Estimulação transcraniana por corrente contínua para melhorar o desempenho matemático em crianças discalculia de desenvolvimento em idade escolar: um único grupo pré-teste-pós-teste, estudo quase experimental / Transcranial direct current stimulation to enhance mathematical performance in school going developmental dyscalculic children: A single group pretest-posttest, quasi experimental study

INTRODUÇÃO: A discalculia do desenvolvimento (DD) lida com o desempenho matemático prejudicado e afeta as atividades educacionais e do dia a dia das crianças. Há evidências de que a estimulação transcraniana por corrente contínua (ETCC) aplicada ao córtex parietal posterior facilita a estrutura neuronal hipoativa e melhora o desempenho matemático em indivíduos com DD. OBJETIVO: O objetivo deste estudo é investigar se tDCS adjuvante com treinamento convencional de numeramento (CNT) aumentaria as habilidades matemáticas de crianças em idade escolar afetadas com DD. MATERIAIS E MÉTODOS: Treze crianças em idade escolar afetadas com DD receberam tDCS e CNT três sessões por semana por até 2 semanas. Foi dada estimulação anódica esquerda e catódica direita na região P3 / P4, com intensidade de 2mA, combinada com CNT por 30 minutos em um dia. O inventário de diagnóstico de deficiência de aprendizagem (LDDI) foi usado como uma medida de resultado e coletado no início e no final da intervenção de 2 semanas. RESULTADOS: Houve melhora significativa no desempenho matemático de crianças em idade escolar. Os resultados mostram uma melhora estatística e clinicamente significativa após 2 semanas de intervenção. CONCLUSÕES: tDCS combinado com CNT é eficaz para melhorar as habilidades matemáticas de crianças em idade escolar afetadas com DD. Os resultados deste estudo fornecem uma nova perspectiva para a reabilitação de crianças com DD em idade escolar.

INTRODUCTION: Developmental dyscalculia (DD) deals with impaired mathematical performance and affects children's educational and day-to-day activities. There is evidence that transcranial direct current stimulation (tDCS) applied to the posterior parietal cortex facilitates the hypoactive neuronal structure and improves mathematical performance in individuals with DD. OBJECTIVE: The objective of this study is to investigate whether tDCS adjuvant with conventional numeracy training (CNT) would enhance the mathematical abilities of school-going children affected with DD. MATERIALS AND METHODS: Thirteen school-going children affected with DD received tDCS and CNT three sessions per week for up to 2 consecutive weeks. Left anodal and right cathodal stimulation at P3/P4 region with 2mA intensity combined with CNT for 30 minutes in a day was given. Learning disability diagnostic inventory (LDDI) was used as an outcome measure and collected at baseline and the end of the 2-week intervention. RESULTS: There was a significant improvement in the mathematical performance of school-going children. The results show statistically as well as a clinically significant improvement after the two weeks of intervention. CONCLUSIONS: tDCS combined with CNT effectively improves the mathematical abilities of school-going children affected with DD. The findings of this study provide a new perspective for the rehabilitation of school-going DD children.

Efficacy of neuropsychological rehabilitation on numerical and calculation abilities: A developmental case study.

Present single case proves the effectiveness of a theory-based cognitive treatment on numerical and calculation abilities in developmental age. Both evaluation and treatment were designed on the bases of current models of numerical cognition, in particular Von Aster's developmental model. At the age of 7.4 years, HT was referred for a serious delay in the acquisition of numerical skills involving all numerical and calculation skills (written calculations, numerical knowledge, accuracy, rapidity). Following the rules of neuropsychological rehabilitation, HT was submitted to an early, intensive, HT-tailored treatment based on analogic representation of amount. After 12 months of treatment, HT showed statistically significant increasing in all the investigated variables: however, even if he correctly performed various numerical tasks, he remained significantly slower compared to his peers. Present case demonstrated the efficacy of theory-based, individually-tailored developmental dyscalculia. Early diagnosis and early intervention are urgently needed to get clinically significant change and to prevent behavioral and emotional symptoms.

A Synthesis of Elementary Mathematics Interventions: Comparisons of Students With Mathematics Difficulty With and Without Comorbid Reading Difficulty.

In this synthesis, we reviewed 65 studies involving elementary students (i.e., grades 1-5) identified with mathematics difficulty (MD) in which authors implemented a mathematics intervention. Of these studies, we identified 33 group designs, 9 quasi-experimental designs, and 23 single-case designs. We aimed to synthesize performance differences between students with MD with and without reading difficulty (RD). We identified three categories of students for analysis: Students with MD+RD, MD-alone, or MD-nonspecified (i.e., no reading information provided). Overall, 80% of studies included students with MD-nonspecified, and the interventions for these students demonstrated strong effects. For the limited number of studies with students with MD+RD or MD-alone, intervention effects were strong for students with MD+RD and variable for students with MD-alone. In the three studies directly comparing the performance of students with MD+RD versus MD-alone, we noted differential patterns of performance. To tailor interventions to student need, more research must be conducted to understand whether students with MD with variable reading profiles respond differentially to mathematics intervention.

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.

SRSD Fractions: Helping Students at Risk for Disabilities Add/Subtract Fractions With Unlike Denominators.

Many students fall below benchmarks in the area of fractions computation, particularly students with disabilities. Self-regulated strategy development (SRSD) is one strategy with proven effectiveness for improving outcomes for students with disabilities, although very few studies have applied SRSD to the area of mathematics. In this study, we used SRSD Fractions to teach adding and subtracting fractions with unlike denominators, simplifying fractions, and converting fractions to mixed numbers using the mnemonics FILMS, CUT, and EDIT. A researcher provided instruction in small groups to fifth-grade students at risk for disabilities. The results from use of a multiple-baseline-across-groups design suggest a functional relationship between SRSD Fractions and 8 fifth-grade students' digits correct on timed fraction probes. Results from treatment fidelity, social validity, and academic engagement during the intervention are also reported. We also discuss limitations and directions for future researchers.

Longitudinal Effects of Reading and/or Mathematical Difficulties: The Role of Special Education in Graduation From Upper Secondary Education.

This study explores the long-term effects of difficulties in reading and mathematical skills on educational achievement and successful graduation from secondary education as well as the role of special education in successful graduation. Study participants were all 16-year-old ninth graders from one Finnish city (N = 595; 302 females, 293 males) who were followed for 5 years after completing compulsory education. Students' reading and mathematical skills were measured at the end of compulsory education and their achieved grades in literacy and mathematics were received from their upper secondary schools. The overall results show that although part-time special education was available throughout both compulsory and upper secondary education, the negative longitudinal consequences of reading difficulties (RDs) and mathematical difficulties (MDs) on school achievement in literacy, mathematics, and rates of graduation can be seen. The regression path models were estimated separately for female and male students and show that among male students with RDs and MDs, the part-time special education that students received in Grades 7 to 9 was significantly related, but for Grades 10 to 11, this relationship is only significant among students with RDs. Moreover, low levels of school achievement in literacy among female students and in literacy and mathematics among male students significantly increased the likelihood of delayed graduation.

Cognitive Rehabilitation of Acquired Calculation Disturbances.

Acalculia is an acquired disorder in calculation abilities, usually associated with left posterior parietal damage. Two types of acalculic disorders are usually distinguished: (1) primary acalculia or anarithmetia, where the patient presents a loss of numerical concepts (difficulties are observed both in oral and written calculations), and (2) secondary acalculia due to a different disturbance in cognition and affecting mathematical abilities. Secondary acalculias are associated with aphasia, alexia, agraphia, executive function disorders, or visuospatial difficulties. This paper is a proposal for clinical intervention to rehabilitation of acquired primary and secondary acalculias.

Embedding Self-Regulation Instruction Within Fractions Intervention for Third Graders With Mathematics Difficulties.

The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering belief that intellectual and academic abilities can be developed) along with SR processes in which students set goals, self-monitor, and use strategies to engage motivationally, metacognitively, and behaviorally through challenging tasks. Students (n = 69) were randomly assigned to business-as-usual control and the two versions of fractions intervention. Multilevel models, accounting for the nested structure of the data, identified a moderation effect on fraction word problems: For students receiving fractions intervention with embedded SR, response to intervention was robust across the continuum of students' pretest word problem skill; by contrast, without SR, response to fractions intervention depended on students' pretest word problem skill. On the remaining outcomes, results reflected stronger outcomes when fractions intervention embedded SR instruction without moderation.

Student Practice Opportunities in Core Mathematics Instruction: Exploring for a Goldilocks Effect for Kindergartners With Mathematics Difficulties.

Opportunities for practice play a critical role in learning complex behaviors. In the context of explicit mathematics instruction, practice facilitates systematic opportunities for students with mathematics difficulties (MD) to learn new mathematics content and apply such knowledge and skills to novel mathematics problems. This study explored whether there is an optimal amount of student practice that teachers should provide in core mathematics instruction to maximize the mathematics achievement of kindergarten students with MD, a so called "Goldilocks effect," as opposed to simply "more is better." Results from observation data collected in a large-scale efficacy trial supported the latter rather than the former. Specifically, we found that three individual practice opportunities for every explicit teacher demonstration of mathematical content was associated with increased mathematics achievement for students with MD relative to fewer practice opportunities. Implications for facilitating frequent student practice opportunities during core mathematics instruction and designing professional development for teachers who work with students with MD are discussed.

Examining the Impact of Group Size on the Treatment Intensity of a Tier 2 Mathematics Intervention Within a Systematic Framework of Replication.

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities and the quality of explicit instruction served as treatment intensity metrics. A total of 465 kindergarten students with mathematics difficulties from 136 intervention groups participated. Results suggested comparable performances between the 2:1 and 5:1 intervention groups on six outcome measures. Observation data indicated that student practice differed by group size. Students in the 5:1 groups received more opportunities to practice with their peers, while students in the 2:1 groups participated in more frequent and higher quality individualized practice opportunities. Implications in terms of delivering Tier 2 interventions in small-group formats and engaging at-risk learners in meaningful practice opportunities are discussed.

Assessment and conceptual remediation of basic calculation skills in elementary school students.

The specific domain model for math disabilities postulates a core number deficit which presents a prime target for remedial interventions. This longitudinal study identified two groups of Grade 3 students based on their basic calculation abilities: students with persistent difficulties through Grade 4 (PD group) and students whose performance improved into the average range (IP group). Baseline data revealed a distinct cognitive profile for students in the PD group featuring predominant deficits in symbolic number processing. A conceptual intervention based on explicit teaching of basic arithmetic procedures was implemented when students attended Grade 5 or 6. Students in the PD group benefited more from the programme, especially in performing written calculations and in multiplication speed. Statement of contribution What is already known on this subject? Most interventions focus on young students' basic arithmetical skills to prevent serious math problems in future. Few interventions target older students who often face persistent math difficulties. These interventions are usually procedural and focus on age-appropriate math skills. What does this study add? A conceptual intervention was implemented to remediate basic calculation deficits at the end of elementary school. The aim was to help students compensate for their gaps in knowledge and motivate them to engage in math activities. Neuropsychological testing of arithmetic abilities revealed difficulties in symbolic number processing.

Fraction Intervention for Students With Mathematics Difficulties: Lessons Learned From Five Randomized Controlled Trials.

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on fractions magnitude understanding may improve learning. They then describe an intervention that relies strongly on this type of understanding about fractions instruction, and they provide an overview of the intervention's overall effects. This is followed by an overview of 5 intervention components for which the authors isolated effects. They conclude by discussing some of the lessons learned from this research program.

Enhancement of numeric cognition in children with low achievement in mathematic after a non-instrumental musical training.

Studies suggest that musical training enhances spatial-temporal reasoning and leads to greater learning of mathematical concepts. The aim of this prospective study was to verify the efficacy of a Non-Instrumental Musical Training (NIMT) on the Numerical Cognition systems in children with low achievement in math. For this purpose, we examined, with a cluster analysis, whether children with low scores on Numerical Cognition would be grouped in the same cluster at pre and post-NIMT. Participants were primary school children divided into two groups according to their scores on an Arithmetic test. Results with a specialized battery of Numerical Cognition revealed improvements for Cluster 2 (children with low achievement in math) especially for number production capacity compared to normative data. Besides, the number of children with low scores in Numerical Cognition decreased at post-NIMT. These findings suggest that NIMT enhances Numerical Cognition and seems to be a useful tool for rehabilitation of children with low achievement in math.

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students With Mathematics Problem-Solving Difficulties.

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.

Remediation for Students With Mathematics Difficulties: An Intervention Study in Middle Schools.

As empirical studies have consistently shown, low achievement in mathematics at the secondary level can often be traced to deficits in the understanding of certain basic arithmetic concepts taught in primary school. The present intervention study in middle schools evaluated whether such learning deficits can be reduced effectively and whether the type of instruction influences students' progress. The sample consisted of 123 students in 34 classes, split among one control group and two intervention groups: (a) small group instruction and (b) independent work partially integrated into regular classrooms. Over a period of 14 weeks, students were taught basic concepts, such as place value and basic operations. In addition, they practiced fact retrieval and counting (in groups). Multilevel regression analyses demonstrated that the interventions can be used to reduce given deficits.

Life on the Number Line: Routes to Understanding Fraction Magnitude for Students With Difficulties Learning Mathematics.

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.

Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children With Mathematics Difficulties.

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children ( N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

The Concept of Magnitude and What It Tells Us About How Struggling Students Learn Fractions.

This commentary summarizes emerging research into fractions instruction for students who are at risk for failure. Each of the three articles emphasizes a measure conception of fractions. Teaching fractions as measurement helps students learn the magnitude of rational numbers. However, measurement is only part of the way that students should conceptualize fractions. Instruction also needs to emphasize fractions as division. The article also draws attention to the teaching qualifications of those who typically instruct at-risk students in Tier 2 and 3 settings. More often than not, these individuals lack the pedagogical content knowledge needed to adapt instruction and address student misconceptions. This is a critical issue going forward as the field attempts to balance procedural understanding with key underlying fractional ideas such a measurement and division.

The Effects of a Tier 3 Intervention on the Mathematics Performance of Second Grade Students With Severe Mathematics Difficulties.

The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and procedures, which are the foundation for later mathematics success. In the previous year, 12 participants had experienced two doses (first and second semesters) of a Tier 2 intervention. In second grade, the participants continued to demonstrate low performance, falling below the 10th percentile on a researcher-designed universal screener and below the 16th percentile on a distal measure, thus qualifying for the intensive intervention. A project interventionist, who met with the students 5 days a week for 10 weeks (9 weeks for one group), conducted the intensive intervention. The intervention employed more intensive instructional design features than the previous Tier 2 secondary instruction, and also included weekly games to reinforce concepts and skills from the lessons. Spring results showed significantly improved mathematics performance (scoring at or above the 25th percentile) for most of the students, thus making them eligible to exit the Tier 3 intervention.

Building Knowledge Structures by Testing Helps Children With Mathematical Learning Difficulty.

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD.