Atypical trajectories of number development: a neuroconstructivist perspective

Exploring relative strengths in people with Down syndrome: Spatial thinking and its role in mathematics

There is convincing evidence that training spatial abilities leads to improved mathematics performance in typically developing (TD) children. However, a lack of information on mathematical development and spatial-mathematical associations in people with Down syndrome (DS) hinders the translation of these interventions. Here, we established developmental trajectories of mathematics and explored whether spatial ability predicts attainment on different mathematics measures in individuals with DS. Participants with DS (n = 36; ages 9-35 years) and TD children (n = 132; ages 4-11 years) completed three groups of tasks: spatial tasks assessing different subdomains of spatial thinking; mathematics tasks assessing early mathematics skills, mathematical reasoning, arithmetic, and geometry; and IQ tasks. The developmental trajectories of mathematics performance against mental age revealed similar starting points of the trajectories and similar rates of development for DS and TD groups. Furthermore, after controlling for verbal skills, spatial skills explained 5.8% to 18.1% of the variation in mathematical performance across different mathematics tasks, and the pattern of spatial-mathematical relations was similar for DS and mental age-matched TD groups. This shows that mathematical development in DS groups appears to mirror that in TD children, indicative of delay only. Strong spatial-mathematical relations were observed for individuals with DS, like those seen for TD participants. This is the vital preliminary knowledge needed to support the design and use of spatial intervention for improving mathematics in individuals with DS.

Dyslexia and dyscalculia: which neuropsychological processes distinguish the two developmental disorders?

This study analyses the specific neuropsychological profiles of children with dyslexia and/or dyscalculia, in particular concerning phonological awareness, lexical access, working memory and numerical processing. Four groups were selected, through a screening process that used strict criteria, from 1568 7-10-year-old children: 90 with typical development, 61 with dyslexia, 13 with dyscalculia, and 14 with dyslexia + dyscalculia. Children with dyslexia show a deficit in phonological processing, lexical access, and verbal working memory, especially with alphabetic stimuli. Children with developmental dyscalculia show a deficit of phonological processing, verbal working memory with digits and visual-spatial working memory. They also show an impairment in spatial representation of numbers and in the automatic access to numerical semantics to a greater extent than those with double disturbance. Children with dyslexia + dyscalculia show a profile generally characterized by the summation of the deficits of the two disorders, although they have a lower deficit in access to numerical semantics and mental representation of numbers.

Different impacts of long-term abacus training on symbolic and non-symbolic numerical magnitude processing in children

Abacus-based mental calculation (AMC) has been shown to be effective in promoting math ability in children. Given that AMC relies on a visuospatial strategy to perform rapid and precise arithmetic, previous studies mostly focused on the promotion of AMC training on arithmetic ability and mathematical visual-spatial ability, as well as its transfer of advanced cognitive ability. However, little attention has been given to its impact on basic numerical comparison ability. Here, we aim to examine whether and how long-term AMC training impacts symbolic and non-symbolic numerical comparisons. The distance effect (DE) was utilized as a marker, indicating that the comparison between two numbers becomes faster as their numerical distance enlarges. In the current study, forty-one children matched for age and sex were recruited at primary school entry and randomly assigned to the AMC group and the control group. After three years of training, the event-related potential (ERP) recording technique was used to explore the temporal dynamics of number comparison, of which tasks were given in symbolic (Arabic number) or non-symbolic (dot array) format. In the symbolic task, the children in the AMC group showed a smaller DE than those in the control group. Two ERP components, N1 and P2p, located in parietal areas (PO7, PO8) were selected as neural markers of numerical processing. Both groups showed DE in the P2p component in both tasks, but only the children in the AMC group showed DE in the N1 component in the non-symbolic task. In addition, the DE size calculated from reaction times and ERP amplitudes was correlated with higher cognitive capacities, such as coding ability. Taken together, the present results provide evidence that long-term AMC training may be beneficial for numerical processing in children, which may be associated with neurocognitive indices of parietal brain regions.

Factor structure of early numeracy: evaluation of a measurement model in greek-speaking children with intellectual disabilities

Exploring the individual differences of the longitudinal growth of early numeracy (EN) in young children with Intellectual disabilities (IDs) prerequires the critical stage of exploring and validating the potential factor structure. Despite the fact that Relational Skills (RS), Counting Skills (CS) and Operations (O) are expected to constitute distinct domains of EN, there is not sufficient evidence to support either the above position or the position that they are different means of assessing a general-informal numeracy skill construct. This study was designed to shed light in the field through the evaluation of a measurement model describing the structure of RS, CS and O domains of EN and their interrelation. The sample included N = 155 children with IDs, enrolled in special school classes, mentally aged between 5;02 (y;m) and 6;10 (M = 5.11, SD = 0.974). Confirmatory Factor Analysis indicated a "good fit" of the two-factor model (RS, CS + O) of EN in ID (RMSEA=.029 < 0.08, CFI = 0.98 ≥ 0.90 and SRMR = 0.000 < 0.08). No measurement invariance across gender was reported for the proposed two-factor model of EN. The nested EN models validated full measurement invariance across gender. Finally, educational implications are discussed.

Quantifying the resolution of spatial and temporal representation in children with 22q11.2 deletion syndrome

OBJECTIVES

Our ability to generate mental representation of magnitude from sensory information affects how we perceive and experience the world. Reduced resolution of the mental representations formed from sensory inputs may generate impairment in the proximal and distal information processes that utilize these representations. Impairment of spatial and temporal information processing likely underpins the non-verbal cognitive impairments observed in 22q11.2 deletion syndrome (22q11DS). The present study builds on prior research by seeking to quantify the resolution of spatial and temporal representation in children with 22q11DS, sex chromosome aneuploidy (SCA), and a typically developing (TD) control group.

PARTICIPANTS AND METHODS

Children (22q11DS = 70, SCA = 49, TD = 46) responded to visual or auditory stimuli with varying difference ratios. The participant's task was to identify which of two sequentially presented stimuli was of larger magnitude in terms of, size, duration, or auditory frequency. Detection threshold was calculated as the minimum difference ratio between the "standard" and the "target" stimuli required to achieve 75% accuracy in detecting that the two stimuli were different.

RESULTS

Children with 22q11DS required larger magnitude difference between spatial stimuli for accurate identification compared with both the SCA and TD groups (% difference from standard: 22q11DS = 14; SCA = 8; TD: 7; F  = 8.42, p < 0.001). Temporal detection threshold was also higher for the 22q11DS group to both visual (% difference from standard: 22q11DS = 14; SCA = 8; TD = 7; F  = 8.33, p < 0.001) and auditory (% difference from standard: 22q11DS = 23; SCA = 12; TD: 8; F  = 8.99, p < 0.001) stimuli compared with both the SCA and TD groups, while the SCA and TD groups displayed equivalent performance on these measures (p's > 0.05). Pitch detection threshold did not differ among the groups (p's > 0.05).

CONCLUSIONS

The observation of higher detection thresholds to spatial and temporal stimuli indicates further evidence for reduced resolution in both spatial and temporal magnitude representation in 22q11DS, that does not extend to frequency magnitude representation (pitch detection), and which is not explained by generalized cognitive impairment alone. These findings generate further support for the hypothesis that spatiotemporal hypergranularity of mental representations contributes to the non-verbal cognitive impairment seen in 22q11DS.

Fronto-parietal numerical networks in relation with early numeracy in young children

Early numeracy provides the foundation of acquiring mathematical skills that is essential for future academic success. This study examined numerical functional networks in relation to counting and number relational skills in preschoolers at 4 and 6 years of age. The counting and number relational skills were assessed using school readiness test (SRT). Resting-state fMRI (rs-fMRI) was acquired in 123 4-year-olds and 146 6-year-olds. Among them, 61 were scanned twice over the course of 2 years. Meta-analysis on existing task-based numeracy fMRI studies identified the left parietal-dominant network for both counting and number relational skills and the right parietal-dominant network only for number relational skills in adults. We showed that the fronto-parietal numerical networks, observed in adults, already exist in 4-year and 6-year-olds. The counting skills were associated with the bilateral fronto-parietal network in 4-year-olds and with the right parietal-dominant network in 6-year-olds. Moreover, the number relational skills were related to the bilateral fronto-parietal and right parietal-dominant networks in 4-year-olds and had a trend of the significant relationship with the right parietal-dominant network in 6-year-olds. Our findings suggested that neural fine-tuning of the fronto-parietal numerical networks may subserve the maturation of numeracy in early childhood.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls' performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Differential Cortical Gray Matter Deficits in Adolescent- and Adult-Onset First-Episode Treatment-Naïve Patients with Schizophrenia

The current study aimed to explore age-variant trait differences of cortical gray matter volume (GMV) in a unique sample of first-episode and treatment-naïve patients with schizophrenia. A total of 158 subjects, including 26 adolescent-onset patients and 49 adult-onset patients as well as 83 age- and gender-matched controls were scanned using a 3T MRI scanner. Voxel-based morphometry (VBM) following Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra (DARTEL) was used to explore group differences between patients and controls in regional GMV. We found that patients with schizophrenia had decreased GMV in the left parietal postcentral region that extended to the left frontal regions, the right middle temporal gyrus, the occipital lobe and the right cerebellum posterior pyramis. Further analysis showed a distinct pattern of gray matter alterations in adolescent-onset patients compared with both healthy controls and adult-onset patients. Relative to healthy controls, adolescent-onset patients showed GMV alterations in the left parietal postcentral gyrus, parahippocampal gyrus and right cerebellum posterior pyramis, while GMV deficits in adult-onset patients were focused on the cingulo-fronto-temporal module and right occipital regions. Our study identified differential cortical gray matter deficits between adolescent- and adulthood-onset patients with schizophrenia, which suggests that the cortical abnormalities in schizophrenia are likely adjusted by the developmental community structure of the human brain.

The Contribution of Numerical Magnitude Comparison and Phonological Processing to Individual Differences in Fourth Graders' Multiplication Fact Ability

Although numerical magnitude processing has been related to individual differences in arithmetic, its role in children’s multiplication performance remains largely unknown. On the other hand, studies have indicated that phonological awareness is an important correlate of individual differences in children’s multiplication performance, but the involvement of phonological memory, another important phonological processing skill, has not been studied in much detail. Furthermore, knowledge about the relative contribution of above mentioned processes to the specific arithmetic operation of multiplication in children is lacking. The present study therefore investigated for the first time the unique contributions of numerical magnitude comparison and phonological processing in explaining individual differences in 63 fourth graders’ multiplication fact ability (mean age = 9.6 years, SD = .67). The results showed that children’s multiplication fact competency correlated significantly with symbolic and nonsymbolic magnitude comparison as well as with phonological short-term memory. A hierarchical regression analysis revealed that, after controlling for intellectual ability and general reaction time, both symbolic and nonsymbolic magnitude comparison and phonological short-term memory accounted for unique variance in multiplication fact performance. The ability to compare symbolic magnitudes was found to contribute the most, indicating that the access to numerical magnitudes by means of Arabic digits is a key factor in explaining individual differences in children’s multiplication fact ability.

A meta-analysis of math performance in Turner syndrome

AIM

Studies investigating the relationship between Turner syndrome and math learning disability have used a wide variation of tasks designed to test various aspects of mathematical competencies. Although these studies have revealed much about the math deficits common to Turner syndrome, their diversity makes comparisons between individual studies difficult. As a result, the consistency of outcomes among these diverse measures remains unknown. The overarching aim of this review is to provide a systematic meta-analysis of the differences in math and number performance between females with Turner syndrome and age-matched neurotypical peers.

METHOD

We provide a meta-analysis of behavioral performance in Turner syndrome relative to age-matched neurotypical populations on assessments of math and number aptitude. In total, 112 comparisons collected across 17 studies were included.

RESULTS

Although 54% of all statistical comparisons in our analyses failed to reject the null hypothesis, our results indicate that meaningful group differences exist on all comparisons except those that do not require explicit calculation.

INTERPRETATION

Taken together, these results help elucidate our current understanding of math and number weaknesses in Turner syndrome, while highlighting specific topics that require further investigation.

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation.

Mathematical difficulties in developmental coordination disorder: Symbolic and nonsymbolic number processing

At school, children with Developmental Coordination Disorder (DCD) struggle with mathematics. However, little attention has been paid to their numerical cognition abilities. The goal of this study was to better understand the cognitive basis for mathematical difficulties in children with DCD. Twenty 7-to-10 years-old children with DCD were compared to twenty age-matched typically developing children using dot and digit comparison tasks to assess symbolic and nonsymbolic number processing and in a task of single digits additions. Results showed that children with DCD had lower performance in nonsymbolic and symbolic number comparison tasks than typically developing children. They were also slower to solve simple addition problems. Moreover, correlational analyses showed that children with DCD who experienced greater impairments in the nonsymbolic task also performed more poorly in the symbolic tasks. These findings suggest that DCD impairs both nonsymbolic and symbolic number processing. A systematic assessment of numerical cognition in children with DCD could provide a more comprehensive picture of their deficits and help in proposing specific remediation.

Link between cognitive neuroscience and education: the case of clinical assessment of developmental dyscalculia

In recent years, cognitive neuroscience research has identified several biological and cognitive features of number processing deficits that may now make it possible to diagnose mental or educational impairments in arithmetic, even earlier and more precisely than is possible using traditional assessment tools. We provide two sets of recommendations for improving cognitive assessment tools, using the important case of mathematics as an example. (1) neurocognitive tests would benefit substantially from incorporating assessments (based on findings from cognitive neuroscience) that entail systematic manipulation of fundamental aspects of number processing. Tests that focus on evaluating networks of core neurocognitive deficits have considerable potential to lead to more precise diagnosis and to provide the basis for designing specific intervention programs tailored to the deficits exhibited by the individual child. (2) implicit knowledge, derived from inspection of variables that are irrelevant to the task at hand, can also provide a useful assessment tool. Implicit knowledge is powerful and plays an important role in human development, especially in cases of psychiatric or neurological deficiencies (such as math learning disabilities or math anxiety).

What standardized tests ignore when assessing individuals with neurodevelopmental disorders

In this article we critique the use of traditional standardized tests for the cognitive assessment of children with neurodevelopmental disorders. Limitations stem from the lack of integrating (a) results from research into the psychological functioning of these populations, and (b) the main arguments underlying models of human development. We identify four secondary issues in this discussion: (1) these instruments cannot be used with children who have particularly low cognitive functioning; (2) little or no variance in the scores obtained by individuals with neurodevelopmental disorders, because all are at floor, prevent adequate interpretations; (3) measurements do not provide information useful for the design of intervention strategies; and (4) different cognitive and/or neural processes may underlie behavioural scores 'in the normal range'. Rethinking traditional assessment methods in favour of technologically-mediated games yields new cognitive assessment possibilities.

Basic numerical processes in very preterm children: a critical transition from preschool to school age

BACKGROUND

Serious difficulties in formal mathematical skills have been identified in preterm children. By contrast, basic-level numerical skills like magnitude judgments have not yet been tested in these children.

AIMS

The aim of the present research was to investigate whether preterm birth also affects these basic numerical abilities, with particular attention to the transition from preschool to formal education.

METHOD

One hundred-forty very preterm children and 60 age-matched controls were recruited in a cross-sectional study at 6 and 8years of age. Magnitude comparison tasks with non-symbolic dot displays or symbolic Arabic-number stimuli, measuring accuracy and reaction time, were administered to participants. We also investigated explicit number knowledge, as well as general cognitive developmental levels, to gain a broader picture of preterm abilities.

RESULTS

Despite no general cognitive delay, the more simple approximate non-symbolic representation of numerical magnitude was affected by preterm birth, with slower reaction times at both ages compared to controls. Additionally, clear difficulties in the construction of the symbolic representation of numerical magnitude and in explicit number knowledge emerged in the 6-year-old preterm children, with a recovery from this serious delay finally by 8years.

CONCLUSIONS

The serious delays identified here in basic numerical abilities in preterm children, despite normal IQ, point to the need for further studies in order to elucidate the relationship between basic numerical abilities and subsequent difficulties in formal mathematic achievement at school.

It's all connected: Pathways in visual object recognition and early noun learning

A developmental pathway may be defined as the route, or chain of events, through which a new structure or function forms. For many human behaviors, including object name learning and visual object recognition, these pathways are often complex and multicausal and include unexpected dependencies. This article presents three principles of development that suggest the value of a developmental psychology that explicitly seeks to trace these pathways and uses empirical evidence on developmental dependencies among motor development, action on objects, visual object recognition, and object name learning in 12- to 24-month-old infants to make the case. The article concludes with a consideration of the theoretical implications of this approach. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Severity of specific language impairment predicts delayed development in number skills

The extent to which mathematical development is dependent upon language is controversial. This longitudinal study investigates the role of language ability in children's development of number skills. Participants were 229 children with specific language impairment (SLI) who were assessed initially at age 7 and again 1 year later. All participants completed measures of psycholinguistic development (expressive and receptive), performance IQ, and the Basic Number Skills subtest of the British Ability Scales. Number skills data for this sample were compared with normative population data. Consistent with predictions that language impairment would impact on numerical development, average standard scores were more than 1 SD below the population mean at both ages. Although the children showed improvements in raw scores at the second wave of the study, the discrepancy between their scores and the population data nonetheless increased over time. Regression analyses showed that, after controlling for the effect of PIQ, language skills explained an additional 19 and 17% of the variance in number skills for ages 7 and 8, respectively. Furthermore, logistic regression analyses revealed that less improvement in the child's language ability over the course of the year was associated with a greater odds of a drop in performance in basic number skills from 7 to 8 years. The results are discussed in relation to the interaction of linguistic and cognitive factors in numerical development and the implications for mathematical education.

Preterm birth: neuropsychological profiles and atypical developmental pathways

Preterm birth is characterized by multiple interacting atypical constraints affecting different aspects of neuropsychological development. In the first years of life, perceptual, motor, and communicative-linguistic abilities, as well as attention, processing speed, and memory are affected by preterm birth resulting in cascading effects on later development. From school age to adolescence, a catch-up of simpler competencies (i.e., receptive lexicon) along with a more selective effect on more complex competencies (i.e., complex linguistic functions, math, motor, and executive functions) are observed, as well as a relevant incidence of behavioral outcomes. A wide heterogeneity in preterm children's neuropsychological profiles is described depending on the interaction among the degree of neonatal immaturity, medical complications, neurological damages/alterations, environmental and social factors. Severe neuromotor and sensory damages are not frequent, while low severity impairments are common among preterm children. It is argued that developmental pathways of preterm children are atypical, and not merely delayed, and are characterized by different developmental patterns and relationships among competencies.

An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities

INTRODUCTION

The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months).

METHODS

EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed.

RESULTS

In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences.

CONCLUSION

Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range.

The development of individuation in autism

Evidence suggests that people with autism rely less on holistic visual information than typical adults. The current studies examine this by investigating core visual processes that contribute to holistic processing--namely, individuation and element grouping--and how they develop in participants with autism and typically developing (TD) participants matched for age, IQ, and gender. Individuation refers to the ability to "see" approximately four elements simultaneously; grouping elements can modify how many elements can be individuated. We examined these processes using two well-established paradigms, rapid enumeration and multiple object tracking (MOT). In both tasks, a performance limit of four elements in typical adults is thought to reflect individuation capacity. Participants with autism displayed a smaller individuation capacity than TD controls, regardless of whether they were enumerating static elements or tracking moving ones. To manipulate the holistic information available via element grouping, elements were arranged into a design in rapid enumeration, or moved together in MOT. Performance in participants with autism was affected to a similar degree as TD participants by element grouping, whether the manipulation helped or hurt performance, consistent with evidence that some types of gestalt/grouping information are processed typically in autism. There was substantial development from childhood to adolescence in the speed of individuation in those with autism, but not from adolescence to adulthood, a pattern distinct from TD participants. These results reveal how core visual processes function in autism, and provide insight into the architecture of vision (i.e., individuation appears distinct from visual strengths in autism, such as visual search).

Time-Resolved and Spatio-Temporal Analysis of Complex Cognitive Processes and their Role in Disorders like Developmental Dyscalculia

The aim of this article is to report on the importance and challenges of a time-resolved and spatio-temporal analysis of fMRI data from complex cognitive processes and associated disorders using a study on developmental dyscalculia (DD). Participants underwent fMRI while judging the incorrectness of multiplication results, and the data were analyzed using a sequence of methods, each of which progressively provided more a detailed picture of the spatio-temporal aspect of this disease. Healthy subjects and subjects with DD performed alike behaviorally though they exhibited parietal disparities using traditional voxel-based group analyses. Further and more detailed differences, however, surfaced with a time-resolved examination of the neural responses during the experiment. While performing inter-group comparisons, a third group of subjects with dyslexia (DL) but with no arithmetic difficulties was included to test the specificity of the analysis and strengthen the statistical base with overall fifty-eight subjects. Surprisingly, the analysis showed a functional dissimilarity during an initial reading phase for the group of dyslexic but otherwise normal subjects, with respect to controls, even though only numerical digits and no alphabetic characters were presented. Thus our results suggest that time-resolved multi-variate analysis of complex experimental paradigms has the ability to yield powerful new clinical insights about abnormal brain function. Similarly, a detailed compilation of aberrations in the functional cascade may have much greater potential to delineate the core processing problems in mental disorders.

The "where" and "what" in developmental dyscalculia

Developmental dyscalculia (DD) is a congenital deficit that affects the ability to acquire arithmetical skills. Individuals with DD have problems learning standard number facts and procedures. Estimates of the prevalence rate of DD are similar to those of developmental dyslexia. Recent reports and discussions suggest that those with DD suffer from specific deficits (e.g., subitizing, comparative judgment). Accordingly, DD has been described as a domain-specific disorder that involves particular brain areas (e.g., intra-parietal sulcus). However, we and others have found that DD is characterized by additional deficiencies and may be affected by domain-general (e.g., attention) factors. Hence "pure DD" might be rather rare and not as pure as one would think. We suggest that the heterogeneity of symptoms that commonly characterize learning disabilities needs to be taken into account in future research and treatment.

Clues to the foundations of numerical cognitive impairments: evidence from genetic disorders

Several neurodevelopmental disorders of known genetic etiology generate phenotypes that share the characteristic of numerical and mathematical cognitive impairments. This article reviews some of the main findings that suggest a possible key role that spatial and temporal information processing impairments may play in the atypical development of numerical cognitive competence. The question of what neural substrate might underlie these impairments is also addressed, as are the challenges for interpreting neural structure/cognitive function mapping in atypically developing populations.

Relationships between number and space processing in adults with and without dyscalculia

A large body of evidence indicates clear relationships between number and space processing in healthy and brain-damaged adults, as well as in children. The present paper addressed this issue regarding atypical math development. Adults with a diagnosis of dyscalculia (DYS) during childhood were compared to adults with average or high abilities in mathematics across two bisection tasks. Participants were presented with Arabic number triplets and had to judge either the number magnitude or the spatial location of the middle number relative to the two outer numbers. For the numerical judgment, adults with DYS were slower than both groups of control peers. They were also more strongly affected by the factors related to number magnitude such as the range of the triplets or the distance between the middle number and the real arithmetical mean. By contrast, adults with DYS were as accurate and fast as adults who never experienced math disability when they had to make a spatial judgment. Moreover, number-space congruency affected performance similarly in the three experimental groups. These findings support the hypothesis of a deficit of number magnitude representation in DYS with a relative preservation of some spatial mechanisms in DYS. Results are discussed in terms of direct and indirect number-space interactions.

Dyscalculia: from brain to education

Recent research in cognitive and developmental neuroscience is providing a new approach to the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their numerosities, which is fundamental to all aspects of elementary school mathematics. The neural bases of numerosity processing have been investigated in structural and functional neuroimaging studies of adults and children, and neural markers of its impairment in dyscalculia have been identified. New interventions to strengthen numerosity processing, including adaptive software, promise effective evidence-based education for dyscalculic learners.

Explorative function in Williams syndrome analyzed through a large-scale task with multiple rewards

This study aimed to evaluate spatial function in subjects with Williams syndrome (WS) by using a large-scale task with multiple rewards and comparing the spatial abilities of WS subjects with those of mental age-matched control children. In the present spatial task, WS participants had to explore an open space to search nine rewards placed in buckets arranged according to three spatial configurations: a cross, a 3 × 3 matrix and a cluster composed by three groups of three buckets each. The findings demonstrate that WS individuals were impaired in efficiently exploring the environment and in building cognitive spatial maps. In exploring the three spatial configurations, they performed worse than control subjects on all parameters analyzed. In fact, WS individuals took more time to complete the task, made more errors, performed a reduced number of error-free trials, displayed lower search efficiency, exhibited shorter spatial spans, showed a higher number of no-visits and displayed marked tendencies to perseverate and to neglect some buckets. Furthermore, WS individuals showed disorganized explorative patterns in comparison to control children. WS influenced performances differentially as a specific effect of the susceptibility of the configurations to being explored in a principled way. In the cross configuration that had strong spatial constraints, both groups exhibited their worst performances. In the matrix configuration, the altered explorative strategies of the WS subjects primarily affected their central exploration. The performances in the cluster configuration indicated that chunking was a strategy of strength in both TD and WS groups. In conclusion, WS individuals' deficits exhibited in the present explorative test may be considered an index of their difficulties in spatial orientation and motion perception displayed in the real world. The marked impairment in spatial information processing is discussed in neuro-anatomical alterations reported in WS.

Mathematics anxiety in children with developmental dyscalculia

BACKGROUND

Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure.

METHODS

Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively.

RESULT

Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group.

CONCLUSION

These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.

22q11.2 microdeletions: linking DNA structural variation to brain dysfunction and schizophrenia

Recent studies are beginning to paint a clear and consistent picture of the impairments in psychological and cognitive competencies that are associated with microdeletions in chromosome 22q11.2. These studies have highlighted a strong link between this genetic lesion and schizophrenia. Parallel studies in humans and animal models are starting to uncover the complex genetic and neural substrates altered by the microdeletion. In addition to offering a deeper understanding of the effects of this genetic lesion, these findings may guide analysis of other copy-number variants associated with cognitive dysfunction and psychiatric disorders.

Atypical functional brain activation during a multiple object tracking task in girls with Turner syndrome: neurocorrelates of reduced spatiotemporal resolution

Turner syndrome is associated with spatial and numerical cognitive impairments. We hypothesized that these nonverbal cognitive impairments result from limits in spatial and temporal processing, particularly as it affects attention. To examine spatiotemporal attention in girls with Turner syndrome versus typically developing controls, we used a multiple object tracking task during functional magnetic resonance (fMRI) imaging. Participants actively tracked a target among six distracters or passively viewed the animations. Neural activation in girls with Turner syndrome during object tracking overlapped with but was dissimilar to the canonical frontoparietal network evident in typically developing controls and included greater limbic activity. Task performance and atypical functional activation indicate anomalous development of cortical and subcortical temporal and spatial processing circuits in girls with Turner syndrome.

Numerical representation in the parietal lobes: abstract or not abstract?

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

Mathematical skills in Williams syndrome: insight into the importance of underlying representations

Williams syndrome (WS) is a developmental disorder characterized by relatively spared verbal skills and severe visuospatial deficits. Serious impairments in mathematics have also been reported. This article reviews the evidence on mathematical ability in WS, focusing on the integrity and developmental path of two fundamental representations, namely those that support judgments of "how much" (i.e., magnitude) and "how many" (i.e., number of objects). Studies on magnitude or "number line" representation in WS suggest that this core aspect of mathematical ability, is atypical in WS throughout development, causing differences on some but not all aspects of math. Studies on the representation of small numbers of objects in WS are also reviewed, given the proposed links between this type of representation and early number skills such as counting. In WS, representation appears to be relatively typical in infancy but limitations become evident by maturity, suggesting a truncated developmental trajectory. The math deficits in WS are consistent with neurological data indicating decreased gray matter and hypoactivation in parietal areas in WS, as these areas are implicated in mathematical processing as well as visuospatial abilities and visual attention. In spite of their deficits in core mathematical representations, people with WS can learn many mathematical skills and show some strengths, such as reading numbers. Thus individuals with WS may be able to take advantage of their relatively strong verbal skills when learning some mathematical tasks. The uneven mathematical abilities found in persons with WS provide insight into not only appropriate remediation for this developmental disorder but also into the precursors of mathematical ability, their neural substrates, and their developmental importance.

Mathematical learning disabilities in children with 22q11.2 deletion syndrome: a review

Mathematical learning disabilities (MLD) occur frequently in children with specific genetic disorders, like Turner syndrome, fragile X syndrome and neurofibromatosis. This review focuses on MLD in children with chromosome 22q11.2 deletion syndrome (22q11DS). This syndrome is the most common known microdeletion syndrome with a prevalence of at least 1:4000 to 1:6000 live births. Although the clinical presentation of 22q11DS is quite variable, its major characteristics include velopharyngeal abnormalities, congenital cardiac anomalies, mild facial dysmorphism and learning difficulties. Children with 22q11DS show considerable difficulties in mathematics, despite relatively normal reading performance. While fact retrieval seems to be preserved, impairments in procedural calculation and word problem solving are particularly prominent. Children with 22q11DS also have substantial difficulties in understanding and representing numerical quantities, possibly related to poor visuospatial attention, which all might stem from their underlying abnormalities in the inferior parietal cortex. This review ends with a discussion on how research on genetic disorders might aid our understanding of MLD in general.

Small and large number processing in infants and toddlers with Williams syndrome

Previous studies have suggested that typically developing 6-month-old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination is successful even when variables continuous with number are systematically controlled for. These findings suggest the existence of different systems underlying small and large number processing in infancy. How do these develop in atypical syndromes? Williams syndrome (WS) is a rare neurocognitive developmental disorder in which numerical cognition has been found to be impaired in older children and adults. Do impairments of number processing have their origins in infancy? Here this question is investigated by testing the small and large number discrimination abilities of infants and toddlers with WS. While infants with WS were able to discriminate between 2 and 3 elements when total area was confounded with numerosity, the same infants did not discriminate between 8 and 16 elements, when number was not confounded with continuous variables. These findings suggest that a system for tracking the features of small numbers of object (object-file representation) may be functional in WS, while large number discrimination is impaired from an early age onwards. Finally, we argue that individual differences in large number processing in infancy are more likely than small number processing to be predictive of later development of numerical cognition.

The predictive value of numerical magnitude comparison for individual differences in mathematics achievement

Although it has been proposed that the ability to compare numerical magnitudes is related to mathematics achievement, it is not clear whether this ability predicts individual differences in later mathematics achievement. The current study addressed this question in typically developing children by means of a longitudinal design that examined the relationship between a number comparison task assessed at the start of formal schooling (mean age=6 years 4 months) and a general mathematics achievement test administered 1 year later. Our findings provide longitudinal evidence that the size of the individual's distance effect, calculated on the basis of reaction times, was predictively related to mathematics achievement. Regression analyses showed that this association was independent of age, intellectual ability, and speed of number identification.

Developmental dyscalculia: heterogeneity might not mean different mechanisms

Research indicates that developmental dyscalculia (DD; a mathematical deficiency) involves a single brain area abnormality - in the intraparietal sulcus. This is surprising because, (i) the behavioural deficits are heterogeneous, (ii) multiple problems are most common in most cases (co-morbidity) and (iii) different aspects of intact number processing are represented in different brain areas. Hence, progress in the study of DD might be limited by conceptual issues. This work looks at biological and cognitive findings within DD and delineates frameworks for studying the neurocognitive basis of DD. We offer three alternative frameworks. These proposed frameworks have the potential of facilitating future discussions, work in the field and have implications for studies of similar disorders like dyslexia and attention-deficit/hyperactivity disorder.

Learning disabilities: definitions, epidemiology, diagnosis, and intervention strategies

Learning problems occur in about 5% of school-aged children. Learning disabilities are specific and life-long but present with different school problems at different ages, depending on such factors as age, medical history, family history, and intelligence quotient. Proper individualized diagnosis and treatment plans are necessary to remediate these problems and to offer adequate coping strategies. Many children who have learning problems can be classified into one of two major categories: the dyslexia group or the nonverbal learning disability group. The role of the medical professional is important to guide parents in the diagnostic and therapeutic process.