Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics

Learning disabilities: Developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

Predicting maths anxiety from mathematical achievement across the transition from primary to secondary education

The primary- to secondary-education transition is a substantive life event for many children. The transition can be associated with changes in the developmental trajectories of both emotional health and academic achievement. The current study looked at whether the trajectory of mathematical attainment and emotional health (anxiety) across this transition predicted later maths anxiety. A secondary analysis of data from the Twin Early Development Study (TEDS) was performed. The statistical models were fit on the 753 participants (one from each twin pair) for which there were measures of mathematical performance across the primary- to secondary-education transition and maths anxiety at age 18. Two multi-level growth models were fit predicting mathematical attainment and anxiety over the primary- to secondary-education transition. The intercepts and slopes for each child were extracted from these models and used as predictors of subsequent maths anxiety at age 18. These effects were adjusted for biological sex, socio-economic status, verbal cognitive ability and general anxiety. Maths anxiety at age 18 was significantly predicted by both pre-transition levels of anxiety and mathematical attainment and their rate of change across the primary- to secondary-education transition. However, the effects were small, suggesting that theories of maths anxiety may have overplayed the role of prior mathematical attainment and general anxiety.

Executive Functions and Visual-Spatial Skills Predict Mathematical Achievement: Asymmetrical Associations Across Age

Children's mathematical achievement depends on their domain-specific abilities and their domain-general skills such as executive functions (EFs) and visual-spatial skills (VSS). Research indicates that these two domain-general skills predict mathematical achievement. However, it is unclear whether these skills are differently associated with mathematical achievement across a large age range. The current cross-sectional study answered this question using a large, representative sample aged 5-20 years (N = 1754). EFs, VSS, and mathematical achievement were assessed using the Intelligence and Development Scales-2. Hierarchical regression analyses were computed with EFs and VSS as predictor variables and mathematical achievement as dependent variable. We examined (non-) linear effects and interactions of EFs and VSS with age. Results indicated that EFs and VSS were distinctly associated with mathematical achievement above and beyond effects of age, sex, maternal education, and verbal reasoning. Effects of EFs were linear and age-invariant. Effects of VSS were curvilinear and stronger in adolescents than in children. Our results indicated that EFs and VSS related differently to mathematical proficiency across age, suggesting a varying impact on mathematics across age.

Improving the Mathematics Performance of Second-Grade Students with Mathematics Difficulties through an Early Numeracy Intervention

The purpose of this study was to determine the effects of an early numeracy Tier 2 intervention on the mathematics performance of second-grade students with persistent mathematics difficulties. Whole number content and instructional design features were used to boost performance in second-grade early numeracy concepts and skills. Researchers employed a pretest-posttest control group design with randomized assignment of 83 students to the treatment condition and 38 students to the comparison condition. The research team’s mathematics interventionists delivered instruction four days per week for 20 weeks to small groups of second-grade students who were identified with persistent mathematics difficulties. Proximal and distal measures were used to determine the effects of the intervention. Findings showed that students in the treatment group outperformed students in the comparison group on the proximal measure of mathematics performance. There were no differences between groups on the problem-solving measures.

Assessing Mathematical School Readiness

Early math skills matter for later formal mathematical performances, academic and professional success. Accordingly, it is important to accurately assess mathematical school readiness (MSR) at the beginning of elementary school. This would help identifying children who are at risk of encountering difficulties in math and then stimulate their acquisition of mathematical skills as soon as possible. In the present study, we present a new test that allows professionals working with children (e.g., teachers, school psychologists, speech therapists, and school doctors) to assess children’s MSR when they enter formal schooling in a simple, rapid and efficient manner. 346 children were assessed at the beginning of 1st Grade (6-to-7-year-olds) with a collective test assessing early mathematical abilities (T1). In addition, children’s math skills were evaluated with classical curriculum math tests at T1 and a year later, in 2nd Grade (T2, 7-to-8-year-olds). After assessing internal consistency, three tasks were retained for the final version of the MSR test. Test performance confirmed to be essentially unidimensional and systematically related to the scores children obtained in classical tests in 1st and 2nd Grade. By using the present MSR test, it is possible to identify pupils at risk of developing low math skills right from the start of formal schooling in 1st Grade. Such a tool is needed, as children’s level in math at school beginning (or school readiness) is known to be foundational for their future academic and professional carrier.

The Role of Learning Difficulties in Adolescents' Academic Emotions and Academic Achievement

The present study examines associations between learning difficulties (LD), academic emotions, and academic achievement among 845 Grade 6 adolescents (455 girls, 390 boys). Reading difficulties (RD) and math difficulties (MD) were identified based on tested reading and math skills in the fall semester of Grade 6. At this time, the students also rated their hope, enjoyment, and anxiety regarding literacy and math. Information on students' achievement in literacy and math, as well as their overall academic achievement, was gathered using questionnaires in both the fall and spring semesters of Grade 6. The results show, first, that students with RD had lower hope and higher anxiety toward reading than those without RD. Also, students with MD reported lower enjoyment, lower hope, and higher anxiety than those without MD. Furthermore, the results show that hope partly played a mediating role between LD and academic achievement in both the literacy and math domains. In addition, enjoyment played a mediating role in the math domain. The present study's results indicate that subject-specific academic emotions should be taken into account when considering relations between LD and academic achievement.

Contributions of Basic Cognitive Processing to Chinese Reading: The Mediation Effect of Basic Language Processing

Prior research has mostly focused on either basic language or basic cognitive precursors of reading development, but relatively little is known about their relative importance for reading, especially for Chinese beginning readers. The present study examined whether and how basic cognitive processing (executive function, attention, and visual-spatial perception) and basic language processing (phonological awareness, morphological awareness, orthographic awareness, and RAN) measured at kindergarten influence Chinese character reading and reading comprehension in the first grade. Results showed that basic language abilities including morphological awareness and rapid automatized naming predicted later Chinese character reading. Only one basic cognitive skill, sustained attention, predicted later reading comprehension. Mediation analysis showed that the overall effects of basic cognitive skills on later character reading and reading comprehension were mediated by basic language skills. These findings supported an integration reading model for early Chinese reading and basic language processing at kindergarten plays an important role in explaining the relation between basic cognitive processing and grade one reading performance.

Developmental influence of unconjugated hyperbilirubinemia and neurobehavioral disorders

Bilirubin-induced brain injury in the neonatal period has detrimental effects on neurodevelopment that persist into childhood and adulthood, contributing to childhood developmental disorders. Unconjugated bilirubin is a potent antioxidant that may be useful for protecting against oxidative injuries, but it becomes a potent neurotoxin once it crosses the blood brain barrier. Because bilirubin toxicity involves a myriad of pathological mechanisms, can damage most types of brain cells, and affects brain circuits or loops that influence cognition, learning, behavior, sensory, and language, the clinical effects of bilirubin-induced neurotoxicity are likely to be manifold. One possible effect that several experts have identified is bilirubin-induced neurological dysfunction (subtle kernicterus). However, the underlying biological mechanisms or pathways by which subtle kernicterus could lead to developmental disorders has not been elucidated previously. Our aim in this review is to describe a spectrum of developmental disorders that may reflect subtle kernicterus and outline plausible biological mechanisms for this possible association. We review existing evidence that support or refute the association between unconjugated hyperbilirubinemia and developmental disorders, and limitations associated with these studies.

Associative Cognitive Factors of Math Problems in Students Diagnosed With Developmental Dyscalculia

The Dutch protocol, 'Dyscalculia: Diagnostics for Behavioral Professionals' (DDBP protocol; Van Luit et al., 2014), describes how behavioral experts can examine whether a student has developmental dyscalculia (DD), based on three criteria: severity, discrepancy, and resistance. In addition to distinguishing the criteria necessary for diagnosis, the protocol provides guidance on formulating hypotheses by describing and operationalising four possible associative cognitive factors of math problems: planning skills, naming speed, short-term and/or working memory, and attention. The current exploratory and descriptive research aims to describe the frequency of these four primary associative cognitive factors in students with DD from the Netherlands. Descriptive data from 84 students aged 8-18 years showed that deficits in naming speed (in particular, in naming numbers) were the most frequent explanation of math problems in children with DD, followed by deficits in short-term/working memory and planning skills. Deficits in attention were the least frequent. The findings are explained in light of current literature, and suggestions for follow-up research are presented.

Individuality in the Early Number Skill Components Underlying Basic Arithmetic Skills

Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age: 75 months) modeled latent performance-level profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), near-average-performing (33%), and high-average-performing children (45%). Although the differences between the groups were statistically significant in all three number skill components and in basic arithmetic, the poorest-performing children seemed to have serious difficulties in accessing the semantic meaning of symbolic numbers that was required in the number comparison and mapping tasks in this study. Interestingly, the tasks demanding processing between quantities and symbols also most differentiated the poorest-performing children from the low-performing children. Due to remarkable and stable individual differences in early number skill components, the findings suggest systematic support and progress monitoring practices in preeducational settings to diminish and avoid potential difficulties in arithmetic and mathematics in general.

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.

Dyslexia and dyscalculia are characterized by common visual perception deficits

A number of studies have investigated the cognitive deficits underlying dyslexia and dyscalculia. Yet, it remains unclear as to whether dyslexia and dyscalculia are associated with the common visual perception deficits. The current investigation analyzed cognitive performance in children with dyslexia, dyscalculia, comorbidity, and typically developing subjects. The results showed that children with dyslexia, dyscalculia and comorbidity exhibited common deficits in numerosity processing and visual perception. Furthermore, visual perception deficits accounted for deficits in numerosity processing in all three groups. The results suggest that visual perception deficits are a common cognitive deficit underlying both developmental dyslexia and dyscalculia.

Raising Early Achievement in Math With Interactive Apps: A Randomized Control Trial

Improving provision and raising achievement in early math for young children is of national importance. Child-centered apps offer an opportunity to develop strong foundations in learning math as they deliver one-to-one instruction. Reported here is the first pupil-level randomized control trial in the United Kingdom of interactive math apps designed for early years education, with 389 children aged 4–5 years. The original and rigorous research design disentangled the impact of the math apps as a form of quality math instruction from additional exposure to math. It was predicted that using the apps would increase math achievement when implemented by teachers in addition to standard math activities (treatment) or instead of a regular small group-based math activity (time-equivalent treatment) compared with standard math practice only (control). After a 12-week intervention period, results showed significantly greater math learning gains for both forms of app implementation compared with standard math practice. The math apps supported targeted basic facts and concepts and generalized to higher-level math reasoning and problem solving skills. There were no significant differences between the 2 forms of math app implementation, suggesting the math apps can be implemented in a well-balanced curriculum. Features of the interactive apps, which are grounded in instructional psychology and combine aspects of direct instruction with play, may account for the observed learning gains. These novel results suggest that structured, content-rich, interactive apps can provide a vehicle for efficiently delivering high-quality math instruction for all pupils in a classroom context and can effectively raise achievement in early math.

In a pupil-level randomized control trial we evaluated the effectiveness of a new math app intervention to support young children’s early math development. The results showed children using the math apps either as a supplementary intervention or instead of a small group teacher-led math activity made significant learning gains in comparison with children receiving standard practice only. This study suggests high-quality math apps can be used as a form of quality math instruction in a well-rounded curriculum to raise achievement in early math for all children.

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.

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement.

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.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Cognitive Profiles Associated With Responsiveness to Fraction Intervention

This study examined differences in cognitive processing between 4^th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or inadequate responders, using as the cut-point the control-group mean on pre-to-post improvement on the relevant measure. Between-group differences identified reasoning, concept formation, and listening comprehension related to all 3 fraction outcomes. On the number-line outcome, within-group profile analysis indicated that inadequate responders experienced low reasoning ability relative to their other forms of cognitive processing.

Identifying the nature of impairments in executive functioning and working memory of children with severe difficulties in arithmetic

An age-matched achievement-matched design was used to examine whether the executive functioning and working memory impairments exhibited by children with severe difficulties in arithmetic (SDA) are better viewed as developmental lags or as cognitive deficits. Three groups of children were included: 20 SDA children, 20 typically achieving children (CM) matched in chronological age with the SDA children, and 20 younger typically achieving children (AM) matched in achievement with the SDA group. While children with SDA did not exhibit impairments in color-word inhibition and verbal working memory, they did demonstrate impairments in shifting, quantity-digits inhibition, and visuospatial working memory. As children with SDA did not perform more poorly than their AM counterparts on any of these tasks, impairments in specific areas of executive functioning and working memory appear to reflect developmental lags rather than cognitive deficits.

Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance

In this chapter, we address one potentially overlooked component of the relation between executive function (EF) skills and early mathematics, a relation for which there is widespread empirical support. Evidence for this relation has, thus far, been largely correlational. Here we emphasize that because positive correlations do not guarantee concordance among all members of a sample or population, a small but meaningful number of children may either fare well in mathematics despite poor EF skills, or may have strong EF skills despite weak mathematics skills. We propose that attention to different profiles of discordance for EF and mathematics may help identify individualized learning needs for students at risk for mathematics difficulties and disabilities.

How Is Working Memory Training Likely to Influence Academic Performance? Current Evidence and Methodological Considerations

Working memory (WM) is one of our core cognitive functions, allowing us to keep information in mind for shorter periods of time and then work with this information. It is the gateway that information has to pass in order to be processed consciously. A well-functioning WM is therefore crucial for a number of everyday activities including learning and academic performance (Gathercole et al., 2003; Bull et al., 2008), which is the focus of this review. Specifically, we will review the research investigating whether improving WM capacity using Cogmed WM training can lead to improvements on academic performance. Emphasis is given to reviewing the theoretical principles upon which such investigations rely, in particular the complex relation between WM and mathematical and reading abilities during development and how these are likely to be influenced by training. We suggest two possible routes in which training can influence academic performance, one through an effect on learning capacity which would thus be evident with time and education, and one through an immediate effect on performance on reading and mathematical tasks. Based on the theoretical complexity described we highlight some methodological issues that are important to take into consideration when designing and interpreting research on WM training and academic performance, but that are nonetheless often overlooked in the current research literature. Finally, we will provide some suggestions for future research for advancing the understanding of WM training and its potential role in supporting academic attainment.

Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children

Rapid automatized naming (RAN) has been found to predict mathematics. However, the nature of their relationship remains unclear. Thus, the purpose of this study was twofold: (a) to examine how RAN (numeric and non-numeric) predicts a subdomain of mathematics (arithmetic fluency) and (b) to examine what processing skills may account for the RAN-arithmetic fluency relationship. A total of 160 third-year kindergarten Chinese children (83 boys and 77 girls, mean age=5.11years) were assessed on RAN (colors, objects, digits, and dice), nonverbal IQ, visual-verbal paired associate learning, phonological awareness, short-term memory, speed of processing, approximate number system acuity, and arithmetic fluency (addition and subtraction). The results indicated first that RAN was a significant correlate of arithmetic fluency and the correlations did not vary as a function of type of RAN or arithmetic fluency tasks. In addition, RAN continued to predict addition and subtraction fluency even after controlling for all other processing skills. Taken together, these findings challenge the existing theoretical accounts of the RAN-arithmetic fluency relationship and suggest that, similar to reading fluency, multiple processes underlie the RAN-arithmetic fluency relationship.

Predictive model for early math skills based on structural equations

Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short-term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short-term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs.

Polyunsaturated fatty acids (PUFAs) for children with specific learning disorders

BACKGROUND

About 5% of school children have a specific learning disorder, defined as unexpected failure to acquire adequate abilities in reading, writing or mathematics that is not a result of reduced intellectual ability, inadequate teaching or social deprivation. Of these events, 80% are reading disorders. Polyunsaturated fatty acids (PUFAs), in particular, omega-3 and omega-6 fatty acids, which normally are abundant in the brain and in the retina, are important for learning. Some children with specific learning disorders have been found to be deficient in these PUFAs, and it is argued that supplementation of PUFAs may help these children improve their learning abilities.

OBJECTIVES

1. To assess effects on learning outcomes of supplementation of polyunsaturated fatty acids (PUFAs) for children with specific learning disorders.2. To determine whether adverse effects of supplementation of PUFAs are reported in these children.

SEARCH METHODS

In November 2015, we searched CENTRAL, Ovid MEDLINE, Embase, PsycINFO, 10 other databases and two trials registers. We also searched the reference lists of relevant articles.

SELECTION CRITERIA

Randomised controlled trials (RCTs) or quasi-RCTs comparing PUFAs with placebo or no treatment in children younger than 18 years with specific learning disabilities, as diagnosed in accordance with the fifth (or earlier) edition of theDiagnostic and Statistical Manual of Mental Disorders (DSM-5), or the 10th (or earlier) revision of the International Classification of Diseases (ICD-10) or equivalent criteria. We included children with coexisting developmental disorders such as attention deficit hyperactivity disorder (ADHD) or autism.

DATA COLLECTION AND ANALYSIS

Two review authors (MLT and KHT) independently screened the titles and abstracts of articles identified by the search and eliminated all studies that did not meet the inclusion criteria. We contacted study authors to ask for missing information and clarification, when needed. We used the GRADE approach to assess the quality of evidence.

MAIN RESULTS

Two small studies involving 116 children, mainly boys between 10 and 18 years of age, met the inclusion criteria. One study was conducted in a school setting, the other at a specialised clinic. Both studies used three months of a combination of omega-3 and omega-6 supplements as the intervention compared with placebo. Although both studies had generally low risk of bias, we judged the risk of reporting bias as unclear in one study, and as high in the other study. In addition, one of the studies was funded by industry and reported active company involvement in the study.None of the studies reported data on the primary outcomes of reading, writing, spelling and mathematics scores, as assessed by standardised tests.Evidence of low quality indicates that supplementation of PUFAs did not increase the risk of gastrointestinal disturbances (risk ratio 1.43, 95% confidence interval 0.25 to 8.15; two studies, 116 children). Investigators reported no other adverse effects.Both studies reported attention deficit hyperactivity disorder (ADHD)-related behaviour outcomes. We were unable to combine the results in a meta-analysis because one study reported findings as a continuous outcome, and the other as a dichotomous outcome. No other secondary outcomes were reported.We excluded one study because it used a cointervention (carnosine), and five other studies because they did not provide a robust diagnosis of a specific learning disorder. We identified one ongoing study and found three studies awaiting classification.

AUTHORS' CONCLUSIONS

Evidence is insufficient to permit any conclusions about the effect of PUFAs on the learning abilities of children with specific learning disorders. Well-designed RCTs with clearly defined populations of children with specific learning disorders who have been diagnosed by standardised diagnostic criteria are needed.

Why Learning Common Fractions Is Uncommonly Difficult: Unique Challenges Faced by Students With Mathematical Disabilities

In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students with math disabilities exhibit a significant delay or deficit in the numerical transcoding of decimal fractions, and I further maintain that they may face unique challenges in developing the ability to effectively translate between different types of fractions and other rational number notational formats-what I call conceptual transcoding. I also argue that characterizing this level of comprehensive understanding of rational numbers as rational number sense is irrational, as it misrepresents this flexible and adaptive collection of skills as a biologically based percept rather than a convergence of higher-order competencies that require intensive, formal instruction.

Untangling the Contribution of the Subcomponents of Working Memory to Mathematical Proficiency as Measured by the National Tests: A Study among Swedish Third Graders

The aim with the present study was to examine the relationship between the subcomponents in working memory (WM) and mathematical performance, as measured by the National tests in a sample of 597 Swedish third-grade pupils. In line with compelling evidence of other studies, individual differences in WM capacity significantly predicted mathematical performance. Dividing the sample into four groups, based on their mathematical performance, revealed that mathematical ability can be conceptualized in terms of different WM profiles. Pupils categorized as High-math performers particularly differed from the other three groups in having a significant higher phonological ability. In contrast, pupils categorized as Low-math performers were particularly characterized by having a significant lower visuo-spatial ability. Findings suggest that it is important for educators to recognize and acknowledge individual differences in WM to support mathematical achievement at an individual level.

Effects of Extreme Prematurity on Numerical Skills and Executive Function in Kindergarten Children: An Application of Partially Ordered Classification Modeling

Although mathematics disabilities (MD) are common in extremely preterm/extremely low birth weight (EPT/ELBW) children, little is known about the nature of these problems. In this study partially ordered set (POSET) models were applied to classify 140 EPT/ELBW kindergarten children (gestational age <28 weeks and/or birth weight <1000 g) and 110 normal birth weight (NBW) controls into profiles of numerical and cognitive skills. Models based on five numerical skills and five executive function and processing speed skills provided a good fit to performance data. The EPT/ELBW group had poorer skills in all areas than NBW controls but the models also revealed substantial individual variability in skill profiles. Weaknesses in executive function were associated with poorer mastery of numerical skills. The findings illustrate the applicability of POSET models to research on MD and suggest distinct types of early numerical deficits in EPT/ELBW children that are related to their impairments in executive function.

Who Is At Risk for Persistent Mathematics Difficulties in the United States?

We analyzed two nationally representative, longitudinal data sets of U.S. children to identify risk factors for persistent mathematics difficulties (PMD). Results indicated that children from low socioeconomic households are at elevated risk of PMD at 48 and 60 months of age, as are children with cognitive delays, identified developmental delays or disabilities, and vocabulary difficulties. In contrast, children attending preschool either in Head Start or non-Head Start classrooms are at initially lower risk of PMD. Kindergarten-aged children experiencing either low socioeconomic status or mathematics difficulties are at greatest risk for PMD across third, fifth, and eighth grades. Also at risk for PMD between third and eighth grades are children displaying reading difficulties or inattention and other learning-related behaviors problems, children with identified disabilities, and those who are retained. Educationally relevant and potentially malleable factors for decreasing young children's risk for PMD may include increasing children's access to preschool, decreasing their risk of experiencing vocabulary or reading difficulties, and avoiding use of grade retention.

Clinical and Cognitive Characteristics Associated with Mathematics Problem Solving in Adolescents with Autism Spectrum Disorder

Mathematics achievement in autism spectrum disorder (ASD) has been understudied. However, the ability to solve applied math problems is associated with academic achievement, everyday problem-solving abilities, and vocational outcomes. The paucity of research on math achievement in ASD may be partly explained by the widely-held belief that most individuals with ASD are mathematically gifted, despite emerging evidence to the contrary. The purpose of the study was twofold: to assess the relative proportions of youth with ASD who demonstrate giftedness versus disability on applied math problems, and to examine which cognitive (i.e., perceptual reasoning, verbal ability, working memory) and clinical (i.e., test anxiety) characteristics best predict achievement on applied math problems in ASD relative to typically developing peers. Twenty-seven high-functioning adolescents with ASD and 27 age- and Full Scale IQ-matched typically developing controls were assessed on standardized measures of math problem solving, perceptual reasoning, verbal ability, and test anxiety. Results indicated that 22% of the ASD sample evidenced a mathematics learning disability, while only 4% exhibited mathematical giftedness. The parsimonious linear regression model revealed that the strongest predictor of math problem solving was perceptual reasoning, followed by verbal ability and test anxiety, then diagnosis of ASD. These results inform our theories of math ability in ASD and highlight possible targets of intervention for students with ASD struggling with mathematics.

Executive Functioning Deficits Increase Kindergarten Children's Risk for Reading and Mathematics Difficulties in First Grade

Whether executive functioning deficits result in children experiencing learning difficulties is presently unclear. Yet evidence for these hypothesized causal relations has many implications for early intervention design and delivery. We used a multi-year panel design, multiple criterion and predictor variable measures, extensive statistical control for potential confounds including autoregressive prior histories of both reading and mathematics difficulties, and additional epidemiological methods to preliminarily examine these hypothesized relations. Results from multivariate logistic regression analyses of a nationally representative and longitudinal sample of 18,080 children (i.e., the Early Childhood Longitudinal Study-Kindergarten Cohort of 2011, or ECLS-K: 2011) indicated that working memory and, separately, cognitive flexibility deficits uniquely increased kindergarten children's risk of experiencing reading as well as mathematics difficulties in first grade. The risks associated with working memory deficits were particularly strong. Experimentally-evaluated, multi-component interventions designed to help young children with reading or mathematics difficulties may also need to remediate early deficits in executive function, particularly in working memory.

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.

Which kindergarten children are at greatest risk for attention-deficit/hyperactivity and conduct disorder symptomatology as adolescents?

We sought to identify which kindergarten children are simultaneously at risk of moderate or severe symptomatology in both attention-deficit/hyperactivity disorder (ADHD) and conduct disorder (CD) as adolescents. These risk factor estimates have not been previously available. We conducted multinomial logistic regression analyses of multiinformant ratings by the end of middle school of a population-based, longitudinal sample of children followed from kindergarten to eighth grade (N = 7,456). Kindergarten children from low SES households, those raised by mothers with depressive symptoms or experiencing emotional problems or substance abuse, or those who were punished by spanking were significantly more likely to later display severe levels of ADHD-CD symptomatology in eighth grade. Kindergarten children frequently engaging in ADHD-CD-type behaviors were more likely to later experience both moderate (covariate adjusted OR = 2.37) and severe (covariate adjusted OR = 3.63) ADHD-CD symptomatology. Low academic achievement uniquely increased the risk of both moderate and severe symptomatology (adjusted OR range = 1.7 to 2.24). The results should guide early screening and school-based intervention efforts for ADHD-CD. Reducing children's risk for adolescent ADHD-CD symptomatology may require remediating low behavioral and academic functioning by the end of kindergarten. When these 2 modifiable factors occur together they increase kindergarten children's odds of experiencing severe ADHD-CD symptomatology in eighth grade by a multiplicative factor of 8.1.

On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies

Even at young ages, children self-report experiencing math anxiety, which negatively relates to their math achievement. Leveraging a large dataset of first and second grade students' math achievement scores, math problem solving strategies, and math attitudes, we explored the possibility that children's math anxiety (i.e., a fear or apprehension about math) negatively relates to their use of more advanced problem solving strategies, which in turn relates to their math achievement. Our results confirm our hypothesis and, moreover, demonstrate that the relation between math anxiety and math problem solving strategies is strongest in children with the highest working memory capacity. Ironically, children who have the highest cognitive capacity avoid using advanced problem solving strategies when they are high in math anxiety and, as a result, underperform in math compared with their lower working memory peers.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1^st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1^st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ESs = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

Program of arithmetic improvement by means of cognitive enhancement: an intervention in children with special educational needs

This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed.

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures.