Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency

BACKGROUND

Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'.

AIMS

The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels.

SAMPLE

Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later).

METHODS

Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured.

RESULTS

Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2.

CONCLUSION

Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.

Affective and cognitive factors associated with Chinese and Italian children's arithmetic performance

BACKGROUND

This study aimed to investigate the cognitive and affective factors associated with cross-cultural differences in arithmetic tasks.

METHODS

A total of 404 third- and fourth- graders were recruited from China and Italy to complete exact arithmetic, arithmetic estimation and cognitive tasks (i.e., short-term memory, executive functions, and fluid reasoning). Their mathematical anxiety was also measured.

RESULTS

The results showed that Chinese children performed better than Italian children in both arithmetic tasks and in shifting task. Italian children performed better in visuospatial updating task and reported higher levels of mathematical anxiety than their Chinese peers. Multi-group path analyses showed that the patterns of relations among cognitive factors (i.e., short-term memory, inhibition and shifting), mathematical anxiety, and arithmetic performance were similar across groups. The only exception was that visuospatial updating uniquely predicted arithmetic estimation for Chinese but not for Italian children.

CONCLUSIONS

Chinese children outperformed their Italian peers in the exact arithmetic task, likely due to the greater emphasis on arithmetic fluency in Chinese mathematics education, both in schools and at home. They also had a slight advantage than Italian peers in the arithmetic estimation task. The unique link between updating and arithmetic estimation found in Chinese children but not Italian children suggests that, although arithmetic estimation is not emphasized in the curricula of either country, instruction and practice in exact arithmetic may enhance Chinese children's efficiency in solving arithmetic estimation problems.

Teaching strategies, cognitive factors and mathematics

Mathematics teaching strategies have a positive impact on learning. However, there is a lack of studies on non-traditional approaches to early mathematics education in the specialized scientific literature. In this theoretical framework, a study to connect teaching methodology with the various cognitive processes implicated in learning has been designed. A total of 114 primary school students aged 74 and 84 months who were taught mathematics either with the method called Open Algorithm Based on Numbers or with the more traditional Closed Algorithm Based on Ciphers, participated in the study. After conducting a thorough examination of cognitive processes and early math performance using well-established assessment instruments, a comparative analysis was undertaken to explore the relationship between cognitive predictors of mathematical performance, while considering the mathematics teaching strategies used. Students were distributed according to their level of mathematical competence and teaching methodology and the type of schools (Charter or Public). The results from the multivariate statistical test showed that the teaching strategy was inconclusive for most of the cognitive factors studied. Significant differences according to mathematical performance were found for fluid intelligence, verbal short-term memory, and visuospatial working memory. Finally, no significant differences were found in the cognitive variables studied when considering the interaction between the teaching approach, school characteristics, and mathematical achievement as a reference.

Let's face it! The role of social anxiety and executive functions in recognizing others' emotions from faces: Evidence from autism and specific learning disorders

Youth with different developmental disorders might experience challenges when dealing with facial emotion recognition (FER). By comparing FER and related emotional and cognitive factors across developmental disorders, researchers can gain a better understanding of challenges and strengths associated with each condition. The aim of the present study was to investigate how social anxiety and executive functioning might underlie FER in youth with and without autism spectrum disorders (ASD) and specific learning disorders (SLD). The study involved 263 children and adolescents between 8 and 16 years old divided into three groups matched for age, sex, and IQ: 60 (52 M) with ASD without intellectual disability, 63 (44 M) with SLD, and 140 (105 M) non-diagnosed. Participants completed an FER test, three executive functions' tasks (inhibition, updating, and set-shifting), and parents filled in a questionnaire reporting their children's social anxiety. Our results suggest that better FER was consistent with higher social anxiety and better updating skills in ASD, while with lower social anxiety in SLD. Clinical practice should focus on coping strategies in autistic youth who could feel anxiety when facing social cues, and on self-efficacy and social worries in SLD. Executive functioning should also be addressed to support social learning in autism.

Verbal but not visual-spatial working memory contributes to complex arithmetic calculation

The contribution of working memory to mathematics has been extensively studied. It has been proposed that verbal working memory (VWM) and visual-spatial working memory (VSWM) have distinct contributions, but results have been inconclusive. Here, we hypothesized that VWM and VSWM contribute differentially to separate sub-domains of mathematics. To test this hypothesis, we enrolled 199 primary school students and measured their VWM and VSWM with number/letter/matrix backward span tasks, and tested mathematics performance with simple subtraction, complex subtraction, multi-step calculation and number series completion, while controlling for several aspects of cognition. We found that while letter backward span had a significant contribution to complex subtraction, multi-step computation and number series completion, number backward span only had a significant contribution to multi-step computation, and matrix span had no effect on any math task. These results suggest that only VWM associated with complex mathematics, which might reflect verbal rehearsal. In contrast, VSWM does not appear to associated with mathematics.

The Role of Working Memory in Early Literacy and Numeracy Skills in Kindergarten and First Grade

The working memory system supports learning processes such as acquiring new information and the development of new skills. Working memory has been found to be related to both early literacy and early numeracy in kindergarten and to linguistic and mathematical academic skills at older ages, but the contribution of each of the memory components at these ages is not yet clear. The purpose of this study is to examine the unique connections among the various systems of WM, early literacy, and early numeracy using various assessment tests of simple WM and complex WM, as well as a variety of tasks in math and language skills administered to the same 250 children in kindergarten and 150 children in first grade. Consistent with the predictions, significant relations among all components of memory and mathematics and language knowledge at both ages were found, although these connections were differential for the different types of tasks and memory systems. The connection of complex WM was stronger in its contribution and more significant in first grade in both mathematics and language domains. Complex WM resources were more important in early literacy at kindergarten age, while simple WM seems to be important in early numeracy. The theoretical and educational implications of these results are discussed accordingly.

A-B-3-Associations and dissociations of reading and arithmetic: Is domain-specific prediction outdated?

Reading and arithmetic are core domains of academic achievement with marked impact on career opportunities and socioeconomic status. While associations between reading and arithmetic are well established, evidence on underlying mechanisms is inconclusive. The main goal of this study was to reevaluate the domain-specificity of established predictors and to enhance our understanding of the (co-)development of reading and arithmetic. In a sample of 885 German-speaking children, standard domain-specific predictors of reading and arithmetic were assessed before and/or at the onset of formal schooling. Reading and arithmetic skills were measured at the beginning and end of second grade. Latent variables were extracted for all relevant constructs: Grapheme-phoneme processing (phonological awareness, letter identification), RAN (RAN-objects, RAN-digits), number system knowledge (number identification, successor knowledge), and magnitude processing (non-symbolic and symbolic magnitude comparison), as well as the criterion measures reading and arithmetic. Four structural equation models tested distinct research questions. Grapheme-phoneme processing was a specific predictor of reading, and magnitude processing explained variance specific to arithmetic. RAN explained variance in both domains, and it explained variance in reading even after controlling for arithmetic. RAN and number system knowledge further explained variance in skills shared between reading and arithmetic. Reading and arithmetic entail domain-specific cognitive components, and they both require tight networks of visual, verbal, and semantic information, as reflected by RAN. This perspective provides a useful background to explain associations and dissociations between reading and arithmetic performance.

Visuo-Spatial Working Memory and Mathematical Skills in Children: A Network Analysis Study

Visuo-spatial working memory is one of the main domain-general cognitive mechanisms underlying mathematical abilities and their development in children. However, if visuo-spatial working memory involves different processes and components, then the term 'mathematics' refers to a broad concept that includes multiple domains and skills. The aim of this present study was to investigate the relationship between different visuo-spatial working memory components and several mathematical abilities in a sample of third- to fifth-grade Italian children. To assess the relationships between different visuo-spatial working memory components and different mathematical abilities, we relied on Network Analysis (NA). Results indicate that some but not all visuo-spatial working memory components are associated with some mathematical abilities.

Multiple influences of working memory capacity on number comprehension: The interplay with metacognition and number-specific prerequisites

A wide literature has studied the predictors of number comprehension and early math learning by considering both domain-general and number-specific prerequisites. However, a consensus has not been reached regarding the specific contribution of these prerequisites. This study aimed to analyze the contribution and interplay of two domain-general functions, working memory (WM) and metacognitive abilities, and number-specific prerequisites in determining number comprehension. The participants, 126 Italian first-graders, were tested on two WM capacity tasks, an early metacognition questionnaire, five number-specific prerequisites tasks (e.g., quantity and/or size comparison; placement of Arabic numeral), and the Number Knowledge Test for whole-number comprehension. We hypothesized that WM capacity would predict number comprehension both directly and indirectly via metacognition and domain-specific prerequisites. This is because both metacognition and domain-specific prerequisites might place an information load on WM to establish schemes for declarative metamemory and metacognitive monitoring and for emerging counting skills, respectively. The results confirmed these hypotheses. WM capacity was positively associated with number comprehension both directly and via increased metacognition and domain-specific prerequisites. These findings offer a model for interpreting the interplay between domain-general and number-specific predictors of whole-number comprehension, but they also underline the multiple ways in which WM capacity affects it.

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.

The differential relationship between visual and spatial working memory in children's mathematics performance

BACKGROUND

Previous research suggests that visuospatial working memory (WM) is a unique predictor of mathematics. However, evidence from neuropsychology and cognitive studies suggests dissociations between visual and spatial WM.

PROCEDURE

We examined the differential relationships between visual and spatial WM with mathematics using a new task that 1) utilized the same paradigm across visual and spatial tasks and 2) required executive WM.

MAIN FINDINGS

We found that our new spatial WM task related to mathematics scores while visual WM did not. Spatial WM related to mathematics scores for fourth-graders and not second graders, consistent with previous findings on the relationship between spatial skills and mathematics as mathematics becomes more complex. No relationship was found between spatial WM and reading scores at either grade level.

CONCLUSIONS

Our results highlight the dynamic relationship between WM components and mathematics over the elementary school years and suggest that spatial WM is a unique predictor of mathematics starting from middle childhood.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (M_age = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

EXPRESS: Arithmetic operations without symbols are unimpaired in adults with math anxiety

This study characterizes a previously unstudied facet of a major causal model of math anxiety. The model posits that impaired "basic number abilities" can lead to math anxiety, but what constitutes a basic number ability remains underdefined. Previous work has raised the idea that our perceptual ability to represent quantities approximately without using symbols constitutes one of the basic number abilities. Indeed, several recent studies tested how participants with math anxiety estimate and compare non-symbolic quantities. However, little is known about how participants with math anxiety perform arithmetic operations (addition and subtraction) on non-symbolic quantities. This is an important question because poor arithmetic performance on symbolic numbers is one of the primary signatures of high math anxiety. To test the question, we recruited 92 participants and asked them to complete a math anxiety survey, two measures of working memory, a timed symbolic arithmetic test, and a non-symbolic "approximate arithmetic" task. We hypothesized that if impaired ability to perform operations was a potential causal factor to math anxiety, we should see relationships between math anxiety and both symbolic and approximate arithmetic. However, if math anxiety relates to precise or symbolic representation, only a relationship between math anxiety and symbolic arithmetic should appear. Our results show no relationship between math anxiety and the ability to perform operations with approximate quantities, suggesting that difficulties performing perceptually based arithmetic operations does not constitute a basic number ability linked to math anxiety.

Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages

Number writing involves transcoding from number words (e.g., "thirty-two") to written digit strings (32) and is an important unique predictor of arithmetic. The existing longitudinal evidence about the relation between transcoding and arithmetic is mostly language specific. In languages with number word inversion (e.g., German), the order of tens and units is transposed in spoken number words compared with Arabic numbers. This makes transcoding more challenging than in languages without number word inversion (e.g., English). In the current study, we aimed to understand whether the contribution of number writing to the development of arithmetic is similar in languages with and without number word inversion. German-speaking children (n = 166) and English-speaking children (n = 201) were followed over the first 3 years of primary school. In a series of multiple linear regressions, we tested whether number writing of multi-digit numbers was a significant unique predictor of arithmetic after controlling for well-known non-numerical predictors (nonverbal reasoning and working memory) and numerical predictors (symbolic and nonsymbolic magnitude comparison). Number writing in Grade 1 predicted arithmetic in Grades 1, 2, and 3 over and above the other predictors. Crucially, number writing performance was of comparable importance for arithmetic development in German- and English-speaking children. Our findings extend previous evidence by showing that transcoding predicts the development of arithmetic skills during the first 3 years of primary school in languages with and without number word inversion.

Discerning Developmental Dyscalculia and Neurodevelopmental Models of Numerical Cognition in a Disadvantaged Educational Context

Developmental Dyscalculia (DD) signifies a failure in representing quantities, which impairs the performance of basic math operations and schooling achievement during childhood. The lack of specificity in assessment measures and respective cut-offs are the most challenging factors to identify children with DD, particularly in disadvantaged educational contexts. This research is focused on a numerical cognition battery for children, designed to diagnose DD through 12 subtests. The aims of the present study were twofold: to examine the prevalence of DD in a country with generally low educational attainment, by comparing z-scores and percentiles, and to test three neurodevelopmental models of numerical cognition based on performance in this battery. Participants were 304 Brazilian school children aged 7–12 years of both sexes (143 girls), assessed by the Zareki-R. Performances on subtests and the total score increase with age without gender differences. The prevalence of DD was 4.6% using the fifth percentile and increased to 7.4% via z-score (in total 22 out of 304 children were diagnosed with DD). We suggest that a minus 1.5 standard deviation in the total score of the Zareki-R is a useful criterion in the clinical or educational context. Nevertheless, a percentile ≤ 5 seems more suitable for research purposes, especially in developing countries because the socioeconomic environment or/and educational background are strong confounder factors to diagnosis. The four-factor structure, based on von Aster and Shalev’s model of numerical cognition (Number Sense, Number Comprehension, Number Production and Calculation), was the best model, with significant correlations ranging from 0.89 to 0.97 at the 0.001 level.

The relationship between numerosity perception and mathematics ability in adults: the moderating role of dots number

Background

It has been proposed that numerosity perception is the cognitive underpinning of mathematics ability. However, the existence of the association between numerosity perception and mathematics ability is still under debate, especially in adults. The present study examined the relationship between numerosity perception and mathematics ability and the moderating role of dots number (i.e., the numerosity of items in dot set) in adults.

Methods

Sixty-four adult participants from Anshun University completed behavioral measures that tested numerosity perception of small numbers and large numbers, mathematics ability, inhibition ability, visual-spatial memory, and set-switching ability.

Results

We found that numerosity perception of small numbers correlated significantly with mathematics ability after controlling the influence of inhibition ability, visual-spatial memory, and set-switching ability, but numerosity perception of large numbers was not related to mathematics ability in adults.

Conclusions

These findings suggest that the dots number moderates the relationship between numerosity perception and mathematics ability in adults and may contribute to explaining the contradictory findings in the previous literature about the link between numerosity perception and mathematics ability.

Children's Verbal, Visual and Spatial Processing and Storage Abilities: An Analysis of Verbal Comprehension, Reading, Counting and Mathematics

The importance of working memory (WM) in reading and mathematics performance has been widely studied, with recent research examining the components of WM (i.e., storage and processing) and their roles in these educational outcomes. However, the differing relationships between these abilities and the foundational skills involved in the development of reading and mathematics have received less attention. Additionally, the separation of verbal, visual and spatial storage and processing and subsequent links with foundational skills and downstream reading and mathematics has not been widely examined. The current study investigated the separate contributions of processing and storage from verbal, visual and spatial tasks to reading and mathematics, whilst considering influences on the underlying skills of verbal comprehension and counting, respectively. Ninety-two children aged 7- to 8-years were assessed. It was found that verbal comprehension (with some caveats) was predicted by verbal storage and reading was predicted by verbal and spatial storage. Counting was predicted by visual processing and storage, whilst mathematics was related to verbal and spatial storage. We argue that resources for tasks relying on external representations of stimuli related mainly to storage, and were largely verbal and spatial in nature. When a task required internal representation, there was a draw on visual processing and storage abilities. Findings suggest a possible meaningful separability of types of processing. Further investigation of this could lead to the development of an enhanced WM model, which might better inform interventions and reasonable adjustments for children who struggle with reading and mathematics due to WM deficits.

Inferencing Skill and Attentional Control Account for the Connection Between Reading Comprehension and Mathematics

We examined the relations of inference, vocabulary, decoding, short-term memory, and attentional control to reading comprehension and mathematics performance for first-grade students in the US (N = 83). The students were composed of 75% Hispanics, 15% Whites, and 6% Asian Americans. Students' performance on mathematics and reading comprehension were very strongly related (r = 0.88). Results from path analysis showed that inference (0.27 ≤ s ≤ 0.38) was independently and positively related to both reading comprehension and mathematics performance after accounting for short-term memory, attentional control, decoding, and vocabulary. Decoding was independently related to reading comprehension, but not mathematics, whereas vocabulary was independently related to mathematics, but not to reading comprehension. Attentional control was directly related to mathematics, and indirectly related to reading comprehension and mathematics via inference, vocabulary, and decoding, with a substantial total effect on reading comprehension and mathematics (0.56 respectively). Short-term memory was not directly nor indirectly related to reading comprehension and mathematics. Overall these results show that language and cognitive skills are shared resources of reading comprehension and mathematics, and highlight the roles of attentional control and inference skill in reading comprehension and mathematics.

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.

Groupitizing Improves Estimation of Numerosity of Auditory Sequences

Groupitizing is a recently described phenomenon of numerosity perception where clustering items of a set into smaller "subitizable" groups improves discrimination. Groupitizing is thought to be rooted on the subitizing system, with which it shares several properties: both phenomena accelerate counting and decrease estimation thresholds irrespective of stimulus format (for both simultaneous and sequential numerosity perception) and both rely on attention. As previous research on groupitizing has been almost completely limited to vision, the current study investigates whether it generalizes to other sensory modalities. Participants estimated the numerosity of a series of tones clustered either by proximity in time or by similarity in frequency. We found that compared with unstructured tone sequences, grouping lowered auditory estimation thresholds by up to 20%. The groupitizing advantage was similar across different grouping conditions, temporal proximity and tone frequency similarity. These results mirror the groupitizing effect for visual stimuli, suggesting that, like subitizing, groupitizing is an a-modal phenomenon.

No evidence for a core deficit in developmental dyscalculia or mathematical learning disabilities

BACKGROUND

Two hypotheses were tested regarding the characteristics of children with mathematical learning disabilities (MLD): (a) that children with MLD would have a 'core deficit' in basic number processing skills; and (b) that children with MLD would be at the end of a developmental continuum and have impairments in many cognitive skills.

METHODS

From a large sample (N = 1,303) of typically developing children, we selected a group definable as having MLD. The children were given measures of basic number processing and domain-general constructs. Differences between the observed sample and a simulated population were estimated using Cohen's d and Bayes factors. Receiver operating characteristic curves were plotted, and the area under the curve was computed to ascertain the diagnostic power of measures.

RESULTS

Results suggest that the differences between the MLD and control group can be defined along with general characteristics of the population rather than assuming single or multiple 'core deficits'. None of the measures of interest exceeded the diagnostic power that could be derived via simulation from the dimensional characteristics of the general population.

CONCLUSIONS

There is no evidence for core deficit(s) in MLD. We suggest that future research should focus on representative samples of typical populations and on carefully tested clinical samples confirming to the criteria of international diagnostic manuals. Clinical diagnoses require that MLD is persistent and resistant to intervention, so studies would deliver results less exposed to measurement fluctuations. Uniform diagnostic criteria would also allow for the easy cross-study comparison of samples overcoming a serious limitation of the current literature.

Data Envelopment Analysis (DEA) in the Educational Sciences

Many of the analytical models commonly used in educational research often aim to maximize explained variance and identify variable importance within models. These models are useful for understanding general ideas and trends, but give limited insight into the individuals within said models. Data envelopment analysis (DEA), is a method rooted in organizational management that makes such insights possible. Unlike models alluded to above, DEA does not explain variance. Instead, it explains how efficiently an individual utilizes their inputs to produce outputs, and identifies which input is not being utilized optimally. This paper provides a history and usages of DEA from fields outside of education, and describes the math and processes behind it. This paper then extends DEA's usage into the educational field using a study on child reading ability. Using students from the Project KIDS dataset (n=1987), DEA is demonstrated using a simple view of reading framework, identifying individual efficiency levels in using reading-based skills to achieve reading comprehension, determining which skills are being underutilized, and classifying new subsets of readers. New subsets of readers were identified using this method, with implications for more targeted interventions.

Executive Functions in Neurodevelopmental Disorders: Comorbidity Overlaps Between Attention Deficit and Hyperactivity Disorder and Specific Learning Disorders

The present study examines the comorbidity between specific learning disorders (SLD) and attention deficit and hyperactivity disorder (ADHD) by comparing the neuropsychological profiles of children with and without this comorbidity. Ninety-seven schoolchildren from 8 to 14 years old were tested: a clinical sample of 49 children with ADHD (n = 18), SLD (n = 18) or SLD in comorbidity with ADHD (n = 13), and 48 typically-developing (TD) children matched for age and intelligence. Participants were administered tasks and questionnaires to confirm their initial diagnosis, and a battery of executive function (EF) tasks testing inhibition, shifting, and verbal and visuospatial updating. Using one-way ANOVAs, our results showed that all children in the clinical samples exhibited impairments on EF measures (inhibition and shifting tasks) when compared with TD children. A more specific pattern only emerged for the updating tasks. Only children with SLD had significant impairment in verbal updating, whereas children with ADHD, and those with SLD in comorbidity with ADHD, had the worst performance in visuospatial updating. The clinical and educational implications of these findings are discussed.

Subitizing and counting impairments in children with developmental coordination disorder

Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.

Using working memory performance to predict mathematics performance 2 years on

A number of previous studies have used working memory components to predict mathematical performance in a variety of ways; however, there is no consideration of the contributions of the subcomponents of visuospatial working memory to this prediction. In this paper we conducted a 2-year follow-up to the data presented in Allen et al. (Q J Exp Psychol 73(2):239–248, 2020b) to ascertain how these subcomponents of visuospatial working memory related to later mathematical performance. 159 children (M age = 115.48 months) completed the maths test for this second wave of the study. Results show a shift from spatial–simultaneous influence to spatial–sequential influence, whilst verbal involvement remained relatively stable. Results are discussed in terms of their potential for education and future research.