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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.

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BACKGROUND AND PURPOSE: In recent years, there has been a growing interest in the study of resting neural networks in different neurological and mental disorders. While previous studies suggest that the default mode network (DMN) may be altered in dyscalculia, the study of resting-state networks in the development of numerical skills, especially in children with developmental dyscalculia (DD), is scarce and relatively recent. Based on this, this study examines differences in resting-state functional connectivity (rs-FC) data of children with DD using functional connectivity multivariate pattern analysis (fc-MVPA), a data-driven methodology that summarizes properties of the entire connectome. METHODS: We performed fc-MVPA on resting-state images of a sample composed of a group of children with DD (n = 19, 8.06 ± 0.87 years) and an age- and sex-matched control group of typically developing children (n = 23, 7.76 ± 0.46 years). RESULTS: Analysis of fc-MVPA showed significant differences between group connectivity profiles in two clusters allocated in both the right and left medial temporal gyrus. Post hoc effect size results revealed a decreased rs-FC between each temporal pole and the DMN in children with DD and an increased rs-FC between each temporal pole and the sensorimotor network. CONCLUSIONS: Our results suggest an aberrant information flow between resting-state networks in children with DD, demonstrating the importance of these networks for arithmetic development.

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Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.

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

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The intraparietal sulcus (IPS) has been associated with numerical processing. A recent study reported that the IPS sulcal pattern was associated with arithmetic and symbolic number abilities in children and adults. In the present study, we evaluated the link between numerical abilities and the IPS sulcal pattern in children with Developmental Dyscalculia (DD) and typically developing children (TD), extending previous analyses considering other sulcal features and the postcentral sulcus (PoCS). First, we confirm the longitudinal sulcal pattern stability of the IPS and the PoCS. Second, we found a lower proportion of left sectioned IPS and a higher proportion of a double-horizontal IPS shape bilaterally in DD compared to TD. Third, our analyses revealed that arithmetic is the only aspect of numerical processing that is significantly related to the IPS sulcal pattern (sectioned vs not sectioned), and that this relationship is specific to the left hemisphere. And last, correlation analyses of age and arithmetic in children without a sectioned left IPS indicate that although they may have an inherent disadvantage in numerical abilities, these may improve with age. Thus, our results indicate that only the left IPS sulcal pattern is related to numerical abilities and that other factors co-determine numerical abilities.

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Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.

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[This corrects the article DOI: 10.3389/fpsyg.2023.1187785.].

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Functional neuroimaging serves as a tool to better understand the cerebral correlates of atypical behaviors, such as learning difficulties. While significant advances have been made in characterizing the neural correlates of reading difficulties (developmental dyslexia), comparatively little is known about the neurobiological correlates of mathematical learning difficulties, such as developmental dyscalculia (DD). Furthermore, the available neuroimaging studies of DD are characterized by small sample sizes and variable inclusion criteria, which make it problematic to compare across studies. In addition, studies to date have focused on identifying single deficits in neuronal processing among children with DD (e.g., mental arithmetic), rather than probing differences in brain function across different processing domains that are known to be affected in children with DD. Here, we seek to address the limitations of prior investigations. Specifically, we used functional magnetic resonance imaging (fMRI) to probe brain differences between children with and without persistent DD; 68 children (8-10 years old, 30 with DD) participated in an fMRI study designed to investigate group differences in the functional neuroanatomy associated with commonly reported behavioral deficits in children with DD: basic number processing, mental arithmetic and visuo-spatial working memory (VSWM). Behavioral data revealed that children with DD were less accurate than their typically achieving (TA) peers for the basic number processing and arithmetic tasks. No behavioral differences were found for the tasks measuring VSWM. A pre-registered, whole-brain, voxelwise univariate analysis of the fMRI data from the entire sample of children (DD and TA) revealed areas commonly associated with the three tasks (basic number processing, mental arithmetic, and VSWM). However, the examination of differences in brain activation between children with and without DD revealed no consistent group differences in brain activation. In view of these null results, we ran exploratory, Bayesian analyses on the data to quantify the amount of evidence for no group differences. This analysis provides supporting evidence for no group differences across all three tasks. We present the largest fMRI study comparing children with and without persistent DD to date. We found no group differences in brain activation using univariate, frequentist analyses. Moreover, Bayesian analyses revealed evidence for the null hypothesis of no group differences. These findings contradict previous literature and reveal the need to investigate the neural basis of DD using multivariate and network-based approaches to brain imaging.

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Current theories postulate that numerical processing depends upon a brain circuit formed by regions and their connections; specialized in the representation and manipulation of the numerical properties of stimuli. It has been suggested that the damage of these network may cause Developmental Dyscalculia (DD): a persistent neurodevelopmental disorder that significantly interferes with academic performance and daily life activities that require mastery of mathematical notions and operations. However, most of the studies on the brain foundations of DD have focused on regions of interest associated with numerical processing, and have not addressed numerical cognition as a complex network phenomenon. The present study explored DD using a Graph Theory network approach. We studied the association between topological measures of integration and segregation of information processing in the brain proposed by Graph Theory; and individual variability in numerical performance in a group of 11 school-aged children with DD (5 of which presented with comorbidity with Developmental Dyslexia, the specific learning disorder for reading) and 17 typically developing peers. A statistically significant correlation was found between the Weber fraction (a measure of numerical representations' precision) and the Clustering Index (a measure of segregation of information processing) in the whole sample. The DD group showed significantly lower Characteristic Path Length (average shortest path length among all pairs of regions in the brain network) compared to controls. Also, differences in critical regions for the brain network performance (hubs) were found between groups. The presence of limbic hubs characterized the DD brain network while right Temporal and Frontal hubs found in controls were absent in the DD group. Our results suggest that the DD may be associated with alterations in anatomical brain connectivity that hinder the capacity to integrate and segregate numerical information.

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BACKGROUND: The role of domain-general cognitive abilities in the etiology of Developmental Dyscalculia (DD) is a hotly debated issue. AIMS: In the present study, we tested whether WISC-IV cognitive profiles can be useful to single out DD. METHODS AND PROCEDURES: Using a stringent 2-SD cutoff in a standardized numeracy battery, we identified children with DD (N = 43) within a clinical sample referred for assessment of learning disability and compared them in terms of WISC cognitive indexes to the remaining children without DD (N = 100) employing cross-validated logistic regression. OUTCOMES AND RESULTS: Both groups showed higher Verbal Comprehension and Perceptual Reasoning than Working Memory and Processing Speed, and DD scores were generally lower. Predictive accuracy of WISC indexes in identifying DD individuals was low (AUC = 0.67) and it dropped to chance level in discriminating DD from selected controls (N = 43) with average math performance but matched on global IQ. The inclusion of a visuospatial memory score as an additional predictor did not improve classification accuracy. CONCLUSIONS AND IMPLICATIONS: These results demonstrate that cognitive profiles do not reliably discriminate DD from non-DD children, thereby weakening the appeal of domain-general accounts.

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Digital game-based training programs have recently been used to train the cognitive abilities of children with neurodevelopmental disorders (NDDs). However, the effects of training remain controversial. The present meta-analysis explored the effectiveness of digital game-based training in children with NDDs and examined the possible moderators of its effects. Twenty-nine studies with cognitive outcomes in 1535 children were included in the present meta-analysis. The results showed that digital game-based training could significantly enhance the core cognitive abilities of children with each type of NDDs and that training could be used remotely. Meanwhile, task content and game features of digital game-based interventions separately make unique and significant contributions to the training effects, suggesting that the combination of training content and game features could efficiently improve children's cognition. Although the present study revealed that the training benefits could be maintained over a period of time, more studies are needed to explore the retention effects of digital game-based training. The present study provides a comprehensive understanding of the training effects of digital game-based interventions and new insights for future cognitive training design and application.

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A long-standing debate concerns whether developmental dyscalculia is characterized by core deficits in processing nonsymbolic or symbolic numerical information as well as the role of domain-general difficulties. Heterogeneity in recruitment and diagnostic criteria make it difficult to disentangle this issue. Here, we selected children (n = 58) with severely compromised mathematical skills (2 SD below average) but average domain-general skills from a large sample referred for clinical assessment of learning disabilities. From the same sample, we selected a control group of children (n = 42) matched for IQ, age, and visuospatial memory but with average mathematical skills. Children with dyscalculia showed deficits in both symbolic and nonsymbolic number sense assessed with simple computerized tasks. Performance in the digit-comparison task and the numerosity match-to-sample task reliably separated children with developmental dyscalculia from controls in cross-validated logistic regression (area under the curve = .84). These results support a number-sense-deficit theory and highlight basic numerical abilities that could be targeted for early identification of at-risk children as well as for intervention.

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Developmental dyscalculia (DD) is a mathematics learning disorder that affects approximately 5% to 7% of the population. This study aimed to detect the underlying domain-specific and domain-general differences between DD and typically developing (TD) children. We recruited 9-year-old primary school children to form the DD group via a 2-year longitudinal screening process. In total, 75 DD children were screened from 1,657 children after the one-time screening, and 13 DD children were screened from 1,317 children through a consecutive 2-year longitudinal screening. In total, 13 experimental tasks were administered to assess their cognitive abilities to test the domain-specific magnitude representation hypothesis (including symbolic and nonsymbolic magnitude comparisons) and four alternative domain-general hypotheses (including working memory, executive function, attention, and visuospatial processing). The DD group had worse performance than the TD group on the number sense task, finger sense task, shifting task, and one-back task after both one-time and two-time screening. Logistic regressions further indicated the differences on the shifting task and the nonsymbolic magnitude comparison task could distinguish DD and TD children. Our findings suggest that domain-specific nonsymbolic magnitude representation and domain-general executive function both contribute to DD. Thus, both domain-specific and domain-general abilities will be necessary to investigate and to intervene in DD groups in the future.

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Research suggests that children with developmental dyscalculia (DD) have deficits in basic numerical skills. However, there is conflicting evidence on whether basic numerical skills in children with DD are qualitatively different from those in typically developing children (TD) or whether basic numerical skills development in children with DD is simply delayed. In addition, there are also competing hypotheses about deficits in basic numerical skills, assuming (1) a general deficit in representing numerosities (Approximate Number System, ANS), (2) specific deficits in an object-based attentional system (Object Tracking System, OTS), or (3) deficits in accessing numerosities from symbols (Access Deficit, AD). Hence, the purpose of this study was to investigate whether deficits in basic numerical skills in children with DD are more indicative of a developmental delay or a dyscalculia-specific qualitative deviation and whether these deficits result from (selective) impairment of core cognitive systems involved in numerical processing. To address this, we tested 480 children (68 DD and 412 TD) in the 2nd, 3rd, and 4th grades with different paradigms for basic numerical skills (subitizing, counting, magnitude comparison tasks, number sets, and number line estimation tasks). The results revealed that DD children's impairments did not indicate qualitatively different basic numerical skills but instead pointed to a specific developmental delay, with the exception of dot enumeration. This result was corroborated when comparing mathematical profiles of DD children in 4th grade and TD children in 2nd grade, suggesting that DD children were developmentally delayed and not qualitatively different. In addition, specific deficits in core markers of numeracy in children with DD supported the ANS deficit rather than the AD and OTS deficit hypothesis.

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Developmental dyscalculia (DD) is characterized by insufficient mathematical learning ability and weaker mathematical performance than peers who are developmentally typical. As a subtype of learning disability, developmental dyscalculia contributes to deep cognitive processing deficits, mainly manifested as a lack of numerical processing ability. This study utilized event-related potentials (ERPs) technology to examine the negative priming effects (NP) between children with and without DD. Behaviorally, trends in mean reaction time (RT) were consistent between children with and without DD under prime and control conditions. The developmental dyscalculia group and the typical developmental (TD) children group showed a significant negative priming effect. However, the magnitude of the NP was significantly different between two groups, with the magnitude being significantly higher in the TD group than the DD group. In terms of the ERPs results, there were significantly larger amplitudes of P100, P200, and P300 in the TD group than that of children with DD. At the same time, in the DD group, N100 and P300 latency were significantly delayed in some electrodes than the TD group. The results indicated that there were characteristic inhibition deficits in children with DD. Inhibition defects in children with DD might be the underlying cause of the development of digital processing ability of children with DD.

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

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

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BACKGROUND: Arithmetic knowledge has long been known as an essential factor for educational and vocational success. AIMS: This study aims to explore the effectiveness of a process-based Executive Function (EF) intervention program on the improvement of components of arithmetic. METHODS AND PROCEDURE: A goal-directed sampling method was applied in this study. Participants were assigned into active control and experimental groups. Semi-experimental design with pre-test, post-test and follow-up was utilized in this research. Participants were included in this study based on their WISC-IV and Key-Math test performance. 30 male students aged 8-10 years with a formal diagnosis of Developmental Dyscalculia (DD), selected from a learning disability center in Ahvaz, Iran, participated in the study. The pre-test took 1 month, the intervention including 17 sessions, took two months and the post-test took 1 month. All the students' arithmetic knowledge were tested in pre-test, post-test, and 3 months after post-test to test the longevity of the intervention effects. Repeated measure Univariate Analysis of Variance was conducted in this study. OUTCOMES AND RESULTS: The results indicate that the students who attended the intervention, outperformed control group in the components of factual and procedural arithmetic in post-test and follow-up, however; the performance of two groups in conceptual knowledge was not different. This study contributes to the emerging evidence that EF intervention may improve factual and procedural arithmetic knowledge in children with DD. CONCLUSIONS AND IMPLICATIONS: Process-based EF interventions can improve arithmetic knowledge of students with DD, which can contribute to the literature of this area WHAT THIS PAPER ADDS?: The current research helps cognitive science to present a more meticulous theoretical and conceptual pattern for EF components and math, using process-based EF intervention programs with arithmetic content. Furthermore, this research allows for specification of cognitive fundamentals of arithmetic development and understanding the mechanisms underlying the transfer effect of EF intervention to math. The findings of this research can contribute to evidence-based EF intervention studies and help educational psychologists in preparation of appropriate curricula based on the fundamental components of arithmetic development in preschool and primary school.

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An ability that is impaired in developmental dyscalculia (DD) is related to number line estimation (NLE). However, due to variability in NLE task performance, group differences do not exemplify the real difficulty level observed in the DD population. Thirty-two of the fifty-two participants posing dyscalculia risk (DR) (mean age = 9.88) experienced difficulties in mathematics. All the children performed two number-to-position tasks and two tasks requiring a verbal estimation of a number indicated on a line, utilizing the ranges 0-100 and 0-1000. The results showed that the estimation error in the verbal task was greater in the DR group than in the typically developed (TD) group for the 0-1000 range. In the number-to-position task, group differences were found for both ranges and the variability within both groups was smaller than it was in the verbal tasks. Analyses of each of the 26 numerical magnitudes revealed a more comprehensive pattern. The majority of the group effects were related to the 0-1000 line. Therefore, considerable data variability, especially in the DD group, suggests this issue must be analyzed carefully in the case of other mathematical capacities. It also critically questions some well-established phenomena and norms in experimental and diagnostic practices.

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Numerical abilities are fundamental in our society. As a consequence, poor numerical skills might have a great impact on daily living. This study analyzes the extent to which the numerical deficit observed in young adults with Developmental Dyscalculia (DD) impacts their activities of everyday life. For this purpose, 26 adults with DD and 26 healthy controls completed the NADL, a standardized battery that assesses numerical skills in both formal and informal contexts. The results showed that adults with DD had poorer arithmetical skills in both formal and informal settings. In particular, adults with DD presented difficulties in time and measure estimation as well as money usage in real-world numerical tasks. In contrast, everyday tasks regarding distance estimation were preserved. In addition, the assessment revealed that adults with DD were aware of their numerical difficulties, which were often related to emotional problems and negatively impacted their academic and occupational decisions. Our study highlights the need to design innovative interventions and age-appropriate training for adults with DD to support their numerical skills as well as their social and emotional well-being.