Dyscalculia: from brain to education

Increased structural covariance in brain regions for number processing and memory in children with developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Several studies demonstrated functional network alterations in DD. Yet, there are no studies, which examined the structural network integrity in DD. We compared whole‐brain maps of volume based structural covariance between 19 (4 males) children with DD and 18 (4 males) typically developing children. We found elevated structural covariance in the DD group between the anterior intraparietal sulcus to the middle temporal and frontal gyrus (p < 0.05, corrected). A hippocampus subfield analysis showed higher structural covariance in the DD group for area CA3 to the parahippocampal and calcarine sulcus, angular gyrus and anterior part of the intraparietal sulcus as well as to the lingual gyrus. Lower structural covariance in this group was seen for the subiculum to orbitofrontal gyrus, anterior insula and middle frontal gyrus. In contrast, the primary motor cortex (control region) revealed no difference in structural covariance between groups. Our results extend functional magnetic resonance studies by revealing abnormal gray matter integrity in children with DD. These findings thus indicate that the pathophysiology of DD is mediated by both structural and functional abnormalities in a network involved in number processing and memory function.

The perception of subset quantity and items in an environment with distractors in a population with mathematical learning difficulties

OBJECTIVE

People often perceive a quantity of specific objects that appear as part of an overall group of items (a subset). This study investigates this type of perception among a population with mathematical leaning difficulties (MLD).

METHOD

Sixty-two participants (mean age: 26.82) reported the general and subset quantity of items using a subset quantity detection task or a conjunction visual search task.

RESULTS

MLD had difficulties perceiving both the general quantity presented and the subset quantity of items. They also had difficulties preforming a conjunction visual search task, even when the task did not involve numerical processing.

CONCLUSIONS

MLD has spatial difficulties in the form of visual search and subset quantity detection. The current study suggests that MLD might experience greater difficulties in daily tasks, which might be related to those tasks (e.g., detecting the amount of forks among other items of silverware on the table).

Neurodevelopmental disorders: An innovative perspective via the response to intervention model

Neurodevelopmental disorders are a group of conditions classified together by the most recent edition of the Diagnostic and Statistical Manual of Mental Disorders which include intellectual disability, communication disorders, autism spectrum disorder, attention-deficit/hyperactivity disorder, specific learning disorder (SLD), and motor disorders. SLD is present in many students, who exhibit significant difficulties in the acquisition of reading, written expression, and mathematics, mostly due to problems with executive functions (EF). The present study is a review of the current situation of neurodevelopmental disorders and SLD focusing on the benefits of the response to intervention model (RtI), which allows the combination of evaluation and intervention processes. It also addresses the key role of EF. The importance of adapting RtI to new possibilities such as the use of virtual reality is discussed and a theoretical framework for carrying that out is provided.

Identified Motivation as a Key Factor for School Engagement During the COVID-19 Pandemic-Related School Closure

On March 16, 2020, French schools suddenly closed due to the COVID-19 pandemic, and middle school students were asked to study from home with no direct interactions with teachers or classmates. However, school plays an important role in the development of social, intellectual, and mental competencies and can counteract the negative effects of adverse life events on learning and early school dropout. In this study, we investigated how the unusual context of school closure during the COVID-19 pandemic affected school engagement. Specifically, we focused on inter-individual differences in the motivational determinants of school engagement. We thus performed an online survey of 170 students focusing on the time spent on mathematics assignments, motivation regulation, implicit theories of intelligence, such as adopting a growth or a fixed mindset about his/her intellectual abilities, and optimism. Importantly, the students participated in the online survey during the first lockdown period, with schools closed (T1), and the second lockdown period, with schools remaining open (T2). During T1, identified motivation positively predicted the time spent on math homework assignments: the more the students thought that working on math exercises was useful for their future life, the more time they spent studying. Importantly, the link between identified motivation and school engagement was specific to T1, when schools were closed, as indicated by a significant interaction between identified motivations by type of lockdown. These results suggest that having self-determined motivation is of particular importance when students are deprived of social and intellectual interactions with classmates and teachers. This finding paves the way toward the development of wise rational interventions that target identified motivation and can be applied during challenging societal times and adverse, common life events to keep students engaged with school.

Kindergarten screening tools filled out by parents and teachers targeting dyslexia. Predictions and developmental trajectories from age 5 to age 15 years

The concept of early 'efforts' has led to discussions for and against introducing language assessment for all kindergarten children. Evidence-based kindergarten screening tools completed by close caregivers could solve this controversy as the children themselves would only be indirectly involved. The aim of this study was to see whether the scores of such early screening tools aiming at developmental dyslexia could predict school marks of literacy competence 10 years later, and to see whether these screening tools would reveal different dyslexia trajectories. The study is part of the Bergen Longitudinal Dyslexia Study, and the results from individual testing are reported elsewhere. Here, the caregivers' views isolated from the rest of the study are focused. Three tools were used: the RI-5, a questionnaire assessing the risk of dyslexia; the TRAS, a non-standardized observation tool of children's communication skills; and the CCC-2, a questionnaire assessing Developmental Language Disorders. Screening was performed at age 5 (TP1), age 11, (TP2) and age 15 (TP3). At TP2, when dyslexia was identified, 13 children formed the dyslexia group, and the rest formed the control group. At TP3, the RI-5 and CCC-2 turned out to be predictive of literacy competence as measured by school marks. Developmental trajectories were seen through the regroupings and scorings into a persistent group, a late onset group and a resolving group. Evidence-based preschool screening tools filled out by close caregivers offer valid information on later literacy developmental trajectories.

Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function

A robust association between young children's early mathematical proficiency and later academic achievement is well established. Less is known about the mechanisms through which early mathematics skills may contribute to later mathematics and especially reading achievement. Using a parallel multiple mediator model, the current study investigated whether executive function (integration of working memory, inhibition, and cognitive flexibility) can explain the relations between early mathematics skills and elementary school mathematics and reading achievement. Data in this longitudinal study were collected from 243 children during the last year of early childhood education and care (kindergarten ages 5 and 6 years), 1 year later in first grade, and 5 years later when the children were in fifth grade. Background variables (maternal education, age, sex, and immigrant status), kindergarten baseline skills, and mediating effects of first-grade mathematics, phonological awareness, vocabulary, and possible omitted variables were controlled. Results showed that first-grade executive function mediated the effects of kindergarten mathematics on fifth-grade mathematics and on reading achievement. These findings suggest that executive function may work as a mechanism that may help to explain the frequently found strong association between children's early mathematics skills and later mathematics and reading achievement.

Mathematics Disability vs. Learning Disability: A 360 Degree Analysis

A fundamental issue for research in mathematics disability (MD) and reading disability (RD) is: If these disabilities are clearly distinct, why is there so high a level of comorbidity, together with the converse; if these disabilities are so similar, why are there clear differences in underlying causes and aetiology? In order to address this puzzle, we introduce the “360 degree analysis” (360DA) framework and apply it to the overlap between RD and MD. The 360DA process starts by analyzing the issue from four perspectives: theoretical, developmental, affective, and pedagogical. Under 360DA, these analyses are then integrated to provide insights for theory, and for individual assessment and support, together with directions for future progress. The analyses confirm extensive similarities between arithmetic and reading development in terms of rote learning, executive function (EF), and affective trauma, but also major differences in terms of the conceptual needs, the motor coordination needs, and the methods of scaffolding. In terms of theory, commonalities are interpreted naturally in terms of initial general developmental delay followed by domain-independent affective trauma following school failure. Dissociations are interpreted in terms of cerebellar vs. hippocampal learning networks, sequential vs. spatial processing, and language vs. spatial scaffolding, with a further dimension of the need for accurate fixation for reading. The framework has significant theoretical and applied implications.

Arithmetic Word-Problem Solving as Cognitive Marker of Progression in Pre-Manifest and Manifest Huntington's Disease

BACKGROUND

Arithmetic word-problem solving depends on the interaction of several cognitive processes that may be affected early in the disease in gene-mutation carriers for Huntington's disease (HD).

OBJECTIVE

Our goal was to examine the pattern of performance of arithmetic tasks in premanifest and manifest HD, and to examine correlations between arithmetic task performance and other neuropsychological tasks.

METHODS

We collected data from a multicenter cohort of 165 HD gene-mutation carriers. The sample consisted of 31 premanifest participants: 16 far-from (>12 years estimated time to diagnosis; preHD-A) and 15 close-to (≤12 years estimated time to diagnosis; preHD-B), 134 symptomatic patients (early-mild HD), and 37 healthy controls (HC). We compared performance between groups and explored the associations between arithmetic word-problem solving and neuropsychological and clinical variables.

RESULTS

Total arithmetic word-problem solving scores were lower in preHD-B patients than in preHD-A (p < 0.05) patients and HC (p < 0.01). Early-mild HD patients had lower scores than preHD patients (p < 0.001) and HC (p < 0.001). Compared to HC, preHD and early-mild HD participants made more errors as trial complexity increased. Moreover, arithmetic word-problem solving scores were significantly associated with measures of global cognition (p < 0.001), frontal-executive functions (p < 0.001), attention (p < 0.001) visual working memory (p < 0.001), mental rotation (p < 0.001), and confrontation naming (p < 0.05).

CONCLUSION

Arithmetic word-problem solving is affected early in the course of HD and is related to deficient processes in frontal-executive and mentalizing-related processes.

The cognitive profiles for different samples of mathematical learning difficulties and their similarity to typical development: Evidence from a longitudinal study

Several cognitive deficits have been suggested to induce mathematical learning difficulties (MLD), but it is unclear whether the cognitive profile for all children with MLD is the same and to what extent it differs from typically developing (TD) children. This study investigated whether such a profile could be distinguished when cognitive skills and math performance are compared between TD children and children with MLD. This was accomplished by employing two-way repeated-measures analyses of covariance in 276 10-year-old participants (60 with MLD) from fourth and fifth grades. In addition, we investigated whether more restrictive selection criteria for MLD result in different mathematical and cognitive profiles by means of independent-samples t tests. Results revealed that cognitive mechanisms for math development are mostly similar for children with MLD and TD children and that variability in sample selection criteria did not produce different mathematical or cognitive profiles. To conclude, the cognitive mechanisms for math development are broadly similar for children with MLD and their TD counterparts even when different MLD samples were selected. This strengthens our idea that MLD can be defined as the worst performance on a continuous scale rather than as a discrete disorder.

Acceptability of Neuroscientific Interventions in Education

Researchers are increasingly applying neuroscience technologies that probe or manipulate the brain to improve educational outcomes. However, their use remains fraught with ethical controversies. Here, we investigate the acceptability of neuroscience applications to educational practice in two groups of young adults: those studying bioscience who will be driving future basic neuroscience research and technology transfer, and those studying education who will be choosing among neuroscience-derived applications for their students. Respondents rated the acceptability of six scenarios describing neuroscience applications to education spanning multiple methodologies, from neuroimaging to neuroactive drugs to brain stimulation. They did so from two perspectives (student, teacher) and for three recipient populations (low-achieving, high-achieving students, students with learning disabilities). Overall, the biosciences students were more favorable to all neuroscience applications than the education students. Scenarios that measured brain activity (i.e., EEG or fMRI) to assess or predict intellectual abilities were deemed more acceptable than manipulations of mental activity by drug use or stimulation techniques, which may violate body integrity. Enhancement up to the norm for low-achieving students and especially students with learning disabilities was more favorably viewed than enhancement beyond the norm for high-achieving students. Finally, respondents rated neuroscientific applications to be less acceptable when adopting the perspective of a teacher than that of a student. Future studies should go beyond the acceptability ratings collected here to delineate the role that concepts of access, equity, authenticity, agency and personal choice play in guiding respondents' reasoning.

Developmental brain dynamics of numerical and arithmetic abilities

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

Resting State EEG Related to Mathematical Improvement After Spatial Training in Children

Spatial cognitive abilities, including mental rotation (MR) and visuo-spatial working memory (vsWM) are correlated with mathematical performance, and several studies have shown that training of these abilities can enhance mathematical performance. Here, we investigated the behavioral and neural correlates of MR and vsWM training combined with number line (NL) training. Fifty-seven children, aged 6–7, performed 25 days of NL training combined with either vsWM or MR and participated in an Electroencephalography (EEG)-session in school to measure resting state activity and steady-state visual evoked potentials during a vsWM task before and after training. Fifty children, aged 6–7, received usual teaching and acted as a control group. Compared to the control group, both training groups improved on a combined measure of mathematics. Cognitive improvement was specific to the training. Significant pre-post changes in resting state-EEG (rs-EEG), common to both training groups, were found for power as well as for coherence, with no significant differences in rs-EEG-changes between the vsWM and MR groups. Two of the common rs-EEG changes were correlated with mathematical improvement: (1) an increase in coherence between the central frontal lobe and the right parietal lobe in frequencies ranging from 16 to 25 Hz, and (2) an increase in coherence between the left frontal lobe and the right parietal lobe ranging from 23 to 25 Hz. These results indicate that changes in fronto-parietal coherence are related to an increase in mathematical performance, which thus might be a useful measure in further investigations of mathematical interventions in children.

Promoting the emergence of tacting three-digit numerals through a chain prompt combined with matrix training

Children with autism spectrum disorder (ASD) have difficulty generalizing from directly trained responses to untrained responses (i.e., emergent responding). In this study, we used a chain prompt combined with matrix training to teach 2 participants with ASD to tact 192 three-digit numerals. We used a multiple-baseline design across matrices to evaluate the treatment effects on trained and untrained tacts of numerals. Both participants mastered all numerals exposed to training and all numerals not exposed to training after 3 to 5 sixteen-trial sessions per matrix. One participant learned to tact 8 numerals for each 1 numeral exposed to direct training, and the other participant learned to tact 12 numerals for each 1 numeral exposed to direct training. We discuss these results relative to the effectiveness and efficiency of our chain prompt combined with matrix training for teaching tacting skills for targets with shared stimulus properties that facilitate generalization to untrained targets.

Predicting learning and achievement using GABA and glutamate concentrations in human development

Previous research has highlighted the role of glutamate and gamma-aminobutyric acid (GABA) in learning and plasticity. What is currently unknown is how this knowledge translates to real-life complex cognitive abilities that emerge slowly and how the link between these neurotransmitters and human learning and plasticity is shaped by development. While some have suggested a generic role of glutamate and GABA in learning and plasticity, others have hypothesized that their involvement shapes sensitive periods during development. Here we used a cross-sectional longitudinal design with 255 individuals (spanning primary school to university) to show that glutamate and GABA in the intraparietal sulcus explain unique variance both in current and future mathematical achievement (approximately 1.5 years). Furthermore, our findings reveal a dynamic and dissociable role of GABA and glutamate in predicting learning, which is reversed during development, and therefore provide novel implications for models of learning and plasticity during childhood and adulthood.

Emerging neurodevelopmental perspectives on mathematical learning

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

A Network Analysis of the Relationship among Reading, Spelling and Maths Skills

Background. Skill learning (e.g., reading, spelling and maths) has been predominantly treated separately in the neuropsychological literature. However, skills (as well as their corresponding deficits), tend to partially overlap. We recently proposed a multi-level model of learning skills (based on the distinction among competence, performance, and acquisition) as a framework to provide a unitary account of these learning skills. In the present study, we examined the performance of an unselected group of third- to fifth-grade children on standard reading, spelling, and maths tasks, and tested the relationships among these skills with a network analysis, i.e., a method particularly suited to analysing relations among different domains. Methods. We administered a battery of reading, spelling, and maths tests to 185 third-, fourth-, and fifth-grade children (103 M, 82 F). Results. The network analysis indicated that the different measures of the same ability (i.e., reading, spelling, and maths) formed separate clusters, in keeping with the idea that they are based on different competences. However, these clusters were also related to each other, so that three nodes were more central in connecting them. In keeping with the multi-level model of learning skills, two of these tests (arithmetic facts subtest and spelling words with ambiguous transcription) relied heavily on the ability to recall specific instances, a factor hypothesised to underlie the co-variation among learning skills. Conclusions. The network analysis indicated both elements of association and of partial independence among learning skills. Interestingly, the study was based on standard clinical instruments, indicating that the multi-level model of learning skills might provide a framework for the clinical analysis of these learning skills.

The Polygenic Nature and Complex Genetic Architecture of Specific Learning Disorder

Specific Learning Disorder (SLD) is a multifactorial, neurodevelopmental disorder which may involve persistent difficulties in reading (dyslexia), written expression and/or mathematics. Dyslexia is characterized by difficulties with speed and accuracy of word reading, deficient decoding abilities, and poor spelling. Several studies from different, but complementary, scientific disciplines have investigated possible causal/risk factors for SLD. Biological, neurological, hereditary, cognitive, linguistic-phonological, developmental and environmental factors have been incriminated. Despite worldwide agreement that SLD is highly heritable, its exact biological basis remains elusive. We herein present: (a) an update of studies that have shaped our current knowledge on the disorder’s genetic architecture; (b) a discussion on whether this genetic architecture is ‘unique’ to SLD or, alternatively, whether there is an underlying common genetic background with other neurodevelopmental disorders; and, (c) a brief discussion on whether we are at a position of generating meaningful correlations between genetic findings and anatomical data from neuroimaging studies or specific molecular/cellular pathways. We conclude with open research questions that could drive future research directions.

Typical Crossmodal Numerosity Perception in Preterm Newborns

Premature birth is associated with a high risk of damage in the parietal cortex, a key area for numerical and non-numerical magnitude perception and mathematical reasoning. Children born preterm have higher rates of learning difficulties for school mathematics. In this study, we investigated how preterm newborns (born at 28-34 weeks of gestation age) and full-term newborns respond to visual numerosity after habituation to auditory stimuli of different numerosities. The results show that the two groups have a similar preferential looking response to visual numerosity, both preferring the incongruent set after crossmodal habituation. These results suggest that the numerosity system is resistant to prematurity.

Parent-based training of basic number skills in children with Down syndrome using an adaptive computer game

BACKGROUND

Numeracy is an area of difficulty for children with Down syndrome (DS). It has been demonstrated that The Number Race, a non-commercial adaptive computer game designed to foster basic mathematical abilities, represents a promising instrument to enhance these skills in children with DS when delivered by an expert in a clinical setting.

AIMS

In the present study, we assessed the efficacy of The Number Race when administered at home by properly instructed and remotely supervised parents.

METHODS AND PROCEDURES

Basic numerical skills were assessed before and after training, as well as at three-months follow-up. Performance of children with DS who worked at home with the parent (PG) was compared with that of children who received the training by an expert (EG). For both groups, the training lasted ten weeks, with two weekly sessions of 20-30 min.

OUTCOMES AND RESULTS

Results show that both groups improved across various measures of numerical proficiency, including the overall score of the numeracy assessment battery, while only the EG showed an improvement in a measure of mental calculation. The improvements were maintained three months after the end of the training.

CONCLUSIONS AND IMPLICATIONS

These findings confirm the efficacy of The Number Race and extend it to an home-based setting, whereby parents administer the training with external supervision.

Spatial Ability in Children with Mathematics Learning Disorder (MLD) and Its Impact on Executive Functions

Mathematics Learning Disorder (MLD) has been found to be related to impairments in cognitive functions. Spatial ability (SA), which is made up of eight single but unified elements can be assumed to have a leading part in different areas of math skills. The first objective of this study was to explore differences in SA factors in 128 school children of third to sixth grade with and without MLD. The Flexibility of Closure, Closure Speed, Perceptual Speed, Visualization, Spatial Relation, Spatial Orientation, Spatial Temporal, and Wayfinding were measured through eight tasks. The second objective of the study was to explore the SA factors' ability to predict the performance of MLD participants in three executive functions. The results revealed that participants with MLD had poorer performance in all the SA tasks and it took longer to finish the visualization, spatial relation, and spatial orientation tasks compared to children with typical development (TD). Regression analysis indicated that some of the SA factors could predict working memory and cognitive flexibility, but they were unable to predict response inhibition. Regarding these results, applying SA factors in cognitive rehabilitation programs of children with MLD seems necessary.

Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.

Neurocognitive modeling of latent memory processes reveals reorganization of hippocampal-cortical circuits underlying learning and efficient strategies

Efficient memory-based problem-solving strategies are a cardinal feature of expertise across a wide range of cognitive domains in childhood. However, little is known about the neurocognitive mechanisms that underlie the acquisition of efficient memory-based problem-solving strategies. Here we develop, to the best of our knowledge, a novel neurocognitive process model of latent memory processes to investigate how cognitive training designed to improve children's problem-solving skills alters brain network organization and leads to increased use and efficiency of memory retrieval-based strategies. We found that training increased both the use and efficiency of memory retrieval. Functional brain network analysis revealed training-induced changes in modular network organization, characterized by increase in network modules and reorganization of hippocampal-cortical circuits. Critically, training-related changes in modular network organization predicted performance gains, with emergent hippocampal, rather than parietal cortex, circuitry driving gains in efficiency of memory retrieval. Our findings elucidate a neurocognitive process model of brain network mechanisms that drive learning and gains in children's efficient problem-solving strategies.

Flipped-OCN Method in Mathematics Learning to Analyze the Attitudes of Pre-Service Teachers

Due to the learning difficulties in mathematics education, a new teaching methodology have been proposed for its improvement. Difficulties in mathematics learning indicate that students are not able to properly deal with resolving calculations and/or problems. This research examines the evolution of the attitudes of pre-service teachers’ (PSTs) toward mathematics learning when an open calculation based on numbers (OCN) method was followed in a flipped classroom. It was conducted in a general mathematics course, Primary Education bachelor’s degree during the course of 2019/2020. A total of 143 students participated in the study (230 students enrolled), with a pre- and post-test survey questionnaire. Based on the analysis of survey questionnaires, the obtained results demonstrated that the attitudes (own beliefs and conceptions (OB), positive (ATP), and negative (ATN) attitudes) of PSTs improved positively after completing the flipped-OCN method toward mathematics learning. Regarding the statistical analyses, all questions had a significant difference that showed the influence of the flipped-OCN method, improving the PSTs attitudes toward mathematics learning (p < 0.005). According to the structural equation modeling—partial least squares (SEM-PLS) analysis, it demonstrated that the components relation effects of OB, ATP, and ATN of PSTs toward mathematics learning, and the influence of their educational background. Finally, with the principal component analysis (PCA), it can be found out that the science and technology background were positively correlated after the flipped-OCN method comparing with the rest of PSTs. The influence of the proposed method indicated a significant improvement in these components. Therefore, the results concluded that this study allowed to draw a promising tendency about the PSTs’ attitudes toward mathematics learning with the OCN method in the flipped classroom. Additionally, these outcomes could advance our comprehension of how to help pre-service education for teachers’ enhancement and maturity of positive attitudes about themselves as future teachers. Then, it would be a fundamental piece in building logical and critical thinking and development for children.

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

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

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Training basic numerical skills in children with Down syndrome using the computerized game "The Number Race"

Individuals with Down syndrome (DS) present reduced basic numerical skills, which have a negative impact on everyday numeracy and mathematical learning. Here, we evaluated the efficacy of the adaptive (non-commercial) computerized game “The Number Race” in improving basic numerical skills in children with DS. The experimental group (EG; N = 30, M_{age-in-months} 118, range 70–149) completed a training playing with “The Number Race”, whereas children in the control group (CG; N = 31, M_{age-in-months} 138, range 76–207) worked with software aiming at improving their reading skills. The training lasted 10 weeks with two weekly sessions of 20–30 min each. We assessed both groups’ numerical and reading skills before and immediately after the end of the training, as well as at a 3-months follow-up. We found weak evidence for post-training groups differences in terms of overall numeracy score. However, the EG displayed substantial improvements in specific numerical skills and in mental calculation, which were maintained over time, and no improvement in reading. Conversely, the CG showed improvements in their reading skills as well as in number skills but to a lesser extent compared to the EG. Overall, “The Number Race” appears as a suitable tool to improve some aspects of numeracy in DS.

Fostering early numerical competencies by playing conventional board games

Recent evidence indicates that playing numerical board games is beneficial for the numerical development of preschoolers. However, board games used in these studies were often specifically developed for training numerical skills. Therefore, we examined whether similar beneficial effects could be observed for playing conventional board games such as Parcheesi. In an intervention study with seven 30-min training sessions over a period of 4 weeks, we observed that 4- to 6-year-old children (M_age = 4 years 11 months) who played conventional board games with traditional number dice (with dot faces numbered from one to six) benefitted more from the board games than children who played board games with color or non-numerical symbol dice. Pretest-posttest comparisons indicated differential effects on counting skills and the ability to recognize and use structures. Beyond these immediate training effects observed in posttest, the differential beneficial effects of playing board games using traditional dot dice on recognizing and using structures was still present in a follow-up test 1 year after the intervention. Thus, playing conventional board games using traditional number dice seems to be an effective low-threshold intervention to foster early numerical competencies.

Measurement of Cognition for the National Children's Study

The National Children's Study Cognitive Health Domain Team developed detailed plans for assessing cognition longitudinally from infancy to early adulthood. These plans identify high-priority aspects of cognition that can be measured efficiently and effectively, and we believe they can serve as a model for future large-scale longitudinal research. For infancy and toddlerhood, we proposed several paradigms that collectively allowed us to assess six broad cognitive constructs: (1) executive function skills, (2) episodic memory, (3) language, (4) processing speed, (5) spatial and numerical processing, and (6) social cognition. In some cases, different trial sequences within a paradigm allow for the simultaneous assessment of multiple cognitive skills (e.g., executive function skills and processing speed). We define each construct, summarize its significance for understanding developmental outcomes, discuss the feasibility of its assessment throughout development, and present our plan for measuring specific skills at different ages. Given the need for well-validated, direct behavioral measures of cognition that can be used in large-scale longitudinal studies, especially from birth to age 3 years, we also initiated three projects focused on the development of new measures.

Effect of Mental Calculation and Number Comparison on a Manual-Pointing Movement

The present study aimed at examining the effect of mental calculation and number comparison on motor performance measured as the movement time of a fast manual-pointing movement. Three experiments, involving a total number of 65 undergraduate subjects, examined the effect of mental subtraction (complex) and, respectively, of (a) mental addition (simple or complex), (b) mental multiplication (simple or complex), and (c) the comparison of dot sets and number comparison. Each number was written in Arabic. The movement times were analyzed by using a multilevel linear mixed-effect model. The results showed significant improvement of manual-pointing movement performance only after the complex calculations and after number comparison. Possible implication of attentional mechanisms specific to this arithmetical activity is further discussed.

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.

Efficacy of a Computer-Based Learning Program in Children With Developmental Dyscalculia. What Influences Individual Responsiveness?

This study presents the evaluation of a computer-based learning program for children with developmental dyscalculia and focuses on factors affecting individual responsiveness. The adaptive training program Calcularis 2.0 has been developed according to current neuro-cognitive theory of numerical cognition. It aims to automatize number representations, supports the formation and access to the mental number line and trains arithmetic operations as well as arithmetic fact knowledge in expanding number ranges. Sixty-seven children with developmental dyscalculia from second to fifth grade (mean age 8.96 years) were randomly assigned to one of two groups (Calcularis group, waiting control group). Training duration comprised a minimum of 42 training sessions à 20 min within a maximum period of 13 weeks. Compared to the waiting control group, children of the Calcularis group demonstrated a higher benefit in arithmetic operations and number line estimation. These improvements were shown to be stable after a 3-months post training interval. In addition, this study examines which predictors accounted for training improvements. Results indicate that this self-directed training was especially beneficial for children with low math anxiety scores and without an additional reading and/or spelling disorder. In conclusion, Calcularis 2.0 supports children with developmental dyscalculia to improve their arithmetical abilities and their mental number line representation. However, it is relevant to further adapt the setting to the individual circumstances.

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

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

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.

Putting a Finger on Numerical Development - Reviewing the Contributions of Kindergarten Finger Gnosis and Fine Motor Skills to Numerical Abilities

The well-documented association between fingers and numbers is not only based on the observation that most children use their fingers for counting and initial calculation, but also on extensive behavioral and neuro-functional evidence. In this article, we critically review developmental studies evaluating the association between finger sensorimotor skills (i.e., finger gnosis and fine motor skills) and numerical abilities. In sum, reviewed studies were found to provide evidential value and indicated that both finger gnosis and fine motor skills predict measures of counting, number system knowledge, number magnitude processing, and calculation ability. Therefore, specific and unique contributions of both finger gnosis and fine motor skills to the development of numerical skills seem to be substantiated. Through critical consideration of the reviewed evidence, we suggest that the association of finger gnosis and fine motor skills with numerical abilities may emerge from a combination of functional and redeployment mechanisms, in which the early use of finger-based numerical strategies during childhood might be the developmental process by which number representations become intertwined with the finger sensorimotor system, which carries an innate predisposition for said association to unfold. Further research is nonetheless necessary to clarify the causal mechanisms underlying this association.

Spatial complexity facilitates ordinal mapping with a novel symbol set

The representation of number symbols is assumed to be unique, and not shared with other ordinal sequences. However, little research has examined if this is the case, or whether properties of symbols (such as spatial complexity) affect ordinal learning. Two studies were conducted to investigate if the property of spatial complexity affects learning ordinal sequences. In Study 1, 46 adults made a series of judgements about two novel symbol sets (Gibson and Sunúz). The goal was to find a novel symbol set that could be ordered by spatial complexity. In Study 2, 84 adults learned to order nine novel symbols (Sunúz) with a paired comparison task, judging which symbol was 'larger' (whereby the larger symbol became physically larger as feedback), and were then asked to rank the symbols. Participants were assigned to either a condition where there was a relationship between spatial complexity and symbol order, or a condition where there was a random relationship. Of interest was whether learning an ordered list of symbols would be facilitated by the spatial complexity of the novel symbols. Findings suggest spatial complexity affected learning ability, and that pairing spatial complexity with relational information can facilitate learning ordinal sequences. This suggests that the implicit cognitive representation of number may be a more general feature of ordinal lists, and not exclusive to number per se.

Development of early domain-specific and domain-general cognitive precursors of high and low math achievers in grade 6

This study investigated from a longitudinal retrospective perspective what characterizes and predicts 6th graders (M_age = 12.95, SD = 0.27) with low (LMA) or high (HMA) math achievement concerning the development of early domain-specific and domain-general cognitive abilities. They were examined and compared to average achievers (n = 88) at four-time points from kindergarten (M_age = 6.58, SD = 0.36) to third grade (M_age = 9.53, SD = 0.33). The LMA (n = 27) or HMA (n = 41) children exhibited persistent multi-weakness and multi-strength profiles, respectively, present already prior to formal schooling. The cognitive profiles of the two groups, and their development, were mostly qualitatively similar, but there were also important qualitative differences. Logistic regression analyzes showed that superior verbal arithmetic, logical reasoning, and executive functions are vital for developing superior mathematical skills while inferior verbal arithmetic, logical reasoning, and spatial processing ability constitute unique potential risk factors for low mathematical skills.

Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research

Achievement in different domains, such as academics, music, or visual arts, plays a central role in all modern societies. Different psychological models aim to describe and explain achievement and its development in different domains. However, there remains a need for a framework that guides empirical research within and across different domains. With the talent-development-in-achievement-domains (TAD) framework, we provide a general talent-development framework applicable to a wide range of achievement domains. The overarching aim of this framework is to support empirical research by focusing on measurable psychological constructs and their meaning at different levels of talent development. Furthermore, the TAD framework can be used for constructing domain-specific talent-development models. With examples for the application of the TAD framework to the domains of mathematics, music, and visual arts, the review provided supports the suitability of the TAD framework for domain-specific model construction and indicates numerous research gaps and open questions that should be addressed in future research.

Visual development

The developing visual brain is an integrated system, linking analysis of the visual input to visuomotor control, visual cognition, and attention. Major points in human visual development are the presence of rudimentary pathways present at birth which can control fixation behavior, with subsequent development of specific functions. These functions include the emergence of cortical selectivity; the integration of local signals to provide global representations of motion, shape, and space; the development of visuomotor modules for eye movements, manual reaching, and locomotion; and the development of distinct attentional systems. Measures of these processes in infancy and early childhood can provide indicators of broader brain development in the at-risk child. A key system in development is the dorsal cortical stream. Measures of global motion processing, visuomotor actions, and attention suggest that this system is particularly vulnerable in children with a wide range of neurodevelopmental disorders. Early disorders of the eye (strabismus, cataract) reveal the level of plasticity in the developing visual system and the ways in which early experience can affect the course of functional development.

Educational fMRI: From the Lab to the Classroom

Functional MRI (fMRI) findings hold many potential applications for education, and yet, the translation of fMRI findings to education has not flowed. Here, we address the types of fMRI that could better support applications of neuroscience to the classroom. This 'educational fMRI' comprises eight main challenges: (1) collecting artifact-free fMRI data in school-aged participants and in vulnerable young populations, (2) investigating heterogenous cohorts with wide variability in learning abilities and disabilities, (3) studying the brain under natural and ecological conditions, given that many practical topics of interest for education can be addressed only in ecological contexts, (4) depicting complex age-dependent associations of brain and behaviour with multi-modal imaging, (5) assessing changes in brain function related to developmental trajectories and instructional intervention with longitudinal designs, (6) providing system-level mechanistic explanations of brain function, so that useful individualized predictions about learning can be generated, (7) reporting negative findings, so that resources are not wasted on developing ineffective interventions, and (8) sharing data and creating large-scale longitudinal data repositories to ensure transparency and reproducibility of fMRI findings for education. These issues are of paramount importance to the development of optimal fMRI practices for educational applications.

Use of numerical and spatial information in ordinal counting by zebrafish

The use of non-symbolic numerical information is widespread throughout the animal kingdom, providing adaptive benefits in several ecological contexts. Here we provide the possible evidence of ordinal numerical skills in zebrafish (Danio rerio). Zebrafish were trained to identify the second exit in a series of five identically-spaced exits along a corridor. When at test the total length of the corridor (Exp. 1) or the distance between exits (Exp. 2) was changed, zebrafish appeared not to use the absolute spatial distance. However, zebrafish relied both on ordinal as well as spatial cues when the number of exits was increased (from 5 to 9) and the inter-exit distance was reduced (Exp. 3), suggesting that they also take into account relative spatial information. These results highlight that zebrafish may provide a useful model organism for the study of the genetic bases of non-symbolic numerical and spatial cognition, and of their interaction.

Screening for learning disabilities in Oman: confirmatory factor analysis of the Arabic version of the learning disabilities diagnostic inventory

Students at risk for learning disabilities (LD) are overidentified in elementary schools in Oman due to the absence of adequate instruments which teachers can use in validating their observations. Teachers need valid instruments so that their judgment of students' behaviours can help in making academic and non-academic decision. The Learning Disabilities Diagnostic Inventory (LDDI) is widely used to examine manifestations of LD as an intrinsic processing disorder. This study aimed to verify the six-factor structure with confirmatory factor analysis, and test its measurement invariance across child gender. Teachers completed the Arabic version of the LDDI for an Omani sample of 1564 children aged 7 to 11. Overall, the six-factor model showed an acceptable fit after performing some post-hoc modifications that were justified on a theoretical ground. Results indicated metric invariance across gender. Zero-order correlations, however, were highly significant, which reflected that the Arabic version of the LDDI showed poor discriminant validity compared to the original LDDI. The Arabic version of the LDDI, however, can be a handy tool to screen for the LD manifestations and help in responding to teachers' academic concerns about students in Key stages 1 and 2 in Oman.

Short-term numerosity training promotes symbolic arithmetic in children with developmental dyscalculia: The mediating role of visual form perception

Studies have shown that numerosity-based arithmetic training can promote arithmetic learning in typically developing children as well as children with developmental dyscalculia (DD), but the cognitive mechanism underlying this training effect remains unclear. The main aim of the current study was to examine the role of visual form perception in arithmetic improvement through an 8-day numerosity training for DD children. Eighty DD children were selected from four Chinese primary schools. They were randomly divided into the intervention and control groups. The intervention group received training on an apple-collecting game, whereas the control group received an English dictation task. Children's cognitive and arithmetic performances were assessed before and after training. The results showed that the intervention group showed a significant improvement in arithmetic performance, approximate number system (ANS) acuity, and visual form perception, but not in spatial processing and sentence comprehension. The control group showed no significant improvement in any cognitive ability. Mediation analysis further showed that training-related improvement in arithmetic performance was fully mediated by the improvement in visual form perception. The results suggest that short-term numerosity training enhances the arithmetic performance of DD children by improving their visual form perception.