Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia

From developmental theory to effective training: long-term and transfer effects of promoting the quantity-to-number word linkage in first-graders at risk for mathematical difficulties

Introduction

The model of quantity-to-number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German "Mengen, zählen, Zahlen" (MZZ)].

Methods

We assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention.

Results and Discussion

Multi-level analyses confirmed both significant short-and long-term effects in the specifically trained quantity-number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6 months and remained stable even 15 months after training. Effect sizes ranged from d = 0.32 to d = 1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model.

Integrated number sense tutoring remediates aberrant neural representations in children with mathematical disabilities

Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, 'inverted U-shaped' neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions.

How understanding and strengthening brain networks can contribute to elementary education

Imaging the human brain during the last 35 years offers potential for improving education. What is needed is knowledge on the part of educators of all types of how this potential can be realized in practical terms. This paper briefly reviews the current level of understanding of brain networks that underlie aspects of elementary education and its preparation for later learning. This includes the acquisition of reading, writing and number processing, improving attention and increasing the motivation to learn. This knowledge can enhance assessment devices, improve child behavior and motivation and lead to immediate and lasting improvements in educational systems.

Symbolic and non-symbolic predictors of number line task in Italian kindergarteners

The number line estimation task (NLE) is often used as a predictor for broader measures of mathematical achievement. In spite of its popularity, it is still not clear whether the task is based on symbolic or non-symbolic numerical competence. In particular, there is only a very limited amount of studies investigating the relationship between NLE performance and symbolic vs. non-symbolic math skills in children who have not yet begun formal schooling. This study investigates the strength of the association between NLE performance and symbolic and non-symbolic tasks in young kindergarteners. Ninety two 5-year-old children completed the NLE task (range 0-100) and a battery of early numerical competence tests including symbolic-lexical tasks, symbolic semantic tasks, and non-symbolic semantic tasks. The relationship between symbolic and non-symbolic early numerical competence and NLE performance was analyzed using a regression model based on the Bayesian Information Criterion (BIC). Results show that only symbolic semantic tasks are significant predictors of NLE performance. These results suggest that symbolic numerical knowledge is involved in number line processing among young children, whilst non-symbolic knowledge is not. This finding brings new data to the debate on the relationship between non-symbolic numeral knowledge and symbolic number processing and supports the evidence of a primary role of symbolic number processing already in young kindergarteners.

Number estimation in Down syndrome: Cognition or experience?

BACKGROUND

The ability to place numbers on a visual "number line" is a hallmark of the understanding of numerical magnitude and it is a strong predictor of mathematical achievement.

AIM

We examined whether the performance in the number line estimation task is more driven by mental age or experience with numbers in a sample of Italian children with Down syndrome (DS).

METHOD AND PROCEDURE

Sixty-three children with DS (M_months = 128.62, SD = 30.73) and sixty-three typically developing children (M_months = 54.98, SD = 6.34) matched one to one for mental age completed number line estimation tasks and other tests to assess their numerical knowledge.

OUTCOMES AND RESULTS

No significant differences emerged between the two groups in terms of accuracy of positioning numbers on the 1-10 and 1-20 interval. In addition, the accuracy on the 1-10 interval was related to the ability to recognize numbers, while the accuracy on the 1-20 line was related to the ability to compare magnitudes.

CONCLUSION AND IMPLICATION

Results suggest that in individuals with DS the linear mapping of numbers is driven by mental age, but the accuracy of positioning numbers is also shaped by the experience with symbolic numbers. Therefore, the improvement of numerical estimation abilities should be a target of intervention programs.

Developing mental number line games to improve young children's number knowledge and basic arithmetic skills

The learning of number knowledge in childhood may directly influence children's mathematics learning ability in subsequent periods. Previous studies also show that the difficulties in mathematics learning faced by schoolchildren are mainly rooted in the lack of number knowledge in early childhood. Focusing on the development of numerical knowledge and basic arithmetic skills in early childhood, this study designed a linear number line game based on the theory of the mental number line. Accordingly, this study examined the effectiveness of the linear number line game in children's learning of number concepts and arithmetic skills and compared the effectiveness of the linear number line game with that of two other games (a nonlinear number line game and a non-number-line game). This study adopted a quasi-experimental research design. A total of 140 young children from remote areas of eastern Taiwan participated and were divided into three experimental groups and one control group, and a pretest-posttest experiment was conducted. The experimental results showed that the linear number line game could help children to acquire numerical knowledge effectively, especially in number line estimation compared with other experimental groups. In terms of the learning effectiveness of basic arithmetic skills (e.g., addition, subtraction), the two number line games (linear and nonlinear number line games) are significantly superior to the non-number-line game (traditional number decomposition and synthesis game). This study recommends that preschool teachers use linear number line games to improve children's numerical knowledge and arithmetic skills.

Assessing young children's national identity through human-computer interaction: A game-based assessment task

As a way of human-computer interaction, game-based assessment is more suitable for young children because it is situational, interesting, and effective. National identity is an important factor affecting the overall development of young children and the future development of a country, which has attracted extensive attention from researchers. Nevertheless, the assessment of young children's national identity is still based on traditional evaluation, including questionnaires and interviews, which have the limitations of being inaccurate, dull, and time-consuming. To understand the characteristics of children's national identity, it is necessary to use scientific and interactive assessment methods. The present study investigated whether the game-based assessment we developed specifically would be an appropriate tool to measure young children's national identity. The results show that the game-based assessment had good item discrimination. Exploratory factor analysis demonstrated the game covered three aspects: national cognition mastery, national emotion engagement, and national behavior tendency. The confirmatory factor analysis suggested that the model with three factors fit the data well. The internal consistency, the split-half reliability, and the test-retest reliability meet standards. Overall, the results indicated that this game can be successfully used to assess young children's national identity with acceptable validity and reliability. Our study provides strong evidence for the use of human-computer interaction in child measurement. These findings are the first to demonstrate the promise of game-based assessment in assessing children's national identity reliably and effectively.

Evaluation of math anxiety and its remediation through a digital training program in mathematics for first and second graders

INTRODUCTION

Math anxiety severely impacts individuals' learning and future success. However, limited is understood about the profile in East Asian cultures where students genuinely show high-level math anxiety, despite that they outperform their Western counterparts. Here, we investigate the relation between math anxiety and math achievement in children as young as first and second graders in Taiwan. Further, we evaluate whether intensive exposure to digital game-based learning in mathematics could ameliorate math anxiety.

METHODS

The study first evaluated a group of 159 first and second graders' math anxiety and its correlation with math performance. Subsequently, a quasi-experimental design was adopted: 77 of the children continued and participated in multi-component digital game training targeting enumeration, speeded calculation, and working memory. Post-assessment was administered afterward for further evaluation of training-associated effects.

RESULTS

Results confirmed that math anxiety was negatively associated with school math achievement, which assessed numerical knowledge and arithmetic calculation. Furthermore, children's math anxiety was remarkably reduced via digital training in mathematics after 6-week intensive remediation. Crucially, this math anxiety relief was more prominent in those with high-level math anxiety. Although the children who underwent the training showed training-induced math achievement and working memory enhancement, this cognitive improvement appeared to be independent of the math anxiety relief.

CONCLUSION

Our findings demonstrate that students can show highly negative emotions and perceptions toward learning even in high-achieving countries. Auspiciously, the feeling of distress toward learning has the feasibility to be relieved from short-term intensive training. Our study suggests a new approach of early treatments to emotional disturbance that can lead to permanent consequences in individuals.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

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.

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 Effects of Musical Training on Mathematical Skills of Children With Developmental Dyscalculia

Musical training (MT) is perceived as a multi-sensory program that simultaneously integrates visual, aural, oral, and kinesthetic senses. Furthermore, MT stimulates cognitive functions in a ludic way instead of tapping straight into the traditional context of school learning, including mathematics. Nevertheless, the efficacy of MT over mathematics remains understudied, especially concerning longstanding effects. For this reason, this longitudinal study explored the impact of MT on numerical cognition and abstract visual reasoning using a double-blind and quasi-experimental design. We assessed two groups of children from primary schools, namely one with developmental dyscalculia [DD; n = 22] and another comprising typically developing children [TD; n = 22], who concomitantly underwent MT. Numerical cognition measurement was carried out at four different time points: Baseline (pre-MT assessment), mid-test (after 7 weeks of MT), post-test (after 14 weeks of MT), and follow-up (10 weeks after the end of MT). Significant interactions were found between time and group for numerical cognition performance, in which the DD group showed higher scores in number comprehension, number production at mid-test, and calculation at post-test compared to baseline. A key finding was that number production, number comprehension, and calculation effects were time-resistant for the DD group since changes remained on follow-up. Moreover, no significant differences over time were found for abstract visual reasoning for both groups. In conclusion, the findings of this study showed that MT appears to be a useful tool for compensatory remediation of DD.

Responsible Research and Innovation as a Novel Approach to Guide Educational Impact of Mind, Brain, and Education Research

We propose a Responsible Research and Innovation (RRI) framework to improve the alignment between mind, brain, and education (MBE) research, the educational practice, and other societal stakeholders. RRI is an approach that has successfully been used in different research fields, but not yet in MBE research. After substantiating the need for, and possibilities of using this framework within MBE research, we report a case study to demonstrate the feasibility and benefits of RRI within an MBE context. This case study entails developing an educational intervention to improve learners' sense of agency regarding their own learning processes using neurofeedback. Using RRI, we found that societal stakeholders (teenagers, parents, and teachers) anticipate different potential impacts of this neurotechnology-based intervention than researchers did, enabling us to adapt the intervention according to these perspectives. This example demonstrates that RRI enables researchers to be reflexive and responsive to the stakeholders needs and values, to ultimately improve the educational and societal value of MBE research.

Assessing Mathematical School Readiness

Early math skills matter for later formal mathematical performances, academic and professional success. Accordingly, it is important to accurately assess mathematical school readiness (MSR) at the beginning of elementary school. This would help identifying children who are at risk of encountering difficulties in math and then stimulate their acquisition of mathematical skills as soon as possible. In the present study, we present a new test that allows professionals working with children (e.g., teachers, school psychologists, speech therapists, and school doctors) to assess children’s MSR when they enter formal schooling in a simple, rapid and efficient manner. 346 children were assessed at the beginning of 1st Grade (6-to-7-year-olds) with a collective test assessing early mathematical abilities (T1). In addition, children’s math skills were evaluated with classical curriculum math tests at T1 and a year later, in 2nd Grade (T2, 7-to-8-year-olds). After assessing internal consistency, three tasks were retained for the final version of the MSR test. Test performance confirmed to be essentially unidimensional and systematically related to the scores children obtained in classical tests in 1st and 2nd Grade. By using the present MSR test, it is possible to identify pupils at risk of developing low math skills right from the start of formal schooling in 1st Grade. Such a tool is needed, as children’s level in math at school beginning (or school readiness) is known to be foundational for their future academic and professional carrier.

"Approximate number system" training: A perceptual learning approach

Recent research suggests that humans perceive quantity using a non-symbolic "number sense." This sense is then thought to provide a foundation for understanding symbolic numbers in formal education. Given this link, there has been interest in the extent to which the approximate number system (ANS) can be improved via dedicated training, as this could provide a route to improving performance in symbolic mathematics. However, current evidence regarding the trainability of the ANS comes largely from studies that have used short training durations, leaving open the question of whether improvements occur over a longer time span. To address this limitation, we utilized a perceptual learning approach to investigate the extent to which long-term (8,000+ trials) training modifies the ANS. Consistent with the general methodological approach common in the domain of perceptual learning (where learning specificity is commonly observed), we also examined whether ANS training generalizes to: (a) untrained locations in the visual field; (b) an enumeration task; (c) a higher-level ratio comparison task; and (d) arithmetic ability. In contrast to previous short-term training studies showing that ANS learning quickly asymptotes, our long-term training approach revealed that performance continued to improve even after thousands of trials. We further found that the training generalized to untrained visual locations. At post-test there was non-significant evidence for generalization to a low-level enumeration task, but not to our high-level tasks, including ratio comparison, multi-object tracking, and arithmetic performance. These results demonstrate the potential utility of long-term psychophysical training, but also suggest that ANS training alone (even long-duration training) may be insufficient to modify higher-level math skills.

Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children's Math Ability

The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children's math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named "123 Bakery" which includes four training modules; non-symbolic numerosity comparison, non-symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, symbolic/non-symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in symbolic, exact calculation, or any other math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to symbolic math ability remains to be further tested.

A Mechanistic Study of the Association Between Symbolic Approximate Arithmetic Performance and Basic Number Magnitude Processing Based on Task Difficulty

Two types of number magnitude processing – semantic and spatial – are significantly correlated with children’s arithmetic performance. However, it remains unclear whether these abilities are independent predictors of symbolic approximate arithmetic performance. The current study addressed this question by assessing 86 kindergartners (mean age of 5 years and 7 months) on semantic number processing (number comparison task), spatial number processing (number line estimation task), and symbolic approximate arithmetic performance with different levels of difficulty. The results showed that performance on both tasks of number magnitude processing was significantly correlated with symbolic approximate arithmetic performance, but the strength of these correlations was moderated by the difficulty level of the arithmetic task. The simple symbolic approximate arithmetic task was equally related to both tasks. In contrast, for more difficult symbolic approximate arithmetic tasks, the contribution of number comparison ability was smaller than that of the number line estimation ability. These results indicate that the strength of contribution of the different types of numerical processing depends on the difficulty of the symbolic approximate arithmetic task.

Influence of initial mathematical competencies on the effectiveness of a classroom-based intervention

BACKGROUND

Students commonly struggle with mathematics and mathematical problem-solving. Therefore, it is necessary to design and implement interventions aimed at improving these essential components of learning. Furthermore, the outcomes of these interventions can vary significantly and appear to be a function of a student's initial competencies in mathematics.

AIM

This study attempts to analyse the influence of initial levels of mathematics competency with respect to the benefits of a specific intervention known as the Integrated Dynamic Representation (IDR).

SAMPLE

Participants were 288 students (aged 6-8 years) who were divided according to their levels of mathematics competency (low-medium-high).

METHODS

Students were assigned to the two primary intervention groups, experimental group (EG; students who received the IDR intervention) and control group (CG; students who followed the traditional instructional methods). All participants completed the Test of Early Mathematics Abilities (TEMA-3) both before and after the intervention.

RESULTS AND CONCLUSIONS

Although all the three competency levels of the EG improved, the progression was different for each level. Results showed that students with low competency level improved substantially more than the students with medium and/or high baseline competency level.

Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter

The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.

Eye-movement patterns during nonsymbolic and symbolic numerical magnitude comparison and their relation to math calculation skills

A growing body of research suggests that the processing of nonsymbolic (e.g. sets of dots) and symbolic (e.g. Arabic digits) numerical magnitudes serves as a foundation for the development of math competence. Performance on magnitude comparison tasks is thought to reflect the precision of a shared cognitive representation, as evidence by the presence of a numerical ratio effect for both formats. However, little is known regarding how visuo-perceptual processes are related to the numerical ratio effect, whether they are shared across numerical formats, and whether they relate to math competence independently of performance outcomes. The present study investigates these questions in a sample of typically developing adults. Our results reveal a pattern of associations between eye-movement measures, but not their ratio effects, across formats. This suggests that ratio-specific visuo-perceptual processing during magnitude processing is different across nonsymbolic and symbolic formats. Furthermore, eye movements are related to math performance only during symbolic comparison, supporting a growing body of literature suggesting symbolic number processing is more strongly related to math outcomes than nonsymbolic magnitude processing. Finally, eye-movement patterns, specifically fixation dwell time, continue to be negatively related to math performance after controlling for task performance (i.e. error rate and reaction time) and domain general cognitive abilities (IQ), suggesting that fluent visual processing of Arabic digits plays a unique and important role in linking symbolic number processing to formal math abilities.

Neuroscience of Childhood Poverty: Evidence of Impacts and Mechanisms as Vehicles of Dialog With Ethics

Several studies have identified associations between poverty and development of self-regulation during childhood, which is broadly defined as those skills involved in cognitive, emotional, and stress self-regulation. These skills are influenced by different individual and contextual factors at multiple levels of analysis (i.e., individual, family, social, and cultural). Available evidence suggests that the influences of those biological, psychosocial, and sociocultural factors on emotional and cognitive development can vary according to the type, number, accumulation of risks, and co-occurrence of adverse circumstances that are related to poverty, the time in which these factors exert their influences, and the individual susceptibility to them. Complementary, during the past three decades, several experimental interventions that were aimed at optimizing development of self-regulation of children who live in poverty have been designed, implemented, and evaluated. Their results suggest that it is possible to optimize different aspects of cognitive performance and that it would be possible to transfer some aspects of these gains to other cognitive domains and academic achievement. We suggest that it is an important task for ethics, notably but not exclusively neuroethics, to engage in this interdisciplinary research domain to contribute analyses of key concepts, arguments, and interpretations. The specific evidence that neuroscience brings to the analyses of poverty and its implications needs to be spelled out in detail and clarified conceptually, notably in terms of causes of and attitudes toward poverty, implications of poverty for brain development, and for the possibilities to reduce and reverse these effects.

Defective Number Sense or Impaired Access? Differential Impairments in Different Subgroups of Children With Mathematics Difficulties

Developmental dyscalculia (DD) is a specific learning disability in mathematics that affects around 6% of the population. Currently, the core deficit of DD remains unknown. While the number sense deficit hypothesis suggests that the core deficit of DD lies in the inability to represent nonsymbolic numerosity, the access deficit hypothesis suggests that the origin of this disability lies in the inability to associate numbers with the underlying magnitude representation. The present study compared the performance of DDs with their low-achieving (LA) and normally achieving peers in nonsymbolic numerosity processing and number-magnitude mapping over 1 year (from kindergarten to 1st grade). The results demonstrated differential impairments in different subgroups of children with mathematics difficulties. While DDs showed deficits in both nonsymbolic numerosity processing and number-magnitude mapping, LAs showed deficit only in the number-magnitude mapping. Furthermore, the deficit in number-magnitude mapping among the DD group was partially explained by their number sense deficit. The number sense deficit hypothesis is supported. Theoretical and practical implications are discussed.

Improving Preschoolers' Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training

The numerical cognition literature offers two views to explain numerical and arithmetical development. The unique-representation view considers the approximate number system (ANS) to represent the magnitude of both symbolic and non-symbolic numbers and to be the basis of numerical learning. In contrast, the dual-representation view suggests that symbolic and non-symbolic skills rely on different magnitude representations and that it is the ability to build an exact representation of symbolic numbers that underlies math learning. Support for these hypotheses has come mainly from correlative studies with inconsistent results. In this study, we developed two training programs aiming at enhancing the magnitude processing of either non-symbolic numbers or symbolic numbers and compared their effects on arithmetic skills. Fifty-six preschoolers were randomly assigned to one of three 10-session-training conditions: (1) non-symbolic training (2) symbolic training and (3) control training working on story understanding. Both numerical training conditions were significantly more efficient than the control condition in improving magnitude processing. Moreover, symbolic training led to a significantly larger improvement in arithmetic than did non-symbolic training and the control condition. These results support the dual-representation view.

Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review

It is widely accepted that human and nonhuman species possess a specialized system to process large approximate numerosities. The theory of an evolutionarily ancient approximate number system (ANS) has received converging support from developmental studies, comparative experiments, neuroimaging, and computational modelling, and it is one of the most dominant and influential theories in numerical cognition. The existence of an ANS system is significant, as it is believed to be the building block of numerical development in general. The acuity of the ANS is related to future arithmetic achievements, and intervention strategies therefore aim to improve the ANS. Here we critically review current evidence supporting the existence of an ANS. We show that important shortcomings and confounds exist in the empirical studies on human and non-human animals as well as the logic used to build computational models that support the ANS theory. We conclude that rather than taking the ANS theory for granted, a more comprehensive explanation might be provided by a sensory-integration system that compares or estimates large approximate numerosities by integrating the different sensory cues comprising number stimuli.

Computer-based training for improving mental calculation in third- and fifth-graders

The literature on intervention programs to improve arithmetical abilities is fragmentary and few studies have examined training on the symbolic representation of numbers (i.e. Arabic digits). In the present research, three groups of 3rd- and 5th-grade schoolchildren were given training on mental additions: 76 were assigned to a computer-based strategic training (ST) group, 73 to a process-based training (PBT) group, and 71 to a passive control (PC) group. Before and after the training, the children were given a criterion task involving complex addition problems, a nearest transfer task on complex subtraction problems, two near transfer tasks on math fluency, and a far transfer task on numerical reasoning. Our results showed developmental differences: 3rd-graders benefited more from the ST, with transfer effects on subtraction problems and math fluency, while 5th-graders benefited more from the PBT, improving their response times in the criterion task. Developmental, clinical and educational implications of these findings are discussed.

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

The prevalence of developmental dyscalculia in Brazilian public school system

ABSTRACT The goal of the study was to assess public school children at the end of the first stage of elementary school. We used a protocol applied concurrently with a writing test in the form of an unexpected activity in 28 public schools; 2,893 children assessed, 687 exhibited performance below 58 points, 184 were excluded due to change of address or lack of consent; 503 children subjected to a test of intellectual capacity and reading assessment and 71 considered intellectually disabled were excluded. 226 (7.8%) children, who could read, write, and had normal intellectual level, met the criteria of developmental dyscalculia (DD), 98 female and 128 male. The most influential factors in the prevalence were socioeconomic levels of the schools neighborhood, education level of parents, and being male, as demonstrated by the odds ratio and multiple logistic regression analysis. Further studies should be done so that educational policies are taken.

Die TUebinger LernPlattform zum Erwerb numerischer und orthografischer Kompetenzen (TULPE)

Zusammenfassung. Digitale Medien haben nicht nur die Kinderzimmer erobert, sondern sind mittlerweile fester Bestandteil einer modernen Schulbildung. Der Einsatz von Online-Lernumgebungen und -spielen, in und außerhalb von pädagogischen Kontexten, erlaubt es selbst traditionelle Lerninhalte spielerisch und unabhängig von Ort und Zeit zu vermitteln. Die im Folgenden vorgestellte «TUebinger LernPlattform zum Erwerb numerischer und orthografischer Kompetenzen (TULPE)» bietet individuelles Lernen zentraler Kulturtechniken auch außerhalb des Klassenraums. Mithilfe adaptiver Verfahren lassen sich die Rechen- und Rechtschreibspiele der TULPE an individuelle Lernermerkmale anpassen: Zuerst wird in einer adaptiven Diagnostik der Lern- und Förderbedarf eingeschätzt. Entsprechend dieser Einschätzung können in einem zweiten Schritt Lernspiele adaptiert bzw. Lern- und Spielpartner mit ähnlichem Leistungsniveau ausgewählt werden. Auf diese Weise soll effektives Lernen ermöglicht werden, das den Bedürfnissen unserer Kinder in ihrer digitalisierten Lebenswirklichkeit entspricht.

Electrocortical Dynamics in Children with a Language-Learning Impairment Before and After Audiovisual Training

Detecting and discriminating subtle and rapid sound changes in the speech environment is a fundamental prerequisite of language processing, and deficits in this ability have frequently been observed in individuals with language-learning impairments (LLI). One approach to studying associations between dysfunctional auditory dynamics and LLI, is to implement a training protocol tapping into this potential while quantifying pre- and post-intervention status. Event-related potentials (ERPs) are highly sensitive to the brain correlates of these dynamic changes and are therefore ideally suited for examining hypotheses regarding dysfunctional auditory processes. In this study, ERP measurements to rapid tone sequences (standard and deviant tone pairs) along with behavioral language testing were performed in 6- to 9-year-old LLI children (n = 21) before and after audiovisual training. A non-treatment group of children with typical language development (n = 12) was also assessed twice at a comparable time interval. The results indicated that the LLI group exhibited considerable gains on standardized measures of language. In terms of ERPs, we found evidence of changes in the LLI group specifically at the level of the P2 component, later than 250 ms after the onset of the second stimulus in the deviant tone pair. These changes suggested enhanced discrimination of deviant from standard tone sequences in widespread cortices, in LLI children after training.

Visual perception can account for the close relation between numerosity processing and computational fluency

Studies have shown that numerosity processing (e.g., comparison of numbers of dots in two dot arrays) is significantly correlated with arithmetic performance. Researchers have attributed this association to the fact that both tasks share magnitude processing. The current investigation tested an alternative hypothesis, which states that visual perceptual ability (as measured by a figure-matching task) can account for the close relation between numerosity processing and arithmetic performance (computational fluency). Four hundred and twenty four third- to fifth-grade children (220 boys and 204 girls, 8.0-11.0 years old; 120 third graders, 146 fourth graders, and 158 fifth graders) were recruited from two schools (one urban and one suburban) in Beijing, China. Six classes were randomly selected from each school, and all students in each selected class participated in the study. All children were given a series of cognitive and mathematical tests, including numerosity comparison, figure matching, forward verbal working memory, visual tracing, non-verbal matrices reasoning, mental rotation, choice reaction time, arithmetic tests and curriculum-based mathematical achievement test. Results showed that figure-matching ability had higher correlations with numerosity processing and computational fluency than did other cognitive factors (e.g., forward verbal working memory, visual tracing, non-verbal matrix reasoning, mental rotation, and choice reaction time). More important, hierarchical multiple regression showed that figure matching ability accounted for the well-established association between numerosity processing and computational fluency. In support of the visual perception hypothesis, the results suggest that visual perceptual ability, rather than magnitude processing, may be the shared component of numerosity processing and arithmetic performance.

Of magnitudes and metaphors: explaining cognitive interactions between space, time, and number

Space, time, and number are fundamental to how we act within and reason about the world. These three experiential domains are systematically intertwined in behavior, language, and the brain. Two main theories have attempted to account for cross-domain interactions. A Theory of Magnitude (ATOM) posits a domain-general magnitude system. Conceptual Metaphor Theory (CMT) maintains that cross-domain interactions are manifestations of asymmetric mappings that use representations of space to structure the domains of number and time. These theories are often viewed as competing accounts. We propose instead that ATOM and CMT are complementary, each illuminating different aspects of cross-domain interactions. We argue that simple representations of magnitude cannot, on their own, account for the rich, complex interactions between space, time and number described by CMT. On the other hand, ATOM is better at accounting for low-level and language-independent associations that arise early in ontogeny. We conclude by discussing how magnitudes and metaphors are both needed to understand our neural and cognitive web of space, time and number.

Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who were matched on age, IQ, reading ability, and working memory. Children with DD were slower and less accurate during problem solving than TD children, and were especially impaired on their ability to solve subtraction problems. Children with DD showed significantly greater activity in multiple parietal, occipito-temporal and prefrontal cortex regions while solving addition and subtraction problems. Despite poorer performance during subtraction, children with DD showed greater activity in multiple intra-parietal sulcus (IPS) and superior parietal lobule subdivisions in the dorsal posterior parietal cortex as well as fusiform gyrus in the ventral occipito-temporal cortex. Critically, effective connectivity analyses revealed hyper-connectivity, rather than reduced connectivity, between the IPS and multiple brain systems including the lateral fronto-parietal and default mode networks in children with DD during both addition and subtraction. These findings suggest the IPS and its functional circuits are a major locus of dysfunction during both addition and subtraction problem solving in DD, and that inappropriate task modulation and hyper-connectivity, rather than under-engagement and under-connectivity, are the neural mechanisms underlying problem solving difficulties in children with DD. We discuss our findings in the broader context of multiple levels of analysis and performance issues inherent in neuroimaging studies of typical and atypical development.

Effect of a virtual environment on the development of mathematical skills in children with dyscalculia

In this study, we show the effectiveness of a virtual environment comprising 18 computer games that cover mathematics topics in a playful setting and that can be executed on the Internet with the possibility of player interaction through chat. An arithmetic pre-test contained in the Scholastic Performance Test was administered to 300 children between 7 and 10 years old, including 162 males and 138 females, in the second grade of primary school. Twenty-six children whose scores showed a low level of mathematical knowledge were chosen and randomly divided into the control (CG) and experimental (EG) groups. The EG participated to the virtual environment and the CG participated in reinforcement using traditional teaching methods. Both groups took a post-test in which the Scholastic Performance Test (SPT) was given again. A statistical analysis of the results using the Student's t-test showed a significant learning improvement for the EG and no improvement for the CG (p≤0.05). The virtual environment allows the students to integrate thought, feeling and action, thus motivating the children to learn and contributing to their intellectual development.

Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school

Research on the improvement of elementary school mathematics has shown that computer-based training of number sense (e.g., processing magnitudes or locating numbers on the number line) can lead to substantial achievement gains in arithmetic skills. Recent studies, however, have highlighted that training domain-general cognitive abilities (e.g., working memory [WM]) may also improve mathematical achievement. This study addressed the question of whether a training of domain-specific number sense skills or domain-general WM abilities is more appropriate for improving mathematical abilities in elementary school. Fifty-nine children (M_age = 9 years, 32 girls and 27 boys) received either a computer-based, adaptive training of number sense (n = 20), WM skills (n = 19), or served as a control group (n = 20). The training duration was 20 min per day for 15 days. Before and after training, we measured mathematical ability using a curriculum-based math test, as well as spatial WM. For both training groups, we observed substantial increases in the math posttest compared to the control group (d = .54 for number sense skills training, d = .57 for WM training, respectively). Whereas the number sense group showed significant gains in arithmetical skills, the WM training group exhibited marginally significant gains in word problem solving. However, no training group showed significant posttest gains on the spatial WM task. Results indicate that a short training of either domain-specific or domain-general skills may result in reliable short-term training gains in math performance, although no stable training effects were found in the spatial WM task.

A new adaptive videogame for training attention and executive functions: design principles and initial validation

A growing body of evidence suggests that action videogames could enhance a variety of cognitive skills and more specifically attention skills. The aim of this study was to develop a novel adaptive videogame to support the rehabilitation of the most common consequences of traumatic brain injury (TBI), that is the impairment of attention and executive functions. TBI patients can be affected by psychomotor slowness and by difficulties in dealing with distraction, maintain a cognitive set for a long time, processing different simultaneously presented stimuli, and planning purposeful behavior. Accordingly, we designed a videogame that was specifically conceived to activate those functions. Playing involves visuospatial planning and selective attention, active maintenance of the cognitive set representing the goal, and error monitoring. Moreover, different game trials require to alternate between two tasks (i.e., task switching) or to perform the two tasks simultaneously (i.e., divided attention/dual-tasking). The videogame is controlled by a multidimensional adaptive algorithm that calibrates task difficulty on-line based on a model of user performance that is updated on a trial-by-trial basis. We report simulations of user performance designed to test the adaptive game as well as a validation study with healthy participants engaged in a training protocol. The results confirmed the involvement of the cognitive abilities that the game is supposed to enhance and suggested that training improved attentional control during play.

Predictors of cognitive enhancement after training in preschoolers from diverse socioeconomic backgrounds

The association between socioeconomic status and child cognitive development, and the positive impact of interventions aimed at optimizing cognitive performance, are well-documented. However, few studies have examined how specific socio-environmental factors may moderate the impact of cognitive interventions among poor children. In the present study, we examined how such factors predicted cognitive trajectories during the preschool years, in two samples of children from Argentina, who participated in two cognitive training programs (CTPs) between the years 2002 and 2005: the School Intervention Program (SIP; N = 745) and the Cognitive Training Program (CTP; N = 333). In both programs children were trained weekly for 16 weeks and tested before and after the intervention using a battery of tasks assessing several cognitive control processes (attention, inhibitory control, working memory, flexibility and planning). After applying mixed model analyses, we identified sets of socio-environmental predictors that were associated with higher levels of pre-intervention cognitive control performance and with increased improvement in cognitive control from pre- to post-intervention. Child age, housing conditions, social resources, parental occupation and family composition were associated with performance in specific cognitive domains at baseline. Housing conditions, social resources, parental occupation, family composition, maternal physical health, age, group (intervention/control) and the number of training sessions were related to improvements in specific cognitive skills from pre- to post-training.

Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics.

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities.