, Mathematics, and Written Expression Disabilities, represent spectrum disorders each occurring in approximately 5–15% of the school-aged population. In addition to risk for academic deficiencies and related functional social, emotional, and behavioral difficulties, those with SLD often have poorer long-term social and vocational outcomes. Given the high rate of occurrence of SLD and their lifelong negative impact on functioning if not treated, it is important to establish and maintain effective prevention, surveillance, and treatment systems involving professionals from various disciplines trained to minimize the risk and maximize the protective factors for SLD.

Fifty years ago, the US federal government, following an advisory committee recommendation ( United States Office of Education, 1968 ), first recognized specific learning disabilities (SLD) as a potentially disabling condition that interferes with adaptation at school and in society. Over these 50 years, a significant research base has emerged on the identification and treatment of SLD, with greater understanding of the cognitive, neurobiological, and environmental causes of these disorders. The original 1968 definition of SLD remains statutory through different reauthorizations of the 1975 special education legislation that provided free and appropriate public education for all children with disabilities, now referred to as the Individuals with Disabilities Education Act (IDEA, 2004). SLD are recognized worldwide as a heterogeneous set of academic skill disorders represented in all major diagnostic nomenclatures, including the Diagnostic and Statistical Manual-5 (DSM-5, American Psychiatric Association, 2013) and the International Statistical Classification of Diseases and Related Health Problems (ICD-11, World Health Organization, 2018).

In the US, the SLD category is the largest for individuals who receive federally legislated support through special education. Children are identified as SLD through IDEA when a child does not meet state-approved age- or grade-level standards in one or more of the following areas: oral expression, listening comprehension, written expression, basic reading skills, reading fluency, reading comprehension, mathematics calculation, and mathematics problem solving. Although children with SLD historically represented about 50% of the children aged 3–21 served under IDEA, percentages have fluctuated across reauthorizations of the special education law, with some decline over the past 10 years ( Figure 1 ).

The Individuals with Disabilities Education Act (IDEA), enacted in 1975 as Public Law 94–142, mandates that children and youth ages 3–21 with disabilities be provided a free and appropriate public school education in the least restricted environment. The percentage of children served by federally mandated special education programs, out of total public school enrollment, increased from 8.3 percent to 13.8 percent between 1976–77 and 2004–05. Much of this overall increase can be attributed to a rise in the percentage of students identified as having SLD from 1976–77 (1.8 percent) to 2004–05 (5.7 percent). The overall percentage of students being served in programs for those with disabilities decreased between 2004–05 (13.8 percent) and 2013–14 (12.9 percent). However, there were different patterns of change in the percentages served with some specific conditions between 2004–05 and 2013–14. The percentage of children identified with SLD declined from 5.7 percent to 4.5 percent of the total public school enrollment during this period. This number is highly variable by state: for example, in 2011 it ranged from 2.3% in Kentucky to 13.8% in Puerto Rico, as there is much variability in the procedures used to identify SLD, and disproportional demographic representation. Figure by Janet Croog.

This review is a consensus statement developed by researchers currently leading the National Institute of Child Health and Human Development (NICHD) supported Consortia of Learning Disabilities Research Centers and Innovation Hubs. This consensus is based on the primary studies we cite, as well as the meta-analytic reviews (*), systematic reviews (**), and first-authored books (***) that provide an overview of the science underlying research and practice in SLD (see references). The hope is that this succinct overview of the current state of knowledge on SLD will help guide an agenda of future research by identifying knowledge gaps, especially as the NICHD embarks on a new strategic plan. The research programs on SLD from which this review is derived represent the integration of diverse, interdisciplinary approaches to behavioral science and human conditions. We start with a brief description of the historical roots of the current view of SLD, then provide definitions as well as prevalence and incidence rates, discuss comorbidity between SLD themselves and SLD and other developmental disorders, comment on methods for SLD identification, present current knowledge on the etiology of SLD, and conclude with evidence-based principles for SLD intervention.

Three Historical Strands of Inquiry that Shaped the Current Field of SLD

Three strands of phenomenological inquiry culminated in the 1968 definition and have continued to shape current terminology and conventions in the field of SLD ( Figure 2 ). The first, a medical strand, originated in 1676, when Johannes Schmidt described an adult who had lost his ability to read (but with preserved ability to write and spell) because of a stroke. Interest in this strand reemerged in the 1870s with the publication of a string of adult cases who had lived through a stroke or traumatic brain injury. Subsequent cases involved children who were unable to learn to read despite success in mathematics and an absence of brain injury, which was termed “word blindness” ( W. P. Morgan, 1896 ). These case studies laid the foundation for targeted investigations into the presentation of specific unexpected difficulties related to reading printed words despite typical intelligence, motivation, and opportunity to learn.

A schematic timeline of the three stands of science and practice in the field of SLD. The colors represent the strands (blue—first, yellow—second, and green—third). Blue: provided phenomenological descriptions and generated hypotheses about the gene-brain bases of SLD (specifically, dyslexia or SRD); it also provided the first evidence that the most effective treatment approaches are skill-based and reflect cognitive models of the conditions. Yellow: differentiated SLD from other comorbid conditions. Green: stressed the importance of focusing on SLD in academic settings and developing both preventive and remediational evidence-based approaches to managing these conditions. Due to space constraints, the names of many highly influential scientists (e.g., Marilyn Adams, Joseph Torgesen, Isabelle Liberman, Keith Stanovich, among others) who shaped the field of SLD have been omitted. Figure by Janet Croog.

The second strand is directly related to the formalization of the American Psychiatric Association’s Diagnostic and Statistical Manual (DSM). Rooted in the work of biologically oriented physicians, the 1952 first edition (DSM-I) referenced a category of chronic brain syndromes of unknown cause that focused largely on behavioral presentations we now recognize as hyperkinesis and Attention Deficit Hyperactivity Disorder (ADHD). The 1968 DSM-II defined “mild brain damage” in children as a chronic brain syndrome manifested by hyperactive and impulsive behavior with reference to a new category, “hyperkinetic reaction of childhood” if the origin is not considered “organic.” As these categories evolved, they expanded to encompass the academic difficulties experienced by many of these children.

After almost 30 years of research into this general category of “minimal brain dysfunction,” representing “... children of near average, average, or above average general intelligence with certain learning or behavioral disabilities ... associated with deviations of function of the central nervous system.” ( Clements, 1966 , pp. 9–10), the field acknowledged the heterogeneity of these children and the failure of general “one size fits all” interventions. As a result, the 1980 DSM-III formally separated academic skill disorders from ADHD. The 1994 DSM-IV differentiated reading, mathematics, and written expression SLD. The DSM-5 reversed that, merging these categories into one overarching category of SLD (nosologically distinct from although comorbid with ADHD), keeping the notion of specificity by stating that SLD can manifest in three major academic domains (reading, mathematics, and writing).

The third strand originated from the development of effective interventions based on cognitive and linguistic models of observed academic difficulties. This strand, endorsed in the 1960s by Samuel Kirk and associates, viewed SLD as an overarching category of spoken and written language difficulties that manifested as disabilities in reading (dyslexia), mathematics (dyscalculia), and writing (dysgraphia). Advances have been made in understanding the psychological and cognitive texture of SLD, developing interventions aimed at overcoming or managing them, and differentiating these disorders from each other, from other developmental disorders, and from other forms of disadvantage. This work became the foundation of the 1968 advisory committee definition of SLD, which linked this definition with that of minimal brain dysfunction via the same “unexpected” exclusionary criteria (i.e., not attributable primarily to intellectual difficulties, sensory disorders, emotional disturbance, or economic/cultural diversity).

Although its exclusionary criteria were well specified, the definition of SLD did not provide clear inclusionary criteria. Thus, the US Department of Education’s 1977 regulatory definition of SLD included a cognitive discrepancy between higher IQ and lower achievement as an inclusionary criterion. This discrepancy was viewed as a marker for unexpected underachievement and penetrated the policy and practice of SLD in the US and abroad. In many settings, the measurement of such a discrepancy is still considered key to identification. Yet, IDEA 2004 and the DSM-5 moved away from this requirement due to a lack of evidence that SLD varies with IQ and numerous philosophical and technical challenges to the notion of discrepancy (Fletcher, Lyon, Fuchs, & Barnes, 2019). IDEA 2004 also permitted an alternative inclusion criterion based on Response-to-Intervention (RTI), in which SLD reflects inadequate response to effective instruction, while the DSM-5 focuses on evidence of persistence of learning difficulties despite treatment efforts.

These three stands of inquiry into SLD use a variety of concepts (e.g., word blindness, strephosymbolia, dyslexia and alexia, dyscalculia and acalculia, dysgraphia and agraphia), which are sometimes differentiated and sometimes used synonymously, generating confusion in the literature. Given the heterogeneity of their manifestation and these diverse historical influences, it has been difficult to agree on the best way to identify SLD, although there is consensus that their core is unexpected underachievement. A source of active research and controversy is whether “unexpectedness” is best identified by applying solely exclusionary criteria (i.e., simple low achievement), inclusionary criteria based on uneven cognitive development (e.g., academic skills lower than IQ or another aptitude measure, such as listening comprehension), or evidence of persisting difficulties (DSM-5) despite effective instruction (IDEA 2004).

Manifestation, Definition, and Etiology

That the academic deficits in SLD relate to other cognitive skills has always been recognized, but the diagnostic and treatment relevance of this connection has remained unclear. A rich literature on cognitive models of SLD ( Elliott & Grigorenko, 2014 ; Fletcher et al., 2019) provides the basis for five central ideas. First, SLD are componential ( Melby-Lervåg, Lyster, & Hulme, 2012 ; Peng & Fuchs, 2016 ): Their academic manifestations arise on a landscape of peaks, valleys, and canyons in various cognitive processes, such that individuals with SLD have weaknesses in specific processes, rather than global intellectual disability ( Morris et al., 1998 ). Second, the cognitive components associated with SLD, just like academic skills and instructional response, are dimensional and normally distributed in the general population ( Ellis, 1984 ), such that understanding typical acquisition should provide insight into SLD and vice versa ( Rayner, Foorman, Perfetti, Pesetsky, & Seidenberg, 2001 ). Third, each academic and cognitive component may have a distinct signature in the brain ( Figure 3 ) and genome ( Figure 4 ). These signatures and etiologies likely overlap because they are correlated, but are not interchangeable, as their unique features substantiate the distinctness of various SLD ( Vandermosten, Hoeft, & Norton, 2016 ). Fourth, the overlap at least partially explains their rates of comorbidity ( Berninger & Abbott, 2010 ; Szucs, 2016 ; Willcutt et al., 2013 ). Fifth, deficiencies in these cognitive and academic processes appear to last throughout the lifespan, especially in the absence of intervention ( Klassen, Tze, & Hannok, 2013 ).

Results of meta-analyses of functional neuroimaging studies that exemplify the distribution of activation patterns in different reading- ( A ) and mathematics- ( B ) related networks, corresponding to componential models of the skills. A (Left panel, light blue): A lexical network in the basal occipito-temporal regions and in the left inferior parietal cortex. A (Middle panel, dark blue): A sublexical network, primarily involving regions of the left temporo-parietal lobe extending from the left anterior fusiform region. A (Right panel): Activation likelihood estimation map of foci from the word>pseudowords (light blue) and pseudowords>words (dark blue) contrasts. The semantic processing cluster is shown in green. B (Left panel): A number-processing network, primarily involving a region of the parietal lobe. B (Middle panel): An arithmetic-processing network, primarily involving regions of the frontal and parietal lobes. B (Right panel): Children (red) and adult (pink) meta-analyses of brain areas associated with numbers and calculations. Figure by Janet Croog.

A schematic representation of the genetic regions and gene-candidates linked to or associated with SRD and reading-related processes (shown in blue), and SMD and mathematics-related processes (shown in red). Dark blue signifies more studied loci and genes. Blue highlighted in red indicate the genes implicated in both SRD and SMD. Figure by Janet Croog.

The DSM-5 and IDEA 2004 reflect agreement that SLD can occur in word reading and spelling (Specific Word Reading Disability; SWRD) and in specific reading comprehension disability (SRCD). SWRD represents difficulties with beginning reading skills due at least in part to phonological processing deficits, while other language indicators (e.g., vocabulary) may be preserved ( Pennington, 2009 ). In contrast, SRCD ( Cutting et al., 2013 ), which is more apparent later in development, is associated with non-phonological language weaknesses ( Scarborough, 2005 ). The magnitude of SRCD is greater than that of vocabulary or language comprehension difficulties, suggesting that other problems, such as weaknesses in executive function or background knowledge, also contribute to SRCD ( Spencer, Wagner, & Petscher, 2018 ).

Math SLDs are differentiated as calculations (SMD) versus problem solving (word problems) SLD, which are associated with distinct cognitive deficits ( L. S. Fuchs et al., 2010 ) and require different forms of intervention ( L. S. Fuchs et al., 2014 ). Calculation is more linked to attention and phonological processing, while problem solving is more linked to language comprehension and reasoning; working memory has been associated with both. Specific written expression disability, SWED ( Berninger, 2004 ; Graham, Collins, & Rigby-Wills, 2017 ) occurs in the mechanical act of writing (i.e., handwriting, keyboarding, spelling), associated with fine motor-perceptual skills, or in composing text (i.e., planning and revising, understanding genre), associated with oral language skills, executive functions, and the automaticity of transcription skills. Although each domain varies in its cognitive correlates, treatment, and neurobiology, there is overlap. By carefully specifying the domain of academic impairment, considerable progress has been made in the treatment and understanding of the factors that lead to SLD.

Identification methods have searched for other markers of unexpected underachievement beyond low achievement, but always include exclusionary factors. Diagnosis solely by exclusion has been criticized due to the heterogeneity of the resultant groups ( Rutter, 1982 ); thus, the introduction of a discrepancy paradigm. One approach relies on the aptitude-achievement discrepancy, commonly operationalized as a discrepancy between measures of IQ and achievement in a specific academic domain. IQ-discrepancy was the central feature of federal regulations for identification from 1977 until 2004, although the approaches used to qualify and quantify the discrepancy varied in the 50 states. Lack of validity evidence ( Stuebing et al., 2015 ; Stuebing et al., 2002 ) resulted in its de-emphasis in IDEA 2004 and elimination from DSM-5.

A second approach focuses on identifying uneven patterns of strengths and weaknesses (PSW) profiles of cognitive functioning to explain observed unevenness in achievement across academic domains ( Flanagan, Alfonso, & Mascolo, 2011 ; Hale et al., 2008 ; Naglieri & Das, 1997 ). According to these methods, a student with SLD demonstrates a weakness in achievement (e.g., word reading), which correlates with an uneven profile of cognitive weaknesses and strengths (e.g., phonological processing deficits with advanced visual-spatial skills). Proponents suggest that understanding these patterns is informative for individualizing interventions that capitalize on student strengths (i.e., maintain and enhance academic motivation) and compensate for weaknesses (i.e., enhance the phonological processing needed for the acquisition and automatization of reading), but little supporting empirical evidence is available ( Miciak, Fletcher, Stuebing, Vaughn, & Tolar, 2014 ; Taylor, Miciak, Fletcher, & Francis, 2017 ). Meta-analytic research suggests an absence of cognitive aptitude by treatment interactions ( Burns et al., 2016 ), and limited improvement in academic skills based on training cognitive deficits such as working memory ( Melby-Lervåg, Redick, & Hulme, 2016 ).

Newer methods of SLD identification are linked to the development of the third historical strand, based on RTI. With RTI, schools screen for early indicators of academic and behavior problems and then progress monitor potentially at-risk children using brief, frequent probes of academic performance. When data indicate inadequate progress in response to adequate classroom instruction (Tier 1), the school delivers supplemental intervention (Tier 2), usually in the form of small-group instruction.

A child who continues to struggle requires more intensive, individualized intervention (Tier 3), which may include special education. An advantage of RTI is that intervention is provided prior to the determination of eligibility for special education placement. RTI juxtaposes the core concept of underachievement with the concept of inadequate response to instruction, that is, intractability to intervention. It prioritizes the presence of functional difficulty and only then considers SLD as a possible source of this difficulty ( Grigorenko, 2009 ). Still, concerns about the RTI approach to identification remain. One concern is that RTI approaches may not identify “high-potential” children who struggle to develop appropriate academic skills ( Reynolds & Shaywitz, 2009 ). Other concerns involve low agreement across different methods for defining inadequate RTI ( D. Fuchs, Compton, Fuchs, Bryant, & Davis, 2008 ; L. S. Fuchs, 2003 ) and challenges schools face in adequately implementing RTI frameworks ( Balu et al., 2015 ; D. Fuchs & Fuchs, 2017 ; Schatschneider, Wagner, Hart, & Tighe, 2016 ).

Prevalence and Incidence

Because the attributes of SLD are dimensional and depend on the thresholds used to subdivide normal distributions ( Hulme & Snowling, 2013 ), estimates of prevalence and incidence vary. SWRD’s prevalence estimates range from 5 to 17% ( Katusic, Colligan, Barbaresi, Schaid, & Jacobsen, 2001 ; Moll, Kunze, Neuhoff, Bruder, & Schulte-Körne, 2014 ). SRCD is less frequent ( Etmanskie, Partanen, & Siegel, 2016 ), but still represents about 42% of all children ever identified with SLD in reading at any grade ( Catts, Compton, Tomblin, & Bridges, 2012 ). Estimates of incidence and prevalence of SMD vary as well: from 4 to 8% ( Moll et al., 2014 ). Cumulative incidence rates by the age of 19 years range from 5.9% to 13.8%. Similar to SWRD, SMD can be differentiated in terms of lower- and higher-order skills and by time of onset. Computation-based SMD manifests earlier; problem-solving SMD later, sometimes in the absence of computation-based SMD ( L. S. Fuchs, D. Fuchs, C. L. Hamlett, et al., 2008 ). SWED is the least studied SLD. Its prevalence estimates range from 6% to 22% ( P. L. Morgan, Farkas, Hillemeier, & Maczuga, 2016 ) and cumulative incidence ranges from 6.9% to 14.7% ( Katusic, Colligan, Weaver, & Barbaresi, 2009 ).

Comorbidity and Co-Occurrence

One reason SLD can be difficult to define and identify is that different SLDs often co-occur in the same child. Comorbidity involving SWRD ranges from 30% ( National Center for Learning Disabilities, 2014 ) to 60% ( Willcutt et al., 2007 ). The most frequently observed co-occurrences are between (1) SWRD and SMD ( Moll et al., 2014 ; Willcutt et al., 2013 ), with 30–50% of children who experience a deficit in one academic domain demonstrating a deficit in the other ( Moll et al., 2014 ); (2) SWRD and early language impairments ( Dickinson, Golinkoff, & Hirsh-Pasek, 2010 ; Hulme & Snowling, 2013 ; Pennington, 2009 ) with 55% of individuals with SWRD exhibiting significant speech and language impairment ( McArthur, Hogben, Edwards, Heath, & Mengler, 2000 ); and (3) SWRD and internalizing and externalizing behavior problems, with 25–50% of children with SWRD meeting criteria for ADHD ( Pennington, 2009 ) and for generalized anxiety disorder and specific test anxiety, depression, and conduct problems ( Cederlof, Maughan, Larsson, D’Onofrio, & Plomin, 2017 ), although comorbid conduct problems are largely restricted to the subset of individuals with both SWRD and ADHD ( Willcutt et al., 2007 ).

The co-occurrence of SMD is less studied, but there are some consistently replicated observations: (1) individuals with SMD exhibit higher rates of ADHD, and math difficulties are observed in individuals with ADHD more frequently than in the general population ( Willcutt et al., 2013 ); (2) math difficulties are associated with elevated anxiety and depression even after reading difficulties are controlled ( Willcutt et al., 2013 ); and (3) SMD are associated with other developmental conditions such as epilepsy ( Fastenau, Shen, Dunn, & Austin, 2008 ) and schizophrenia ( Crow, Done, & Sacker, 1995 ).

SLD is clearly associated with difficulties in adaptation, in school and in larger spheres of life associated with work and overall adjustment. Longitudinal research reports poorer vocational outcomes, lower graduation rates, higher rates of psychiatric difficulties, and more involvement with the justice system for individuals with SWRD ( Willcutt et al., 2007 ). Importantly, there is evidence of increased comorbidity across forms of SLD with age, with accumulated cognitive burden ( Costa, Edwards, & Hooper, 2016 ). Individuals with comorbid SLDs have poorer emotional adjustment and school functioning than those identified with a single impairment ( Martinez & Semrud-Clikeman, 2004 ).

Identification (Diagnosis)

Comorbidity indicates that approaches to assessment should be broad and comprehensive. For SLD, the choice of a classification model directly influences the selection of assessments for diagnostic purposes. Although all three models are used, the literature (Fletcher et al., 2019) demonstrates that a single indicator model, based either on cut-off scores, other formulae, or assessment of instructional response, does not lead to reliable identification regardless of the method employed. SLD can be identified reliably only in the context of multiple indicators. A step in this direction is a hybrid method that includes three sets of criteria, two inclusionary and one exclusionary, recommended by a consensus group of researchers (Bradley, Danielson, & Hallahan, 2002). The two inclusionary criteria are evidence of low achievement (captured by standardized tests of academic achievement) and evidence of inadequate RTI (captured by curriculum-based progress-monitoring measures or other education records). The exclusionary criterion should demonstrate that the documented low achievement is not primarily attributable to “other” (than SLD) putative causes such as (a) other disorders (e.g., intellectual disability, sensory or motor disorders) or (b) contextual factors (e.g., disadvantaged social, religious, economic, linguistic, or family environment). In the future, it is likely that multi-indicator methods will be extended, with improved identification accuracy, by the addition of other indicators, neurobiological, genetic, or behavioral. It is also possible that assessment of specific cognitive processes beyond academic achievement will improve identification, but presently there is little evidence that such testing adds value to identification ( Elliott & Grigorenko, 2014 ; Fletcher et al., 2019). All identification methods for SLD assume that children referred for assessment are in good health or are being treated and that their physical health, including hearing and vision, is monitored. Currently, there are no laboratory tests (i.e., DNA or brain structure/activity) for SLD. There are also no tests that can be administered by an optometrist, audiologist, or physical therapist to diagnose or treat SLD.

Etiological Factors

Neural structure and function.

Since the earliest reports of reading difficulties, it has been assumed that the loss of function (i.e., acquired reading disability) or challenges in the acquisition of function (i.e., congenital reading disability) are associated with the brain. Functional patterns of activation in response to cognitive stimuli show reliable differences in degrees of activation between typically developing children and those identified with SWRD, and reveal different spatial distributions in relation to children identified with SMD and ADHD ( Dehaene, 2009 ; Seidenberg, 2017 ). In SWRD, there are reduced gray matter volumes, reduced integrity of white matter pathways, and atypical sulcal patterns/curvatures in the left-hemispheric frontal, occipito-temporal, and temporo-parietal regions that overlap with areas of reduced brain activation during reading.

These findings together indicate the presence of atypicalities in the structures (i.e., grey matter) that form the neural system for reading and their connecting pathways (i.e., white matter). These structural atypicalities challenge the emergence of the cognitive—phonological, orthographic, and semantic—representations required for the assembly and automatization of the reading system. Although some have interpreted the atypicalities as a product of reading instruction ( Krafnick, Flowers, Luetje, Napoliello, & Eden, 2014 ), there is also evidence that atypicalities can be observed in pre-reading children at risk for SWRD due to family history or speech and language difficulties ( Raschle et al., 2015 ), sometimes as early as a few days after birth with electrophysiological measures ( Molfese, 2000 ). What emerges in a beginning reader, if not properly instructed at developmentally important periods, is a suboptimal brain system that is inefficient in acquiring and practicing reading. This system is complex, representing multiple networks aligned with different reading-related processes ( Figure 3 ). The system engages cooperative and competitive brain mechanisms at the sublexical (phonological) and lexical levels, in which the phonological, orthographic, and semantic representations are utilized to rapidly form representations of a written stimulus. Proficient readers process words on sight with immediate access to meaning ( Dehaene, 2009 ). In addition to malleability in development, there is strong evidence of malleability through instruction in SWRD, such that the neural processes largely normalize if the intervention is successful ( Barquero, Davis, & Cutting, 2014 ).

The functional neural networks for SMD also vary depending on the mathematical operation being performed, just as the neural correlates of SWRD and SRCD do ( Cutting et al., 2013 ). Neuroimaging studies on the a(typical) acquisition of numeracy posit SMD ( Arsalidou, Pawliw-Levac, Sadeghi, & Pascual-Leone, 2017 ) as a brain disorder engaging multiple functional systems that together substantiate numeracy and its componential processes ( Figure 3 ). First, the intraparietal sulcus, the posterior parietal cortex, and regions in the prefrontal cortex are important for representing and processing quantitative information. Second, mnemonic regions anchored in the medial temporal lobe and hippocampus are involved in the retrieval of math facts. Third, additional relevant regions include visual areas implicated in visual form judgement and symbolic processing. Fourth, prefrontal areas are involved in higher-level processes such as error monitoring, and maintaining and manipulating information. As mathematical processes become more automatic, reliance on the parietal network decreases and reliance on the frontal network increases. All these networks, assembled in a complex functional brain system, appear necessary for the acquisition and maintenance of numeracy, and various aberrations in the functional interactions between networks have been described. Thus, SMD can arise as a result of disturbances in one or multiple relevant networks, or interactions among them ( Arsalidou et al., 2017 ; Ashkenazi, Black, Abrams, Hoeft, & Menon, 2013 ). There is also evidence of malleability and the normalization of neural networks with successful intervention in SMD ( Iuculano et al., 2015 ).

Genetic and environmental factors

Early case studies of reading difficulties identified their familial nature, which has been confirmed in numerous studies utilizing genetically-sensitive designs with various combinations of relatives—identical and fraternal twins, non-twin siblings, parent-offspring pairs and trios, and nuclear and extended families. The relative risk of having SWRD if at least one family member has SWRD is higher for relatives of individuals with the condition, compared to the risk to unrelated individuals; higher for children in families where at least one relative has SWRD; even higher for families where a first-degree relative (i.e., a parent or a sibling) has SWRD; and higher still for children in families where both parents have SWRD ( Snowling & Melby-Lervåg, 2016 ). Quantitative-genetic studies estimate that 30–80% of the variance in reading, math or spelling outcomes is explained by heritable factors ( Willcutt et al., 2010 ).

Since the 1980s, there have been systematic efforts to identify the sources of structural variation in the genome, i.e., genetic susceptibility loci that can account for the strong heritability and familiality of SWRD ( Figure 4 ). These efforts have yielded the identification of nine regions of the genome thought to harbor genes, or other genetic material, whose variation is associated with the presence of SWRD and individual differences in reading-related processes. Within these regions, a number of candidate genes have been tapped, but no single candidate has been unequivocally replicated as a causal gene for SWRD, and observed effects are small. In addition, multiple other genes located outside of the nine linked regions have been observed to be relevant to the manifestation of SWRD and related difficulties. Currently there are ongoing efforts to interrogate candidate genes for SWRD and connect their structural variation to individual differences in the brain system underlying the acquisition and practice of reading.

There are only a few molecular-genetic studies of SMD and its related processes ( Figure 4 ). Unlike SWRD, no “regions of interest” have been identified. Only one study investigated the associations between known single-nuclear polymorphisms (SNP) and a composite measure of mathematics performance derived from various assessments of SMD-related componential processes and teacher ratings. The study generated a set of SNPs that, when combined, accounted for 2.9% of the phenotypic variance ( Figure 4 shows the genes in which the three most statistically significant SNPs from this set are located). Importantly, when this SNP set was used to study whether the association between the 10-SNP set and mathematical ability differs as a function of characteristics of the home and school, the association was stronger for indicators of mathematical performance in chaotic homes and in the context of negative parenting.

Finally, studies have investigated the pleiotropic (i.e., impacting multiple phenotypes) effects of SWRD candidate genes on SMD, ADHD, and related processes. These effects are seemingly in line with the “generalist genes” hypothesis, asserting the pleiotropic influences of some genes to multiple SLD ( Plomin & Kovas, 2005 ).

Environmental factors are strong predictors of SLD. These factors penetrate all levels of a child’s ecosystem: culture, demonstrated in different literacy and numeracy rates around the world; social strata, captured by social-economic indicators across different cultures; characteristics of schooling, reflected by pedagogies and instructional practices; family literacy environments through the availability of printed materials and the importance ascribed to reading at home; and neighborhood and peer influences. Interactive effects suggest that reading difficulties are magnified when certain genetic and environmental factors co-occur, but there is evidence of neural malleability even in SWDE ( Overvelde & Hulstijn, 2011 ). Neural and genetic factors are best understood as risk factors that variably manifest depending on the home and school environment and child attributes like motivation.

Intervention

Although the content of instruction varies depending on whether reading, math, and/or writing are impaired, general principles of effective intervention apply across SLD i . First, intervention for SLD is explicit ( Seidenberg, 2017 ): Teachers formally present new knowledge and concepts with clear explanations, model skills and strategies, and teach to mastery with cumulative practice with ongoing guidance and feedback. Second, intervention is individualized: Instruction is formatively adjusted in response to systematic progress-monitoring data ( Stecker, Fuchs, & Fuchs, 2005 ). Third, intervention is comprehensive and differentiated, addressing the multiple components underlying proficient skill as well as comorbidity. Comprehensive approaches address the multifaceted nature of SLD and provide more complex interventions that are generally more effective than isolated skills training in reading ( Mathes et al., 2005 ) and math ( L. S. Fuchs et al., 2014 ). For example, children with SLD and ADHD may need educational and pharmacological interventions ( Tamm et al., 2017 ). Anxiety can develop early in children who struggle in school, and internalizing problems must be treated ( Grills, Fletcher, Vaughn, Denton, & Taylor, 2013 ). Differentiation through individualization in the context of a comprehensive intervention also permits adjustments of the focus of an intervention on specific weaknesses.

Fourth, intervention adjusts intensity as needed to ensure success, by increasing instructional time, decreasing group size, and increasing individualization ( L. S. Fuchs, Fuchs, & Malone, 2017 ). Such specialized intervention is typically necessary for students with SLD ( L. S. Fuchs et al., 2015 ). Yet, effective instruction for SLD begins with differentiated general education classroom instruction ( Connor & Morrison, 2016 ), in which intervention is coordinated with rather than supplanting core instruction ( L. S. Fuchs, D. Fuchs, C. Craddock, et al., 2008 ).

In addition, intervention is more effective when provided early in development. For example, intervention for SWRD was twice as effective if delivered in grades 1 or 2 than if started in grade 3 ( Lovett et al., 2017 ). This is underscored by neuroimaging research ( Barquero et al., 2014 ) showing that experience with words and numbers is needed to develop the neural systems that mediate reading and math proficiency. A child with or at risk for SWRD who cannot access print because of a phonological processing problem will not get the reading experience needed to develop the lexical system for whole word processing and immediate access to word meanings. This may be why remedial programs are less effective after second grade; with early intervention, the child at risk for SLD develops automaticity because they have gained the experience with print or numbers essential for fluency. Even with high quality intensive intervention, some children with SLD do not respond adequately, and students with persistent SLD may profit from assistive technology (e.g., computer programs that convert text-to-speech; Wood, Moxley, Tighe, & Wagner, 2018 ).

Finally, interventions for SLD must occur in the context of the academic skill itself. Cognitive interventions that do not involve print or numbers, such as isolated phonological awareness training or working memory training without application to mathematical operations do not improve reading or math skill ( Melby-Lervåg et al., 2016 ). Physical exercises (e.g., cerebellar training), optometric training, special lenses or overlays, and other proposed interventions that do not involve teaching reading or math are ineffective ( Pennington, 2009 ). Pharmacological interventions are effective largely due to their impact on comorbid symptoms, with little evidence of a direct effect on the academic skill ( Tamm et al., 2017 ).

No evaluations of recovery rate from SLD have been performed. Intervention success has been evaluated as closing the age-grade discrepancy, placing children with SLD at an age-appropriate grade level, and maintaining their progress at a rate commensurate with typical development. Meta-analytic studies estimate effect sizes of academic interventions at 0.49 for reading ( Scammacca, Roberts, Vaughn, & Stuebing, 2015 ), 0.53 for math ( Dennis et al., 2016 ), and 0.74 for writing ( Gillespie & Graham, 2014 ).

Implications for Practice and Research

Practitioners should recognize that the psychological and educational scientific evidence base supports specific approaches to the identification and treatment of SLD. In designing SLD evaluations, assessments must be timely to avoid delays in intervention; they must consider comorbidities as well as contextual factors, and data collected in the context of previous efforts to instruct the child. Practitioners should use the resulting assessment data to ensure that intervention programs are evidence-based and reflect explicitness, comprehensiveness, individualization, and intensity. There is little evidence that children with SLD benefit from discovery, exposure, or constructivist instructional approaches.

With respect to research, the most pressing issue is understanding individual differences in development and intervention from neurological, genetic, cognitive, and environmental perspectives. This research will ultimately lead to earlier and more precise identification of children with SLD, and to better interventions and long-term accommodations for the 2–6% of the general population who receive but do not respond to early prevention efforts. More generally, other human conditions may benefit from the examples of progress exemplified by the integrated, interdisciplinary approaches that underlie the progress of the past 50 years in the scientific understanding of SLD.

Acknowledgments

The authors are the Principal Investigators of the currently funded Learning Disabilities Research Centers ( https://www.nichd.nih.gov/research/supported/ldrc ) and Innovation Hubs ( https://www.nichd.nih.gov/research/supported/ldhubs ), the two key NICHD programs supporting research on Specific Learning Disabilities. The preparation of this articles was supported by P20 HD090103 (PI: Compton), P50 HD052117 (PI: Fletcher), P20 HD075443 (PI: Fuchs), P20 HD091005 (PI: Grigorenko), P50 HD052120 (PI: Wagner), and P50 HD27802 (PI: Willcutt). Grantees undertaking such projects are encouraged to express their professional judgment. Therefore, this article does not necessarily reflect the position or policies of the abovementioned agencies, and no official endorsement should be inferred.

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Working memory and specific learning disability: Math

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There is much debate surrounding the definition of Specific Learning Disabilities in mathematics (SLD-math). This debate centers on the inconsistent terminology used to describe mathematics-related disabilities and difficulties (as reviewed by Lewis and Fisher, 2016; and Mazzocco, 2007), the many cognitive abilities that synergistically support mathematics learning and performance (Berch and Mazzocco, 2007), the complexity of mathematics as a discipline, and the multi-dimensionality of mathematics skills and processes (e.g., Petrill et al., 2012). The potential underpinnings and manifestations of mathematics disabilities are reflected in the broad, skill-based diagnostic criteria for SLD-math reported in the DSM-5 (American Psychiatric Association, 2013). Similar to other Specific Learning Disorders addressed in this volume (i.e., SLD-reading or writing; see Chapters 6 and 7), the DSM-5 defines SLD-math as: a developmental disorder that begins by school-age, … involves ongoing problems learning key academic skills (like) … math calculation and math problem solving, (and) is not simply a result of lack of instruction or poor instruction.

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• Working Memory Keyphrases 100%
• Memory-based Learning Keyphrases 100%
• Specific Learning Disabilities Keyphrases 100%
• Mathematics Social Sciences 100%
• Learning Disabilities Social Sciences 100%
• Learning Disability Psychology 100%
• Learning Disabilities in Mathematics Keyphrases 75%
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PY - 2018/1/1

Y1 - 2018/1/1

N2 - There is much debate surrounding the definition of Specific Learning Disabilities in mathematics (SLD-math). This debate centers on the inconsistent terminology used to describe mathematics-related disabilities and difficulties (as reviewed by Lewis and Fisher, 2016; and Mazzocco, 2007), the many cognitive abilities that synergistically support mathematics learning and performance (Berch and Mazzocco, 2007), the complexity of mathematics as a discipline, and the multi-dimensionality of mathematics skills and processes (e.g., Petrill et al., 2012). The potential underpinnings and manifestations of mathematics disabilities are reflected in the broad, skill-based diagnostic criteria for SLD-math reported in the DSM-5 (American Psychiatric Association, 2013). Similar to other Specific Learning Disorders addressed in this volume (i.e., SLD-reading or writing; see Chapters 6 and 7), the DSM-5 defines SLD-math as: a developmental disorder that begins by school-age, … involves ongoing problems learning key academic skills (like) … math calculation and math problem solving, (and) is not simply a result of lack of instruction or poor instruction.

AB - There is much debate surrounding the definition of Specific Learning Disabilities in mathematics (SLD-math). This debate centers on the inconsistent terminology used to describe mathematics-related disabilities and difficulties (as reviewed by Lewis and Fisher, 2016; and Mazzocco, 2007), the many cognitive abilities that synergistically support mathematics learning and performance (Berch and Mazzocco, 2007), the complexity of mathematics as a discipline, and the multi-dimensionality of mathematics skills and processes (e.g., Petrill et al., 2012). The potential underpinnings and manifestations of mathematics disabilities are reflected in the broad, skill-based diagnostic criteria for SLD-math reported in the DSM-5 (American Psychiatric Association, 2013). Similar to other Specific Learning Disorders addressed in this volume (i.e., SLD-reading or writing; see Chapters 6 and 7), the DSM-5 defines SLD-math as: a developmental disorder that begins by school-age, … involves ongoing problems learning key academic skills (like) … math calculation and math problem solving, (and) is not simply a result of lack of instruction or poor instruction.

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Specific Learning Disability - Impairment in Mathematics in Children and Adolescents

ICD-10 code: F81.2

Specific Learning Disorder, Impairment in Mathematics is part of a cluster of diagnoses called Specific Learning Disorders. Specific Learning Disorders are a group of psychiatric conditions that include:

• Impairment in Reading
• Impairment in Written Expression
• Impairment in Mathematics

These disorders are categorized by a persistent difficulty learning keystone academic skills with an onset during the years of formal schooling. Key academic skills include reading of single words accurately and fluently, reading comprehension, written expression and spelling, arithmetic calculation, and mathematical reasoning. Difficulties learning to map letters with the sound of one’s language- to read printed words- is one of the most common manifestations of specific learning disorder. Children and adolescents with specific learning disorder experience a persistent, or restricted progress in learning for at least six months despite intervention. The learning difficulties are usually readily apparent in the early school years in most children.

Children and adolescents with Specific Learning Disorders also perform well below average for their age, and average achievement is only attained through extraordinarily high levels of effort or support. The low academic skills cause significant interference with school skills that is usually indicated by school report or teacher’s grades. These learning difficulties are considered “specific” for four reasons: (1) they are not attributable to an intellectual disability; (2) the difficulty cannot be attributed to external factors such as economic or environmental disadvantage, chronic absenteeism, or lack of education in the individual’s community context; (3) it cannot be attributed to a neurological or motor disorder and (4) the difficulty must be restricted to one academic skill or domain (i.e., reading single words, retrieving or calculating number facts).

Note that Dyscalculia is a general term used to describe difficulty in mathematics. If dyscalculia is used to specify this particular pattern of difficulties, it is important to specify what difficulties are present.

What is Specific Learning Disorder, Impairment in Mathematics?

Approximately 5-5% of individuals in the general population have a learning disorder. Of the children who have a specific learning disability, approximately half have a math impairment.

Math impairments are characterized by one or more of the following domains:

• Number sense: has poor understanding of numbers, their magnitude, and relationships.  
• Memorization of math facts: counts on fingers to add single-digit numbers instead of recalling the math fact as peers do.
• Accurate or fluent calculation: gets lost in the midst of arithmetic computation and may switch procedures.
• Accurate math reasoning: has severe difficulty applying mathematical concepts, facts, or procedures to solve quantitative problems.

Common characteristics of children with a math impairment are:

• Shows difficulty understanding concepts of place value, and quantity, number lines, positive and negative value, carrying and borrowing
• Has difficulty understanding and doing word problems
• Has difficulty sequencing information or events
• Exhibits difficulty using steps involved in math operations
• Shows difficulty understanding fractions
• Is challenged making change and handling money
• Displays difficulty recognizing patterns when adding, subtracting, multiplying, or dividing
• Has difficulty putting language to math processes
• Has difficulty understanding concepts related to time such as days, weeks, months, seasons, quarters, etc.
• Exhibits difficulty organizing problems on the page, keeping numbers lined up, following through on long division problems

Understanding Impairment in Mathematics

Impairment in Math is a condition that makes it difficult to make sense of numbers and math concepts. Children with math impairments have difficulty learning and memorizing basic number facts. They struggle to understand the logic behind math and how to apply their knowledge to solving problems.

Impairments in mathematics severity can range from mild to severe. The most common problem seen with children is with “number sense.” This is an intuitive understanding of how numbers work, and how to compare and estimate quantities on a number line. It is not uncommon for children to have difficulties learning skills in one or two academic domains, such as math and reading. Children and adolescents with impairments with mathematics may also have neurodevelopmental disabilities such as attention-deficit/hyperactivity disorder (ADHD), anxiety and genetic disorders such as fragile X syndrome, Gerstmann’s syndrome and Turner’s Syndrome.

As with most learning disabilities, the exact cause of math disabilities is unknown. Research has indicated that it is a brain-based condition. Possible causes of math impairments include genetics and heredity. Researchers have found that a child with a math impairment often has a parent or sibling with a similar math issue. Studies have also found differences between children with math impairments and matched controls in the surface area, thickness, and volume in parts of the brain that are linked to learning and memory, setting up and monitoring tasks, and remembering math facts.

How is Impairment in Mathematics treated?

Impairments in mathematics are treatable using a targeted, individualized intervention. The intervention is uniquely tailored to remedy the child’s weaknesses in a targeted area of mathematics (e.g., number sense, memorization of math facts, accurate or fluent calculation, accurate math reasoning).

Although interventions should be individualized to take into account a child’s academic strengths and weaknesses, there are recommendations of what a math intervention should include: Math Interventions ; Instructional Interventions .

First Line Treatments

• Individualized Direct Instruction: Instruction in the classroom should include the following methods: explicit and direct instruction on computation and word problems; basic facts fluency practice; instruction on word problems is based on common underlying structure; provide visual representations of math ideas; at least 10 minutes per session to building fluent retrieval of basic arithmetic facts.
• Remediation using learning technology: Computer-assisted instructional software designed to help the learner make the link between digits and their meaning. Number Race emphasizes numerical comparison and designed to train number sense.  Graphogame-Math emphasizes training in matching verbal labels to visual patterns and number symbols.
• Adaptation to general curriculum: Teachers will differentiate instructional content and activities to ensure student is provided practice on core objectives that have already been taught
• Common adjustments are: allowing the use of scratch paper; assistive technology (i.e., calculator, digital and talking clocks, calendars and time management programs); use of diagrams; teacher assistance with use of graph paper and colored pencils to differentiate problems and steps; assistance with and use of manipulatives; schedule computer time for drill and practice; draw pictures of word problems

Second Line Treatments

When patients do not respond adequately to the first line treatments described above, other strategies might include:

• Evaluation for special education eligibility through school district’s Child Study Team

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Disabilities in math affect many students — but get little attention

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Laura Jackson became seriously concerned about her daughter and math when the girl was in third grade. While many of her classmates flew through multiplication tests, Jackson’s daughter struggled to complete her 1 times table. She relied on her fingers to count, had difficulty reading clocks and frequently burst into tears when asked at home to practice math flashcards. At school, the 9-year-old had been receiving help from a math specialist for two years, with little improvement. “We hit a point where she was asking me, ‘Mom, am I stupid?’” Jackson recalled. 

Then, when Jackson was having lunch with a friend one day, she heard for the first time about a disorder known as dyscalculia. After lunch, she went to her computer, looked up the term, and quickly came across a description of the learning disability, which impacts a child’s ability to process numbers, retain math knowledge and complete math problems. “I was like, ‘Oh my gosh, this is my kid,’” Jackson said.

Nationwide, hundreds of thousands of students face challenges learning math due to math disabilities like dyscalculia, a neurodevelopmental learning disorder caused by differences in the parts of the brain that are involved with numbers and calculations . There are often obstacles to getting help.

America’s schools have long struggled to identify and support students with learning disabilities of all kinds: Kids often languish while waiting to receive a diagnosis; families frequently have to turn to private, often pricey, providers to get one; and even with a diagnosis, some children still don’t get the supports they need because their schools are unable to provide them.

That’s slowly changing — for some disabilities. A majority of states have passed laws that mandate screening early elementary students for the most common reading disability, dyslexia, and countless districts train teachers how to recognize and teach struggling readers. Meanwhile, parents and experts say school districts continue to neglect students with math disabilities like dyscalculia, which affects up to 7 percent of the population and often coexists with dyslexia.

“Nobody uses the proper term for it, it’s not diagnosed frequently,” said Sandra Elliott, a former special education teacher and current chief academic officer at TouchMath, a multisensory math program. “We’re all focused on literacy.”

The Math Problem  

Sluggish growth in math scores for U.S. students began long before the pandemic, but the problem has snowballed into an education crisis. This back-to-school season, the Education Reporting Collaborative, a coalition of eight newsrooms, will be documenting the enormous challenge facing our schools and highlighting examples of progress. The three-year-old Reporting Collaborative includes AL.com, The Associated Press, The Christian Science Monitor, The Dallas Morning News, The Hechinger Report, Idaho Education News, The Post and Courier in South Carolina, and The Seattle Times.

AI might disrupt math and computer science classes – in a good way

Racial gaps in math have grown. could detracking help, dollars and sense: can financial literacy help students learn math .

Nationwide, teachers report that up to 40 percent of their students perform below grade level in math. And while students with math disabilities may be especially far behind , math scores for all students have remained dismal for years , showing that more attention needs to be paid to math instruction. Experts say learning the most effective methods for teaching students with math disabilities could significantly strengthen math instruction for all students. “You’ve got a huge number of students that are in the middle ground,” when it comes to math achievement but may not have a disability, Elliott added. Those students could also be helped by having explicit, multisensory instruction in math. “If it works for the students with the most severe disconnections and slower processing speeds, it’s still going to work for the kids that are in the ‘middle’ with math difficulties.”

“It’s not the fault of schools. I think it has to do with the amount of resources schools have to provide intervention to children, and reading takes priority over math.” Lynn Fuchs, research professor at Vanderbilt University

Covid exacerbated the nation’s problem with math achievement. The number of children who are several years behind in math has increased over the past few years and achievement gaps have widened. For some students, learning struggles may be due to an underlying disability like dyscalculia or other math learning disabilities that affect math calculation or problem solving skills. Yet only 15 percent of teachers report that their students have been screened for dyscalculia.

“There’s not as much research on math disorders or dyscalculia,” as there is on reading disabilities, said Karen Wilson, a clinical neuropsychologist who works with the organization Understood.org and specializes in the assessment of children with learning differences. “That also trickles down into schools.”

Related: Why it matters that Americans are comparatively bad at math

There are a host of reasons why math disabilities receive less attention than reading disabilities. Elementary teachers report more anxiety when it comes to teaching math, which can make it harder to teach struggling learners. Advocacy focused on math disabilities has been less widespread than that for reading disabilities. There is also a deep-seated societal belief that some people have a natural aptitude for math. “A lot of times, [parents] let it go for a long time because it’s culturally acceptable to be bad at math,” said Heather Brand, a math specialist and operations manager for the tutoring organization Made for Math.  

Some signs of dyscalculia are obvious at an early age, if parents and educators know what to look for. In the earliest years , a child might have difficulty recognizing numbers or patterns. Children may also struggle to connect a number’s symbol with what it represents, like knowing the number 3 corresponds to three blocks, for example. In elementary school, students may have trouble with math functions like addition and subtraction, word problems, counting money, or remembering directions.

Still, schools may be resistant to assessing math disabilities, or unaware of their prevalence. Even after Jackson learned about dyscalculia on her own, her daughter’s Seattle-area public school was doubtful that the third grader had a learning disability because she was performing so well in all other areas. Teachers suggested Jackson spend extra time on math at home. “For so many parents, they assume the school would let them know there’s an issue, but that’s just not how it works,” said Jackson. (She ultimately wrote a book, “Discovering Dyscalculia” about her family’s journey, and now runs workshops for parents of children with dyscalculia.)

Experts say universal screening, like those provided in many states for dyslexia, should be in place for math disabilities. Early diagnosis is crucial to provide children a stronger foundation in the early concepts that all math builds on. “Many times, if a student is caught early with the interventions that we all know work … these children can perform math, if not equal to their typically developing peers, they can get very, very close,” said Elliott from TouchMath.

Solving the Math Problem: Helping kids find joy and success in math

The Education Reporting Collaborative will host “Solving the Math Problem: Helping kids find joy and success in math,” a live expert panel, on Tuesday, Oct. 17 at 8 p.m. Eastern, 7 p.m. Central, 5 p.m. Pacific. This webinar is designed for families seeking strategies to help kids engage and excel in math.

Panelists include:Melissa Hosten , a Mathematics Outreach Co-Director at the University of Arizona, in the Department of Mathematics at the Center for Recruitment and Retention of Mathematics Teachers.

Elham Kazemi , a professor of mathematics education in the College of Education at the University of Washington.

The event registration shortlink is:  https://st.news/mathwebinar

As with other learning disabilities, a diagnosis is only the first step to getting children the help they need in school. In particular, students with dyscalculia often need a more structured approach to learning math that, like reading, involves “systematic and explicit” instruction and provides ample time to practice counting and recognizing numbers, said Lynn Fuchs, a research professor in special education and human development at Vanderbilt University. These students also may need strategies to help them commit math facts to memory, she added. To do this well, they often need small-group or one-on-one teaching, which is non-existent in many schools’ math instruction. “It’s not the fault of schools. I think it has to do with the amount of resources schools have to provide intervention to children, and reading takes priority over math,” said Fuchs.

Part of the problem is that teachers don’t receive the training needed to work with children with math disabilities. Teacher training programs offer little instruction on disabilities of any kind, and even less on math. In a 2023 survey by Education Week, nearly 75 percent of teachers reported that they had received little to no preservice or in-service training on supporting students with math disabilities. At least one state, Virginia, requires dyslexia awareness training for teacher licensure renewal, but has no similar requirement for math disability training. “It’s pretty rare for undergraduate degrees or even master’s degrees to focus on math learning disabilities with any level of breadth, depth, quality or rigor,” said Amelia Malone, director of research and innovation at the National Center for Learning Disabilities.

Nearly 75 percent of teachers reported in a 2023 Education Week survey that they had received little to no preservice or in-service training on supporting students with math disabilities..

Without more widespread knowledge of and support for dyscalculia, many parents have had to look for specialists and tutors on their own, which they say can be particularly challenging for math, and costly. Even after her daughter received a diagnosis, Jackson felt the girl’s school wasn’t supporting her enough. At school, her daughter’s math teacher demanded “tidy” math notebooks and discouraged drawing or doodling, activities that often helped the girl work through problems. In 2019, Jackson started pulling her daughter out of school for part of each day to teach her math at home. “I am not a math teacher, but I was so desperate,” Jackson said. “There’s no one who knows anything and we have to figure this out.”

Jackson pored over materials online and reached out to math disability experts in America and abroad for help. She started infusing her daughter’s math lessons with games and brought out physical objects, like small wooden rods, to help her practice counting. She worked with her daughter on the core foundations of math, including number sense and basic operations, to help establish the solid grounding that the girl was missing.

Experts say it’s possible to improve math outcomes for those who struggle, if more attention and resources are poured into math in the early years to ensure children do not reach third grade — or beyond — without the support they need.

Yet early childhood teachers are often the least equipped to teach math, especially for children with dyscalculia, said Marilyn Zecher, a dyslexia specialist who created a multisensory approach to math based on the popular Orton-Gillingham approach in reading. Zecher offers training on dyscalculia-related teaching strategies for teachers of all grade levels. Many of her strategies for early educators emphasize that math instruction starts through language. Children learn the basics of mathematics when teachers give them opportunities to verbally compare similarities and differences between objects, and describe how items or activities occur in relation to each other, such as “before” or “after.”

“The early ed teachers are the giants upon whose shoulders everybody else stands,” Zecher said. Early educators, like preschool teachers, not only teach foundational skills, they are also “so critical to identifying children who are having difficulties.”

Related: For teachers who fear math, banishing bad memories can help

At Brand’s organization, Made for Math , intensive tutoring based on Zecher’s approach often stands in for a lack of school-based support. Teachers create individualized lesson plans for students during each tutoring session, employing a variety of items to help students better understand math concepts. Students might use craft sticks bundled together to learn place value, cubes to learn subtraction or addition, and items that can be physically cut apart, like foam stickers, to learn fractions. Math specialists at the organization have found that children with dyscalculia need repetition, especially to understand math facts. Some students attend tutoring up to four days a week, at a cost of up to $1,000 a month . “It’s hard because it’s not something schools are offering, and kids deserve it,” said Brand.

In recent years, a handful of states, including Alabama , West Virginia and Florida , have introduced legislation that would require schools to identify and support younger students who struggle with math. Elliott’s company, TouchMath, introduced a screener earlier this year that can identify signs of math disabilities, like dyscalculia, in children as young as age 3.

“Many times, if a student is caught early with the interventions that we all know work…these children can perform math if not equal to their typically developing peers,” Sandra Elliott, a former special education teacher and current chief academic officer at TouchMath

Malone, from the National Center for Learning Disabilities, said, there are pockets of progress around the country in screening more children for math disabilities, but movement at the federal level — and in most states — is “nonexistent.”

New York City is one district that has prioritized math disability screening and math instruction in the early years. In 2015 and 2016, the city spent $6 million to roll out a new math curriculum featuring games, building blocks, art projects and songs. The district has also introduced universal math and reading screeners to try to identify students who may be behind.

Experts say that there are ways that all schools can make math instruction more accessible. In elementary schools, activities that involve more senses should be used more widely, including whole-body motions and songs for teaching numbers and hands-on materials for math operations. All students, and not only those with dyscalculia, could benefit from using manipulatives to help visualize problems and graph paper to assist in lining up numbers.  

As with dyslexia, figuring out better ways to teach kids with math disabilities will shore up math instruction across the board – and better meet students where they are. “Some kids won’t use [the strategies],” said Wilson, the neuropsychologist. “It’s really about having the option, so the student who’s struggling will be able to find a method that works for them.”

Jackson said her daughter could have benefited from a wider variety of methods at school. After several years of learning math at home, she was ready to try to re-join grade-level math classes. When the teen returned to school-based math classes in high school, she achieved an A in Algebra. “When you really understand what it is to be dyscalculic, then you can look around and decide what this person needs to succeed,” Jackson said. “It’s not just that you’re ‘bad at math’ and need to buckle down and try harder.”

This story about  dyscalculia  was produced by  The Hechinger Report , a nonprofit, independent news organization focused on inequality and innovation in education, as part of The Math Problem, an ongoing series about math instruction. The series is a collaboration with the Education Reporting Collaborative, a coalition of eight newsrooms that includes AL.com, The Associated Press, The Christian Science Monitor, The Dallas Morning News, The Hechinger Report, Idaho Education News, The Post and Courier in South Carolina, and The Seattle Times. Sign up for the Hechinger newsletter .

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What are strategies for teaching a student with a math-related learning disability?

Dyscalculia is a mathematics-related disability resulting from neurological dysfunction. Students who are diagnosed with Dyscalculia have average to above-average intellectual functioning and a significant discrepancy between their math skills and their chronological-age-peer norms. For a diagnosis of Dyscalculia, it must be determined that the math deficit is not simply related to issues such as poor instruction, vision, hearing or other physical problems, cultural or language differences, or developmental delays.

In Accommodating Math Students with Learning Disabilities , author Rochelle Kenyon lists the following strategies for teaching a student with math-related learning disabilities.

• Avoid memory overload. Assign manageable amounts of work as skills are learned.
• Build retention by providing review within a day or two of the initial learning of difficult skills.
• Provide supervised practice to prevent students from practicing misconceptions and "misrules."
• Make new learning meaningful by relating practice of subskills to the performance of the whole task.
• Reduce processing demands by preteaching component skills of algorithms and strategies.
• Help students to visualize math problems by drawing.
• Use visual and auditory examples.
• Use real-life situations that make problems functional and applicable to everyday life.
• Do math problems on graph paper to keep the numbers in line.
• Use uncluttered worksheets to avoid too much visual information.
• Practice with age-appropriate games as motivational materials.
• Have students track their progress.
• Challenge critical thinking about real problems with problem solving.
• Use manipulatives and technology such as tape recorders or calculators.

This list was adapted from the following source: Garnett, K., Frank, B., & Fleischner, J. X. (1983). A strategies generalization approach to basic fact learning (addition and subtraction lessons, manual #3; multiplication lessons, manual #5). Research Institute for the Study of Learning Disabilities. New York, NY: Teacher's College, Columbia University.

For additional resources on how to make mathematics accessible to students with disabilities, consult the DO-IT Knowledge Base article Where can I find tips on making math accessible to students with disabilities?

For more information regarding challenges faced by students with math-related learning disabilities, consult the DO-IT Knowledge Base article What are typical challenges students with math-related learning disabilities face?

Nonverbal Learning Disorder, Explained

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Laura Lemle watched how some teachers didn’t always understand how to teach her daughter, who has nonverbal learning disability. Some were incredibly empathetic, others were not. Special education schools weren’t the right fit, but neither was mainstream education. She felt her daughter never ultimately got what she needed.

Lemle knew she wanted to do something to help other children like her daughter. She thought somebody had to be working to raise awareness. But it didn’t seem like anyone was. She decided it had to be her.

But now, there’s an unexpected spotlight on nonverbal learning disability, or NVLD. After some on social media fixated on the teenage son of Minnesota Gov. Tim Walz, Gus, who had an emotional reaction as Walz accepted the Democratic nomination for vice president, there’s been heightened awareness of what NVLD is.

The Walz family has previously said that Gus has attention deficit hyperactivity disorder, anxiety disorder, and nonverbal learning disability.

Lemle—the founder of the NVLD Project, a nonprofit that seeks to raise awareness of the condition and pursue formal diagnosis recognition in the Diagnostic and Statistical Manual of Mental Disorders—said the outspokenness of the Walz family has shed a light on NVLD. The DSM is used by mental health professionals in the United States for standard classifications of mental disorders.

“It’s really been under the radar, and it’s a problem for this population,” she said. “Getting it into the DSM is, to me, the beginning, because a lot more work needs to be done.”

Without recognition in the DSM, NVLD is not covered by the Individuals with Disabilities Education Act—meaning students can’t get accommodations if they don’t have another diagnosable disability.

When it comes to learning disabilities, there’s a lack of research for disabilities outside of dyslexia, said Monica McHale-Small, the director of education for the Learning Disabilities of America Association.

“A lot of times we talk about it as the most common learning disability is dyslexia, but we don’t have good data to support that it is indeed. It’s the one we have the most information about, the most research on,” McHale-Small said. “We need a lot more research specific to learning disabilities and how they manifest in the classroom, and in life.”

There is a push for more visibility and research—and eventual inclusion in the DSM. Here are some common questions, answered.

What is nonverbal learning disability?

NVLD refers to a condition that a group of kids or adults have, which includes difficulty with visual and spatial reasoning, and problem-solving, leading to functional impairments in their everyday life, said Amy Margolis, a professor of pediatric neuropsychiatry at Columbia University. The NVLD Project funds Margolis’s research.

A common misconception, because it is called nonverbal learning disability, is that people with NVLD have problems with language and speech, or that it is an autism spectrum disorder. Researchers havestudied how the disorders are similar and how they’re different. You could have both, Margolis said, but they’re distinct.

In research a few years ago, Margolis asked parents with kids who have NVLD and those with autism spectrum disorder to rate their children on social functioning. When the researchers looked at the children’s brain functions, the social functioning issues were coming from “different problems in a circuit that underlies social functioning,” said Margolis. The fancy term is different pathophysiology, she said. But basically, the brain basis is different.

What are common signs of NVLD that educators might see in the classroom?

A classic example is difficulty with math, said Margolis, either in understanding numerosity and the concepts behind math, or the mechanics of learning the procedures for things to line up on the page—for instance, if you’re writing an addition problem, and the columns don’t align.

As students with NVLD get older, they might struggle with certain kinds of math that require visual or spatial problem-solving, like geometry, or in science where they may have to read and draw graphs.

Students who learned to read easily in 1st and 2nd grade may now have difficulty reading to learn—they could struggle to grasp the main idea or big picture of what they’ve read, Margolis said.

In gym class, children with NVLD may run in the wrong direction during a soccer game. They may have trouble packing their backpacks, creating Lego structures, or trouble gauging when it is safe to cross the street.

These are students who, oftentimes, have stronger language-based skills than visual-spatial skills, Margolis said. Giving a student the diagram and helping them label it, rather than drawing it, is one way teachers can create an inclusive space.

“For a lot of kids, copying down the square in the circles is not going to be such a huge effort. But for this kid, it is,” she said. “You want to take away that part of the challenge and let them focus on learning what the shapes represent.”

The NVLD project also devised a toolkit for educators to understand NVLD and how it may appear in class.

These students may also struggle with higher-order comprehension, said McHale-Small, who was an educator for nearly 30 years. Rewording directions or explaining concepts in a different way, are ways to help.

Social skills are also essential for success in and after school, McHale-Small added. It’s important for educators to help facilitate friendships and model working through social conflict, too.

Is there a diagnosis for NVLD?

Because NVLD isn’t in the diagnostic nomenclature, it is hard for students to get diagnosed, Margolis said. Clinicians are forced to classify people based on “downstream problems”-—like if they also meet criteria for ADHD, anxiety, or specific learning disorders in math. This means students often won’t have accommodations specific to NVLD under the IDEA Act.

In research published in 2020 , Margolis and her colleagues found that potentially 3 percent of kids in North America meet the criteria for this disorder. A lot of the kids in that sample had other diagnoses, but about 10 percent did not.

“If you extrapolate out, that could mean 300,000 kids who have no access to care because they don’t meet the criteria for some other diagnosis,” she said.

Right now, to get a diagnosis, individuals have to get a neuropsychological assessment, she said. There are efforts to have NVLD included in the DSM as a diagnosis, and recontextualized as developmental visual spatial disorder (DVSD).

“What we’re hoping also by getting into the book is to really enhance access for people,” she said. “We’re recommending that this diagnosis could be made based on interviews, the same way ADHD is made based on interviews, rather than requiring testing.”

Right now, Margolis and colleagues are working to prove that people can use their new definition reliably. Getting into the DSM would not only increase access to health care services, Margolis said, but it would also increase research interest.

“If it’s not covered in the DSM and it’s not recognized, then people aren’t going to study it, because it’s going to be very hard to get research dollars to study it, and why would you want to develop treatments for things nobody can be diagnosed with?” she said.

Coverage of students with learning differences and issues of race, opportunity, and equity is supported in part by a grant from the Oak Foundation, at www.oakfnd.org . Education Week retains sole editorial control over the content of this coverage.

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