Representation and retrieval of arithmetical facts: developmental difficulties

Deafness and early language deprivation influence arithmetic performances

It has been consistently reported that deaf individuals experience mathematical difficulties compared to their hearing peers. However, the idea that deafness and early language deprivation might differently affect verbal (i.e., multiplication) vs. visuospatial (i.e., subtraction) arithmetic performances is still under debate. In the present paper, three groups of 21 adults (i.e., deaf signers, hearing signers, and hearing controls) were therefore asked to perform, as fast and as accurately as possible, subtraction and multiplication operations. No significant group effect was found for accuracy performances. However, reaction time results demonstrated that the deaf group performed both arithmetic operations slower than the hearing groups. This group difference was even more pronounced for multiplication problems than for subtraction problems. Weaker language-based phonological representations for retrieving multiplication facts, and sensitivity to interference are two hypotheses discussed to explain the observed dissociation.

No evidence for a core deficit in developmental dyscalculia or mathematical learning disabilities

BACKGROUND

Two hypotheses were tested regarding the characteristics of children with mathematical learning disabilities (MLD): (a) that children with MLD would have a 'core deficit' in basic number processing skills; and (b) that children with MLD would be at the end of a developmental continuum and have impairments in many cognitive skills.

METHODS

From a large sample (N = 1,303) of typically developing children, we selected a group definable as having MLD. The children were given measures of basic number processing and domain-general constructs. Differences between the observed sample and a simulated population were estimated using Cohen's d and Bayes factors. Receiver operating characteristic curves were plotted, and the area under the curve was computed to ascertain the diagnostic power of measures.

RESULTS

Results suggest that the differences between the MLD and control group can be defined along with general characteristics of the population rather than assuming single or multiple 'core deficits'. None of the measures of interest exceeded the diagnostic power that could be derived via simulation from the dimensional characteristics of the general population.

CONCLUSIONS

There is no evidence for core deficit(s) in MLD. We suggest that future research should focus on representative samples of typical populations and on carefully tested clinical samples confirming to the criteria of international diagnostic manuals. Clinical diagnoses require that MLD is persistent and resistant to intervention, so studies would deliver results less exposed to measurement fluctuations. Uniform diagnostic criteria would also allow for the easy cross-study comparison of samples overcoming a serious limitation of the current literature.

Predicting individual differences in reading, spelling and maths in a sample of typically developing children: A study in the perspective of comorbidity

We examined reading, spelling, and mathematical skills in an unselected group of 129 Italian fifth graders by testing various cognitive predictors for each behaviour. As dependent variables, we measured performance in behaviours with a clear functional value in everyday life, such as reading a text, spelling under dictation and doing mental and written computations. As predictors, we selected cognitive dimensions having an explicit relation with the target behaviour (called proximal predictors), and prepared various tests in order to select which task had the best predictive power on each behaviour. The aim was to develop a model of proximal predictors of reading (speed and accuracy), spelling (accuracy) and maths (speed and accuracy) characterized by efficacy also in comparison to the prediction based on general cognitive factors (i.e., short-term memory, phonemic verbal fluency, visual perceptual speed, and non-verbal intelligence) and parsimony, pinpointing the role of both common and unique predictors as envisaged in the general perspective of co-morbidity. With one exception (reading accuracy), the proximal predictors models (based on communality analyses) explained a sizeable amount of variance, ranging from 27.5% in the case of calculation (accuracy) to 48.7% of reading (fluency). Models based on general cognitive factors also accounted for some variance (ranging from 6.5% in the case of spelling to 19.5% in the case of reading fluency) but this was appreciably less than that explained by models based on the hypothesized proximal predictors. In general, results confirmed the efficacy of proximal models in predicting reading, spelling and maths although they offered only limited support for common predictors across different learning skills; namely, performance in the Orthographic Decision test entered as a predictor of both reading and spelling indicating that a single orthographic lexicon may account for performance in reading and spelling. Possible lines of research to expand on this approach are illustrated.

Specific Mental Arithmetic Difficulties and General Arithmetic Learning Difficulties: The Role of Phonological Working Memory

The aim of this paper was to examine the role of phonological working memory in specific mental arithmetic difficulties and general arithmetic learning difficulties (ALD; difficulties presenting in both mental arithmetic and written arithmetic). In Study 1, we categorized 53 sixth graders into a control group, a group with specific mental arithmetic difficulties, and a group with general ALD. The findings indicated the group with specific mental arithmetic difficulties performed significantly worse on the task involving phonological working memory than did the control group. However, a significant difference was not found between the group with general ALD and the control group. In Study 2 involving 54 sixth graders, we decreased the load of phonological working memory by changing the format of the problems from horizontal (more reliance on phonological codes) to vertical (more reliance on visual resources). We found that the group with specific mental arithmetic difficulties performed comparably to the control group. In other words, when the working memory load is reduced, they no longer lag significantly behind on mental arithmetic. However, the group with general ALD still performed significantly worse than the control group when the problems were presented vertically, indicating that reduced phonological working memory load did not alleviate their arithmetic difficulties. The findings in both studies suggested that poor phonological working memory might contribute to the underlying mechanism for specific mental arithmetic difficulties but not as much for general ALD.

The role of short-term memory and visuo-spatial skills in numerical magnitude processing: Evidence from Turner syndrome

Most studies on magnitude representation have focused on the visual modality with no possibility of disentangling the influence of visuo-spatial skills and short-term memory (STM) abilities on quantification processes. This study examines this issue in patients with Turner syndrome (TS), a genetic condition characterized by a specific cognitive profile frequently associating poor mathematical achievement, low spatial skills and reduced STM abilities. In order to identify the influence of visuo-spatial and STM processing on numerical magnitude abilities, twenty female participants with TS and twenty control female participants matched for verbal IQ and education level were administered a series of magnitude comparison tasks. The tasks differed on the nature of the magnitude to be processed (continuous, discrete and symbolic magnitude), on visuo-spatial processing requirement (no/high) and on STM demands (low in simultaneous presentation vs. high in sequential presentation). Our results showed a lower acuity when participants with TS compared the numerical magnitudes of stimuli presented sequentially (low visuo-spatial processing and high STM load: Dot sequence and Sound sequence) while no difference was observed in the numerical comparison of sets presented simultaneously. In addition, the group difference in sequential tasks disappeared when controlling for STM abilities. Finally, both groups demonstrated similar performance when comparing continuous or symbolic magnitude stimuli and they exhibited comparable subitizing abilities. These results highlight the importance of STM abilities in extracting numerosity through a sequential presentation and underline the importance of considering the impact of format presentation on magnitude judgments.

Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children

Rapid automatized naming (RAN) has been found to predict mathematics. However, the nature of their relationship remains unclear. Thus, the purpose of this study was twofold: (a) to examine how RAN (numeric and non-numeric) predicts a subdomain of mathematics (arithmetic fluency) and (b) to examine what processing skills may account for the RAN-arithmetic fluency relationship. A total of 160 third-year kindergarten Chinese children (83 boys and 77 girls, mean age=5.11years) were assessed on RAN (colors, objects, digits, and dice), nonverbal IQ, visual-verbal paired associate learning, phonological awareness, short-term memory, speed of processing, approximate number system acuity, and arithmetic fluency (addition and subtraction). The results indicated first that RAN was a significant correlate of arithmetic fluency and the correlations did not vary as a function of type of RAN or arithmetic fluency tasks. In addition, RAN continued to predict addition and subtraction fluency even after controlling for all other processing skills. Taken together, these findings challenge the existing theoretical accounts of the RAN-arithmetic fluency relationship and suggest that, similar to reading fluency, multiple processes underlie the RAN-arithmetic fluency relationship.

Limited Near and Far Transfer Effects of Jungle Memory Working Memory Training on Learning Mathematics in Children with Attentional and Mathematical Difficulties

The goal of this randomized controlled trial was to investigate whether Jungle Memory working memory training (JM) affects performance on working memory tasks, performance in mathematics and gains made on a mathematics training (MT) in school aged children between 9-12 years old (N = 64) with both difficulties in mathematics, as well as attention and working memory. Children were randomly assigned to three groups and were trained in two periods: (1) JM first, followed by MT, (2) MT first, followed by JM, and (3) a control group that received MT only. Bayesian analyses showed possible short term effects of JM on near transfer measures of verbal working memory, but none on visual working memory. Furthermore, support was found for the hypothesis that children that received JM first, performed better after MT than children who did not follow JM first or did not train with JM at all. However, these effects could be explained at least partly by frequency of training effects, possibly due to motivational issues, and training-specific factors. Furthermore, it remains unclear whether the effects found on improving mathematics were actually mediated by gains in working memory. It is argued that JM might not train the components of working memory involved in mathematics sufficiently. Another possible explanation can be found in the training's lack of adaptivity, therefore failing to provide the children with tailored instruction and feedback. Finally, it was hypothesized that, since effect sizes are generally small, training effects are bound to a critical period in development.

Arithmetical Difficulties and Low Arithmetic Achievement: Analysis of the Underlying Cognitive Functioning

This study analyzed the cognitive functioning underlying arithmetical difficulties and explored the predictors of arithmetic achievement in the last three grades of Spanish Primary Education. For this purpose, a group of 165 students was selected and divided into three groups of arithmetic competence: Mathematical Learning Disability group (MLD, n = 27), Low Achieving group (LA, n = 39), and Typical Achieving group (TA, n = 99). Students were assessed in domain-general abilities (working memory and PASS cognitive processes), and numerical competence (counting and number processing) during the last two months of the academic year. Performance of children from the MLD group was significantly poorer than that of the LA group in writing dictated Arabic numbers (d = –0.88), reading written verbal numbers (d = –0.84), transcoding written verbal numbers to Arabic numbers (–0.75) and comprehension of place value (d = –0.69), as well as in simultaneous (d = –0.62) and successive (d = –0.59) coding. In addition, a specific developmental sequence was observed in both groups, the implications of which are discussed. Hierarchical regression analysis revealed simultaneous coding (β = .47, t(155) = 6.18, p < .001) and number processing (β = .23, t(155) = 3.07, p < .01) as specific predictors of arithmetical performance.

The processing of number scales beyond whole numbers in development: Dissociations in arithmetic in Turner's syndrome

The arithmetical skills in two children with Turner's syndrome (TS), each the focus of a case study, were analysed in whole numbers and other number scales that have not been systematically explored previously, fractions, decimals, percentages, and negative numbers. The intention was to identify the fractionation of arithmetical skills. The two girls with TS showed dissociations of arithmetical skill in the calculation system of whole numbers that support its modular organization. Fractionation of skills was observed in some components of the other number scales, suggesting an analogous organization within these scales. The operational specificity of impairment within number scales but not others argued against a unitary arithmetical system but rather for autonomous operational scales within distinct number scales. A general model of arithmetic is proposed.

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.

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes With Different Cognitive Profiles and Deficits

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with arithmetic fact dyscalculia (AFD) and a group with general dyscalculia (GD). Several different aspects of number magnitude processing were assessed in these two groups and compared with age-matched typically achieving children. The GD group displayed weaknesses with both symbolic and nonsymbolic number processing, whereas the AFD group displayed problems only with symbolic number processing. These findings provide evidence that the origins of DD in children with different profiles of mathematical problems diverge. Children with GD have impairment in the innate approximate number system, whereas children with AFD suffer from an access deficit. These findings have implications for researchers' selection procedures when studying dyscalculia, and also for practitioners in the educational setting.

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures.

Development of magnitude processing in children with developmental dyscalculia: space, time, and number

Developmental dyscalculia (DD) is a learning disorder associated with impairments in a preverbal non-symbolic approximate number system (ANS) pertaining to areas in and around the intraparietal sulcus (IPS). The current study sought to enhance our understanding of the developmental trajectory of the ANS and symbolic number processing skills, thereby getting insight into whether a deficit in the ANS precedes or is preceded by impaired symbolic and exact number processing. Recent work has also suggested that humans are endowed with a shared magnitude system (beyond the number domain) in the brain. We therefore investigated whether children with DD demonstrated a general magnitude deficit, stemming from the proposed magnitude system, rather than a specific one limited to numerical quantity. Fourth graders with DD were compared to age-matched controls and a group of ability-matched second graders, on a range of magnitude processing tasks pertaining to space, time, and number. Children with DD displayed difficulties across all magnitude dimensions compared to age-matched peers and showed impaired ANS acuity compared to the younger, ability-matched control group, while exhibiting intact symbolic number processing. We conclude that (1) children with DD suffer from a general magnitude-processing deficit, (2) a shared magnitude system likely exists, and (3) a symbolic number-processing deficit in DD tends to be preceded by an ANS deficit.

Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

Working memory in children with reading disabilities and/or mathematical disabilities

Elementary school children with reading disabilities (RD; n = 17), mathematical disabilities (MD; n = 22), or combined reading and mathematical disabilities (RD+MD; n = 28) were compared to average achieving (AA; n = 45) peers on working memory measures. On all working memory components, 2 (RD vs. no RD) × 2 (MD vs. no MD) factorial ANCOVAs revealed clear differences between children with and without RD. Children with MD had lower span scores than the AA children on measures of the phonological loop and the central executive. A significant interaction effect between RD and MD was found only for listening recall and had a small, partial effect size. In addition, analyses showed that the best logistic regression model consisted of a visuospatial and a central executive task. The model significantly distinguished between the AA and clinical groups and between the MD and RD+MD groups. Evidence was found for domain-general working memory problems in children with learning disabilities. Management of working memory loads in structured learning activities in the classroom, at home, or during therapy may help these children to cope with their problems in a more profound manner.

Prediction and stability of mathematics skill and difficulty

The present study evaluated the stability of math learning difficulties over a 2-year period and investigated several factors that might influence this stability (categorical vs. continuous change, liberal vs. conservative cut point, broad vs. specific math assessment); the prediction of math performance over time and by performance level was also evaluated. Participants were 144 students initially identified as having a math difficulty (MD) or no learning difficulty according to low achievement criteria in the spring of Grade 3 or Grade 4. Students were reassessed 2 years later. For both measure types, a similar proportion of students changed whether assessed categorically or continuously. However, categorical change was heavily dependent on distance from the cut point and so more common for MD, who started closer to the cut point; reliable change index change was more similar across groups. There were few differences with regard to severity level of MD on continuous metrics or in terms of prediction. Final math performance on a broad computation measure was predicted by behavioral inattention and working memory while considering initial performance; for a specific fluency measure, working memory was not uniquely related, and behavioral inattention more variably related to final performance, again while considering initial performance.

Exceptional lexical skills but executive language deficits in school starters and young adults with Turners syndrome: implications for X chromosome effects on brain function

TS school starters had enhanced receptive and expressive language on standardised assessment (CELF-P) and enhanced rhyme judgements, spoonerisms, and lexical decision, indicating enhanced phonological skills and word representations. There was marginal but consistent advantage across lexico-semantic tasks. On executive tasks, speeded naming of numbers was impaired but not pictures. Young TS adults had enhanced naming and receptive vocabulary, indicating enhanced semantic skills. There were consistent deficits in executive language: phonemic oral fluency, rhyme fluency, speeded naming of pictures, numbers and colours; sentence completion requiring supression of prepotent responses. Haploinsufficiency of X-chromosome drives mechanisms that affect the anatomical and neurochemical development of the brain, resulting in enhanced temporal lobe aspects of language. These strengths co-exist with impaired development of frontal lobe executive language systems. This means not only that these elements of language can decouple in development but that their very independence is driven by mechanisms linked to the X-chromosome.

Cognitive processing and mathematical achievement: a study with schoolchildren between fourth and sixth grade of primary education

This investigation analyzed the relation between cognitive functioning and mathematical achievement in 114 students in fourth, fifth, and sixth grades. Differences in cognitive performance were studied concurrently in three selected achievement groups: mathematical learning disability group (MLD), low achieving group (LA), and typically achieving group (TA). For this purpose, performance in verbal memory and in the PASS cognitive processes of planning, attention, and simultaneous and successive processing was assessed at the end of the academic course. Correlational analyses showed that phonological loop and successive and simultaneous processing were related to mathematical achievement at all three grades. Regression analysis revealed simultaneous processing as a cognitive predictor of mathematical performance, although phonological loop was also associated with higher achievement. Simultaneous and successive processing were the elements that differentiated the MLD group from the LA group. These results show that, of all the variables analyzed in this study, simultaneous processing was the best predictor of mathematical performance.

Cognitive profile of adolescents with math disabilities: are the profiles different from those with reading disabilities?

Adolescents (ages 14-17) with math disabilities (MD, n=12), reading disabilities (RD, n=19), math+reading disabilities (MD+RD, n=12), and average achievers (n=15) were compared on measures of visual-spatial processing, random generation (inhibition), writing speed, short-term memory (STM), and working memory (WM). Adolescents with MD performed significantly lower than adolescents with RD on measures of visual-spatial processing and visual WM. Adolescents with MD outperformed adolescents with RD +MD on measures of random generation and motor speed. Performance of all three low-achieving groups was inferior to average achievers on measures of random generation, motor speed, and verbal WM. The results were interpreted within a multicomponent model that attributed deficits related to MD in adolescents to deficits related the visual-spatial sketchpad of WM.

Coherent motion sensitivity predicts individual differences in subtraction

Recent findings suggest deficits in coherent motion sensitivity, an index of visual dorsal stream functioning, in children with poor mathematical skills or dyscalculia, a specific learning disability in mathematics. We extended these data using a longitudinal design to unravel whether visual dorsal stream functioning is able to predict individual differences in subsequent specific mathematical skills, i.e., single-digit subtraction and multiplication. We measured children's sensitivity to coherent motion in kindergarten (mean age: 5 years 8 months) and evaluated their subtraction and multiplication skills in third grade (mean age 8 years 3 months). Findings revealed an association between subtraction but not multiplication performance and coherent motion sensitivity. This association remained significant even when intellectual ability and reading ability were additionally controlled for. Subtractions are typically solved by means of quantity-based procedural strategies, which reliably recruit the intraparietal sulcus. Against the background of a neural overlap between the intraparietal sulcus and visual dorsal stream functioning, we hypothesize that low-level visuospatial mechanisms might set constraints on the development of quantity representations, which are used during calculation, particularly in subtraction.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: a developmental study

Background

The development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also children's knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory.

Methods

The magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task.

Results and discussion

Verbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks.

Conclusion

We conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable.

Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties

Errors in written multi-digit computation were investigated in children with math difficulties. Third- and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low average achievement in math, and no learning difficulties. Math fact errors were related to the severity of the math difficulties, not to reading status. Contrary to predictions, children with poorer reading, regardless of math achievement, committed more visually based errors. Operation switch errors were not systematically related to group membership. Teacher ratings of behavioral inattention were related to accuracy, math fact errors, and procedural bugs. The findings are discussed with respect to hypotheses about the cognitive origins of arithmetic errors and in relation to current discussions about how to conceptualize math disabilities.

Aberrant functional activation in school age children at-risk for mathematical disability: a functional imaging study of simple arithmetic skill

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same network of brain regions; however, children in the MD group had significantly increased activation in parietal, frontal, and cingulate cortices during both calculation tasks. A majority of the differences occurred in anatomical brain regions associated with cognitive resources such as executive functioning and working memory that are known to support higher level arithmetic skill but are not specific to mathematical processing. We propose that these findings are evidence that children with MD use the same types of problem solving strategies as TD children, but their weak mathematical processing system causes them to employ a more developmentally immature and less efficient form of the strategies.

Math Disabilities and Reading Disabilities

This article synthesizes some of the published literature that selectively compares the cognitive functioning of children with math disabilities (MDs) with average-achieving children and poor readers (children with reading disabilities [RDs] or comorbid disabilities [RDs + MDs]). All studies in the synthesis report reading, IQ, and math scores for children with MDs and poor readers. A random coefficients model of effect sizes (ESs) show that (a) ESs between MD and normal achievers were moderated by variations in working memory and literacy, (b) ESs between MD- and RD-only children were moderated by working memory and problem solving, and (c) ESs between MD and MD + RD children were moderated by long-term memory and IQ scores. No support was found for the notion that the differentiation between MD children and poor readers (RD and MD + RD) was related to variations in reading across the reviewed studies.

Mental arithmetic in children with mathematics learning disabilities: the adaptive use of approximate calculation in an addition verification task

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the proposed and the correct answer was manipulated. Both typically achieving groups were sensitive to answer plausibility on simple problems, were faster at rejecting extremely incorrect results than at accepting correct answers on complex addition problems, and showed a reduction of the complexity effect on implausible problems, attesting to the use of approximate calculation. Conversely, children with mathematics disabilities were unaffected by answer plausibility on simple addition problems, processed implausible and correct sums with equal speed on complex problems, and exhibited a smaller reduction of the complexity effect on implausible problems. They also made more errors on implausible problems. Different hypotheses are discussed to account for these results.

Optimized voxel-based morphometry in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability affecting the normal acquisition of arithmetic skills. Current studies estimate that 3-6% of the school population is affected by DD. Genetic, neurobiological, and epidemiologic evidence indicates that dyscalculia is a brain-based disorder. Imaging studies suggest the involvement of parietal and prefrontal cortices in arithmetic tasks. The aim of the present study was to analyze if children with DD show structural differences in parietal, frontal, and cingulate areas compared to typically achieving children. Magnetic resonance imaging was obtained from 12 children with DD aged 9.3+/-0.2 years and 12 age-matched control children without any learning disabilities on a 1.5 T whole-body scanner. Voxel-based morphometry analysis with an optimization of spatial segmentation and normalization procedures was applied to compare the two groups in order to find differences in cerebral gray and white matter. Compared to controls, children with DD show significantly reduced gray matter volume in the right intraparietal sulcus (IPS), the anterior cingulum, the left inferior frontal gyrus, and the bilateral middle frontal gyri. White matter comparison demonstrates clusters with significantly less volume in the left frontal lobe and in the right parahippocampal gyrus in dyscalculic children. The decreased gray and white matter volumes in the frontoparietal network might be the neurological substrate of impaired arithmetic processing skills. The white matter volume decrease in parahippocampal areas may have influence on fact retrieval and spatial memory processing.

Patterns of developmental dyscalculia with or without dyslexia

This study has been conducted in order to investigate the extent to which some characteristics of dyscalculia may be common to dyslexia. Seven multiple single-cases were studied: two children with dyslexia only, two with dyscalculia only, and three more children with comorbidity of dyslexia and dyscalculia. Each participant was assessed with a standardized comprehensive battery of arithmetical, reading, and cognitive tests. We observed that a clinical impairment in mental and written calculations, arithmetical facts retrieval, number comparison, number alignment, and identification of arithmetical signs may appear with a normal reading capacity and independently of a short-term verbal memory deficit. These findings add convergent support to the evidence mainly obtained from group comparisons that the more distinctive characteristics of dyscalculia are functionally independent of dyslexia.

Turner Syndrome

Turner syndrome is a neurogenetic disorder characterized by partial or complete monosomy-X. It is associated with certain physical and medical features, including estrogen deficiency, short stature, and increased risk for several diseases, with cardiac conditions being among the most serious. The cognitive-behavioral phenotype associated with the syndrome includes strengths in verbal domains with impairments in visuospatial, executive function, and emotion processing. Less is known regarding psychosocial and psychiatric functioning in Turner syndrome, but essential aspects of psychotherapeutic treatment plans are suggested. Future investigations should include continued genetic studies and determination of candidate genes for physical and cognitive features. Multimodal, interdisciplinary studies are essential for identifying optimal, syndrome-specific interventions for improving the lives of individuals who have Turner syndrome.

Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.

The Origins of Diverse Domains of Mathematics: Generalist Genes but Specialist Environments

The authors assessed 2,502 ten-year-old children, members of 1,251 pairs of twins, on a Web-based battery of problems from 5 diverse aspects of mathematics assessed as part of the U.K. national curriculum. This 1st genetic study into the etiology of variation in different domains of mathematics showed that the heritability estimates were moderate and highly similar across domains and that these genetic influences were mostly general. Environmental factors unique to each twin in a family (rather than shared by the 2 twins) explained most of the remaining variance, and these factors were mostly specific to each domain.