Visual sustained attention and numerosity sensitivity correlate with math achievement in children

The effect of a 2-month abacus training on students with developmental dyscalculia

Developmental dyscalculia (DD) is a specific mathematics learning disorder, characterized by the atypical development of number sense, arithmetic calculation, and atypical development of brain structures and brain activations in core brain regions for number processing. The current study examined the intervention effect of a 2-month abacus training on DD students. Results showed that compared with the non-trained control group, the DD students with abacus training showed higher scores in number sense, calculation, and sustained attention abilities. Additionally, a larger percentage of students in the abacus group showed improvements in the DD screening tasks compared to the control group. The current finding indicated that abacus training or abacus courses can be used as a tool for further DD intervention.

What Predicts Early Math in Autism? A Study of Cognitive and Linguistic Factors

This study aimed to examine early mathematical abilities in young children with autism aged four to seven without intellectual disabilities and their connection with autism severity, non-verbal intelligence, and linguistic abilities (receptive vocabulary and grammar). The study involved 42 children with autism. We assessed participants' cognitive, mathematical, and linguistic abilities. Their mathematical performance was compared with that of typically developing children using standardized measures. Statistical analyses were conducted to identify potential cognitive or linguistic differences across groups based on mathematical performance, and to determine predictive factors for mathematical abilities in children with autism. The findings indicated a higher prevalence of mathematical difficulties among the participants compared to typically developing children. A classification based on mathematical performance revealed statistically significant differences in cognitive and linguistic variables across groups, particularly in the low-performance group. However, no significant differences were found according to autism severity between the groups. The analysis further identified that a combination of visuo-spatial and linguistic abilities was the most predictive factor for mathematical performance. The study suggests that young children with autism without intellectual disabilities may be more likely to experience mathematical difficulties compared to typically developing children. Assessing cognitive and linguistic abilities could serve as a predictive measure for mathematical difficulties of children with autism, even without a formal diagnosis. Future research, with larger samples or longitudinal approaches, could validate these findings or explore which specific mathematical abilities are more related to non-verbal intelligence and which ones to structural language.

Subitizing endures in sequential rather than simultaneous comparison tasks

Subitizing is the ability to appraise a number of small quantities (up to four) rapidly and precisely. This system, however, can be impaired by distractors presented along with targets to be enumerated. To better understand whether this limitation arises in perceptual circuits or in the response selection stage, we investigated whether subitizing can endure in simultaneous comparison tasks. Participants were asked to compare the number of dots in two sets on the left and right sides of the screen, presented either simultaneously or sequentially. For comparing within the numerosity range (6-32 dots), both the error rate and reaction time increased steadily as the ratio between the two numbers compared approached "1." Namely, a phenomenon labeled the ratio effect was revealed. For comparison with small numbers (<5), the sequential comparison task was errorless despite the ratio, suggesting the feature of subitizing. Individual efficiency (measured by the inverse efficiency score [IES]) did not correlate between number ranges in sequential comparison, suggesting that distinct mechanisms were involved. However, we found that in simultaneous tasks, error rate and efficiency showed an increase as the ratios of the two numbers compared approached "1." This is similar to the ratio effect revealed in the comparison for moderate numbers. Individual efficiency within these two ranges correlated, indicating that the enumeration within these two ranges was based on a single mechanism. These results suggest that subitizing cannot process sets in parallel, and numerosity takes the job whenever subitizing fails.

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.

Academic skills in children with cerebral palsy and specific learning disorders

AIM

To investigate the prevalence and clinical manifestations of reading, writing, and mathematics disorders in children with cerebral palsy (CP). We explored how the clinical profile of these children differed from those with specific learning disorders (SLDs), taking into account several factors, particularly IQ scores, neuropsychological aspects, and the presence of a visual impairment.

METHOD

A prospective cross-sectional study was conducted in 42 children with CP (mean age 9 years 8 months; SD = 2 years 2 months) and 60 children with SLDs (mean age 10 years; SD = 1 year 7 months). Clinical characteristics, neuromotor and cognitive profiles, neuropsychological aspects (speech performance, academic skills, visual attention, phonological awareness, working memory), and signs of visual impairment (visual acuity, contrast sensitivity, visual field, oculomotor functions) were assessed. A machine learning approach consisting of a random forest algorithm, where the outcome was the diagnosis and the covariates were the clinical variables collected in the sample, was used for the analyses.

RESULTS

About 59% of the children with CP had reading, writing, or mathematics disorders. Children with CP with learning disorders had a low performance IQ, normal phonological awareness, and working memory difficulties, whereas children with SLDs had normal performance IQ, impaired phonological awareness, and mild working memory difficulties. There were no differences in verbal IQ between the two groups.

INTERPRETATION

Learning disorders are frequently associated with CP, with different clinical characteristics, compared with SLDs. Assessment of academic skills is mandatory in these children, even if the IQ is normal. At school age, specific interventions to promote academic skills in children with CP could be a major rehabilitative goal.

WHAT THIS PAPER ADDS

Reading, writing, and mathematics disorders in cerebral palsy have specific clinical characteristics. Their underlying mechanisms differ from those described in specific learning disorders. Working memory impairment can be considered a hallmark of learning disorders in children with cerebral palsy.

Developmental Dyscalculia in Relation to Individual Differences in Mathematical Abilities

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

Form perception is a cognitive correlate of the relation between subitizing ability and math performance

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).

Cognitive Predictors of the Overlap of Reading and Math in Middle School

Math and reading skills are known to be related, and predictors of each are well researched. What is less understood is the extent to which these predictors, uniquely and collectively, overlap with one another, are differentially important for different academic skills, and account for the overlap of math and reading. We examined 20 potential predictors from four domains (working memory, processing speed, attention, and language) using latent variables and both timed and untimed achievement skill, in a sample (N=212) of at-risk middle schoolers, half of whom were English learners. The predictors accounted for about half of the overlap among achievement skills, suggesting that other factors (e.g., domain specific skills) might also be relevant for the overlap. We also found some differential prediction (language for reading, working memory for math). The present results extend and refine our understanding of the contribution of these cognitive predictors for reading and math.

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

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

The Impact of Audio-Visual, Visual and Auditory Cues on Multiple Object Tracking Performance in Children with Autism

Previous studies have documented differences in processing multisensory information by children with autism compared to typically developing children. Furthermore, children with autism have been found to track fewer multiple objects on a screen than those without autism, suggesting reduced attentional control. In the present study, we investigated whether children with autism (n = 33) and children without autism (n = 33) were able to track four target objects moving amongst four indistinguishable distractor objects while sensory cues were presented. During tracking, we presented various types of cues - auditory, visual, or audio-visual or no cues while target objects bounced off the inner boundary of a centralized circle. We found that children with autism tracked fewer targets than children without autism. Furthermore, children without autism showed improved tracking performance in the presence of visual cues, whereas children with autism did not benefit from sensory cues. Whereas multiple object tracking performance improved with increasing age in children without autism, especially when using audio-visual cues, children with autism did not show age-related improvement in tracking. These results are in line with the hypothesis that attention and the ability to integrate sensory cues during tracking are reduced in children with autism. Our findings could contribute valuable insights for designing interventions that incorporate multisensory information.

The componential nature of arithmetical cognition: some important questions

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

The Association Between Screen Time and Outdoor Time on Adolescent Mental Health and Academic Performance: Evidence from Rural China

Purpose

We examine how adolescent free time allocation-namely, screen time and outdoor time-is associated with mental health and academic performance in rural China.

Methods

This paper used a large random sample of rural junior high school students in Ningxia (n = 20,375; age=13.22), with data collected from self-reported demographic questionnaires (to assess free time allocation), the Strengths and Difficulties Questionnaire (to assess mental health), and a standardized math test (to measure academic performance). We utilized a multivariate OLS regression model to examine associations between free time allocation and adolescent outcomes, controlling for individual and family characteristics.

Results

Our sample's screen time and outdoor time both averaged around 1 hour. About 10% of the sample adolescents reported behavioral difficulties, while a similar percentage (11%) reported abnormal prosocial behaviors. Adolescents with higher levels of screen time (>2 hours) were 3 percentage points more likely to have higher levels of behavioral difficulties (p<0.001), indicating that excessive screen time was associated with worse mental health. Meanwhile, outdoor time was associated with better mental health, and positive correlations were observed at all levels of outdoor time (compared to no outdoor time, decreasing the likelihood of higher levels of behavioral difficulties by between 3 and 4 percentage points and of lower prosocial scores by between 6 and 8 percentage points; all p's<0.001). For academic performance, average daily screen times of up to 1 hour and 1-2 hours were both positively associated with standardized math scores (0.08 SD, p<0.001; 0.07 SD, p<0.01, respectively), whereas there were no significant associations between outdoor time and academic performance.

Conclusion

Using a large sample size, this study was the first to examine the association between adolescent free time allocation with mental health and academic performance, providing initial insights into how rural Chinese adolescents can optimize their free time.

Longitudinal relations between self-regulatory skills and mathematics achievement in early elementary school children from Chinese American immigrant families

Drawing from two waves (∼1.5-2.5 years apart) of longitudinal data, the current study investigated the bidirectional associations between self-regulatory skills and mathematics achievement among a socioeconomically diverse sample of school-age Chinese American children from immigrant families (N = 258; 48.1% girls; ages 5.8-9.1 years; first to third grades at Wave 1). Children's self-regulatory skills were assessed with task-based measures of attention focusing, inhibitory control, behavioral persistence, and comprehensive executive function as well as parent- and teacher-reported effortful control. Multiple regressions showed that behavioral persistence and parent-reported effortful control positively predicted math achievement over time. Math achievement positively predicted comprehensive executive function over time. These effects were found when controlling for child age, sex, generation status, family socioeconomic status, parents' cultural orientations, and prior levels of math achievement or self-regulation. The prospective relation of math achievement predicting comprehensive executive function remained significant after a false discovery rate correction.

Numerical Cognition after Brain Injury: Is There a Relationship between Subitizing and Arithmetical Abilities?

Subitizing is the ability to enumerate small quantities efficiently and automatically. Counting is a strategy adopted for larger numerosities resulting in a near linear increase in response time with each increase in quantity. Some developmental studies suggest that being able to subitize efficiently may be a predictor of later arithmetical ability. Being able to enumerate small quantities efficiently may be necessary for at least some aspects of arithmetical skill and understanding to develop. According to this view, arithmetic ability ultimately depends upon subitizing. If this were the case, when acquired brain injury results in impaired performance on subitizing tasks, mathematical performance may also be impaired. The following study tested eleven healthy control participants and nine chronic patients with acquired brain injury on tasks focused on visual enumeration, addition and multiplication to explore a potential relationship between subitizing ability and calculation performance. No overall correlations were found between subitizing and addition or multiplication speed. However, a very clear subitizing impairment was found in two patients who then demonstrated very different levels of preserved addition skills. The dissociations found and the large inter-individual variability supports a more componential view of arithmetical ability.

Contribution of sustained attention abilities to real-world academic skills in children

Sustained attention is a critical cognitive ability that improves over the course of development and predicts important real-world outcomes, such as academic achievement. However, the majority of work demonstrating links between sustained attention and academic skills has been conducted in lab-based settings that lack the ecological validity of a more naturalistic environment, like school. Further, most studies focus on targeted academic measures of specific sub-skills and have not fully examined whether this relationship generalizes to broad measures of academic achievement that are used for important, real-world, academic advancement decisions, such as standardized test scores. To address this gap, we examined the role of sustained attention in predicting targeted and broad assessments of academic abilities, where all skills were assessed in group-based environments in schools. In a sample of over 700 students aged 9-14, we showed that attention was positively related to performance on targeted assessments (math fluency and reading comprehension), as well as broad academic measures (statewide standardized test scores). Moreover, we found that attention was more predictive of targeted math sub-skills compared to assessments of broad math abilities, but was equally predictive of reading for both types of measures. Our findings add to our understanding of how sustained attention is linked to academic skills assessed in more 'real-world', naturalistic school environments and have important implications for designing tools to support student's academic success.

Phonological Processing, Visuospatial Skills, and Pattern Understanding in Chinese Developmental Dyscalculia

A number of previous studies have identified cognitive deficits in developmental dyscalculia (DD). Yet, most of these studies were in alphabetic languages, whereas few of them examined Chinese DD. Here, we conducted a study aiming to determine the cognitive factors associated with DD in Chinese children. Five candidate cognitive factors of DD-phonological retrieval, phonological awareness, visual-spatial attention, spatial thinking, and pattern understanding-were examined in the present study. A total of 904 Chinese children ages 8 to 11 years participated in this study. From the sample, 97 children were identified with DD through tests of arithmetic ability, and 93 age- and IQ-matched typically developing children were selected as controls. Logistic regression analysis revealed that phonological retrieval, pattern understanding, visual-spatial attention, and phonological awareness significantly predicted DD, whereas spatial thinking failed to do so. Results of logistic relative weights analysis showed that all five factors explained statistically significant amounts of variance in arithmetic scores. Phonological retrieval had the most influence on DD, followed by pattern understanding, visual-spatial attention, phonological awareness, and spatial thinking. These findings have important clinical implications for diagnosis and intervention of Chinese DD.

Math difficulties in attention deficit hyperactivity disorder do not originate from the visual number sense

There is ample evidence from literature and clinical practice indicating mathematical difficulties in individuals with ADHD, even when there is no concomitant diagnosis of developmental dyscalculia. What factors underlie these difficulties is still an open question. Research on dyscalculia and neurotypical development suggests visual perception of numerosity (the number sense) as a building block for math learning. Participants with lower numerosity estimation thresholds (higher precision) are often those with higher math capabilities. Strangely, the role of numerosity perception in math skills in ADHD has been neglected, leaving open the question whether math difficulties in ADHD also originate from a deficitary visual number sense. In the current study we psychophysically measured numerosity thresholds and accuracy in a sample of children/adolescents with ADHD, but not concomitant dyscalculia (N = 20, 8-16 years). Math abilities were also measured by tasks indexing different mathematical competences. Numerosity performance and math scores were then compared to those obtained from an age-matched control group (N = 20). Bayesian statistics indicated no difference between ADHD and controls on numerosity perception, despite many of the symbolic math tasks being impaired in participants with ADHD. Moreover, the math deficits showed by the group with ADHD remained substantial even when numerosity thresholds were statistically regressed out. Overall, these results indicate that math difficulties in ADHD are unlikely to originate from an impaired visual number sense.

The effects of university students' fragmented reading on cognitive development in the new media age: evidence from Chinese higher education

Introduction

The impacts of fragmented reading have been felt on a huge scale during the new media age. An increasingly fast-paced society and a corresponding drop in theoretical reading have affected reading literacy and cognitive development across communities-and among university students in particular. This study sought to identify the components of fragmented reading and cognitive development and investigate the former's effects on the latter among university students in the new media age.

Methods

Paper-based and electronic surveys were used to gather demographic and related-reading data from undergraduates at six Chinese universities in early 2021. After testing the data from 916 samples for reliability and validity, descriptive statistics were obtained and path analysis was undertaken using structural equation modeling.

Results

The students reported relatively high levels of fragmented reading, particularly in its temporal form. Significant associations were found between the constructs of fragmented reading and cognitive development. Specifically, the fragmentation of content, time, and attention in reading behavior had significant, positive effects on cognitive breadth. However, each of these components was somewhat negatively associated with cognitive depth.

Conclusions

The findings disclosed the dual effects of fragmented reading on the cognitive development of students, opening a new perspective on this debate. As fragmented reading in the new media age grows inexorably, the study highlights the need to utilize its positive effects on cognitive development by integrating and classifying fragmented information into the mental maps of learners.

Attention drives human numerosity-selective responses

Numerosity, the set size of a group of items, helps guide behavior and decisions. Previous studies have shown that neural populations respond selectively to numerosities. How numerosity is extracted from the visual scene is a longstanding debate, often contrasting low-level visual with high-level cognitive processes. Here, we investigate how attention influences numerosity-selective responses. The stimuli consisted of black and white dots within the same display. Participants' attention was focused on either black or white dots, while we systematically changed the numerosity of black, white, and total dots. Using 7 T fMRI, we show that the numerosity-tuned neural populations respond only when attention is focused on their preferred numerosity, irrespective of the unattended or total numerosities. Without attention, responses to preferred numerosity are suppressed. Unlike traditional effects of attention in the visual cortex, where attention enhances already existing responses, these results suggest that attention is required to drive numerosity-selective responses.

The association between non-symbolic number comparison and mathematical abilities depends on fluency

Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.

Mathematics and Numerosity but Not Visuo-Spatial Working Memory Correlate with Mathematical Anxiety in Adults

Many individuals, when faced with mathematical tasks or situations requiring arithmetic skills, experience exaggerated levels of anxiety. Mathematical anxiety (MA), in addition to causing discomfort, can lead to avoidance behaviors and then to underachievement. However, the factors inducing MA and how MA deploys its detrimental effects are still largely debated. There is evidence suggesting that MA affects working memory capacity by further diminishing its limited processing resources. An alternative account postulates that MA originates from a coarse early numerical cognition capacity, the perception of numerosity. In the current study, we measured MA, math abilities, numerosity perception and visuo-spatial working memory (VSWM) in a sample of neurotypical adults. Correlational analyses confirmed previous studies showing that high MA was associated with lower math scores and worse numerosity estimation precision. Conversely, MA turned out to be unrelated to VSWM capacities. Finally, partial correlations revealed that MA fully accounted for the relationship between numerosity estimation precision and math abilities, suggesting a key role for MA as a mediating factor between these two domains.

Patterns of Attention and Anxiety in Predicting Arithmetic Fluency among School-Aged Children

Although the interaction between anxiety and attention is considered crucial for learning and performance in mathematics, few studies have examined these cognitive and affective predictors in a single framework or explored the role of sustained attention in promoting children’s arithmetic performance, using traditional linear analyses and latent profile analysis (LPA). In this paper, state anxieties (in a math test and in an attention test situation), general anxiety traits, sustained attention (performance-based test and attention deficit/hyperactivity disorder (ADHD) self-ratings) and math achievement of 403 fourth and fifth graders (55.8% girls) were assessed. A negative correlation between state anxiety prior to the math test and arithmetic achievements was identified, even when controlling for other non-math related state anxieties and general anxiety. Sustained attention was a strong predictor of arithmetic achievement and functioned as a moderator in the anxiety-performance link. LPA identified six distinct profiles that revealed a complex relationship with arithmetic fluency. The weakest achievement was found for a specific math anxiety subgroup. The findings highlight the important role of the interaction of anxiety and sustained attention in children’s ability to perform math and enable new conclusions about the specific nature of math anxiety. Implications for future research are discussed.

The dynamics of grouping-induced biases in apparent numerosity revealed by a continuous tracking technique

Connecting pairs of items causes robust underestimation of the numerosity of an ensemble, presumably by invoking grouping mechanisms. Here we asked whether this underestimation in numerosity judgments could be revealed and further explored by continuous tracking, a newly developed technique that allows for fast and efficient data acquisition and monitors the dynamics of the responses. Participants continuously reproduced the perceived numerosity of a cloud of dots by moving a cursor along a number line, while the number of dots and the proportion connected by lines varied over time following two independent random walks. The technique was robust and efficient, and correlated well with results obtained with a standard psychophysics task. Connecting objects with lines caused an underestimation of approximately 15% during tracking, agreeing with previous studies. The response to the lines was slower than the response to the physical numerosity, with a delay of approximately 150 ms, suggesting that this extra time is necessary for processing the grouping effect.

Short-Term Exposure to Nature and Benefits for Students’ Cognitive Performance: a Review

There is growing interest recently in the outdoor environment surrounding schools where students spent time during breaks, in-school activities, and after-school programs. Several reviews have examined the impact of long-term exposures to nearby nature on students’ academic achievement, but none has focused on the effects of short-term contacts with nature on students’ cognitive performance. The aim of this review is to understand the context in which short-term passive exposures to greenness occur, how cognitive performance is measured, and the conditions under which cognitive benefits emerge at various educational levels. We reviewed 14 studies in the extant literature that report investigations involving students at different educational levels, from elementary school to university, in a short exposure to nature lasting from 10 to 90 min during a study day. The review shows that in 12 out of the 14 studies, across educational levels, cognitive benefits emerge in terms of directed attention restoration from mental fatigue due to contact with nature. A no-cost opportunity to sustain students’ cognition is a break in a green environment after mentally demanding activities.

Cross- and Within-Domain Associations of Early Reading and Mathematical Skills: Changes Across the Preschool Years

Existing research has mainly examined the role of cognitive correlates of early reading and mathematics from a stationary perspective that does not consider how these skills unfold and interact over time. This approach constraints the interpretation of cross-domain associations and the specificity of domain-specific covariates. In this study, we disentangle the role of these predictors and investigate cross-domain associations between reading, math, and two related domain-specific predictors (phonological awareness and fluency with number sets) over the kindergarten years (n=512, Mage=54months, SDage=3.5, 52% females). Results reveal that the overlap between reading and math skills changes over development. Reciprocal associations between reading and math abilities are observed at earlier stages; then, reading abilities become the lead force. Findings also show that phonological awareness and fluency with number sets are domain-specific predictors that do not contribute to cross-domain gains in academic skills. Indeed, there is a trend for domain-specific skills to be more strongly related to achievement at the beginning of formal education than at the beginning of kindergarten, which suggests an increasing differentiation of domains over the kindergarten years. Such findings have implications for the timing and nature of interventions that aim to support children's reading and mathematical development.

How physical activity, fitness, and motor skills contribute to math performance: Working memory as a mediating factor

PURPOSE

The purpose of this study was to examine whether physical activity, fitness, and motor skills have an indirect association with math performance via cognitive outcomes and if so, through which aspects of cognition?

METHODS

This study comprised 311 6th-9th grade adolescents (12-17 years [M age = 14.0 years], 59% girls) from seven schools throughout Finland in 2015. Math performance was measured via a teacher-rated math achievement and the Basic Arithmetic test. Cognitive functions were measured by broad cognitive test battery. Physical activity was assessed with a self-reported questionnaire and a hip-worn accelerometer. Aerobic fitness was estimated using a maximal 20-m shuttle run test, muscular fitness with curl-up and push-up tests, and motor skills with a 5-leaps test and a throwing-catching combination test. Structural equation modeling was applied to examine the associations.

RESULTS

In both boys and girls, motor skills had a positive indirect association with math outcomes through visuospatial working memory. Among girls, muscular fitness had a positive indirect association with math outcomes through visuospatial working memory. Aerobic fitness was positively associated with math achievement, but the indirect path via cognition was not observed. Self-reported physical activity had a borderline indirect positive association with math outcomes through visuospatial working memory. Accelerometer-based physical activity did not correlate with math performance.

CONCLUSION

Motor skills and muscular fitness had indirect positive associations with math performance, mediated by visuospatial working memory. The results give support to the viewpoints that the connections between motor skills, fitness, and physical activity to academic skills are mediated via specific cognitive skills.

Neural basis of approximate number in congenital blindness

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.

Approximate Number Sense in Students With Severe Hearing Loss: A Modality-Neutral Cognitive Ability

The Approximate Number System (ANS) allows humans and non-human animals to estimate large quantities without counting. It is most commonly studied in visual contexts (i.e., with displays containing different numbers of dots), although the ANS may operate on all approximate quantities regardless of modality (e.g., estimating the number of a series of auditory tones). Previous research has shown that there is a link between ANS and mathematics abilities, and that this link is resilient to differences in visual experience (Kanjlia et al., 2018). However, little is known about the function of the ANS and its relationship to mathematics abilities in the absence of other types of sensory input. Here, we investigated the acuity of the ANS and its relationship with mathematics abilities in a group of students from the Sichuan Province in China, half of whom were deaf. We found, consistent with previous research, that ANS acuity improves with age. We found that mathematics ability was predicted by Non-verbal IQ and Inhibitory Control, but not visual working memory capacity or Attention Network efficiencies. Even above and beyond these predictors, ANS ability still accounted for unique variance in mathematics ability. Notably, there was no interaction with hearing, which indicates that the role played by the ANS in explaining mathematics competence is not modulated by hearing capacity. Finally, we found that age, Non-verbal IQ and Visual Working Memory capacity were predictive of ANS performance when controlling for other factors. In fact, although students with hearing loss performed slightly worse than students with normal hearing on the ANS task, hearing was no longer significantly predictive of ANS performance once other factors were taken into account. These results indicate that the ANS is able to develop at a consistent pace with other cognitive abilities in the absence of auditory experience, and that its relationship with mathematics ability is not contingent on sensory input from hearing.

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

BACKGROUND

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

AIMS

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

METHODS AND PROCEDURES

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

OUTCOMES AND RESULTS

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

CONCLUSIONS AND IMPLICATIONS

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

Location- and object-based attention enhance number estimation

Humans and non-humans can extract an estimate of the number of items in a collection very rapidly, raising the question of whether attention is necessary for this process. Visual attention operates in various modes, showing selectivity both to spatial location and to objects. Here, we tested whether each form of attention can enhance number estimation, by measuring whether presenting a visual cue to increase attentional engagement will lead to a more accurate and precise representation of number, both when attention is directed to location and when it is directed to objects. Results revealed that enumeration of a collection of dots in the location previously cued led to faster, more precise, and more accurate judgments than enumeration in un-cued locations, and a similar benefit was seen when the cue and collection appeared on the same object. This work shows that like many other perceptual tasks, numerical estimation may be enhanced by the spread of active attention inside a pre-cued object.

The contribution of attentional processes to calculation skills in second and third grade in a typically developing sample

Attention is an important, multifaceted cognitive domain that includes many key cognitive processes involved in learning. This study aimed to identify the predictive links between different components of attentional skills and core calculation skills development, using two standardized measures assessing calculation (AC-MT 6–11) and attention skills (CAS) in a sample of 143 typically developing children of age range from 7.6 years to 9.4 years. The results showed that in 2nd grade, selective visuo-spatial attention emerged as an important predictor in the written calculation task, while the ability to inhibit distracting information seemed to better predict accuracy in oral calculation. In 3rd grade, visuo-spatial components of attention emerged as no longer predictive, whereas planning and active visuo-spatial attention abilities emerged as predictive of accuracy in the oral calculation task. These results confirm previous findings about the contribution that attentional skills may have in calculation skills development, supporting evidence for progressive automation attentional components over time.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.

Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability

Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children's visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children's precision in a visual ANS task related to their math performance - replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.

"Groupitizing": a strategy for numerosity estimation

Previous work has shown that when arrays of objects are grouped within clusters, participants can enumerate their numerosity more rapidly than when objects are randomly scattered, a phenomenon termed "groupitizing". Importantly, the magnitude of the grouping advantage correlates with math abilities in children. Here we show that sensory precision of numerosity estimation is also improved when grouping cues are available, by up to 20%. The grouping can be induced by color and/or spatial proximity, and occurs in temporal sequences as well as spatial arrays. The improvement is strongest for participants with the highest thresholds in the random, ungrouped conditions. Taken together with previous research, our data suggest that measurements correlations between numerosity estimation and formal math skills may be driven by grouping strategies, which require a minimal level of basic arithmetic.

Using a multidimensional model of attention to predict low-income preschoolers' early academic skills across time

The current study examines the organization of attention skills across the preschool year before kindergarten, and tests how distinct attention subcomponents predict early academic skills in a sample of low-income children (n = 99). Children completed well-validated attention tasks in fall at 4.5 years old and spring at 5 years old, capturing the abilities to selectively focus, sustain attention, and employ executive control. Exploratory factor analyses at both time points support a 2-factor model differentiating selective and sustained attention from attention processing speed and executive attention, suggesting that attention in low-income preschoolers may have a simpler organization than the 3-factor structure found in adulthood. Multiple regression models find children's ability to selectively focus and sustain attention serves as a robust concurrent and longitudinal predictor of academic skills. These results highlight the role of selective and sustained attention processes in supporting school readiness for economically vulnerable children.

The association between visual attention and arithmetic competence: The mediating role of enumeration

The current study aimed at clarifying the nature of relation between visual attention and arithmetic competence. A group of 301 Chinese second graders was assessed. Children's visual attention was measured using two versions of a visual search task, with efficient visual search (the similarity between the target and the distractors is low) tapping automatic, stimulus-driven visual attention and inefficient visual search (the similarity between the target and the distractors is high) tapping effortful, goal-directed visual attention. Children's arithmetic competence, enumeration skills (assessed in about half of the participants), and other domain-general cognitive abilities were also assessed. The results suggest that only inefficient visual search significantly predicted children's arithmetic competence, and such a relation was mediated through their enumeration skills. The findings highlight the role of fundamental cognitive capacities in mathematics learning and provide insights into potential interventions for improving children's arithmetic competence.

Math Anxiety Mediates the Link Between Number Sense and Math Achievements in High Math Anxiety Young Adults

In the past few years, many studies have suggested that subjects with high sensory precision in the processing of non-symbolic numerical quantities (approximate number system; ANS) also have higher math abilities. At the same time, there has been interest in another non-cognitive factor affecting mathematical learning: mathematical anxiety (MA). MA is defined as a debilitating emotional reaction to mathematics that interferes with the manipulation of numbers and the solving of mathematical problems. Few studies have been dedicated to uncovering the interplay between ANS and MA and those have provided conflicting evidence. Here we measured ANS precision (numerosity discrimination thresholds) in a cohort of university students with either a high (>75th percentile; n = 49) or low (<25th percentile; n = 39) score on the Abbreviate Math Anxiety Scale (AMAS). We also assessed math proficiency using a standardized test (MPP: Mathematics Prerequisites for Psychometrics), visuo-spatial attention capacity by means of a Multiple Objects Tracking task (MOT) and sensory precision for non-numerical quantities (disk size). Our results confirmed previous studies showing that math abilities and ANS precision correlate in subjects with high math anxiety. Neither precision in size-discrimination nor visuo-spatial attentional capacity were found to correlate with math capacities. Interestingly, within the group with high MA, our data also revealed a relationship between ANS precision and MA, with MA playing a key role in mediating the correlation between ANS and math achievement. Taken together, our results suggest an interplay between extreme levels of MA and the sensory precision in the processing of non-symbolic numerosity.

Numeracy skills in child synaesthetes: Evidence from grapheme-colour synaesthesia

Grapheme-colour synaesthesia is a neurological trait that causes lifelong colour associations for letter and numbers. Synaesthesia studies have demonstrated differences between synaesthetes and non-synaesthetes in ways that extend beyond synaesthesia itself (e.g., differences in their cognition, personality, and creativity). This research has focused almost exclusively on adult synaesthetes, and little is known about the profiles of synaesthetic children. By and large, findings suggest advantages for synaesthetes (e.g., Chun & Hupé, 2016; Havlik, Carmichael, & Simner, 2015; Rothen, Meier, & Ward, 2012; Rouw & Scholte, 2016; Simner & Bain, 2018) although differences in mathematical ability are unclear: some research indicates advantages (e.g., Green & Goswami, 2008) whilst others suggest difficulties (e.g., Rich et al., 2005). In the current study, we tested numerical cognition in a large group of children with grapheme-colour synaesthesia. Synaesthetes with coloured numbers showed advantages over their peers in their sense of numerosity, but not in their curriculum mathematics ability. We discuss how our findings speak to models for synaesthesia, to methodologies for assessing number cognition (e.g., dot numerosity tasks), and to the wider educational practice of using coloured number-tools in schools (e.g., Numicon; Oxford University Press, 2018).

Three-systems for visual numerosity: A single case study

Humans possess the remarkable capacity to assess the numerosity of a set of items over a wide range of conditions, from a handful of items to hundreds of them. Recent evidence is starting to show that judgments over such a large range is possible because of the presence of three mechanisms, each tailored to specific stimulation conditions. Previous evidence in favour of this theory comes from the fact that discrimination thresholds and estimation reaction times are not constants across numerosity levels. Likewise, attention is capable of dissociating the three mechanisms: when healthy adult observers are asked to perform concurrently a taxing task, the judgments of low numerosities (<4 dots) or of high numerosities is affected greatly, not so however for intermediate numerosities. Here we bring evidence from a neuropsychological perspective. To this end we measured perceptual performance in PA, a 41 year-old patient who suffers simultanagnosia after a hypoxic brain injury. PA showed a profound deficit in attentively tracking objects over space and time (multiple object tracking), even in very simple conditions where controls made no errors. PA also showed a massive deficit on sensory thresholds when comparing dot-arrays containing extremely low (3 dots) or extremely high (64, 128 dots) numerosities as well as in comparing dot-distances. Surprisingly, PA discrimination thresholds were relatively spared for intermediate numerosity (12 and 16 dots). Overall his deficit on the numerosity task results in a U-shape function across numerosity which, combined with the attentional deficit and the inability to judge dot-distances, confirms previously suggested three-systems for numerosity judgments.

Do the Colors of Educational Number Tools Improve Children's Mathematics and Numerosity?

This study examined how colored educational tools improve children's numerosity ("number sense") and/or mathematics. We tested children 6-10 years (n = 3,236) who had been exposed to colored numbers from the educational tools Numicon (Oxford University Press, 2018) or Numberjacks (Ellis, 2006), which map colors to magnitudes or Arabic numerals, respectively. In a free association task pairing numbers with colors, a subset of children spontaneously provided colors matching one of these schemas. These children, who had internalized Numicon (colored magnitude), showed significantly better numerosity but not mathematics compared to peers. There was no similar benefit from internalizing Numberjacks (colored numerals). These data support a model in which colored number tools provide benefits at different levels of numerical cognition, according to their different levels of cross-modal mappings.

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

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

Spontaneous perception of numerosity in pre-school children

There is strong evidence that humans can make rough estimates of the numerosity of a set of items, almost from birth. However, as numerosity covaries with many non-numerical variables, the idea of a direct number sense has been challenged. Here we applied two different psychophysical paradigms to demonstrate the spontaneous perception of numerosity in a cohort of young pre-school children. The results of both tasks showed that even at that early developmental stage, humans spontaneously base the perceptual choice on numerosity, rather than on area or density. Precision in one of these tasks predicted mathematical abilities. The results reinforce strongly the idea of a primary number sense and provide further evidence linking mathematical skills to the sensory precision of the spontaneous number sense, rather than to mechanisms involved in handling explicit numerosity judgements or extensive exposure to mathematical teaching.