Mathematical Disabilities Research Articles

Phonological Awareness and Rapid Naming Skills of Children with Reading Disabilities and Children with Reading Disabilities Who Are At Risk for Mathematics Difficulties.

Limited research has examined the skills of children with a reading disability (RD) and children with RD and a mathematics disability (MD). Even less research has examined the phonological awareness (PA) and rapid automatized naming (RAN) skills in these two groups of children and how these skills relate to reading and math achievement. Additionally, various classification criteria are frequently implemented to classify children with MD. The purpose of this study, therefore, was to examine the PA and RAN skills in children who met different criteria for RD only and children with RD who are at-risk for mathematics difficulties (MDR). Participants were 114 second or third grade students with RD from public elementary schools in three large metropolitan areas. Students were classified as at-risk for mathematics difficulties utilizing a 25th percentile cutoff and a 15th percentile cutoff as assessed by the KeyMath-Revised Test (Connolly, 1988). A series of PA and RAN measures were administered along with a range of reading and mathematics measures. Hierarchical regression analyses indicated that children with RD only evidenced a different pattern of results compared to children with RD + MDR. Additionally, using a more stringent criterion to classify children at-risk for mathematics difficulties resulted in a differential pattern of results when compared to a less stringent classification criterion.

Intensive Intervention for Students with Mathematics Disabilities: Seven Principles of Effective Practice

The focus of this article is intervention for third - grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for students in the primary grades: number combinations and story problems. We then focus on seven principles of effective intervention. First, we describe a validated, intensive remedial intervention for number combinations and another for story problems. Then, we use these interventions to illustrate the first six principles for designing intensive tutoring protocols for students with mathematics disabilities. Next, using the same validated interventions, we report the percentage of students whose learning outcomes were inadequate despite the overall efficacy of the interventions and explain how ongoing progress monitoring represents a seventh, and perhaps the most essential, principle of intensive intervention. We conclude by identifying issues and directions for future research in the primary and later grades.

Implementing CRA With Secondary Students With Learning Disabilities in Mathematics

Students with learning disabilities struggle to acquire essential mathematical concepts and skills, especially at the secondary level. One effective approach to improving secondary math performance supported by research is the concrete-to-representational-to-abstract (CRA) sequence of instruction. Although CRA is an evidenced-based instructional practice, it is somewhat complicated for teachers to implement in their day-to-day instruction.To better assist implementation of the CRA, an instructional approach with the mnemonic CRA-MATH was developed as a flexible roadmap to help math teachers better address student deficits using the CRA sequence of instruction. The purpose of this article is to describe the seven-step strategy used to guide curricular CRA modifications in secondary mathematics.

Mental Arithmetic in Children With Mathematics Learning Disabilities

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the proposed and the correct answer was manipulated. Both typically achieving groups were sensitive to answer plausibility on simple problems, were faster at rejecting extremely incorrect results than at accepting correct answers on complex addition problems, and showed a reduction of the complexity effect on implausible problems, attesting to the use of approximate calculation. Conversely, children with mathematics disabilities were unaffected by answer plausibility on simple addition problems, processed implausible and correct sums with equal speed on complex problems, and exhibited a smaller reduction of the complexity effect on implausible problems. They also made more errors on implausible problems. Different hypotheses are discussed to account for these results.

Rote Numeric Skills May Mask Underlying Mathematical Disabilities in Girls With Fragile X Syndrome

Mathematical learning disabilities (MLD) have been reported for elementary school age girls with fragile X syndrome who do not have mental retardation. Yet girls with fragile X demonstrate age-appropriate rote math skills, sometimes outperforming other children with MLD. We examined whether MLD and strengths in rote math skills persist during middle school among girls with fragile X. Middle school children were individually administered the Ranking Proportions Task (RPT), which involves fractions and decimals. Such problems, although difficult for many students, yield different performance profiles between children with versus without MLD. We hypothesized that girls with fragile X would outperform children with MLD on rote skills (e.g., naming decimals) despite conceptual difficulties, regardless of effects of FSIQ. To address the influence of fragile X versus MLD or FSIQ, several comparison groups were included. Children from a normative sample outperformed girls with fragile X on conceptual, but not rote, skills. However, their performance resembled that of children with MLD on conceptual skills, such as identifying equal quantities with different symbols (e.g., 0.5 and 1/2). Fragile X syndrome provides a compelling model of the heterogeneity of MLD, as the associated profile resembles that of both children with or without MLD. In terms of applications to serving girls with fragile X, it is important to consider that efficient rote skills may not only fail to enhance math achievement, they may hinder achievement by masking underlying conceptual deficiencies.

Teaching Conceptual Model—Based Word Problem Story Grammar to Enhance Mathematics Problem Solving

Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching word problem (WP) story grammar on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or at risk for mathematics disabilities in two urban public elementary schools in the Midwest. An adapted multiple-probe-across-participants design was used to assess the functional relation between the intervention and students' problem-solving performance. The results indicated that conceptual model—based representation prompted by WP story grammar improved students' performance on arithmetic WP solving and promoted prealgebra concept and skill acquisition. The practical implications of integrating algebraic reasoning in elementary mathematics are discussed.

Basic number processing and difficulties in single-digit arithmetic: Evidence from Velo-Cardio-Facial Syndrome

It has been suggested that mathematical disabilities (MD) emerge as a consequence of impairments in basic number processing skills. The aim of the present study was to investigate basic number processing skills in children with Velo-Cardio-Facial Syndrome (VCFS), a common genetic disorder with a high prevalence of MD, and to examine whether these basic low-level skills account for their performance in single-digit arithmetic. Twenty-five children with VCFS and 25 individually matched controls (age range: 6–12 years) participated. They all completed two basic number processing tasks (number reading, number comparison) and three single-digit arithmetic tasks comprising addition, subtraction and multiplication. In the latter tasks, strategy use was recorded next to accuracy and speed. Our data revealed that children with VCFS were significantly slower than controls on number comparison but not on number reading. Analysis of the single-digit arithmetic data revealed that children with VCFS performed more poorly than controls on large addition and subtraction problems. Both groups did not differ on multiplication and small additions and subtractions. At the strategy level, children with VCFS were significantly slower in executing backup strategies in addition and subtraction, but showed preserved retrieval of arithmetic facts. Taken together, children with VCFS show a consistent pattern of deficits at the level of number representations, arithmetic operations and strategy use, which suggests an impaired quantity subsystem in terms of Dehaene et al.'s model (2003). Most importantly, the correlational analyses showed that basic number processing skills directly accounted for single-digit arithmetic performance and strategy use in the children of the present study.

A Critical Examination of Learning Disabilities in Mathematics: Applying the Lens of Ableism

Introduction Background and Rationale Over half of the students who receive special education services are labeled as learning disabled (LD); they comprise approximately five to six percent of the entire K-12 student population (Hehir, 2005). Most students are labeled LD in reading; however, approximately twenty percent are either labeled as LD in mathematics or LD in both reading and mathematics (G. Williamson, personal communication on March 9, 2006). Therefore, it is likely that one in every one hundred students in American public schools carries the label of LD in mathematics. Many may perceive one percent to be a small and insignificant slice of the K-12 population and may wonder why I would choose to focus my on such a small group of students. My response is three-fold. First, federal legislation such as the No Child Left Behind Act (NCLB, 2001) and the Individuals with Disabilities in Education Act (IDEA, 2004) require us to pay attention to the quality of all students' education and (probably more so) their academic performance. Second, not much literature exists in mathematics education on this topic. As a field, we have published mathematics education work relating to race, gender, and socioeconomic status, but on the subgroup of special education, particularly students carrying the label of LD in mathematics, we remain largely silent. Lastly, the social, emotional, educational and political realities for those involved--the labeled student him/herself, his/her parents, the labeled student's general education mathematics teacher as well as his/her special education teacher, the administrators and in fact the labeled student's entire school--are extremely significant. I am deeply concerned with issues of equity and the power differentials inherent in our society, and I want our schools to seek ways to eradicate practices in mathematics education that privilege some at the expense of others. Theoretical Perspective In this article, I apply a critical pedagogy (Kincheloe & McLaren, 1994; Freire, 1997) perspective looking through the lens of ableism (Rauscher & McClintock, 1977; Hehir, 2005) to examine current educational policy, research and practice regarding the identification of and labeling of students as LD in mathematics. Kincheloe and McLaren (1994, p. 453) state, inquiry that aspires to the name critical must be connected to an to confront the injustice of a particular society or public sphere within the society. A critical pedagogy perspective, then, seeks to uncover hegemonic (power) relations, ideologies, and inequities in education, critique instrumental rationality, and inspire a movement for toward social justice. The following are assumptions from a critical pedagogy perspective that are pertinent to this article: 1. Acknowledging schooling as a form of cultural politics that endorses only particular forms of knowledge, thus creating a dominant group of successful knowers and others (Brantlinger, 1997, 2001); 2. Challenging the traditional view of education as a neutral and just process, and instead, recognizing it serves as an oppressive social structure (Freire, 1997) for some students; 3. Believing that self and social empowerment should precede mastery of technical skills tied to the marketplace and that educators should attempt to see and experience education from the perspective of those who are not dominant and work towards positive social change (Pasco, 2003, p. 5). Hehir (2005) discusses how the ideology of ableism negatively affects the education of children labeled with disabilities and urges educators and policymakers to focus on making just and equitable decisions about the policies and practices that support the educational, emotional and social progress of individual children. In his book on eliminating ableism, he utilizes (and in this paper I adopt) the following definition for ableism: Ableism is a pervasive system of discrimination and exclusion that oppresses people who are perceived to have cognitive, emotional, and/or physical disabilities. …

Arithmetical impairments related to domain-specific working memory updating

Event Abstract Back to Event Arithmetical impairments related to domain-specific working memory updating Teresa Iuculano1*, R. Moro1, 2 and B. Butterworth1 1 Institute of Cognitive Neuroscience, University College London, United Kingdom 2 Institute of Psychiatry, King’s College, United Kingdom The ability to perform simple arithmetic, such as single-digits additions, evolves with practice from algorithmic computation to direct retrieval from memory (Geary, 1994). Mathematical disabilities have often been associated with poor general working memory capacities (Geary, 1993; Koontz & Berch, 1996; McLean & Hitch, 1999). Moreover, there is also evidence of a specific working memory deficit in relation to processing numerical information in children with arithmetical disabilities (Siegel & Ryan, 1989). However, previous studies investigating working memory in relation to mathematical ability have not accounted for the possibility of other confounding numerical impairments. Using the Dyscalculia Screener standardized testing battery (Butterworth, 2003) we identified a group of children who presented a selective impairment in single-digit addition. This group with Poor Arithmetical ability (PA) scored in the lowest 7% of the population for children between the ages of eight and nine compared to Normal Achievement children (NA). The impairment in PA was specific to arithmetic: they displayed normal scores on symbolic and non-symbolic numerosity comparisons, on continuous magnitude comparisons, as well as on non-symbolic approximate arithmetic. This group also obtained IQ and reading scores within the normal range of the population for their age group. In a series of behavioural tests on ten PA and twenty-three NA children, we aimed to find if the selective impairment in arithmetic was due to a working memory impairment and, if so, whether it was generalized or domain-specific. No significant differences were found between PA and NA for digit span and word span tests. In order to assess their ability of working memory to continually update relevant information and to inhibit irrelevant information, a modified version of a working memory updating task was used (Palladino et al., 2001). In this test, participants were presented with a set of oral stimuli (word or number task) with increasing memory load and were required to retain the relevant stimuli based on a ongoing magnitude criteria (i.e. report smallest number or subset of numbers within a trial). Repeated measures ANOVA revealed a significant group by task interaction (p < 0.05), where PA displayed significantly decreased accuracy for number tasks, but increased accuracy for word tasks when compared to NA. This result suggests that the PA group might experience a specific working memory impairment related to numerosity. Furthermore, such impairment doesn’t seem to be due to a low working memory capacity for numbers, but instead may derive from the inability to continually update and modify numerical information. Conference: 10th International Conference on Cognitive Neuroscience, Bodrum, Turkey, 1 Sep - 5 Sep, 2008. Presentation Type: Poster Presentation Topic: Memory & Learning Citation: Iuculano T, Moro R and Butterworth B (2008). Arithmetical impairments related to domain-specific working memory updating. Conference Abstract: 10th International Conference on Cognitive Neuroscience. doi: 10.3389/conf.neuro.09.2009.01.282 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 09 Dec 2008; Published Online: 09 Dec 2008. * Correspondence: Teresa Iuculano, Institute of Cognitive Neuroscience, University College London, London, United Kingdom, t.iuculano@ucl.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Teresa Iuculano R. Moro B. Butterworth Google Teresa Iuculano R. Moro B. Butterworth Google Scholar Teresa Iuculano R. Moro B. Butterworth PubMed Teresa Iuculano R. Moro B. Butterworth Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

The Inhibition Capacities of Children with Mathematical Disabilities

Several authors have argued that mathematical disabilities might result from difficulties in inhibiting irrelevant information. The present study addresses this issue by assessing three inhibition functions in 40 ten-year-old children: suppression of irrelevant information from working memory, inhibition of prepotent responses, and interference control. We found no significant differences between children with math disabilities and typically achieving controls, or between children with arithmetic facts disabilities and children with above-average arithmetic facts skills. These findings, along with other empirical evidence and with theoretical considerations, cast doubt on the inhibition deficit hypothesis.

Computational Fluency Performance Profile of High School Students With Mathematics Disabilities

The purpose of this descriptive study was to develop a computational fluency performance profile of 224 high school (Grades 9—12) students with mathematics disabilities (MD). Computational fluency performance was examined by grade-level expectancy (Grades 2—6) and skill area (whole numbers: addition, subtraction, multiplication, division; rational numbers: fractions, decimals) using the Mathematics Operations Test— Revised (MOT-R). The findings indicated that these high school students with MD were fluent only in computational skills at the second- and third-grade levels. Computational fluency was found with most whole number basic facts in addition, subtraction, multiplication, and division. Lack of computational fluency was demonstrated on many items dealing with subtraction of multiple digits or items requiring regrouping, most multiplication and division items, and rational number items involving fractions and decimals. The results are discussed in regard to instructional programs and curriculum organization for high school students with MD.

Overlap and specificity of genetic and environmental influences on mathematics and reading disability in 10-year-old twins.

To what extent do genetic and environmental influences on reading disability overlap with those on mathematics disability? Multivariate genetic research on the normal range of variation in unselected samples has led to a Generalist Genes Hypothesis which posits that the same genes largely affect individual differences in these abilities in the normal range. However, little is known about the etiology of co-morbidity for the disability extremes of reading and mathematics. From 2596 pairs of 10-year-old monozygotic and dizygotic twins assessed on a web-based battery of reading and mathematics tests, we selected the lowest 15% on reading and on mathematics. We conducted bivariate DeFries-Fulker (DF) extremes analyses to assess overlap and specificity of genetic and environmental influences on reading and mathematics disability defined by a 15% cut-off. Both reading and mathematics disability are moderately heritable (47% and 43%, respectively) and show only modest shared environmental influence (16% and 20%). There is substantial phenotypic co-morbidity between reading and mathematics disability. Bivariate DF extremes analyses yielded a genetic correlation of .67 between reading disability and mathematics disability, suggesting that they are affected largely by the same genetic factors. The shared environmental correlation is .96 and the non-shared environmental correlation is .08. In line with the Generalist Genes Hypothesis, the same set of generalist genes largely affects mathematical and reading disabilities. The dissociation between the disabilities occurs largely due to independent non-shared environmental influences.

An Evolutionary Perspective on Learning Disability in Mathematics

A distinction between potentially evolved, or biologically-primary forms of cognition, and the culturally-specific, or biologically-secondary forms of cognition that are built from primary systems is used to explore mathematical learning disability (MLD). Using this model, MLD could result from deficits in the brain and cognitive systems that support biologically-primary mathematical competencies, or from the brain and cognitive systems that support the modification of primary systems for the creation of secondary knowledge and secondary cognitive competencies. The former include visuospatial long-term and working memory and the intraparietal sulcus, whereas the latter include the central executive component of working memory and the anterior cingulate cortex and lateral prefrontal cortex. Different forms of MLD are discussed as related to each of the cognitive and brain systems.

Learning disabilities: from identification to intervention

Introduction. History of the Field. Classification, Definition, and Identification of Learning Disabilities. Assessment of Learning Disabilities. Reading Disabilities: Word Recognition. Reading Disabilities: Fluency. Reading Disabilities: Comprehension. Mathematics Disabilities. Written Expression Disabilities. Conclusions and Future Directions

Teaching mathematics to middle school students with learning difficulties

Montague, Jitendra, Introduction. Bryant, Kim, Hartman, Bryant, Standards-based Mathematics Instruction and Teaching Middle School Students with Mathematical Disabilities. Woodward, Making Reform-based Mathematics Work for Academically Low-achieving Middle School Students. Xin, Jitendra, Teaching Problem-solving Skills to Middle School Students with Learning Difficulties: Schema-based Strategy Instruction. van Garderen, Teaching Visual Representation for Mathematics Problem Solving. Montague, Self-regulation Strategies for Better Math Performance in Middle School. Foegen, Evaluating Instructional Effectiveness: Tools and Strategies for Monitoring Student Progress. Kinder, Stein, Quality Mathematics Programs for Students with Disabilities. Parmar, DeSimone, Facilitating Teacher Collaboration in Middle School Mathematics Classrooms with Special-Needs Students.

Extending Responsiveness to Intervention to Mathematics at First and Third Grades

Responsiveness to intervention (RTI) is an innovative approach to the identification of learning disabilities (LD). The central assumption is that RTI can differentiate between two explanations for low achievement: poor instruction versus disability. If the child responds poorly to validated instruction, then the assessment eliminates instructional quality as a viable explanation for poor academic growth and instead provides evidence of a disability. For children who do respond nicely, RTI serves a critical prevention function. Most of RTI research has been focused on early reading. In this article, we describe two ongoing programs of research on RTI in the area of mathematics: one on a comprehensive mathematics curriculum at first grade and the other focused on word problems at third grade. For each research program, we describe the sample, explain how students are identified as at risk for mathematics disability, provide an overview of the interventions to which responsiveness is gauged, and describe some results to date.

The Effects of Peer–Mediated Instruction in Mathematics for Students with Learning Problems: A Research Synthesis

The purpose of this synthesis is to summarize the effectiveness of peer–mediated interventions on the mathematics performance of both students with disabilities and those at risk for mathematics disabilities. Meta–analytic techniques were used to calculate mean effect sizes for 17 studies that met inclusion criteria. Results indicate that peer–mediated interventions in mathematics are moderately effective for improving students’ mathematics performance. Also, findings are strongest for students at risk for mathematics disabilities, elementary–aged participants, and mathematics computation content. Recommendations for future research and practical implications are discussed.

Factors affecting learning disabilities in mathematics: a study of central region of Nepal

The students whose achievement lagged behind their intellectual potential presents a serious problem to the parents, society and finally to the nation; instead of being the contributing members they turn out to be social problem and get involved in the most common social malaise-student on rest. Describing groups who have average or above average intelligence continuously failing to maintain normal progress in school subjects as learning disabled students, the teacher education programs in western countries like U.S.A. and Europe started the identification, diagnosis and serve them since 1963. But in developing countries, for example, in Nepal and India, although the efforts are directed towards this direction, no the considerable progress has yet been observed. So the present investigation was concerned with the identification of the causes of primary school children learning disabilities in mathematics (CLDM). 58 LD boys and 46 LD girls from 29 rural and 15 urban schools situated in different parts of central region of Nepal participated in this study. The analysis of these 104 LD students' bio-data revealed that the factors related to the children with learning disabilities in mathematics were the poor instruction, parents' adverse behavior to them, teacher's negligence in the class. It was suggested that the quality of teaching strategies and quality of instruction in the schools must be improved. Further research is needed for the generalization of the findings throughout the nation.&#x0D; Tribhuvan University Journal 2004/1 pp. 13-19

Mathematical disabilities in children with velo-cardio-facial syndrome

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system located in the angular gyrus, which underlies the retrieval of arithmetic facts, and a quantity system located in the intraparietal sulcus, which subserves operations that involve semantic manipulations of quantity. According to this model, subtypes of math disability (MD) should be traceable to differential impairments in these subsystems. The present study investigated MD in children with velo-cardio-facial syndrome (VCFS) and aimed to verify which of these subsystems of number processing is impaired in these children. Eleven children with VCFS and 11 individually matched controls, selected from the same classes, completed a large battery of mathematical tests.Our data revealed that children with VCFS had preserved number reading abilities and preserved retrieval of arithmetic facts, both of which indicate that the verbal subsystem is not impaired in VCFS. By contrast, children with VCFS showed difficulties in number comparison, the execution of a calculation strategy and word problem solving, all of which involve the semantic manipulation of quantities. This provides evidence for a specific deficit in the quantity subsystem in children with VCFS, suggesting underlying abnormalities in the intraparietal sulcus.

Learnmaths: A case study of the development of learning software to support social inclusion

This paper discusses the role of technology in overcoming existing barriers to education and employment faced by people with specific learning disabilities and illustrates the discussion by the example of the LearnMaths toolbox for people with specific learning disabilities in mathematics. The context of the toolbox is respect for equality and diversity and consequently recognition that different approaches to learning are equally valid and that the cognitive processes of people with specific learning disabilities can lead to creativity and innovation.