Arithmetic fluency and number processing skills in identifying students with mathematical learning disabilities.

BACKGROUND: Students with mathematical learning disabilities (MLD) struggle with number processing skills (e.g., enumeration and number comparison) and arithmetic fluency. Traditionally, MLD is identified based on arithmetic fluency. However, number processing skills are suggested to differentiate low achievement (LA) from MLD. AIMS: This study investigated the accuracy of number processing skills in identifying students with MLD and LA, based on arithmetic fluency, and whether the classification ability of number processing skills varied as a function of grade level. METHODS AND PROCEDURES: The participants were 18,405 students (girls = 9080) from Grades 3-9 (ages 9-15). Students' basic numerical skills were assessed with an online dyscalculia screener (Functional Numeracy Assessment -Dyscalculia Battery, FUNA-DB), which included number processing and arithmetic fluency as two factors. OUTCOMES AND RESULTS: Confirmatory factor analyses supported a two-factor structure of FUNA-DB. The two-factor structure was invariant across language groups, gender, and grade levels. Receiver operating characteristics curve analyses indicated that number processing skills are a fair classifier of MLD and LA status across grade levels. The classification accuracy of number processing skills was better when predicting MLD (cut-off < 5 %) compared to LA (cut-off < 25 %). CONCLUSIONS AND IMPLICATIONS: Results highlight the need to measure both number processing and arithmetic fluency when identifying students with MLD.

Auditory time perception impairment in children with developmental dyscalculia.

Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.

Mathematical learning deficits originate in early childhood from atypical development of a frontoparietal brain network.

Mathematical learning deficits are defined as a neurodevelopmental disorder (dyscalculia) in the International Classification of Diseases. It is not known, however, how such deficits emerge in the course of early brain development. Here, we conducted functional and structural magnetic resonance imaging (MRI) experiments in 3- to 6-year-old children without formal mathematical learning experience. We followed this sample until the age of 7 to 9 years, identified individuals who developed deficits, and matched them to a typically developing control group using comprehensive behavioral assessments. Multivariate pattern classification distinguished future cases from controls with up to 87% accuracy based on the regional functional activity of the right posterior parietal cortex (PPC), the network-level functional activity of the right dorsolateral prefrontal cortex (DLPFC), and the effective functional and structural connectivity of these regions. Our results indicate that mathematical learning deficits originate from atypical development of a frontoparietal network that is already detectable in early childhood.

Dystypia Associated with Diaschisis of the Middle Frontal Gyri after Left Angular Infarction.

Dystypia without aphasia, agraphia, or apraxia is a rare symptom and has been suggested to result from a lesion in the left middle frontal cortex. We herein describe a man with dystypia with agraphia due to infarction of the left angular gyrus. His dystypia seemed to result from the convergence failure of the kana into the alphabetical spellings. During dystypia, hypoperfusion of the bilateral middle frontal cortices was discovered. However, after his symptoms improved, blood flow in the middle frontal cortices returned to normal. This case suggests that the middle frontal cortex is downstream of the angular gyrus in the dictating pathway and a lesion in the left middle frontal cortex could cause pure dystypia.

Excessive visual crowding effects in developmental dyscalculia.

Visual crowding refers to the inability to identify objects when surrounded by other similar items. Crowding-like mechanisms are thought to play a key role in numerical perception by determining the sensory mechanisms through which ensembles are perceived. Enhanced visual crowding might hence prevent the normal development of a system involved in segregating and perceiving discrete numbers of items and ultimately the acquisition of more abstract numerical skills. Here, we investigated whether excessive crowding occurs in developmental dyscalculia (DD), a neurodevelopmental disorder characterized by difficulty in learning the most basic numerical and arithmetical concepts, and whether it is found independently of associated major reading and attentional difficulties. We measured spatial crowding in two groups of adult individuals with DD and control subjects. In separate experiments, participants were asked to discriminate the orientation of a Gabor patch either in isolation or under spatial crowding. Orientation discrimination thresholds were comparable across groups when stimuli were shown in isolation, yet they were much higher for the DD group with respect to the control group when the target was crowded by closely neighbouring flanking gratings. The difficulty in discriminating orientation (as reflected by the combination of accuracy and reaction times) in the DD compared to the control group persisted over several larger target flanker distances. Finally, we found that the degree of such spatial crowding correlated with impairments in mathematical abilities even when controlling for visual attention and reading skills. These results suggest that excessive crowding effects might be a characteristic of DD, independent of other associated neurodevelopmental disorders.

Early Cognitive Precursors of Children's Mathematics Learning Disability and Persistent Low Achievement: A 5-Year Longitudinal Study.

Mathematical difficulties have been distinguished as mathematics learning disability (MLD) and persistent low achievement (LA). Based on 1,880 Finnish children who were followed from kindergarten (age 6) to fourth grade, this study examined the early risk factors for MLD and LA. Distinct groups of MLD (6.0% of the sample) and LA (25.7%) children were identified on the basis of their mathematics performance between first and fourth grades with latent class growth modeling. Impairment in the same set of cognitive skills, including language, spatial, and counting skills, was found to underlie MLD and LA. The finding highlights the importance of monitoring mathematical development across the early grades and identifying early cognitive precursors of MLD and LA for screening and intervention efforts.

Substantiating synesthesia: a novel aid in a case of grapheme-colour synesthesia and concomitant dyscalculia.

Here we present the case of SP, a 21-year-old female with life-long dyscalculia. SP was subsequently diagnosed with grapheme-color synesthesia, a diagnosis that serendipitously catalyzed our development of a novel aid:The digit-color calculator (DCC). The DCC substantiates SP's color concurrents, dramatically ameliorating her difficulties with basic calculations. We envisage the DCC and its analogues may assist others in educational settings, particularly if they experience difficulties with the acquisition of literacy and numeracy. Further devices that leverage synesthesia may also have the potential to improve the quality of life for others with trait synesthesia regardless of concomitant disorder.

Modal-independent Pattern Recognition Deficit in Developmental Dyscalculia Adults: Evidence from Tactile and Visual Enumeration.

Developmental dyscalculia (DD) is characterized by lower numerical and finger-related skills. Studies of enumeration among those DD that suggested core deficiency in pattern recognition, working memory or/and attention were mostly carried out in the visual modality. In our study, we examined visual (dots) enumeration of 1-10 stimuli and tactile (vibration) enumeration of 1-10 fingers among DD and matched-control adults. We used 800-ms stimuli exposure time of either random/non-neighboring or canonical/neighboring stimuli arrangements (visual/tactile). Compared to controls, those with DD responded faster in visual random enumeration and did not differ in reaction time (RT) of canonical stimuli arrangements. However, while the control group had near perfect accuracy in random stimuli arrangements of up to five stimuli, DD participants performed accurately for only up to four stimuli, and they were less accurate in the canonical stimuli arrangements in the counting range. In the tactile task, DD participants showed less accurate tactile enumeration only for neighboring arrangements, more profoundly for finger counting (FC) patterns. The longer exposure time in the visual task enabled us to explore pattern recognition effects when working memory and attention loads were low. We discuss possible modal-independent deficits in pattern recognition and working memory on enumeration performance among those with DD and the unique role of fingers in ordinal and cardinal representation of numbers.

Understanding Comorbidity Between Specific Learning Disabilities.

Current definitions of specific learning disability (SLD) identify a heterogeneous population that includes individuals with weaknesses in reading, math, or writing, and these academic difficulties often co-occur in many of the same individuals. The Colorado Learning Disabilities Research Center (CLDRC) is an interdisciplinary, multisite research program that uses converging levels of analysis to understand the genetic and environmental etiology, neuropsychology, and developmental outcomes of SLDs in reading (RD), math (MD), and writing (WD), along with the comorbidity between these SLDs and other developmental disorders. The latest results from the CLDRC twin study suggest that shared genetic influences contribute to the significant covariance between all aspects of reading (word reading, reading fluency, and reading comprehension) and math (calculations, math fluency, and word problems), and distinct genetic or environmental influences also contribute to weaknesses in each specific academic domain. RD and MD are associated with a range of negative outcomes on both concurrent measures and measures of functional outcomes completed 5 years after the twins were first assessed. Over the next several years the CLDRC will continue to expand on this work by administering a comprehensive test battery that includes measures of all dimensions of academic achievement that are described in current definitions of SLD and incorporating these measures in new neuroimaging and molecular genetic studies.

Connections Between Reading Comprehension and Word-Problem Solving via Oral Language Comprehension: Implications for Comorbid Learning Disabilities.

In this article, we discuss the approach adopted within the Vanderbilt University Learning Disabilities Innovation Hub, which focuses on students with higher-order comorbidity: students with concurrent difficulty with reading comprehension and word-problem solving. The aim of the Hub's Research Project is to test what we refer to as the higher-order comorbidity hypothesis: that language comprehension plays a critical role in reading comprehension and word-problem solving. In the Hub's study, we test the hypothesize that language comprehension offers a coordinated approach for improving both outcomes and that this approach thus provides direction for understanding higher-order comorbidity and support for the validity of reading comprehension and word-problem solving comorbidity as a learning disabilities subtyping framework. In the first segment of this article, we describe a model that connects reading comprehension and word-problem solving development via oral language comprehension, and we provide a brief overview of prior related research on these connections. This first section provides the basis for the second segment of this article, in which we discuss the Vanderbilt Hub's innovative approach for investigating these connections. This study tests a theoretically-coordinated framework on students' performance in both high-priority domains of academic development, while exploring effects for boys versus girls and for linguistically diverse learners.

Spontaneous representation of numerosity in typical and dyscalculic development.

Animals including humans are endowed with a remarkable capacity to estimate rapidly the number of items in a scene. Some have questioned whether this ability reflects a genuine sense of number, or whether numerosity is derived indirectly from other covarying attributes, such as density and area. In previous work we have demonstrated that adult observers are more sensitive to changes in numerosity than to area or density, particularly changes that leave numerosity constant, pointing to a spontaneous sensitivity to numerosity, not attributable to area and density. Here we extend this line of research with a novel technique where participants reproduce the size and density of a dot-array. They were given no explicit instructions of what to match, but could regulate freely all combinations of area and density by trackpad. If the task is mediated by matching separately area and texture-density, the errors in the two attributes have to be independent. Contrarily to this prediction, we found that errors in area and density were negatively correlated, suggesting that subjects matched numerosity, rather than area and density. We employed this technique to investigate processing of number in adolescents with typical and low math abilities (dyscalculia). Interestingly, we found that dyscalculics also reproduced numerosity rather than area or density. However, compared to typicals, dyscalculics had longer reaction times, a tendency to rely also on area, and their performance did not improve over sessions. Taken together, the data demonstrate that numerosity emerges as the most spontaneous and sensitive dimension, supporting the existence of a dedicated number sense and confirm numerosity atypicalities in dyscalculia.

Quality of Explanation as an Indicator of Fraction Magnitude Understanding.

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students' explanations of those comparisons, as well as the relation between those measures and scores on a criterion test: released fraction items from the National Assessment of Educational Progress. We also considered the extent to which reasoning and language contribute to the prediction. Results indicated a significant moderate correlation between accuracy and explanation quality. Commonality analyses indicated that explanation quality accounts for little variance in National Assessment of Educational Progress scores beyond what is accounted for by traditional measures of magnitude understanding. Implications for instruction and assessment are discussed.

Multi-method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia.

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.

A Cognitive Dimensional Approach to Understanding Shared and Unique Contributions to Reading, Math, and Attention Skills.

Disorders of reading, math, and attention frequently co-occur in children. However, it is not yet clear which cognitive factors contribute to comorbidities among multiple disorders and which uniquely relate to one, especially because they have rarely been studied as a triad. Thus, the present study considers how reading, math, and attention relate to phonological awareness, numerosity, working memory, and processing speed, all implicated as either unique or shared correlates of these disorders. In response to findings that the attributes of all three disorders exist on a continuum rather than representing qualitatively different groups, this study employed a dimensional approach. Furthermore, we used both timed and untimed academic variables in addition to attention and activity level variables. The results supported the role of working memory and phonological awareness in the overlap among reading, math, and attention, with a limited role of processing speed. Numerosity was related to the comorbidity between math and attention. The results from timed variables and activity level were similar to those from untimed and attention variables, although activity level was less strongly related to cognitive and academic/attention variables. These findings have implications for understanding cognitive deficits that contribute to comorbid reading disability, math disability, and/or attention-deficit/hyperactivity disorder.

Tactile enumeration: A case study of acalculia.

Enumeration is one of the building blocks of arithmetic and fingers are used as a counting tool in early steps. Subitizing-fast and accurate enumeration of small quantities-has been vastly studied in the visual modality, but less in the tactile modality. We explored tactile enumeration using fingers, and gray matter (GM) changes using voxel-based morphometry (VBM), in acalculia. We examined JD, a 22-year-old female with acalculia following a stroke to the left inferior parietal cortex. JD and a neurologically healthy normal comparison (NC) group reported how many fingers were stimulated. JD was tested at several time points, including at acute and chronic phases. Using the sensory intact hand for tactile enumeration, JD showed deficit in the acute phase, compared to the NC group, and improvement in the chronic phase of (1) the RT slope of enumerating up to four stimuli, (2) enumerating neighboring fingers, and (3) arithmetic fluency performance. Moreover, VBM analysis showed a larger GM volume for JD relative to the NC group in the right middle occipital cortex, most profoundly in the chronic phase. JD's performance serves as a first glance of tactile enumeration in acalculia. Pattern-recognition-based results support the suggestion of subitizing being the enumeration process when using one hand. Moreover, the increase in GM in the occipital cortex lays the groundwork for studying the innate and primitive ability to perceive and evaluate sizes or amounts-"sense of magnitude"- as a multisensory magnitude area and as part of a recovery path for deficits in basic numerical abilities.

Developmental Dyscalculia is Characterized by Order Processing Deficits: Evidence from Numerical and Non-Numerical Ordering Tasks.

This study tested the hypothesis that individuals with dyscalculia have an order processing deficit. The ordering measures included both numerical and non-numerical ordering tasks, and ordering of both familiar and novel sequences was assessed. Magnitude processing/estimation tasks and measures of inhibition skills were also administered. The participants were 20 children with developmental dyscalculia, and 20 children without maths difficulties. The two groups were closely matched on age, gender, socio-economic status, educational experiences, IQ and reading ability. The findings revealed differences between the groups in both ordering and magnitude processing skills. Nevertheless, diagnostic status was best predicted by order processing abilities.

Acute stroke presenting with isolated acalculia.

Acalculia is defined as the inability to mentally manipulate numbers for simple calculations. It may occur in dementia, central nervous system (CNS) neoplasm, and stroke (Bermejo-Velasco and Castillo-Moreno, 2006). Lesions of the left parietal cortex are the principal cause. When acalculia occurs in stroke, it is generally associated with other deficits in speech, sensation, or motor function. We report the case of a 63-year-old male with a 1 day history of isolated acalculia that was found to have a left parietal lobe infarct with several smaller infarcts in the left occipital lobe. The diagnosis of stroke should be considered in all patients experiencing acute difficulty with mathematics, reading, or writing, even in the absence of other deficits.

A cognitive model for multidigit number reading: Inferences from individuals with selective impairments.

We propose a detailed cognitive model of multi-digit number reading. The model postulates separate processes for visual analysis of the digit string and for oral production of the verbal number. Within visual analysis, separate sub-processes encode the digit identities and the digit order, and additional sub-processes encode the number's decimal structure: its length, the positions of 0, and the way it is parsed into triplets (e.g., 314987 → 314,987). Verbal production consists of a process that generates the verbal structure of the number, and another process that retrieves the phonological forms of each number word. The verbal number structure is first encoded in a tree-like structure, similarly to syntactic trees of sentences, and then linearized to a sequence of number-word specifiers. This model is based on an investigation of the number processing abilities of seven individuals with different selective deficits in number reading. We report participants with impairment in specific sub-processes of the visual analysis of digit strings - in encoding the digit order, in encoding the number length, or in parsing the digit string to triplets. Other participants were impaired in verbal production, making errors in the number structure (shifts of digits to another decimal position, e.g., 3,040 â†’ 30,004). Their selective deficits yielded several dissociations: first, we found a double dissociation between visual analysis deficits and verbal production deficits. Second, several dissociations were found within visual analysis: a double dissociation between errors in digit order and errors in the number length; a dissociation between order/length errors and errors in parsing the digit string into triplets; and a dissociation between the processing of different digits - impaired order encoding of the digits 2-9, without errors in the 0 position. Third, within verbal production, a dissociation was found between digit shifts and substitutions of number words. A selective deficit in any of the processes described by the model would cause difficulties in number reading, which we propose to term "dysnumeria".