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.

Linear and nonlinear profiles of weak behavioral and neural differentiation between numerical operations in children with math learning difficulties.

Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.

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

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

Learning disabilities: Developmental dyscalculia.

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

Quantitative analysis of heterogeneity in academic achievement of children with autism.

Autism spectrum disorders (ASD) represent a quintessential example of a clinical population with diverse symptom presentations and marked variation in cognitive abilities. However, the extent literature lacks rigorous quantitative procedures for characterizing heterogeneity of cognitive abilities in these individuals. Here we employ novel clustering and cross-validation procedures to investigate the stability of heterogeneous patterns of cognitive abilities in reading and math in a relatively large sample (N=114) of children with ASD and matched controls (N=96). Our analysis revealed a unique profile of heterogeneity in ASD, consisting of a low-achieving subgroup with poor math skills compared to reading, and a high-achieving subgroup who showed superior math skills compared to reading. Verbal and central executive working memory skills further differentiated these subgroups. Findings provide insights into distinct profiles of academic achievement in children with ASD, with implications for educational practice and intervention, and provide a novel framework for quantifying heterogeneity in the disorder.

Short-term cognitive training recapitulates hippocampal functional changes associated with one year of longitudinal skill development.

Objective: A goal of developmental cognitive neuroscience is to uncover brain mechanisms underlying successful learning. While longitudinal studies capture brain changes following 'schooling as usual', short-term training studies can more directly link learning to brain changes. We investigated whether eight weeks of cognitive training recapitulates longitudinal changes in hippocampal engagement and connectivity. Methods: Nineteen children underwent a training program focused on improving arithmetic skills, along with fifteen children in a no-contact control group. Before and after training, or no-contact, both groups performed an arithmetic task during neuroimaging and a strategy assessment. Results: Training increased activity in the anterior hippocampus, and gains in memory-based strategies were associated with decreased lateral fronto-parietal activity and increased hippocampus-parietal connectivity. No changes were observed in the no-contact control group. Conclusions: Our results demonstrate that short-term training can recapitulate long-term neurodevelopmental changes accompanying learning and identifies plasticity of hippocampal responses as a common locus of cognitive skill development in children.

Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities.

Competency with numbers is essential in today's society; yet, up to 20% of children exhibit moderate to severe mathematical learning disabilities (MLD). Behavioural intervention can be effective, but the neurobiological mechanisms underlying successful intervention are unknown. Here we demonstrate that eight weeks of 1:1 cognitive tutoring not only remediates poor performance in children with MLD, but also induces widespread changes in brain activity. Neuroplasticity manifests as normalization of aberrant functional responses in a distributed network of parietal, prefrontal and ventral temporal-occipital areas that support successful numerical problem solving, and is correlated with performance gains. Remarkably, machine learning algorithms show that brain activity patterns in children with MLD are significantly discriminable from neurotypical peers before, but not after, tutoring, suggesting that behavioural gains are not due to compensatory mechanisms. Our study identifies functional brain mechanisms underlying effective intervention in children with MLD and provides novel metrics for assessing response to intervention.

Remediation of Childhood Math Anxiety and Associated Neural Circuits through Cognitive Tutoring.

Math anxiety is a negative emotional reaction that is characterized by feelings of stress and anxiety in situations involving mathematical problem solving. High math-anxious individuals tend to avoid situations involving mathematics and are less likely to pursue science, technology, engineering, and math-related careers than those with low math anxiety. Math anxiety during childhood, in particular, has adverse long-term consequences for academic and professional success. Identifying cognitive interventions and brain mechanisms by which math anxiety can be ameliorated in children is therefore critical. Here we investigate whether an intensive 8 week one-to-one cognitive tutoring program designed to improve mathematical skills reduces childhood math anxiety, and we identify the neurobiological mechanisms by which math anxiety can be reduced in affected children. Forty-six children in grade 3, a critical early-onset period for math anxiety, participated in the cognitive tutoring program. High math-anxious children showed a significant reduction in math anxiety after tutoring. Remarkably, tutoring remediated aberrant functional responses and connectivity in emotion-related circuits anchored in the basolateral amygdala. Crucially, children with greater tutoring-induced decreases in amygdala reactivity had larger reductions in math anxiety. Our study demonstrates that sustained exposure to mathematical stimuli can reduce math anxiety and highlights the key role of the amygdala in this process. Our findings are consistent with models of exposure-based therapy for anxiety disorders and have the potential to inform the early treatment of a disability that, if left untreated in childhood, can lead to significant lifelong educational and socioeconomic consequences in affected individuals. Significance statement: Math anxiety during early childhood has adverse long-term consequences for academic and professional success. It is therefore important to identify ways to alleviate math anxiety in young children. Surprisingly, there have been no studies of cognitive interventions and the underlying neurobiological mechanisms by which math anxiety can be ameliorated in young children. Here, we demonstrate that intensive 8 week one-to-one cognitive tutoring not only reduces math anxiety but also remarkably remediates aberrant functional responses and connectivity in emotion-related circuits anchored in the amygdala. Our findings are likely to propel new ways of thinking about early treatment of a disability that has significant implications for improving each individual's academic and professional chances of success in today's technological society that increasingly demands strong quantitative skills.

Preliminary evidence for performance enhancement following parietal lobe stimulation in Developmental Dyscalculia.

Nearly 7% of the population exhibit difficulties in dealing with numbers and performing arithmetic, a condition named Developmental Dyscalculia (DD), which significantly affects the educational and professional outcomes of these individuals, as it often persists into adulthood. Research has mainly focused on behavioral rehabilitation, while little is known about performance changes and neuroplasticity induced by the concurrent application of brain-behavioral approaches. It has been shown that numerical proficiency can be enhanced by applying a small-yet constant-current through the brain, a non-invasive technique named transcranial electrical stimulation (tES). Here we combined a numerical learning paradigm with transcranial direct current stimulation (tDCS) in two adults with DD to assess the potential benefits of this methodology to remediate their numerical difficulties. Subjects learned to associate artificial symbols to numerical quantities within the context of a trial and error paradigm, while tDCS was applied to the posterior parietal cortex (PPC). The first subject (DD1) received anodal stimulation to the right PPC and cathodal stimulation to the left PPC, which has been associated with numerical performance's improvements in healthy subjects. The second subject (DD2) received anodal stimulation to the left PPC and cathodal stimulation to the right PPC, which has been shown to impair numerical performance in healthy subjects. We examined two indices of numerical proficiency: (i) automaticity of number processing; and (ii) mapping of numbers onto space. Our results are opposite to previous findings with non-dyscalculic subjects. Only anodal stimulation to the left PPC improved both indices of numerical proficiency. These initial results represent an important step to inform the rehabilitation of developmental learning disabilities, and have relevant applications for basic and applied research in cognitive neuroscience, rehabilitation, and education.

Brain organization underlying superior mathematical abilities in children with autism.

BACKGROUND: Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by social and communication deficits. While such deficits have been the focus of most research, recent evidence suggests that individuals with ASD may exhibit cognitive strengths in domains such as mathematics. METHODS: Cognitive assessments and functional brain imaging were used to investigate mathematical abilities in 18 children with ASD and 18 age-, gender-, and IQ-matched typically developing (TD) children. Multivariate classification and regression analyses were used to investigate whether brain activity patterns during numerical problem solving were significantly different between the groups and predictive of individual mathematical abilities. RESULTS: Children with ASD showed better numerical problem solving abilities and relied on sophisticated decomposition strategies for single-digit addition problems more frequently than TD peers. Although children with ASD engaged similar brain areas as TD children, they showed different multivariate activation patterns related to arithmetic problem complexity in ventral temporal-occipital cortex, posterior parietal cortex, and medial temporal lobe. Furthermore, multivariate activation patterns in ventral temporal-occipital cortical areas typically associated with face processing predicted individual numerical problem solving abilities in children with ASD but not in TD children. CONCLUSIONS: Our study suggests that superior mathematical information processing in children with ASD is characterized by a unique pattern of brain organization and that cortical regions typically involved in perceptual expertise may be utilized in novel ways in ASD. Our findings of enhanced cognitive and neural resources for mathematics have critical implications for educational, professional, and social outcomes for individuals with this lifelong disorder.

The mental cost of cognitive enhancement.

Noninvasive brain stimulation provides a potential tool for affecting brain functions in the typical and atypical brain and offers in several cases an alternative to pharmaceutical intervention. Some studies have suggested that transcranial electrical stimulation (TES), a form of noninvasive brain stimulation, can also be used to enhance cognitive performance. Critically, research so far has primarily focused on optimizing protocols for effective stimulation, or assessing potential physical side effects of TES while neglecting the possibility of cognitive side effects. We assessed this possibility by targeting the high-level cognitive abilities of learning and automaticity in the mathematical domain. Notably, learning and automaticity represent critical abilities for potential cognitive enhancement in typical and atypical populations. Over 6 d, healthy human adults underwent cognitive training on a new numerical notation while receiving TES to the posterior parietal cortex or the dorsolateral prefrontal cortex. Stimulation to the the posterior parietal cortex facilitated numerical learning, whereas automaticity for the learned material was impaired. In contrast, stimulation to the dorsolateral prefrontal cortex impaired the learning process, whereas automaticity for the learned material was enhanced. The observed double dissociation indicates that cognitive enhancement through TES can occur at the expense of other cognitive functions. These findings have important implications for the future use of enhancement technologies for neurointervention and performance improvement in healthy populations.

Genetics and mathematics: FMR1 premutation female carriers.

Neuropsychological investigations of FMR1 premutation carriers without FXTAS present one domain resulting in contradictory findings, namely that of mathematical skills. One reason for this might be that standard clinical batteries used so far may be inadequate to uncover precise deficits within specific mathematical skills. In fact, these batteries do not clearly distinguish between specific mathematical abilities and are therefore likely to provide only a generic indication of a deficit. Mathematical skills in a group of females with FMR1 premutation were investigated through the use of an extensive, theoretically grounded battery of mathematical tasks, encompassing counting, number comprehension, numerical transcoding, calculation skills and arithmetic principles. Moreover, the mental representation of numbers was assessed by studying the Spatial Numerical Association of Response Codes (SNARC) effect and mental number line (MNL) bisection. The FMR1 premutation group (N=18) comprised 29-50 years old women of normal intelligence, who were individually matched on age, sex and education to a group of healthy participants (N=18). Specific yet subtle weaknesses were detected on processes of basic number understanding such as dealing with analogue scales and certain aspects of number transcoding, in the presence of otherwise spared calculation abilities.

Understanding the real value of fractions and decimals.

Understanding fractions and decimals is difficult because whole numbers are the most frequently and earliest experienced type of number, and learners must avoid conceptualizing fractions and decimals in terms of their whole-number components (the "whole-number bias"). We explored the understanding of fractions, decimals, two-digit integers, and money in adults and 10-year-olds using two number line tasks: marking the line to indicate the target number, and estimating the numerical value of a mark on the line. Results were very similar for decimals, integers, and money in both tasks for both groups, demonstrating that the linear representation previously shown for integers is also evident for decimals already by the age of 10. Fractions seem to be "task dependent" so that when asked to place a fractional value on a line, both adults and children displayed a linear representation, while this pattern did not occur in the reverse task.

Mapping numerical magnitudes along the right lines: differentiating between scale and bias.

Previous investigations on the subjective scale of numerical representations assumed that the scale type can be inferred directly from stimulus-response mapping. This is not a valid assumption, as mapping from the subjective scale into behavior may be nonlinear and/or distorted by response bias. Here we present a method for differentiating between logarithmic and linear hypotheses robust to the effect of distorting processes. The method exploits the idea that a scale is defined by transformational rules and that combinatorial operations with stimulus magnitudes should be closed under admissible transformations on the subjective scale. The method was implemented with novel variants of the number line task. In the line-marking task, participants marked the position of an Arabic numeral within an interval defined by various starting numbers and lengths. In the line construction task, participants constructed an interval given its part. Two alternative approaches to the data analysis, numerical and analytical, were used to evaluate the linear and log components. Our results are consistent with the linear hypothesis about the subjective scale with responses affected by a bias to overestimate small magnitudes and underestimate large magnitudes. We also observed that in the line-marking task, participants tended to overestimate as the interval start increased, and in the line construction task, they tended to overconstruct as the interval length increased. This finding suggests that magnitudes were encoded differently in the 2 tasks: in terms of their absolute magnitudes in the line-marking task and in terms of numerical differences in the line construction task.

Modulating neuronal activity produces specific and long-lasting changes in numerical competence.

Around 20% of the population exhibits moderate to severe numerical disabilities [1-3], and a further percentage loses its numerical competence during the lifespan as a result of stroke or degenerative diseases [4]. In this work, we investigated the feasibility of using noninvasive stimulation to the parietal lobe during numerical learning to selectively improve numerical abilities. We used transcranial direct current stimulation (TDCS), a method that can selectively inhibit or excitate neuronal populations by modulating GABAergic (anodal stimulation) and glutamatergic (cathodal stimulation) activity [5, 6]. We trained subjects for 6 days with artificial numerical symbols, during which we applied concurrent TDCS to the parietal lobes. The polarity of the brain stimulation specifically enhanced or impaired the acquisition of automatic number processing and the mapping of number into space, both important indices of numerical proficiency [7-9]. The improvement was still present 6 months after the training. Control tasks revealed that the effect of brain stimulation was specific to the representation of artificial numerical symbols. The specificity and longevity of TDCS on numerical abilities establishes TDCS as a realistic tool for intervention in cases of atypical numerical development or loss of numerical abilities because of stroke or degenerative illnesses.

Core information processing deficits in developmental dyscalculia and low numeracy.

There are two different conceptions of the innate basis for numerical abilities. On the one hand, it is claimed that infants possess a 'number module' that enables them to construct concepts of the exact numerosities of sets upon which arithmetic develops (e.g. Butterworth, 1999; Gelman & Gallistel, 1978). On the other hand, it has been proposed that infants are equipped only with a sense of approximate numerosities (e.g. Feigenson, Dehaene & Spelke, 2004), upon which the concepts of exact numerosities are constructed with the aid of language (Carey, 2004) and which forms the basis of arithmetic (Lemer, Dehaene, Spelke & Cohen, 2003). These competing proposals were tested by assessing whether performance on approximate numerosity tasks is related to performance on exact numerosity tasks. Moreover, performance on an analogue magnitude task was tested, since it has been claimed that approximate numerosities are represented as analogue magnitudes. In 8-9-year-olds, no relationship was found between exact tasks and either approximate or analogue tasks in normally achieving children, in children with low numeracy or in children with developmental dyscalculia. Low numeracy was related not to a poor grasp of exact numerosities, but to a poor understanding of symbolic numerals.