Working memory in children's math learning and its disruption in dyscalculia

The mathematical word problem-solving performance gap between children with and without math difficulties: does working memory mediate and/or moderate treatment effects?

This study determined the extent to which working memory (WM) played a moderating and/or mediating role in word-problem-solving (WPS) instructional outcomes between children with and without math difficulties (MD). A randomized pretest-posttest control group study investigated the effects of 8-week strategy instruction in one of four treatment conditions on WPS accuracy of third graders with MD (N = 136) when compared to children with (N = 28) and without MD (N = 43). Comparisons were made of three strategy conditions that included overt cues (e.g. underlining key sentences, filling in diagrams), another treatment condition that removed the overt cues (material-only), and two control conditions (children with and without MD). Four important findings emerged. First, posttest WM significantly predicted posttest WPS, computation, and schema accuracy independent of pretest and treatment conditions. Second, posttest WM mediated posttest WPS treatment outcomes when the control conditions included children without MD. Third, strategy conditions that included overt cues (e.g. crossing out irrelevant sentences) decreased WM demands compared to the Materials-Only condition (without overt cues) for children with MD. Finally, incremental attention allocation training within treatment conditions improved posttest WM in children with MD but not posttest WPS. Results indicated that WPS differences between children with and without MD across treatment conditions were mediated by posttest WM performance.

Mathematics Skills in Epilepsy: A Systematic Review and Meta-Analysis

Mathematics incorporates a broad range of skills, which includes basic early numeracy skills, such as subitizing and basic counting to more advanced secondary skills including mathematics calculation and reasoning. The aim of this review was to undertake a detailed investigation of the severity and pattern of early numeracy and secondary mathematics skills in people with epilepsy. Searches were guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Twenty adult studies and 67 child studies were included in this review. Overall, meta-analyses revealed significant moderate impairments across all mathematics outcomes in both adults (g= -0.676), and children (g= -0.593) with epilepsy. Deficits were also observed for specific mathematics outcomes. For adults, impairments were found for mathematics reasoning (g= -0.736). However, two studies found that mathematics calculation was not significantly impaired, and an insufficient number of studies examined early numeracy skills in adults. In children with epilepsy, significant impairments were observed for each mathematics outcome: early numeracy (g= -0.383), calculation (g= -0.762), and reasoning (g= -0.572). The gravity of impairments also differed according to the site of seizure focus for children and adults, suggesting that mathematics outcomes were differentially vulnerable to the location of seizure focus.

Digital rhythm training improves reading fluency in children

Musical instrument training has been linked to improved academic and cognitive abilities in children, but it remains unclear why this occurs. Moreover, access to instrument training is not always feasible, thereby leaving less fortunate children without opportunity to benefit from such training. Although music-based video games may be more accessible to a broader population, research is lacking regarding their benefits on academic and cognitive performance. To address this gap, we assessed a custom-designed, digital rhythm training game as a proxy for instrument training to evaluate its ability to engender benefits in math and reading abilities. Furthermore, we tested for changes in core cognitive functions related to math and reading to inform how rhythm training may facilitate improved academic abilities. Classrooms of 8-9 year old children were randomized to receive either 6 weeks of rhythm training (N = 32) or classroom instruction as usual (control; N = 21). Compared to the control group, results showed that rhythm training improved reading, but not math, fluency. Assessments of cognition showed that rhythm training also led to improved rhythmic timing and language-based executive function (Stroop task), but not sustained attention, inhibitory control, or working memory. Interestingly, only the improvements in rhythmic timing correlated with improvements in reading ability. Together, these results provide novel evidence that a digital platform may serve as a proxy for musical instrument training to facilitate reading fluency in children, and that such reading improvements are related to enhanced rhythmic timing ability and not other cognitive functions associated with reading performance. RESEARCH HIGHLIGHTS: Digital rhythm training in the classroom can improve reading fluency in 8-9 year old children Improvements in reading fluency were positively correlated with enhanced rhythmic timing ability Alterations in reading fluency were not predicted by changes in other executive functions that support reading A digital platform may be a convenient and cost-effective means to provide musical rhythm training, which in turn, can facilitate academic skills.

Cognitive processes that underlie mathematically gifted emergent bilinguals

The purpose of this study was to determine those cognitive measures that increase the likelihood of identifying mathematically gifted students who are emerging bilinguals. Elementary school children (Grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory, inhibition, and working memory in their first language (L1: Spanish) and second language (L2: English). Multilevel polytomous logistic modeling compared mathematically gifted children with children who were average math achievers or low math achievers. The results indicated that cognitive parameters that included estimation and working memory in the L2 and problem-solving in the L1 were unique predictors that significantly influenced whether a child was categorized as gifted relative to average achievers. Relative to average achievers, L2 parameters (magnitude judgment) and English reading were significantly related to the identification of children with low math computation. The results are discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the ability to correctly identify children who score in the gifted range in both their L1 and L2.

Neurocognitive mechanisms of co-occurring math difficulties in dyslexia: Differences in executive function and visuospatial processing

Children with dyslexia frequently also struggle with math. However, studies of reading disability (RD) rarely assess math skill, and the neurocognitive mechanisms underlying co-occurring reading and math disability (RD+MD) are not clear. The current study aimed to identify behavioral and neurocognitive factors associated with co-occurring MD among 86 children with RD. Within this sample, 43% had co-occurring RD+MD and 22% demonstrated a possible vulnerability in math, while 35% had no math difficulties (RD-Only). We investigated whether RD-Only and RD+MD students differed behaviorally in their phonological awareness, reading skills, or executive functions, as well as in the brain mechanisms underlying word reading and visuospatial working memory using functional magnetic resonance imaging (fMRI). The RD+MD group did not differ from RD-Only on behavioral or brain measures of phonological awareness related to speech or print. However, the RD+MD group demonstrated significantly worse working memory and processing speed performance than the RD-Only group. The RD+MD group also exhibited reduced brain activations for visuospatial working memory relative to RD-Only. Exploratory brain-behavior correlations along a broad spectrum of math ability revealed that stronger math skills were associated with greater activation in bilateral visual cortex. These converging neuro-behavioral findings suggest that poor executive functions in general, including differences in visuospatial working memory, are specifically associated with co-occurring MD in the context of RD. RESEARCH HIGHLIGHTS: Children with reading disabilities (RD) frequently have a co-occurring math disability (MD), but the mechanisms behind this high comorbidity are not well understood. We examined differences in phonological awareness, reading skills, and executive function between children with RD only versus co-occurring RD+MD using behavioral and fMRI measures. Children with RD only versus RD+MD did not differ in their phonological processing, either behaviorally or in the brain. RD+MD was associated with additional behavioral difficulties in working memory, and reduced visual cortex activation during a visuospatial working memory task.

Working memory and math skills in children with and without ADHD

OBJECTIVE

Children with attention-deficit/hyperactivity disorder (ADHD) frequently demonstrate deficits in working memory and in multiple domains of math skills, including underdeveloped problem-solving and computation skills. The Baddeley model of working memory posits a multicomponent system, including a domain-general central executive and two domain-specific subsystems-phonological short-term memory and visuospatial short-term memory. Extant literature indicates a strong link between neurocognitive deficits in working/short-term memory and math skills; however, the extent to which each component of working/short-term memory may account for this relation is unclear.

METHOD

The present study was the first to use bifactor (S·I-1) modeling to examine relations between each working/short-term memory subcomponent (i.e., central executive, phonological short-term memory, and visuospatial short-term memory), ADHD symptoms, and math skills in a clinically evaluated sample of 186 children ages 8-13 (Myears = 10.40, SD = 1.49; 62 girls; 69% White/non-Hispanic).

RESULTS

Structural equation modeling indicated that all three working/short-term memory components exert a significant and approximately equal effect on latent math skills (β = .29-.50, all p < .05) and together explain 56% of the variance in children's math achievement (R² = .56). Exploratory analyses indicated that teacher-reported ADHD inattentive symptoms provided a small but significant contribution to predicting latent math skills (ΔR² = .07) and accounted for 24% of the central executive/math association.

CONCLUSIONS

These findings suggest that math difficulties in children with ADHD and clinically evaluated children without ADHD are associated, in large part, with their neurocognitive vulnerabilities in working/short-term memory and, to a lesser extent, overt ADHD symptoms. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Unique profile of academic learning difficulties in Wiedemann-Steiner syndrome

BACKGROUND

Wiedemann-Steiner syndrome (WSS) is a rare genetic disorder caused by heterozygous variants in KMT2A. To date, the cognitive profile associated with WSS remains largely unknown, although emergent case series implicate increased risk of non-verbal reasoning and visual processing deficits. This study examines the academic and learning concerns associated with WSS based on a parent-report screening measure.

PARTICIPANTS AND METHODS

A total of 25 parents of children/adults with a molecularly-confirmed diagnosis of WSS (mean age = 12.85 years, SD = 7.82) completed the Colorado Learning Difficulties Questionnaire (CLDQ), a parent-screening measure of learning and academic difficulties. Parent ratings were compared to those from a normative community sample to determine focal areas in Math, Reading and Spatial skills that may be weaker within this clinical population.

RESULTS

On average, parent ratings on the Math (mean Z = -3.08, SD = 0.87) and Spatial scales (mean Z = -2.52, SD = 0.85) were significantly more elevated than that of Reading (mean Z = -1.31, SD = 1.46) (Wilcoxon sign rank test Z < -3.83, P < 0.001), reflecting relatively more challenges observed in these areas. Distribution of parent ratings in Math items largely reflect a positively skewed distribution with most endorsing over three standard deviations below a community sample. In contrast, distributions of parent ratings in Reading and Spatial domains were more symmetric but flat. Ratings for Reading items yielded much larger variance than the other two domains, reflecting a wider range of performance variability.

CONCLUSIONS

Parent ratings on the CLDQ suggest more difficulties with Math and Spatial skills among those with WSS within group and relative to a community sample. Study results are consistent with recent case reports on the neuropsychological profile associated with WSS and with Kabuki syndrome, which is caused by variants in the related gene KMT2D. Findings lend support for overlapping cognitive patterns across syndromes, implicating potential common disease pathogenesis.

Parent ratings on the MEMRY questionnaire predict children's academic performance

Given the high rates of learning challenges in children with medical conditions, efficient and reliable screening methods are crucial. This study examined whether parent report of daily learning and memory predicts academic achievement in youth. Parents of 213 youth (aged 6-18) with varied medical diagnoses completed the Multidimensional Everyday Memory Ratings for Youth (MEMRY), and youth completed subtests from the Wechsler Individual Achievement Test-Third Edition (WIAT-III) as part of a comprehensive assessment. All scales of the MEMRY (Learning, Daily Memory, Executive/Working Memory) correlated significantly with WIAT-III Spelling, Word Reading, and Numerical Operations, while only the MEMRY Learning subscale correlated significantly with WIAT-III Pseudoword Decoding. Regression analyses indicated that MEMRY Learning significantly predicted WIAT-III Word Reading and Spelling, while both the MEMRY Learning and MEMRY Daily Memory scales significantly predicted WIAT-III Numerical Operations. When Full Scale IQ was entered into the models first, the MEMRY Learning subscale accounted for an additional 4% of variance in WIAT-III Word Reading and 7% of variance in WIAT-III Spelling, but did not account for additional variance in WIAT-III Numerical Operations or Pseudoword Decoding. Analyses in a subset of children with broadly normal intellectual functioning demonstrated very similar results, with even higher variance in academic testing accounted for by the MEMRY. In sum, the MEMRY questionnaire may serve as an efficient screen to identify children at risk for reading, spelling, and math deficits.

Emergent math difficulties among English learners: can the odds be reduced?

Solving word problems in mathematics presents difficulties for many English learners (ELs), including those who use Spanish as a home language. In the early stage of learning to solve mathematics word problems, some children, including ELs, experience difficulties. By English status, EL refers to those children whose home language was Spanish while in the process of developing English at school. Math difficulties (MD) refers to those children with low normative mathematical problem-solving scores in both English and Spanish. The purpose of this study was to determine those measures that increase the odds of identifying EL children with emergent MD. Elementary school children (grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, working memory [WM]) in both Spanish (L1) and English (L2) in Year 1 and again one year later. Multilevel growth modeling compared MD children identified one year later who manifested MD to children who were average math achievers or poor math achievers across the two testing waves (year 1 and year 2). The results indicated that significant growth parameters (i.e., measures of estimation, WM) increased the odds of identifying emergent MD relative to children with Persistent math deficits and average achievers. The results were discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the odds of identifying later math difficulties.

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.

A Neuropsychological Profile of Developmental Dyscalculia: The Role of Comorbidity

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

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria

Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8–12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.

The contributions of working memory domains and processes to early mathematical knowledge between preschool and first grade

Working Memory (WM) plays a crucial role in supporting children's mathematical learning. However, there is no consensus on the relative contributions of different WM domains (i.e., verbal, visuo-spatial, and numerical-verbal) and processes (i.e., low-control and high-control) to mathematical performance, specifically before and after the onset of formal education. This cross-sectional study examined the relations between WM domains and processes and early mathematical knowledge, comparing a group of children in the second year of preschool (N = 66) to a group of first graders (N = 110). Results of multigroup path analysis showed that whereas visuo-spatial low-control WM significantly predicted early mathematical knowledge only among preschoolers, verbal low-control WM was a significant predictor only among first graders. Instead, the contribution of visuo-spatial high-control WM emerged as significant for both age groups, as well as that of numerical-verbal WM, although the latter to a greater extent among preschoolers. These findings provide new insights into the WM domains and processes most involved in early mathematical knowledge at different developmental stages, with potential implications for the implementation of age-appropriate training interventions targeting specific WM skills before and after the onset of formal education.

Patterns of symbolic numerical magnitude processing and working memory as predictors of early mathematics performance

Although the roles of symbolic numerical magnitude processing (SNMP) and working memory (WM) in mathematics performance are well acknowledged, studies examining their joint effects are few. Here, we investigated the profiles of SNMP (1- and 2-digit comparison) and WM (verbal, visual and central executive) among Norwegian first graders (N = 256), and how these predict performance in counting, arithmetic facts and word problem–solving. Using latent class cluster analysis, four groups were identified: (1) weak SNMP (33.6%), (2) strong SNMP (25.8%), (3) weak SNMP and WM (23.4%) and (4) strong WM (17.2%). Group differences in mathematics performance were significant with explained variance ranging from 7 to 16%, even after controlling for relevant demographics and domain-general cognitive skills. Our findings suggest that children may display relative strengths in SNMP and WM, and that they both have a unique, even compensatory role in mathematics performance.

Numerical Training Videos and Early Numerical Achievement: A Study on 3-Year-Old Preschoolers

Early numerical abilities predict later math achievement and could be improved in children by using various training methods. As the literature on the use of training videos to develop numerical abilities is still surprisingly scant, the aim of the present study was to test the efficacy of a numerical training video on the development of counting and number line knowledge in 3-year-old preschoolers. Far transfer effects to cardinality and working memory were also examined. The study involved 86 children randomly assigned to two intervention groups: a numerical training group exposed to videos on counting and number lines; and a control group exposed to videos on colors and animal names in a foreign language. After the video training, there was an improvement in the numerical training group's counting skills, but not in their number line knowledge, and this improvement persisted six months later. The numerical training group also showed a far-transfer enhancement of cardinality six months after the intervention. Based on our results, numerical training videos could be effective in helping to enhance early numeracy skills in very young preschoolers.

Resources Underlying Visuo-Spatial Working Memory Enable Veridical Large Numerosity Perception

Humans can quickly approximate how many objects are in a visual image, but no clear consensus has been achieved on the cognitive resources underlying this ability. Previous work has lent support to the notion that mechanisms which explicitly represent the locations of multiple objects in the visual scene within a mental map are critical for both visuo-spatial working memory and enumeration (at least for relatively small numbers of items). Regarding the cognitive underpinnings of large numerosity perception, an issue currently subject to much controversy is why numerosity estimates are often non-veridical (i.e., susceptible to biases from non-numerical quantities). Such biases have been found to be particularly pronounced in individuals with developmental dyscalculia (DD), a learning disability affecting the acquisition of arithmetic skills. Motivated by findings showing that DD individuals are also often impaired in visuo-spatial working memory, we hypothesized that resources supporting this type of working memory, which allow for the simultaneous identification of multiple objects, might also be critical for precise and unbiased perception of larger numerosities. We therefore tested whether loading working memory of healthy adult participants during discrimination of large numerosities would lead to increased interference from non-numerical quantities. Participants performed a numerosity discrimination task on multi-item arrays in which numerical and non-numerical stimulus dimensions varied congruently or incongruently relative to each other, either in isolation or in the context of a concurrent visuo-spatial or verbal working memory task. During performance of the visuo-spatial, but not verbal, working memory task, precision in numerosity discrimination decreased, participants' choices became strongly biased by item size, and the strength of this bias correlated with measures of arithmetical skills. Moreover, the interference between numerosity and working memory tasks was bidirectional, with number discrimination impacting visuo-spatial (but not verbal) performance. Overall, these results suggest that representing visual numerosity in a way that is unbiased by non-numerical quantities relies on processes which explicitly segregate/identify the locations of multiple objects that are shared with visuo-spatial (but not verbal) working memory. This shared resource may potentially be impaired in DD, explaining the observed co-occurrence of working memory and numerosity discrimination deficits in this clinical population.

Differentiation of Two Working Memory Tasks Normed on a Large U.S. Sample of Children 2-7 Years Old

The Wechsler Preschool and Primary Scale of Intelligence, 4th ed. includes two measures of working memory normed on children 2;6-7;7. The present analyses of the typically developing children (N = 1,591, 812 female, 779 male, with an ethnic distribution approximating the United States) provide new, theoretically important information about these working memory tasks, Picture Memory and Zoo Locations. These new analyses establish developmental trends, individual-difference properties, and cognitive task properties. They show comparable developmental trends for the two tasks, but Picture Memory picks up more individual-difference variation and is more sensitive to knowledge. This analysis of normed tasks starting very young makes possible new methods for research on the early stages of childhood working memory development, about which little is currently known.

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.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Shared Neural Circuits for Visuospatial Working Memory and Arithmetic in Children and Adults

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of frontoparietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

Early Stopping in Experimentation With Real-Time Functional Magnetic Resonance Imaging Using a Modified Sequential Probability Ratio Test

Introduction: Functional magnetic resonance imaging (fMRI) often involves long scanning durations to ensure the associated brain activity can be detected. However, excessive experimentation can lead to many undesirable effects, such as from learning and/or fatigue effects, discomfort for the subject, excessive motion artifacts and loss of sustained attention on task. Overly long experimentation can thus have a detrimental effect on signal quality and accurate voxel activation detection. Here, we propose dynamic experimentation with real-time fMRI using a novel statistically driven approach that invokes early stopping when sufficient statistical evidence for assessing the task-related activation is observed. Methods: Voxel-level sequential probability ratio test (SPRT) statistics based on general linear models (GLMs) were implemented on fMRI scans of a mathematical 1-back task from 12 healthy teenage subjects and 11 teenage subjects born extremely preterm (EPT). This approach is based on likelihood ratios and allows for systematic early stopping based on target statistical error thresholds. We adopt a two-stage estimation approach that allows for accurate estimates of GLM parameters before stopping is considered. Early stopping performance is reported for different first stage lengths, and activation results are compared with full durations. Finally, group comparisons are conducted with both early stopped and full duration scan data. Numerical parallelization was employed to facilitate completion of computations involving a new scan within every repetition time (TR). Results: Use of SPRT demonstrates the feasibility and efficiency gains of automated early stopping, with comparable activation detection as with full protocols. Dynamic stopping of stimulus administration was achieved in around half of subjects, with typical time savings of up to 33% (4 min on a 12 min scan). A group analysis produced similar patterns of activity for control subjects between early stopping and full duration scans. The EPT group, individually, demonstrated more variability in location and extent of the activations compared to the normal term control group. This was apparent in the EPT group results, reflected by fewer and smaller clusters. Conclusion: A systematic statistical approach for early stopping with real-time fMRI experimentation has been implemented. This dynamic approach has promise for reducing subject burden and fatigue effects.

Working memory growth predicts mathematical problem-solving growth among emergent bilingual children

An area of mathematics found to be difficult for emergent bilingual children whose first language (L1) is Spanish in the United States is solving mathematical word problems. The purpose of this study was to determine the relationship between growth in the executive component of working memory (WM) and growth in mathematical word-problem solving in children whose L1 is Spanish. Elementary school children (Grades 1, 2, and 3) were administered a battery of mathematical, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, and WM) in both Spanish (L1) and English (second language [L2]) in Year 1 and again 1 year later. Multilevel growth modeling showed that growth in WM significantly predicted growth in L1 and L2 mathematical word-problem solving. Furthermore, the contributions of WM to mathematical word-problem-solving growth in both L1 and L2 were independent of language skills in vocabulary, reading, estimation, naming speed, inhibition, STM, and calculation. Overall, the results suggest that the mental activities that underlie WM play a significant role in predictions of L1 and L2 mathematical word-problem-solving accuracy.

Persistent Differences in Brain Structure in Developmental Dyscalculia: A Longitudinal Morphometry Study

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2-10.4 years) and 10 typically developing (TD) children (8.0-10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas.

Damage to the Intraparietal Sulcus Impairs Magnitude Representations of Results of Complex Arithmetic Problems

Past research investigating the role of the intraparietal sulcus (IPS) in numerical processes focused mainly on quantity and numerical comparisons as well on single digit arithmetic. The present study investigates the involvement of the IPS in estimating the results of multi-digit multiplication problems. For this purpose, the performance a 24-year-old female (JD) with brain damage in the left IPS was compared to an age-matched control group in the computation estimation task. When required to estimate whether the results of multi-digit multiplication problems are smaller or larger than given reference numbers, JD, in contrast to controls, did not show the common patterns of distance and size effects. Her strategy use was also atypical. Most control participants used both the approximated calculation strategy that involves rounding and calculation procedures and the sense of magnitude strategy that relies on an intuitive approximated magnitude representation of the results. In contrast, JD used only the former but not the latter strategy. Together, these findings suggest that the damage to the IPS impaired JD's representations of magnitude that play an important role in this computation estimation task.

Predicting individual differences in reading, spelling and maths in a sample of typically developing children: A study in the perspective of comorbidity

We examined reading, spelling, and mathematical skills in an unselected group of 129 Italian fifth graders by testing various cognitive predictors for each behaviour. As dependent variables, we measured performance in behaviours with a clear functional value in everyday life, such as reading a text, spelling under dictation and doing mental and written computations. As predictors, we selected cognitive dimensions having an explicit relation with the target behaviour (called proximal predictors), and prepared various tests in order to select which task had the best predictive power on each behaviour. The aim was to develop a model of proximal predictors of reading (speed and accuracy), spelling (accuracy) and maths (speed and accuracy) characterized by efficacy also in comparison to the prediction based on general cognitive factors (i.e., short-term memory, phonemic verbal fluency, visual perceptual speed, and non-verbal intelligence) and parsimony, pinpointing the role of both common and unique predictors as envisaged in the general perspective of co-morbidity. With one exception (reading accuracy), the proximal predictors models (based on communality analyses) explained a sizeable amount of variance, ranging from 27.5% in the case of calculation (accuracy) to 48.7% of reading (fluency). Models based on general cognitive factors also accounted for some variance (ranging from 6.5% in the case of spelling to 19.5% in the case of reading fluency) but this was appreciably less than that explained by models based on the hypothesized proximal predictors. In general, results confirmed the efficacy of proximal models in predicting reading, spelling and maths although they offered only limited support for common predictors across different learning skills; namely, performance in the Orthographic Decision test entered as a predictor of both reading and spelling indicating that a single orthographic lexicon may account for performance in reading and spelling. Possible lines of research to expand on this approach are illustrated.

Growth in Math Computation among Monolingual and English Language Learners:Does the Executive System have a Role?

This cohort-sequential study explored the components of working memory that underlie math calculation in elementary school children who are monolingual (English) or English language learners (ELLs) whose first language is Spanish. To this end, children (N = 789) in grades 1, 2, and 3 at wave 1 were administered a battery of math, vocabulary, reading and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again one year and two years later to the same participants. Three important findings emerged. First, along with naming speed, the results suggest that growth in the executive component of WM was significantly related to growth in calculation performance. Second, performance on measures of reading, fluid intelligence, naming speed and executive processes in wave 1 were significantly related to wave 3 math calculation performance. Finally, the full latent growth model showed that monolingual and ELL children were statistically comparable in computation at wave 3. Thus, strong support was found for the notion that the executive component of WM was related to math computation but weak support for the notion ELL children experienced a math achievement gap.

Cognitive and Behavioural Weaknesses in Children with Reading Disorder and AD(H)D

Working memory capacity, an essential prerequisite for language learning and the development of arithmetic skills, has been reported as deficient in children with reading disorder (RD) and attention deficit (hyperactivity) disorder (AD(H)D). However, few studies to date have explored potential associations of working memory impairments and foreign language learning, mathematical skills and school achievement in these groups, in particular in children with a comorbidity of both. In the present study, we assessed working memory, language learning, arithmetic fluency and academic achievement in children (N = 166; Mage = 14.3, range 8-18 y), including typically-developing children (n = 89), subjects with RD (n = 27), AD(H)D (n = 43), and a comorbidity (n = 15). While children with AD(H)D performed similar to typically developing children on all tasks, RD children performed weakly on various language learning and working memory tasks, with major deficits in non-word span, phonetic memory and vocabulary learning. Combining weaknesses of the two groups, children with a comorbidity further performed significantly worse on arithmetic skills, learning of sound-symbol combinations and simple digit span forward. The findings suggest a reconsideration of working memory and learning impairments in AD(H)D, while highlighting the additional weaknesses of comorbid children and pointing out severe foreign language learning difficulties in RD children.

Math problem-solving and cognition among emerging bilingual children at risk and not at risk for math difficulties

Cognitive processes that underlie individual differences in mathematical problem-solution accuracy in elementary emerging bilingual children (English Learners) at risk and not at risk for math problem-solving difficulties (MD) were examined. A battery of tests was administered in both English and Spanish that assessed problem-solving, achievement, and cognitive processing in children in first (N = 155/MD N = 23), second (N = 129/MD N = 44) and third grades (N = 110/MD N = 39). The results were that (a) the executive component of working memory (WM) predicted MD status independent of measures of fluid intelligence, reading, calculation, knowledge of algorithms, processing speed, short-term memory, and inhibition, (b) low performance on Spanish measures of numeracy and executive component of WM were major predictors of the odds of being classified as MD and (c) bilingual proficiency primarily moderated English rather than Spanish measures of cognition. The results support the notion that the executive system of WM is an important predictor of emerging bilingual children's math problem-solving difficulties.

Individual differences in math problem solving and executive processing among emerging bilingual children

This study identified cognitive processes that underlie individual differences in working memory (WM) and mathematical problem-solving accuracy in emerging bilingual children (English learners). A battery of tests was administered in both English and Spanish that assessed problem solving, achievement, and cognitive processing in children in first grade (n = 155), second grade (n = 129), and third grade (n = 110). The results were that (a) the executive component of WM predicted solution accuracy of word problems independent of first language and second language measures of vocabulary, reading, domain-specific knowledge (e.g., calculation, estimation), and short-term memory and (b) first language (Spanish) measures of the executive component of WM and magnitude comparisons were major predictors of math problem-solving accuracy in both languages. The results support the notion that the executive system of WM is a unique predictor of emerging bilingual children's math problem-solving accuracy in both languages.

Applied Problem Solving in Children with ADHD: The Mediating Roles of Working Memory and Mathematical Calculation

The difficulties children with ADHD experience solving applied math problems are well documented; however, the independent and/or interactive contributions of cognitive processes underlying these difficulties are not fully understood and warrant scrutiny. The current study examines two primary cognitive processes integral to children's ability to solve applied math problems: working memory (WM) and math calculation skills (i.e., the ability to utilize specific facts, skills, or processes related to basic math operations stored in long-term memory). Thirty-six boys with ADHD-combined presentation and 33 typically developing (TD) boys aged 8-12 years old were administered multiple counterbalanced tasks to assess upper (central executive [CE]) and lower level (phonological [PH STM] and visuospatial [VS STM] short-term memory) WM processes, and standardized measures of mathematical abilities. Bias-corrected, bootstrapped mediation analyses revealed that CE ability fully mediated between-group differences in applied problem solving whereas math calculation ability partially mediated the relation. Neither PH STM nor VS STM was a significant mediator. When modeled together via serial mediation analysis, CE in tandem with math calculation ability fully mediated the relation, explained 79% of the variance, and provided a more parsimonious explication of applied mathematical problem solving differences among children with ADHD. Results suggest that interventions designed to address applied math difficulties in children with ADHD will likely benefit from targeting basic knowledge of math facts and skills while simultaneously promoting the active interplay of these skills with CE processes.

Annual Research Review: Educational neuroscience: progress and prospects

Educational neuroscience is an interdisciplinary research field that seeks to translate research findings on neural mechanisms of learning to educational practice and policy and to understand the effects of education on the brain. Neuroscience and education can interact directly, by virtue of considering the brain as a biological organ that needs to be in the optimal condition to learn ('brain health'); or indirectly, as neuroscience shapes psychological theory and psychology influences education. In this article, we trace the origins of educational neuroscience, its main areas of research activity and the principal challenges it faces as a translational field. We consider how a pure psychology approach that ignores neuroscience is at risk of being misleading for educators. We address the major criticisms of the field comprising, respectively, a priori arguments against the relevance of neuroscience to education, reservations with the current practical operation of the field, and doubts about the viability of neuroscience methods for diagnosing disorders or predicting individual differences. We consider future prospects of the field and ethical issues it raises. Finally, we discuss the challenge of responding to the (welcome) desire of education policymakers to include neuroscience evidence in their policymaking, while ensuring recommendations do not exceed the limitations of current basic science.

Math Anxiety in Combination With Low Visuospatial Memory Impairs Math Learning in Children

Math anxiety impairs academic achievements in mathematics. According to the processing efficiency theory (PET), the adverse effect is the result of reduced processing capacity in working memory (WM). However, this relationship has been examined mostly with correlational designs. Therefore, using an intervention paradigm, we examined the effects of math anxiety on math learning. Twenty-five 5th graders underwent seven training sessions of multiplication over the course of 2 weeks. Children were faster and made fewer errors in solving trained problems than untrained problems after learning. By testing the relationship between math anxiety, WM, and math learning, we found that if children have little or no math anxiety, enough WM resources are left for math learning, so learning is not impeded. If they have high math anxiety and high visuospatial WM, some WM resources are needed to deal with math anxiety but learning is still supported. However, if they have high math anxiety and low visuospatial WM capacity, math learning is significantly impaired. These children have less capacity to learn new math content as cognitive resources are diverted to deal with their math anxiety. We conclude that math anxiety not only hinders children's performance in the present but potentially has long-lasting consequences, because it impairs not only math performance but also math learning. This intervention study partially supports the PET because only the combination of high math anxiety and low WM capacity seems critical for hindering math learning. Moreover, an adverse effect of math anxiety was observed on performance effectiveness (response accuracy) but not processing efficiency (response time).

Increased arithmetic complexity is associated with domain-general but not domain-specific magnitude processing in children: A simultaneous fNIRS-EEG study

The investigation of the neural underpinnings of increased arithmetic complexity in children is essential for developing educational and therapeutic approaches and might provide novel measures to assess the effects of interventions. Although a few studies in adults and children have revealed the activation of bilateral brain regions during more complex calculations, little is known about children. We investigated 24 children undergoing one-digit and two-digit multiplication tasks while simultaneously recording functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG) data. FNIRS data indicated that one-digit multiplication was associated with brain activity in the left superior parietal lobule (SPL) and intraparietal sulcus (IPS) extending to the left motor area, and two-digit multiplication was associated with activity in bilateral SPL, IPS, middle frontal gyrus (MFG), left inferior parietal lobule (IPL), and motor areas. Oscillatory EEG data indicated theta increase and alpha decrease in parieto-occipital sites for both one-digit and two-digit multiplication. The contrast of two-digit versus one-digit multiplication yielded greater activity in right MFG and greater theta increase in frontocentral sites. Activation in frontal areas and theta band data jointly indicate additional domain-general cognitive control and working memory demands for heightened arithmetic complexity in children. The similarity in parietal activation between conditions suggests that children rely on domain-specific magnitude processing not only for two-digit but-in contrast to adults-also for one-digit multiplication problem solving. We conclude that in children, increased arithmetic complexity tested in an ecologically valid setting is associated with domain-general processes but not with alteration of domain-specific magnitude processing.

Math Difficulties and Working Memory Growth in English Language Learner Children: Does Bilingual Proficiency Play a Significant Role?

Purpose

The purpose of this study was to determine those components of working memory (WM) that play a significant role in predicting math growth in children who are English language learners ( N = 157) with serious math difficulties (MD).

Method

A battery of tests was administered in English and Spanish that assessed computation, reading, vocabulary, inhibition, and components of WM in Grade 1 children with follow-up testing in Grades 2 and 3.

Results

The results indicated that growth in the executive component of WM was related to growth in math performance. Proficient bilingual children (proficient in both Spanish and English vocabulary) with MD outperformed less proficient bilingual children with MD on measures of math calculation, fluid intelligence, reading, and Spanish WM at Grade 3.

Conclusion

Growth in the executive component of WM is significantly related to growth in math computation, and increased bilingual proficiency across testing waves yielded positive gains in both math and cognitive performance in children with MD.

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Memory and cognitive control circuits in mathematical cognition and learning

Numerical cognition relies on interactions within and between multiple functional brain systems, including those subserving quantity processing, working memory, declarative memory, and cognitive control. This chapter describes recent advances in our understanding of memory and control circuits in mathematical cognition and learning. The working memory system involves multiple parietal-frontal circuits which create short-term representations that allow manipulation of discrete quantities over several seconds. In contrast, hippocampal-frontal circuits underlying the declarative memory system play an important role in formation of associative memories and binding of new and old information, leading to the formation of long-term memories that allow generalization beyond individual problem attributes. The flow of information across these systems is regulated by flexible cognitive control systems which facilitate the integration and manipulation of quantity and mnemonic information. The implications of recent research for formulating a more comprehensive systems neuroscience view of the neural basis of mathematical learning and knowledge acquisition in both children and adults are discussed.