The role of executive attention in the acquisition of mathematical skills for children in Grades 2 through 4

Children's arithmetic strategy use trajectories: Exploring the roles of executive functions and sociodemographic characteristics

Although young children often use counting to solve arithmetic problems, over time they move toward more efficient strategies such as direct retrieval and decomposition. Strategy selection has longitudinal associations with children's math achievement. Existing research indicates that children's executive functions (EFs) support inhibiting unnecessary strategies and adaptively switching between strategies. Moreover, research has documented gender differences in strategy use, but prior literature does not account for the contributions of socioeconomic factors in children's strategy trajectories. The current study examined the unique roles of preschoolers' EFs, gender, household income, and maternal education for the trajectories of strategy use on arithmetic problems across early elementary school. Preschoolers' EFs were assessed at 5 years 3 months of age, and children completed addition and subtraction problems in first, second, and third grades. Children's strategies were categorized as retrieval, counting, decomposition, and sign flipping. Results indicated that children with higher EFs were more likely to use retrieval and sign flipping in first grade compared with children with lower EFs, and this advantage was maintained into third grade. Boys used more retrieval and decomposition, whereas girls used more counting strategies, in first grade, and this pattern held longitudinally. Finally, children whose mothers had more years of education were likely to use decomposition and sign flipping in first grade, with an advantage through third grade. Overall, the current study sheds light on how cognitive and sociodemographic factors differentially contribute to children's accurate strategy use, with implications for how to best target early interventions to support children's math achievement.

Developmental Dyscalculia in Relation to Individual Differences in Mathematical Abilities

There is still much debate about the exact nature and frequency of developmental dyscalculia, and about how it should be defined. This article examines several key questions in turn: Is developmental dyscalculia a distinct disorder, or should it be seen as the lower end of a continuum-or possibly more than one continuum-of numerical ability? Do individuals with developmental dyscalculia show atypical brain structure or function? Does the study of acquired dyscalculia have anything to teach us about developmental dyscalculia? In studying dyscalculia, should we look less at arithmetical ability as a single entity, and more at separable components of arithmetical ability? How heterogeneous is developmental dyscalculia, and how important is it to study individual profiles? To what extent is developmental dyscalculia influenced by domain-specific versus domain-general abilities? The conclusion is that, though a significant amount has been discovered through existing research, and though this has some important implications for screening and diagnosis of dyscalculia, there is much more research that still needs to be conducted if we are to answer all of these questions fully. In particular, the study of developmental dyscalculia must be more integrated with the study of individual differences in mathematics in the population as a whole.

Motor activities to improve maths performance in pre-school children with typical development

Poor maths skills are associated with negative outcomes throughout life, such as lower academic qualifications, decreased professional success and socio-economic results. Mathematical skills emerge continuously throughout childhood and those that children acquire in pre-school are crucial for activities that support analytical thinking, problem-solving and reasoning and argumentation skills. Many of these activities are related to motor skills, since certain cognitive and motor areas of the brain are activated simultaneously when solving maths problems. Of all motor skills, visuomotor integration skills have been documented as those that are most consistently positively and significantly associated with maths performance in pre-school children. These skills are influenced by visual perception (spatial and attention skills), fine motor coordination and gross motor skills. Early intervention can improve visuomotor integration skills in pre-school children. Of all skills that make up visuomotor integration, spatial skills, in addition to being the first skills to influence numerical knowledge and the recognition of geometric shapes, are also those skills that form part of the majority of programs and activities to be worked on with pre-school children for the development of mathematical concepts. However, most intervention programs or activities to develop spatial skills are carried out in the classroom, usually through activities involving handling small objects. In this sense and given the significant association between visuomotor integration skills and gross motor skills, the main objective of this study was to list a set of activities to develop spatial skills, with a strong involvement of gross motor skills, in a classroom, playground or home context.

Far Transfer Effects of Trainings on Executive Functions in Neurodevelopmental Disorders: A Systematic Review and Metanalysis

Executive Functions are a set of interrelated, top-down processes essential for adaptive goal-directed behaviour, frequently impaired across different neurodevelopmental disorders with variable degrees of severity. Many executive-function-training studies in children with neurodevelopmental disorders have focused on near effects, investigating post-treatment improvements on directly trained processes, while enhancements of skills not directly trained, defined as far effects, are less considered, albeit these could be extremely relevant for reducing the negative impact of a disorder's core symptomatology. This systematic review and metanalysis aims to investigate the far effect outcomes after EF training in children with different types of neurodevelopmental disorders. 17 studies met the inclusion criteria for the systematic review, while 15 studies were selected in the metanalysis. An overall statistically significant effect size was found in the majority of far effect outcome measures considered in the studies. In particular, trainings on executive functions determine significant far effects on daily life functioning (0.46, 95% CI: [0.05-0.87]) and clinical symptoms (0.33, 95% CI: [0.15-0.51]). Despite a high variability of the results, intensity, frequency and the laboratory/life contexts dimension seem to be the most influential variables in determining far effects. This systematic review and metanalysis highlights the need to measure far effects of executive function training in neurodevelopmental disorders, selecting treatments not only on directly targeted processes, but also according to far impacts on the functional weakness of the disorder.

Attending to what's important: what heat maps may reveal about attention, inhibitory control, and fraction arithmetic performance

Math proficiency is an important predictor of educational attainment and life success. However, developing mathematical competency is challenging, and some content (e.g., fractions) can be enigmatic. Numerous factors are suspected to influence math performance, including strategy knowledge, attention, and executive functions. In two online studies, we investigated the relationship between adults' fraction arithmetic performance, confidence judgments, inhibitory control (a component of executive functions), and attention to strategy-relevant fraction components. We explored the utility of heat maps (based on mouse clicks) to measure adults' attention to strategy-relevant fraction arithmetic components (operationalized according to each mathematical operation). In Study 1, attending to strategy-relevant fraction components was correlated with inhibitory control, but this finding did not replicate in Study 2. Across both studies, inhibitory control and attention to strategy-relevant fraction components were correlated with arithmetic accuracy. Intraindividual variability in participants' attention to strategy-relevant fraction components was also found. Our findings suggest that heat map questions may be a viable alternative to assess participants' attention during fraction tasks and that attention to specific fraction-arithmetic problem features is related to problem-solving accuracy.

The Longitudinal Contributions of Preschool Executive Functions and Early Math Abilities to Arithmetic Skills in Elementary School

Executive functions (EFs) are linked to children's overall math performance, although few studies have considered the joint role of prior math abilities for specific math subskills, such as arithmetic. The current study examined the longitudinal contributions of preschool EFs and early math abilities to children's accuracy and reaction time on arithmetic problems. Two hundred and eighty-three children completed EF and numeracy assessments at 5.25 years old. Children completed an arithmetic problem task in first (Mage = 7.14), second (Mage = 8.09), and third grade (Mage = 9.08). Results indicated that preschool EFs and math abilities are uniquely linked to children's accuracy and reaction time at age 7, whereas preschool EFs alone continue to predict accuracy at age 8 and reaction time at age 9, even after accounting for intervening arithmetic performance. The study highlights the sustained, unique importance of early EFs for children's arithmetic acquisition.

The componential nature of arithmetical cognition: some important questions

Research on typically developing children and adults and people with developmental and acquired dyscalculia converges in indicating that arithmetical ability is not unitary but is made up of many different components. Categories of components include non-symbolic quantity representation and processing; symbolic quantity representation and processing; counting procedures and principles; arithmetic operations; arithmetical knowledge and understanding; multiple forms and applications of conceptual knowledge of arithmetic; and domain-general abilities such as attention, executive functions and working memory. There is much evidence that different components can and often do show considerable functional independence, not only in developmental and acquired dyscalculia, but in typically achieving children and adults. At the same time, it is possible to find complex interactions and bidirectional relationships between the different components, including between domain-specific and apparently domain-general abilities. There is a great deal that still needs to be discovered. In particular, we need to learn more about the origins in infancy of subitizing and approximate magnitude comparison, the extent to which these interact, the extent to which they may be further divisible, and the extent and ways in which they themselves may develop with age and the extent to which they may influence later-developing components. There also needs to be a lot more research on exactly how domain-general and domain-specific abilities contribute to mathematical development, and how they interact with one another.

Monolingual and bilingual children's performance on arithmetic fluency varies by language fluency

Research has demonstrated that learning two or more languages during development (i.e., becoming bilingual) shapes children's cognition in myriad ways. However, because such studies have largely been conducted using laboratory experiments, it is unclear how bilingualism may modulate more naturalistic cognitive skills such as arithmetic fluency. Moreover, how the relationship between speaking two (or more) languages and arithmetic varies with language fluency-specifically, the degree of bilingualism-has been understudied. Therefore, this study examined third- to fifth-grade monolingual (n = 70) and bilingual (n = 51) children's performance on an arithmetic fluency task. Monolinguals' and bilinguals' performance on the arithmetic fluency task did not differ. However, individual differences in the relation between children's arithmetic fluency and their language fluency were found, suggesting that bilingual children's skill in their nondominant language was associated with arithmetic fluency. These findings point to the importance of examining individual differences in language fluency among bilinguals to understand how bilingualism may shape cognitive skills.

The association between working memory and mathematical problem solving: A three-level meta-analysis

Although working memory (WM) is an important factor in mathematical problem solving (MPS), it remains unclear how well WM relates to MPS. Thus, we aimed to determine this relationship by using a meta-analysis. We searched electronic databases for studies published between 2000 and 2020 and established operational criteria. We conducted Egger’s regression tests and created funnel plots to test for publication bias. Finally, a three-level meta-analytic model analysis of data from 130 studies involving 43,938 participants and 1,355 effect sizes revealed a moderate relationship between WM and MPS (r = 0.280, 95% CI = [0.263, 0.314]). Moreover, moderator analyses showed that: (1) dressed-up word problems were more strongly tied to WM than to intra-mathematical problems; (2) the central executive function showed the strongest relation with MPS, whereas the phonological loop had the weakest; (3) gender ratio had significant moderating effects; and (4) some of the above-mentioned significant moderating effects were unique after controlling for other factors. Implications for research and practice were also discussed.

Training and asymmetrical transfer effects of working memory and inhibitory control in primary school children

Working memory (WM) and inhibitory control (IC) are two fundamental and supportive components of executive function (EF) that are critical for school-age children. However, the direct comparison of the training and transfer effects of WM and IC training in school-age children still needs to be improved. This study adopted a "pre-, post-, and delayed posttest" design to compare the training, near-transfer, and far-transfer effects of WM and IC in school-age children. A total of 60 children aged 8 to 10 years were randomly assigned to the WM training group, IC training group, or control group. Children in the WM and IC training groups completed 12 sessions of multiple adaptive training tasks tapping different subcomponents of WM (visual-spatial and verbal WM) and IC (interference control and response inhibition) separately. In the pretraining, posttraining, and 6-month follow-up stages, we used WM and IC tasks to evaluate training and near-transfer effects and used analogical reasoning tasks to evaluate far-transfer effects. Results showed significant training effects on visual-spatial and verbal WM, near-transfer effects on response inhibition, and far-transfer effects on analogical reasoning for WM training in the posttraining stage. The improvements in verbal WM and analogical reasoning were maintained for 6 months, whereas for IC training only the training effects on response inhibition and the far-transfer effects on analogical reasoning were observed in the posttraining stage and only the training effects on response inhibition were maintained for 6 months. Results suggested positive training and asymmetrical transfer effects of WM and IC training, which provide new evidence for the effectiveness of WM and IC training in school-age children.

The role of executive function in shaping the longitudinal stability of math achievement during early elementary grades

There is substantial rank-order stability in children's mathematical skills throughout development. Research has shown that children who enter school with relatively low math skills are unlikely to catch up to peers who begin kindergarten with more developed math skills. Emerging evidence suggests that children's executive function skills might play an important role in shaping the rate and stability of mathematical skill development during early development. Therefore in the present study, we used data from the Early Childhood Longitudinal Study-Kindergarten Cohort 2010-11-a prospective sample of over 18,000 children in the United States-to examine executive function as an antecedent to characteristics of growth in math skills and to test whether executive function moderates the longitudinal stability of math achievement from kindergarten through second grade. Latent growth curve models reveal that executive function is related to not only the level of math skills at school entry but also to the rate of growth in early elementary years. Moreover, we found that executive function moderated the stability of math achievement from kindergarten to second grade, suggesting that early executive function skills can serve as a compensatory mechanism for children who enter school with lower levels of mathematical skills. These findings might have important implications for narrowing gaps in math achievement during early elementary school.

The Relationship between Working Memory and Arithmetic in Primary School Children: A Meta-Analysis

Working memory (WM) plays a crucial role in the development of arithmetic ability. However, research findings related to which factors influence the relationship between WM and arithmetic skills are inconsistent. The present meta-analysis aimed to examine the links between WM and arithmetic in primary school children and investigate whether this is dependent on WM domains (i.e., verbal, visual, spatial), child age, arithmetic operation type, and arithmetic task type. A total of 11,224 participants with an age range of 6- to 12 years, from 55 independent samples were included in the meta-analysis. Analysis of 46 studies with 187 effect sizes revealed an overall significant and medium correlation between WM and arithmetic. Heterogeneity analyses indicated that verbal WM showed a stronger correlation with arithmetic than visuospatial WM, and that correlations between verbal WM and arithmetic declined with age, whereas correlations between spatial-sequential, and spatial-simultaneous WM and arithmetic remained stable throughout development. Addition and subtraction were more involved in verbal WM than multiplication and division. Moreover, mental and written arithmetic showed comparable correlations with WM in all domains. These findings suggest moderation effects of WM domains, age, and operation types in the WM-arithmetic relationship and highlight the significant role of verbal WM in arithmetic ability in primary school children.

Theta Band Transcranial Alternating Current Stimulation Enhances Arithmetic Learning: A Systematic Comparison of Different Direct and Alternating Current Stimulations

Over the last decades, interest in transcranial electrical stimulation (tES) has grown, as it might allow for causal investigations of the associations between cortical activity and cognition as well as to directly influence cognitive performance. The main objectives of the present work were to assess whether tES can enhance the acquisition and application of arithmetic abilities, and whether it enables a better assessment of underlying neurophysiological processes. To this end, the present, double-blind, sham-controlled study assessed the effects of six active stimulations (three tES protocols: anodal transcranial direct current stimulation (tDCS), alpha band transcranial alternating current stimulation (tACS), and theta band tACS; targeting the left dorsolateral prefrontal cortex or the left posterior parietal cortex) on the acquisition of an arithmetic procedure, arithmetic facts, and event-related synchronization/desynchronization (ERS/ERD) patterns. 137 healthy adults were randomly assigned to one of seven groups, each receiving one of the tES-protocols during learning. Results showed that frontal theta band tACS reduced the repetitions needed to learn novel facts and both, frontal and parietal theta band tACS accelerated the decrease in calculation times in fact learning problems. The beneficial effect of frontal theta band tACS may reflect enhanced executive functions, allowing for better control and inhibition processes and hence, a faster acquisition and integration of novel fact knowledge. However, there were no significant effects of the stimulations on procedural learning or ERS/ERD patterns. Overall, theta band tACS appears promising as a support for arithmetic fact training, but effects on procedural calculations and neurophysiological processes remain ambiguous.

Nutrients for executive function development and related brain connectivity in school-aged children

Executive functions refer to a set of higher-order cognitive processes involved in the control and organization of information to serve goal-directed behaviors. Skills in executive functioning are developed throughout childhood and adolescence and have been shown to be predictive of academic achievement. The coordination of these complex processes is critically dependent on brain maturation and connectivity, including key neurodevelopmental processes like myelination and synaptogenesis. Among other factors, research highlights the influential effect of nutrition and diet on these neurodevelopmental processes, which may impact executive function performance in healthy and deficient populations. This review considers the research to date on the role of key nutrients that have been identified for executive function development and their underlying neurophysiological processes in school-aged children.

The relationship between cognition and mathematics in children with attention-deficit/hyperactivity disorder: a systematic review

Cognitive processes play an imperative role in children's mathematics learning. Difficulties in cognitive functioning are a core feature of Attention Deficit Hyperactivity Disorder (ADHD) in children, who also tend to show lower levels of mathematics attainment than their typically developing peers. This review (registration number: CRD42020169708) sought to aggregate findings from studies assessing the relationship between cognition and mathematics in children with a clinical ADHD diagnosis aged 4-12 years. A total of 11,799 studies published between 1992 and August 2020 were screened for eligibility using various database (PsycINFO, PubMed, SCOPUS, EMBASE, ERIC, Web of Science, and additional sources), from which four studies met inclusion criteria. A narrative synthesis was conducted on the correlations between mathematics and cognitive domains, including an evaluation of the risk of bias within the studies. Across four studies meeting inclusion criteria, memory, inhibitory control, and processing speed were assessed. The results showed a positive association between cognition and mathematics performance in this population. The strength of associations across these studies varied as a function of the cognitive domain in question, means by which mathematics performance was assessed, as well as whether confounding factors such as age and IQ were controlled for. Collectively, this review demonstrates a lack of research in this area and points to various methodological considerations for identifying the association between cognition and mathematics performance in ADHD.

Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4-6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.

Executive Function, Language Dominance and Literacy Skills in Spanish-speaking Language-minority Children: A Longitudinal Study

In the U.S., children whose home language is Spanish are at increased risk for the development of reading difficulties. Studies have reported a link between executive function (EF) and reading; few studies have examined this linkage in Spanish-speaking language-minority (LM) children. This longitudinal study examined the association between preschool EF and kindergarten reading-related skills in 241 Spanish-speaking LM children (M-age in preschool = 54.23 months, SD = 6.17). In preschool, children completed measures of inhibitory control (IC) and working memory (WM) in their dominant language, and early literacy skills in Spanish and English. In the fall of their kindergarten year, children completed code- and language-related literacy measures in both languages. A two-factor model (IC and WM) accounted for children's preschool EF. Most zero-order correlations between EF factors and kindergarten outcomes in Spanish (rs = .03-.40) and English (rs = .05-.35) were statistically significant. For English-language outcomes, WM was more strongly associated with code-related skills and IC with language-related skills; for Spanish-language outcomes, WM was more strongly related to both code- and language- related skills than IC. There was little difference in the associations between EF and reading outcomes based on the language in which EF was measured (i.e., the child's dominant language). When controlling for early literacy skills in the same language as the kindergarten outcomes, EF contributed significant unique variance to kindergarten skills in English but not in Spanish. For Spanish language outcomes, early literacy skills appear to mediate the role of preschool EF. The results suggest that children's development in cognitive domains, such as EF, may have an important role in the acquisition of core early reading skills for Spanish-speaking LM children.

Integrating Embodied Cognition and Information Processing: A Combined Model of the Role of Gesture in Children's Mathematical Environments

Children learn and use various strategies to solve math problems. One way children's math learning can be supported is through their use of and exposure to hand gestures. Children's self-produced gestures can reveal unique, math-relevant knowledge that is not contained in their speech. Additionally, these gestures can assist with their math learning and problem solving by supporting their cognitive processes, such as executive function. The gestures that children observe during math instructions are also linked to supporting cognition. Specifically, children are better able to learn, retain, and generalize knowledge about math when that information is presented within the gestures that accompany an instructor's speech. To date, no conceptual model provides an outline regarding how these gestures and the math environment are connected, nor how they may interact with children's underlying cognitive capacities such as their executive function. In this review, we propose a new model based on an integration of the information processing approach and theory of embodied cognition. We provide an in-depth review of the related literature and consider how prior research aligns with each link within the proposed model. Finally, we discuss the utility of the proposed model as it pertains to future research endeavors.

Perceptual reasoning skills mediate the relationship between attention and math proficiency in individuals with a neurodevelopmental condition

BACKGROUND

An important component of academic success in typically developing students is the development of math skills, which is associated with attention and perceptual reasoning (PR) skills. For children with a neurodevelopmental condition (NDC), the relationship is confounded by diagnostic-specific cognitive characteristics. Specifically, enhanced PR is specific to individuals with Autism Spectrum Disorder (ASD).

AIMS

The purpose of this study was to test: (i) a mediation model where PR skills would mediate the relationship between attention and math proficiency for students with an NCD, and (ii) whether this mediation model is moderated by a diagnostic profile.

METHODS AND PROCEDURES

One hundred and thirty-seven students with an NDC participated in a school-based study examining the effectiveness of using a standardized measure of attention in predicting math capabilities.

OUTCOMES AND RESULTS

PR mediated the relationship between attention and math proficiency for students diagnosed with an NDC. However, the model was not moderated by diagnostic profile.

CONCLUSIONS AND IMPLICATIONS

The results of this study provide a better understanding of the roles of higher-level cognitive ability specific to students with NDCs. Additionally, the superior PR skills demonstrated by the ASD sample further supports the research suggesting this population possesses cognitive strengths in this domain.

How Cognitive Strengths Compensate Weaknesses Related to Specific Learning Difficulties in Fourth-Grade Children

The goal of the present study was to investigate whether children's cognitive strengths can compensate the accompanied weaknesses related to their specific learning difficulties. A Bayesian multigroup mediation SEM analysis in 281 fourth-grade children identified a cognitive compensatory mechanism in children with mathematical learning difficulties (n = 36): Children with weak number sense, but strong rapid naming performed slightly better on mathematics compared to peers with weak rapid naming. In contrast, a compensatory mechanism was not identified for children with a comorbid mathematical and reading difficulty (n = 16). One explanation for the latter finding could relate to the lack of ability to compensate, because of the difficulties these children experience in both academic domains. These findings lead to a new direction in research on learning difficulties in mathematics and/or reading by suggesting that children with a learning disability each have a unique profile of interrelated cognitive strengths and weaknesses. Children might compensate with these strengths for their weaknesses, which could lead to (small) learning gains in the affected domain.

Developmental Trajectories of Adaptive Behavior From Toddlerhood to Middle Childhood in Autism Spectrum Disorder

Longitudinal growth modeling was utilized to examine adaptive behavior over eight years across the three time points (i.e., ages 2-10). Seventy-six parents completed the Vineland Adaptive Behavior Scales interviews of adaptive behavior. Child participants completed standardized developmental testing and an executive function task in toddlerhood and the Autism Diagnostic Observation Schedule across all time points. Growth models were specified for communication, daily living skills, and socialization domains of adaptive behavior. Mental age in toddlerhood was a significant predictor of trajectories of communication, daily living skills, and socialization. Executive function and autism severity were significant predictors of socialization. Findings suggest executive function as a potential target for promoting the growth of adaptive behavior skills in addition to autism symptomology.

Relationships between cardiorespiratory fitness, inhibition, and math fluency: A cluster analysis

This study identified clusters of adolescents who share similar cardiorespiratory fitness levels and analysed the relationships between cardiorespiratory fitness, inhibition, and math fluency in each of the clusters. The subjects were 490 high-school students aged 10-16 years. The mean age was 13.82 years (SD = 1.12). Latent class analysis identified three clusters with high, medium, and low levels of cardiorespiratory fitness. The high-fitness cluster achieved higher scores in inhibition and math fluency than the low-fitness cluster. Path analysis revealed that the influence of cardiorespiratory fitness on inhibition was non-existent in the three clusters. The effect of inhibition on math fluency was positive and significant in all three cardiorespiratory fitness levels. Cardiorespiratory fitness had a direct, positive, and significant effect on math fluency only in the high-fitness cluster. Therefore, a high level of cardiorespiratory fitness is a significant determining factor in the explanation of math fluency. These results indicate that inhibition does not mediate the relationship between cardiorespiratory fitness and math fluency. However, the benefits of cardiorespiratory fitness affect math fluency, which has important implications for the educational environment and the teaching/learning process.

Assessment of Mathematics Difficulties for Second and Third Graders: Cognitive and Psychological Parameters

Mathematical achievement during the first years of primary school seems to be a reliable predictor of students’ later performance. In addition, cognitive, metacognitive, and psychological parameters are considered to be factors related to mathematical achievement. However, in the Greek educational system, there is a shortage of valid and reliable tools for the assessment of mathematics difficulties and as a consequence, identification of children with these difficulties does not take place before the last years of primary school. This study aims to investigate the relationship between working memory, sustained attention, executive functions, and math anxiety with mathematical achievement in 2nd and 3rd graders. The design of the study was based on the parameters of mathematics difficulties, as they arise from the literature review. Ninety-one Year 2 and Year 3 primary school students (mean age 8.06 years) from three public schools situated in Attica, Greece participated in the study. The students completed three different scales including educational, cognitive, and psychological tasks. Results showed that mathematical skills were significantly correlated with sustained attention, inductive reasoning, math anxiety, and working memory. Moreover, mental arithmetic ability, sustained attention, and working memory predicted mathematical achievement of second and third graders. The study’s outcomes verify that sustained attention, inductive reasoning, working memory, and math anxiety are correlated with young students’ mathematical performance. The implications of the results for the development of an assessment tool for early detection of mathematics difficulties will be discussed.

The Relationship Between Reading Fluency and Arithmetic Fact Fluency and Their Shared Cognitive Skills: A Developmental Perspective

This study investigated the underlying cognitive abilities which are related to both fluency in reading and arithmetic across different developmental phases of their acquisition. An unselected sample of children in first (N = 83), second (N = 66), and third (N = 67) grades completed several reading and arithmetic fluency tasks, as well as rapid automatized naming (RAN), working memory (WM), and inhibition measures. The results of a stepwise regression analysis revealed differences in the predictive models of fluency in both academic domains in first grade. However, similar patterns were found in the second and third grades. Specifically, in first grade reading fluency was predicted by inhibition and WM, while arithmetic fact fluency was predicted by RAN and WM. In contrast, in second grade both types of fluency were predicted by RAN and WM, and in third grade only RAN was found to be a predictor. Alongside the gradual reduction in the cognitive components participating in reading and arithmetic fluency, the results of the present study suggest that both fluencies share the same underlying cognitive mechanisms. Practical implications of the current results are discussed.

Cognitive Abilities and Mathematical Competencies at School Entry

The aim of this study was to identify mathematical competencies in early childhood and cognitive correlates of those competencies in a prospective longitudinal sample of children (N=1292) in predominantly low-income and nonurban communities in the United States. General mental ability (IQ), processing speed, vocabulary, and the working memory, inhibitory control, and cognitive flexibility components of executive function (EF) were assessed when children were ages 4 and 5. Math ability was assessed prior to school entry using a norm-referenced assessment. Exploratory factor analysis indicated that items from the math assessment loaded onto factors representing conceptual and procedural skill. IQ, processing speed, vocabulary, and a unitary EF composite all related to both conceptual and procedural skill. When EF components were examined separately, however, only the inhibitory control aspect of EF was related to conceptual skill and only the working memory aspect of EF was related to procedural skill.

Taking Language out of the Equation: The Assessment of Basic Math Competence Without Language

While numerical skills are fundamental in modern societies, some estimated 5-7% of children suffer from mathematical learning difficulties (MLD) that need to be assessed early to ensure successful remediation. Universally employable diagnostic tools are yet lacking, as current test batteries for basic mathematics assessment are based on verbal instructions. However, prior research has shown that performance in mathematics assessment is often dependent on the testee's proficiency in the language of instruction which might lead to unfair bias in test scores. Furthermore, language-dependent assessment tools produce results that are not easily comparable across countries. Here we present results of a study that aims to develop tasks allowing to test for basic math competence without relying on verbal instructions or task content. We implemented video and animation-based task instructions on touchscreen devices that require no verbal explanation. We administered these experimental tasks to two samples of children attending the first grade of primary school. One group completed the tasks with verbal instructions while another group received video instructions showing a person successfully completing the task. We assessed task comprehension and usability aspects both directly and indirectly. Our results suggest that the non-verbal instructions were generally well understood as the absence of explicit verbal instructions did not influence task performance. Thus we found that it is possible to assess basic math competence without verbal instructions. It also appeared that in some cases a single word in a verbal instruction can lead to the failure of a task that is successfully completed with non-verbal instruction. However, special care must be taken during task design because on rare occasions non-verbal video instructions fail to convey task instructions as clearly as spoken language and thus the latter do not provide a panacea to non-verbal assessment. Nevertheless, our findings provide an encouraging proof of concept for the further development of non-verbal assessment tools for basic math competence.

Innate or Acquired? - Disentangling Number Sense and Early Number Competencies

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.

Reliability and Validity of Nonsymbolic and Symbolic Comparison Tasks in School-Aged Children

Basic numerical processing has been regularly assessed using numerical nonsymbolic and symbolic comparison tasks. It has been assumed that these tasks index similar underlying processes. However, the evidence concerning the reliability and convergent validity across different versions of these tasks is inconclusive. We explored the reliability and convergent validity between two numerical comparison tasks (nonsymbolic vs. symbolic) in school-aged children. The relations between performance in both tasks and mental arithmetic were described and a developmental trajectories' analysis was also conducted. The influence of verbal and visuospatial working memory processes and age was controlled for in the analyses. Results show significant reliability (p < .001) between Block 1 and 2 for nonsymbolic task (global adjusted RT (adjRT): r = .78, global efficiency measures (EMs): r = .74) and, for symbolic task (adjRT: r = .86, EMs: r = .86). Also, significant convergent validity between tasks (p < .001) for both adjRT (r = .71) and EMs (r = .70) were found after controlling for working memory and age. Finally, it was found the relationship between nonsymbolic and symbolic efficiencies varies across the sample's age range. Overall, these findings suggest both tasks index the same underlying cognitive architecture and are appropriate to explore the Approximate Number System (ANS) characteristics. The evidence supports the central role of ANS in arithmetic efficiency and suggests there are differences across the age range assessed, concerning the extent to which efficiency in nonsymbolic and symbolic tasks reflects ANS acuity.

Measuring arithmetic: A psychometric approach to understanding formatting effects and domain specificity

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a sample of 1314 3rd grade students (age M=103.24 months, SD=5.41 months), Abstract Code Theory, Encoding Complex Theory, Triple Code Theory, and the Exact versus Approximate Calculations Hypothesis were evaluated, using 11 measures of arithmetic with symbolic problem formats (e.g., Arabic numeral and language-based formats) and various problem demands (e.g., requiring both exact and approximate calculations). In general, results provided support for both Triple Code Theory and Encoding Complex Theory. As predicted by Triple Code Theory, arithmetic outcomes with language formatting, Arabic numeral formatting, and estimation demands (across formats) were related but distinct from one another. As predicted by Encoding Complex Theory, executive attention was a direct predictor of all arithmetic outcomes. Language was no longer a direct predictor of arithmetic outcomes when executive attention was accounted for in the model; however, a strong and enduring relationship between language and executive attention suggested that language may play a facilitative role in reasoning during numeric processing. These findings have important implications for assessing arithmetic in educational settings and suggest that in addition to arithmetic-focused interventions, interventions targeting executive attention, language, and/or the interplay between them (i.e., internal speech during problem-solving) may be a promising avenues of mathematical problem-solving intervention.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection”) in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

[Formula: see text]Cognitive and behavioral rating measures of executive function as predictors of academic outcomes in children

Interrelations of two measurement methods (cognitive versus behavioral ratings) for executive function (EF) were examined and related to reading comprehension and math calculations in fourth and fifth grade students (n = 93) in the context of a diverse urban student population. Relations among measures within four EF processes (working memory, planning, inhibition and shifting) were modest; relations to academics were stronger. EF measures contributed to both academic outcomes even in the context of relevant covariates (age, language and educational program). Working memory was particularly important for reading comprehension across measurement type. Cognitive measures from all EF processes, particularly inhibition and planning, and behavioral ratings of working memory were important for math.

Impact of Attention Training on Academic Achievement, Executive Functioning, and Behavior: A Randomized Controlled Trial

Children with intellectual and developmental disabilities (IDD) experience significant difficulties in attention, learning, executive functions, and behavioral regulation. Emerging evidence suggests that computerized cognitive training may remediate these impairments. In a double blind controlled trial, 76 children with IDD (4-11 years) were randomized to either an attention training (n = 38) or control program (n = 38). Both programs were completed at home over a 5-week period. Outcome measures assessed literacy, numeracy, executive functioning, and behavioral/emotional problems, and were conducted at baseline, post-training, and 3-month follow-up. No training effects were observed at post-training; however, children in the training group showed greater improvements in numeracy skills at the 3-month follow-up. These results suggest that attention training may be beneficial for children with IDD; however, the modest nature of the intervention effects indicate that caution should be taken when interpreting clinical significance.

The DREME Network: Research and Interventions in Early Childhood Mathematics

The DREME Network was created to advance the field of early mathematics research and improves the opportunities to develop math competencies offered to children birth through age 8 years, with an emphasis on the preschool years. All four main Network projects will have implications for interventions. Section 1 introduces the Network and its four projects. The remainder of the chapter focuses on one of these four projects, Making More of Math (MMM), in depth. MMM is directly developing an intervention for children, based on selecting high-quality instructional activities culled from the burgeoning curriculum resources. We first report a review of 457 activities from 6 research-based curricula, which describes the number of activities by content focus, type (nature), and setting of each activity. Given the interest in higher-order thinking skills and self-regulation, we then identified activities that had the potential to, develop both mathematics and executive function (EF) proficiencies. We rated these, selecting the top 10 for extensive coding by mathematics content and EF processes addressed. We find a wide divergence across curricula in all these categories and provide comprehensive reports for those interested in selecting, using, or developing early mathematics curricula.

The impact of behavioural executive functioning and intelligence on math abilities in children with intellectual disabilities

BACKGROUND

Little is known about the role of behavioural executive functioning (EF) skills and level of intelligence (IQ) on math abilities in children with mild to borderline intellectual disabilities.

METHOD

Teachers of 63 children attending a school for special education (age: 10 to 13 years; IQ: 50 to 85) filled out a Behaviour Rating Inventory for Executive Function for each student. Furthermore, students took a standardised national composite math test and a specific math test on measurement and time problems. Information on level of intelligence was gathered through school records. Multiple regression analyses were performed to test direct, moderating and mediating effects of EF and IQ on math performance.

RESULTS

Behavioural problems with working memory and flexibility had a direct negative effect on math outcome, while concurrently, level of intelligence had a positive effect. The effect of IQ on math skills was moderated by problems with inhibition: in children with a clinical level of inhibition problems, there was no effect of level of intelligence on math performance.

CONCLUSIONS

Findings suggest that in students with mild to borderline intellectual disabilities and math difficulties, it is important to address their strengths and weaknesses with respect to EF and adjust instruction and remedial intervention accordingly.

Neural Markers of the Development of Executive Function: Relevance for Education

Executive functions are involved in the development of academic skills and are critical for functioning in school settings. The relevance of executive functions to education begins early and continues throughout development, with clear impact on achievement. Diverse efforts increasingly suggest ways in which facilitating development of executive function may be used to improve academic performance. Such interventions seek to alter the trajectory of executive development, which exhibits a protracted course of maturation that stretches into young adulthood. As such, it may be useful to understand how the executive system develops normally and abnormally in order to tailor interventions within educational settings. Here we review recent work investigating the neural basis for executive development during childhood and adolescence.

Are Individual Differences in Arithmetic Fact Retrieval in Children Related to Inhibition?

Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processing. We administered measures of cognitive inhibition (i.e., numerical and non-numerical stroop tasks) and a complementary, more ecologically valid measure of children’s inhibition in the classroom (i.e., teacher questionnaire), as well as numerical magnitude processing (i.e., symbolic and non-symbolic numerical magnitude comparison) and arithmetic fact retrieval (i.e., two verification tasks) in 86 typically developing third graders. We used a correlation, a regression and a Bayesian analysis. This study failed to observe a significant association between inhibition and arithmetic fact retrieval. Consequently, our results did not reveal a unique contribution of inhibition to arithmetic fact retrieval in addition to numerical magnitude processing. On the other hand, symbolic numerical magnitude processing turned out to be a very powerful predictor of arithmetic fact retrieval, as indicated by both frequentist and Bayesian approaches.