Exploring the impact of a fraction sense intervention in authentic school environments: An initial investigation.

A solid understanding of fractions is the cornerstone for acquiring proficiency with rational numbers and paves the way for learning advanced mathematical concepts such as algebra. Fraction difficulties limit not only students' educational and vocational opportunities but also their ability to solve everyday problems. Students who exit sixth grade with inadequate understanding of fractions may experience far-reaching repercussions that lead to lifelong avoidance of mathematics. This article presents the results of a randomized controlled trial focusing on the first two cohorts of a larger efficacy investigation aimed at building fraction sense in students with mathematics difficulties. Teachers implemented an evidence-informed fraction sense intervention (FSI) within their sixth-grade intervention classrooms. The lessons draw from research in cognitive science as well as mathematics education research. Employing random assignment at the classroom level, multilevel modeling revealed a significant effect of the intervention on posttest fractions scores after controlling for pretest fractions scores, working memory, vocabulary, proportional reasoning, and classroom attentive behavior. Students in the FSI group outperformed their counterparts in the control group, with noteworthy effect sizes on most fraction measures. Challenges associated with carrying out school-based intervention research are addressed.

The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study.

Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia.

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

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.

Dyscalculia and Typical Math Achievement Are Associated With Individual Differences in Number-Specific Executive Function.

Deficits in numerical magnitude perception characterize the mathematics learning disability developmental dyscalculia (DD), but recent studies suggest the relation stems from inhibitory control demands from incongruent visual cues in the nonsymbolic number comparison task. This study investigated the relation among magnitude perception during differing congruency conditions, executive function, and mathematics achievement measured longitudinally in children (n = 448) from ages 4 to 13. This relation was investigated across achievement groups and as it related to mathematics across the full range of achievement. Only performance on incongruent trials related to achievement. Findings indicate that executive function in a numerical context, beyond magnitude perception or executive function in a non-numerical context, relates to DD and mathematics across a wide range of achievement.

A Rare Clinical Antity; Pure Gerstmann Syndrome.

Gerstmann syndrome is defined as a tetrad including agraphia, acalculia, finger agnosia, and right-left disorientation. In the case studies presented in the literature, it has been reported that Gerstmann syndrome usually appears as an incomplete tetrad of symptoms or accompanied by cognitive deficits including aphasia, alexia, apraxia and some perceptual disorders. Here, we present of the patient with left angular and supramarginal gyrus infarction affecting the parietal lobe. In addition to the symptoms mentioned above, the patient had alexia and anomic aphasia as well. We discussed the clinic appearance and reviewed the current literature.

Altered association between executive functions and reading and math fluency tasks in children with reading difficulties compared with typical readers.

Fluent reading in children relies on executive functions (EF). Recent research suggests that EF skills also affect arithmetic abilities. Children with reading difficulties (RD) experience deficits in EF. It is still unknown to what extent these EF deficits are the basis for both reading and arithmetic skills in children with RD compared with typical readers. To define the role of EF in reading and arithmetic in children with RD and typical readers, EF measures and reading and arithmetic fluency and non-fluency measures were assessed in 8 to 12-year-old children with RD and age-matched typical readers. Comparison and correlation analyses were performed within and between the two groups. Children with RD scored lower on reading and arithmetic fluency and non-fluency tasks compared with typical readers. For both groups, fluency measures were lower than non-fluency measures. Strong correlations were found within the entire study population between fluency measures and EF, as well as between non-fluency measures and EF compared with mixed correlations observed for the groups separately. Fluency was related to subcomponents of EF expressed in both reading and arithmetic domains for the two groups. The role of each domain and comparison with non-fluency results for each group are discussed.

Effectiveness of working memory training among children with dyscalculia: evidence for transfer effects on mathematical achievement-a pilot study.

We examined whether the working memory (WM) capacity of developmentally dyscalculic children can be improved by a WM training program and whether outcomes relate to mathematical performance. The experimental design comprised two groups with developmental dyscalculia with grade 4 schooling: an experimental group (n = 14; mean age = 115.29 months) and a control group (n = 14; mean age = 116.07 months). All participants were assessed on measures of WM, mathematic attainment, and nonverbal mental ability (Raven test) before and after training. The WM training program focused on manipulating and maintaining arithmetic information. The results show that both WM and mathematical performances improved significantly after intervention, indicating a strong relationship between these two constructs. The control group improved slightly in Raven's progressive matrices and a reading number task. These findings are discussed in terms of near and far transfer toward trained and untrained skills and stress the positive impact of WM training on learning mathematics in children with dyscalculia.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test).

The ability to compare symbolic numerical magnitudes correlates with children's concurrent and future mathematics achievement. We developed and evaluated a quick timed paper-and-pencil measure that can easily be used, for example in large-scale research, in which children have to cross out the numerically larger of two Arabic one- and two-digit numbers (SYMP Test). We investigated performance on this test in 1,588 primary school children (Grades 1-6) and examined in each grade its associations with mathematics achievement. The SYMP Test had satisfactory test-retest reliability. The SYMP Test showed significant and stable correlations with mathematics achievement for both one-digit and two-digit comparison, across all grades. This replicates the previously observed association between symbolic numerical magnitude processing and mathematics achievement, but extends it by showing that the association is observed in all grades in primary education and occurs for single- as well as multi-digit processing. Children with mathematical learning difficulties performed significantly lower on one-digit comparison and two-digit comparison in all grades. This all suggests satisfactory construct and criterion-related validity of the SYMP Test, which can be used in research, when performing large-scale (intervention) studies, and by practitioners, as screening measure to identify children at risk for mathematical difficulties or dyscalculia.

[Differential diagnosis of primary and secondary mathematical learning disability ­ indications from the dyscalculia test Basis-Math 4­8]. / Differenzialdiagnose zwischen primärer Rechenstörung und sekundärer Rechenschwäche: Hinweise aus dem Basis-Math 4-8.

Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4­8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4­8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.

Basic numerical processing, calculation, and working memory in children with dyscalculia and/or ADHD symptoms.

Objective: Deficits in basic numerical skills, calculation, and working memory have been found in children with developmental dyscalculia (DD) as well as children with attention-deficit/hyperactivity disorder (ADHD). This paper investigates cognitive profiles of children with DD and/or ADHD symptoms (AS) in a double dissociation design to obtain a better understanding of the comorbidity of DD and ADHD. Method: Children with DD-only (N = 33), AS-only (N = 16), comorbid DD+AS (N = 20), and typically developing controls (TD, N = 40) were assessed on measures of basic numerical processing, calculation, working memory, processing speed, and neurocognitive measures of attention. Results: Children with DD (DD, DD+AS) showed deficits in all basic numerical skills, calculation, working memory, and sustained attention. Children with AS (AS, DD+AS) displayed more selective difficulties in dot enumeration, subtraction, verbal working memory, and processing speed. Also, they generally performed more poorly in neurocognitive measures of attention, especially alertness. Children with DD+AS mostly showed an additive combination of the deficits associated with DD-only and A_Sonly, except for subtraction tasks, in which they were less impaired than expected. Conclusions: DD and AS appear to be related to largely distinct patterns of cognitive deficits, which are present in combination in children with DD+AS.

[Specific learning disabilities - from DSM-IV to DSM-5]. / Spezifische lernstörungen.

The publication of the DSM-5 means changes in the classification and recommendations for diagnosis of specific learning disabilities. Dyslexia and dyscalculia have been reintroduced into the DSM. Three specific learning disorders - impairment in reading, impairment in the written expression, and impairment in mathematics, described by subskills - are now part of the DSM-5. Three subcomponents of the reading disorder are expressly differentiated: word reading accuracy, reading rate, and fluency and reading comprehension. Impaired subskills of the specific learning disorder with impairment in written expression are spelling accuracy, grammar and punctuation accuracy, and clarity and organization of written expression. Four subskills are found in the mathematics disorder: number sense, memorization of arithmetic facts, accurate or fluent calculation, and accurate math reasoning. Each impaired academic domain and subskill should be recorded. A description of the severity degree was also included. The diagnosis is based on a variety of methods, including medical history, clinical interview, school report, teacher evaluation, rating scales, and psychometric tests. The IQ discrepancy criterion was abandoned, though that of age or class discrepancy criterion was retained. The application of a discrepancy is recommended by 1 to 2.5 SD. All three specific developmental disorders are common (prevalence 5 %-15 %), occur early during the first years of formal schooling, and persist into adulthood.

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.

Dyslexia and dyscalculia: which neuropsychological processes distinguish the two developmental disorders?

This study analyses the specific neuropsychological profiles of children with dyslexia and/or dyscalculia, in particular concerning phonological awareness, lexical access, working memory and numerical processing. Four groups were selected, through a screening process that used strict criteria, from 1568 7-10-year-old children: 90 with typical development, 61 with dyslexia, 13 with dyscalculia, and 14 with dyslexia + dyscalculia. Children with dyslexia show a deficit in phonological processing, lexical access, and verbal working memory, especially with alphabetic stimuli. Children with developmental dyscalculia show a deficit of phonological processing, verbal working memory with digits and visual-spatial working memory. They also show an impairment in spatial representation of numbers and in the automatic access to numerical semantics to a greater extent than those with double disturbance. Children with dyslexia + dyscalculia show a profile generally characterized by the summation of the deficits of the two disorders, although they have a lower deficit in access to numerical semantics and mental representation of numbers.

[Symptoms diagnosis and treatment of dyscalulia]. / Symptomatik, diagnostik und behandlung der rechenstörung..

Children with dyscalculia show deficits in basic numerical processing which cause difficulties in the acquisition of mathematical skills. This article provides an overview of current research findings regarding the symptoms, cause, and prognosis of dyscalculia, and it summarizes recent developments in the diagnosis, early intervention, and treatment thereof. Diagnosis has improved recently because newly developed tests focus not only on the math curriculum, but also on basic skills found to be impaired in dyscalculia. A controversial debate continues with regard to IQ achievement discrepancy. International studies have demonstrated the effectiveness of specialized interventions. This article summarizes the research findings from intervention studies, describes different treatment approaches, and discusses implications for clinical practice.

[Changes in psychological stress after interventions in children and adolescents with mathematical learning disabilities]. / Veränderungen psychischer Belastung durch die Förderung von rechenschwachen Kindern und Jugendlichen.

OBJECTIVE: The present study examined the effects of the Waterglass Intervention Program on children with mathematical learning disabilities compared to dyscalculic children who received private tutoring. METHOD: In a pre-post-control group design, N = 46 children (age 7-12) and their parents were questioned about changes in test anxiety, school reluctance, anxiety disorder, and internal and external abnormality. RESULTS: Children who attended the Waterglass Intervention Program reported a higher reduction of test anxiety, school reluctance, and attention problems. A trend toward a higher reduction of the CBCL-score was also found. These changes were mediated by the changes in math school grades. Furthermore, results showed that more children showed internal disorders than would be expected. CONCLUSIONS: An intervention specific for children with mathematical learning disabilities has positive effects on the psychological stress level of these children. Further research is required to investigate the mechanisms related to these changes and the effects on mathematical achievement.

Low discriminative power of WISC cognitive profile in developmental dyscalculia.

BACKGROUND: The role of domain-general cognitive abilities in the etiology of Developmental Dyscalculia (DD) is a hotly debated issue. AIMS: In the present study, we tested whether WISC-IV cognitive profiles can be useful to single out DD. METHODS AND PROCEDURES: Using a stringent 2-SD cutoff in a standardized numeracy battery, we identified children with DD (N = 43) within a clinical sample referred for assessment of learning disability and compared them in terms of WISC cognitive indexes to the remaining children without DD (N = 100) employing cross-validated logistic regression. OUTCOMES AND RESULTS: Both groups showed higher Verbal Comprehension and Perceptual Reasoning than Working Memory and Processing Speed, and DD scores were generally lower. Predictive accuracy of WISC indexes in identifying DD individuals was low (AUC = 0.67) and it dropped to chance level in discriminating DD from selected controls (N = 43) with average math performance but matched on global IQ. The inclusion of a visuospatial memory score as an additional predictor did not improve classification accuracy. CONCLUSIONS AND IMPLICATIONS: These results demonstrate that cognitive profiles do not reliably discriminate DD from non-DD children, thereby weakening the appeal of domain-general accounts.

A Neuropsychological Profile of Developmental Dyscalculia: The Role of Comorbidity.

Developmental dyscalculia (DD) has long been thought to be determined by multiple components. Dyscalculia has high comorbidity with other learning and developmental disabilities, including reading and writing disorders, attention deficits, and problems in visual/spatial skills, short memory, and working memory. This study aims to assess prevalence rates for isolated as well as comorbid DD in a sample of Italian-speaking children. In addition, we studied the neuropsychological profile of children with isolated or combined dyscalculia. We tested 380 children (176 males and 204 females) between the ages of 8.17 and 9.33 years using an extensive battery to determine the neuropsychological profile. The assessment included an arithmetic battery and nonverbal intelligence, short-term memory, reading, and writing tests. The results indicated that children with DD more frequently have a reading disorder and writing disorder. They also have a lower nonverbal intelligence quotient (IQ) and obtain significantly lower scores in short-term memory tests and on a visuospatial skills questionnaire. They also had significantly higher scores (indicative of greater attentional difficulties) on the Conners subscale for attentional problems. Children with DD present different cognitive and neuropsychological profiles.

Symbolic and non symbolic numerical representation in adults with and without developmental dyscalculia.

BACKGROUND: The question whether Developmental Dyscalculia (DD; a deficit in the ability to process numerical information) is the result of deficiencies in the non symbolic numerical representation system (e.g., a group of dots) or in the symbolic numerical representation system (e.g., Arabic numerals) has been debated in scientific literature. It is accepted that the non symbolic system is divided into two different ranges, the subitizing range (i.e., quantities from 1-4) which is processed automatically and quickly, and the counting range (i.e., quantities larger than 4) which is an attention demanding procedure and is therefore processed serially and slowly. However, so far no study has tested the automaticity of symbolic and non symbolic representation in DD participants separately for the subitizing and the counting ranges. METHODS: DD and control participants undergo a novel version of the Stroop task, i.e., the Enumeration Stroop. They were presented with a random series of between one and nine written digits, and were asked to name either the relevant written digit (in the symbolic task) or the relevant quantity of digits (in the non symbolic task) while ignoring the irrelevant aspect. RESULT: DD participants, unlike the control group, didn't show any congruency effect in the subitizing range of the non symbolic task. CONCLUSION: These findings suggest that DD may be impaired in the ability to process symbolic numerical information or in the ability to automatically associate the two systems (i.e., the symbolic vs. the non symbolic). Additionally DD have deficiencies in the non symbolic counting range.

Microgenetic patterns of children's multiplication learning: confirming the overlapping waves model by latent growth modeling.

Variability in strategy selection is an important characteristic of learning new skills such as mathematical skills. Strategies gradually come and go during this development. In 1996, Siegler described this phenomenon as "overlapping waves." In the current microgenetic study, we attempted to model these overlapping waves statistically. In addition, we investigated whether development in strategy selection is related to development in accuracy and to what degree working memory is related to both. We expected that children with poor working memory are limited in their possibilities to make the associations that are necessary to progress to more mature strategies. This limitation would explain the often-found relationship between working memory and mathematical abilities. To this aim, the strategy selection and accuracy of 98 children who were learning single-digit multiplication was assessed eight times on a weekly basis. Using latent growth modeling for categorical data, we confirmed Siegler's hypothesis of overlapping waves. Moreover, both the intercepts and the slopes of strategy selection and accuracy were strongly interrelated. Finally, working memory predicted both strategy selection and accuracy, confirming that working memory is related to mathematical problem solving in two ways because it influences both the maturity of strategy choice and the probability of making procedural mistakes.