Basic number processing and difficulties in single-digit arithmetic: Evidence from Velo-Cardio-Facial Syndrome

Extent of magnitude representation deficit and relationship with arithmetic skills in children with 22q11.2DS

BACKGROUND

Previous studies have produced conflicting results concerning the extent of magnitude representation deficit and its relationship with arithmetic achievement in children with 22q11.2 deletion syndrome. More specifically, it remains unclear whether deficits are restricted to visuospatial content or are more general and whether they could explain arithmetical impairment.

METHODS

Fifteen 5- to 12-year-old children with 22q11.2 deletion syndrome and 23 age-matched healthy controls performed a non-symbolic magnitude comparison task. Depending on the trial, participants had to compare stimuli with high or low visuospatial load (visuospatial stimuli or temporal sequence of visual stimuli). The participants also completed a battery of arithmetic skills (ZAREKI-R) and a battery of global cognitive functioning (WISC-V or WPPSI-IV), from which working memory and visuospatial indices were derived.

RESULTS

Children with 22q11.2DS responded as fast as healthy controls did but received fewer correct responses, irrespective of visuospatial load. In addition, their performance in the non-symbolic magnitude comparison task did not correlate with the ZAREKI total score, while the working memory index did.

CONCLUSION

Children with 22q11.2DS might suffer from a global magnitude representation deficit rather than a specific deficit due to visuospatial load. However, this deficit alone does not seem to be related to arithmetic achievement. Working memory might be a better concern of interest in favoring arithmetic skills in patients with 22q11.2 deletion syndrome.

TRIAL REGISTRATION

Clinicaltrials, NCT04373226 . Registered 16 September 2020.

Temporal-spatial deciphering mental subtraction in the human brain

Mental subtraction, involving numerical processing and operation, requires a complex interplay among several brain regions. Diverse studies have utilized scalp electroencephalograph, electrocorticogram, or functional magnetic resonance imaging to resolve the structure pattern and functional activity during subtraction operation. However, a high resolution of the spatial-temporal understanding of the neural mechanisms involved in mental subtraction is unavailable. Thus, this study obtained intracranial stereoelectroencephalography recordings from 20 patients with pharmacologically resistant epilepsy. Specifically, two sample-delayed mismatch paradigms of numeric comparison and subtracting results comparison were used to help reveal the time frame of mental subtraction. The brain sub-regions were chronologically screened using the stereoelectroencephalography recording for mental subtraction. The results indicated that the anterior cortex, containing the frontal, insular, and parahippocampous, worked for preparing for mental subtraction; moreover, the posterior cortex, such as parietal, occipital, limbic, and temporal regions, cooperated during subtraction. Especially, the gamma band activities in core regions within the parietal-cingulate-temporal cortices mediated the critical mental subtraction. Overall, this research is the first to describe the spatiotemporal activities underlying mental subtraction in the human brain. It provides a comprehensive insight into the cognitive control activity underlying mental arithmetic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09937-z.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

How does working memory matter in young children's arithmetic skills: The mediating role of basic number processing

The current study investigated whether and how each component of the working memory model was associated with kindergarten children's arithmetic performance. A total of 103 Chinese kindergarten children were administered tests of the visuospatial sketchpad, the phonological loop, the central executive, and basic number processing (i.e., number line estimation, nonverbal numerosity estimation and numerical magnitude comparison). The results showed that among the three working memory components, the central executive accounted for a significant proportion of the variance in young children's arithmetic performance. In terms of basic number processing, number line estimation and numerical magnitude comparison had significant influences on young children's arithmetic performance. Furthermore, numerical magnitude comparison played a mediating role between the visuospatial sketchpad and early arithmetic skills. These findings highlight the importance of working memory and basic number processing in early arithmetic skills and reveal different pathways through which the three working memory components influence young children's arithmetic performance.

Working memory and arithmetic impairments in children with FMR1 premutation and gray zone alleles

Expansive mutations in familial mental retardation 1 (FMR1) gene have been associated with different phenotypes. Full mutations are associated with intellectual disability and autism spectrum disorder; premutations are associated with math learning difficulties and working memory impairments. In gray zone, neuropsychological development has not yet been described.

Objectives

This study aimed to describe the frequency of FMR1 premutation and gray zone alleles in a school population sample representing a broad spectrum of variation in math achievement and detail school achievement and cognitive performance in the children identified with FMR1 premutation or gray zone alleles.

Methods

We described a two-phase study. In the first phase, 2,195 school-age children were screened for math achievement. In the second phase, 378 children with normal intelligence were neuropsychologically assessed and genotyped for FMR1. Of these, 121 children (61 girls) performed below percentile 25 in mathematics (MD group) and 257 children (146 girls) performed above percentile 25 (control group).

Results

Four pupils presented expanded alleles, one premutation and three gray zone alleles. The girl with the premutation and one boy with a gray zone allele presented impairments in working memory and arithmetic performance below percentile 6, compatible with the diagnosis of developmental dyscalculia. These children's difficulties were not associated with inaccuracy of nonsymbolic number representations or literacy impairments. Dyscalculia in these children seems to be associated mainly with working memory impairments.

Conclusions

FMR1 expansions in the gray zone may contribute to dyscalculia in otherwise healthy and normally intelligent children.

Magnitude processing in populations with spina-bifida: The role of visuospatial and working memory processes

People with Spina Bifida usually experience difficulties with mathematics. In a series of other developmental disorders, a magnitude processing deficit was considered to be the main source of subsequent difficulties in mathematics. The processing of magnitude could be numerical (which is the larger number) or non-numerical such as spatial (e.g., which is the longer?) or temporal (which one last longer?) for instance. However, no study yet has examined directly magnitude processes in a population with Spina Bifida. On the other hand, recent studies in people with genetic syndromes have suggested that visuospatial and working memory processes play an important role in magnitude processing, including number magnitude. Therefore, in this study we explored for the first time magnitude representation using several tasks with different visuospatial and working memory processing requirements, cognitive skills frequently impaired in Spina Bifida. Results showed children with SB presented a global magnitude processing deficit for non-numerical and numerical comparison tasks, but not in symbolic number magnitude tasks compared to controls. Importantly, visuospatial skills and working memory abilities could partially explain the differences between groups in comparison and estimation tasks. This study proposes that magnitude processing difficulties in children with SB could be due to higher cognitive factors such as visuospatial and working memory processes.

Numerical Processing Impairment in 22q11.2 (LCR22-4 to LCR22-5) Microdeletion: A Cognitive-Neuropsychological Case Study

Although progress has been made, the cognitive, biological and, particularly, the genetic underpinnings of math learning difficulties (MD) remain largely unknown. This difficulty stems from the heterogeneity of MD and from the large contribution of environmental factors to its etiology. Understanding endophenotypes, e.g., the role of the Approximate Number System (ANS), may help understanding the nature of MD. MD associated with ANS impairments has been described in some genetic conditions, e.g., 22q11.2 deletion syndrome (22q11.2DS or Velocardiofacial syndrome, VCFS). Recently, a girl with MD was identified in a school population screening. She has a new syndrome resulting from a microdeletion in 22q11.2 (LCR22-4 to LCR22-5), a region adjacent to but not overlapping with region 22q11.2 (LCR22-2 to LCR22-4), typically deleted in VCFS. Here, we describe her cognitive-neuropsychological and numerical-cognitive profiles. The girl was assessed twice, at 8 and 11 years. Her numerical-cognitive performance at both times was compared to demographically similar girls with normal intelligence in a single-case, quasi-experimental study. Neuropsychological assessment was normal, except for relatively minor impairments in executive functions. She presented severe and persistent difficulties in the simplest single-digit calculations. Difficulties in commutative operations improved from the first to the second assessment. Difficulties in subtraction persisted and were severe. No difficulties were observed in Arabic number writing. Difficulties in single-digit calculation co-occurred with basic numerical processing impairments in symbolic and non-symbolic (single-digit comparison, dot sets size comparison and estimation) tasks. Her difficulties suggest ANS impairment. No difficulties were detected in visuospatial/visuoconstructional and in phonological processing tasks. The main contributions of the present study are: (a) this is the first characterization of the neuropsychological phenotype in 22q11.2DS (LCR22-4 to LCR22.5) with normal intelligence; (b) mild forms of specific genetic conditions contribute to persistent MD in otherwise typical persons; (c) heterogeneity of neurogenetic underpinnings of MD is suggested by poor performance in non-symbolic numerical processing, dissociated from visuospatial/visuoconstructional and phonological impairments; (d) similar to what happens in 22q11.2DS (LCR22-2 to LCR22-4), ANS impairments may also characterize 22q11.2DS (LCR22-4 to LCR22-5).

Neurodevelopmental outcome in 22q11.2 deletion syndrome and management

The 22q11.2 deletion syndrome (22q11.2 DS) places affected individuals at an increased risk for neurodevelopmental/cognitive, behavioral and social-emotional difficulties. Poor cognitive functioning and intellectual disabilities, attention and executive functioning deficits, learning disorders, emotional dysregulation and impairments in social processing are common among individuals with 22q11.2 DS. Identifying risk and protective/resilience factors that can be detected in early life and can predict neurodevelopmental outcomes for people with 22q11.2 DS is of significant clinical relevance and might allow for early detection and intervention. Given the focus of this review, we will discuss the possible contributing factors that influence the neurodevelopmental outcome in 22q1.2 DS, the cognitive phenotype in 22q11.2 DS, the different developmental trajectories across life span, and the implications for clinical practice and management.

Arithmetic difficulties in children with mild traumatic brain injury at the subacute stage of recovery

AIM

Arithmetic difficulties have been reported in children with mild traumatic brain injury (mTBI), but the electrophysiological abnormalities underlying these impairments remain unknown. We therefore used event-related potentials (ERPs) to investigate brain functioning during arithmetic in children in the subacute phase after mTBI.

METHOD

The participants comprised 16 children with mTBI at the subacute phase of recovery (10 males, mean age 10y 8mo; six females, mean age 10y 8mo) and 16 well-matched comparison children (11 males, mean age 10y 11mo; five females, mean age 10y 6mo). All children were asked to solve single-digit addition problems of small (sum ≤10) and large problem size (sum >10) and ERPs were simultaneously recorded.

RESULTS

Children with mTBI performed significantly less accurately (mean 81%) than comparison children (mean 91%) on the large (p=0.026) but not on the small problems (p=0.171). We observed no group differences in the early ERP components P1, N1, P2, and N2 (all p values ≥0.241), yet significant group differences (p=0.019) emerged for the late positivity component (LPC), which showed smaller mean amplitudes (mean 8.35μV) in mTBI patients than comparison children (mean 12.95μV).

INTERPRETATION

Immediately after the injury, arithmetic difficulties in children with mTBI are particularly pronounced on more complex arithmetical problems that are less automated. This is reflected in the ERP pattern, with decreased LPC but normal N2 and early ERP components.

Are 22q11.2 distal deletions associated with math difficulties?

Approximately 6% of school-aged children have math difficulties (MD). A neurogenetic etiology has been suggested due to the presence of MD in some genetic syndromes such as 22q11.2DS. However, the contribution of 22q11.2DS to the MD phenotype has not yet been investigated. This is the first population-based study measuring the frequency of 22q11.2DS among school children with MD. Children (1,564) were identified in the schools through a screening test for language and math. Of these children, 152 (82 with MD and 70 controls) were selected for intelligence, general neuropsychological, and math cognitive assessments and for 22q11.2 microdeletion screening using MLPA. One child in the MD group had a 22q11.2 deletion spanning the LCR22-4 to LCR22-5 interval. This child was an 11-year-old girl with subtle anomalies, normal intelligence, MD attributable to number sense deficit, and difficulties in social interactions. Only 19 patients have been reported with this deletion. Upon reviewing these reports, we were able to characterize a new syndrome, 22q11.2 DS (LCR22-4 to LCR22-5), characterized by prematurity; pre- and postnatal growth restriction; apparent hypotelorism, short/upslanting palpebral fissures; hypoplastic nasal alae; pointed chin and nose; posteriorly rotated ears; congenital heart defects; skeletal abnormalities; developmental delay, particularly compromising the speech; learning disability (including MD, in one child); intellectual disability; and behavioral problems. These results suggest that 22q11.2 DS (LCR22-4 to LCR22-5) may be one of the genetic causes of MD.

Cognitive phenotype of velocardiofacial syndrome: a review

The behavioural phenotype of velocardiofacial syndrome (VCFS), one of the most common human multiple anomaly syndromes, includes developmental disabilities, frequently including intellectual disability (ID) and high risk of diagnosis of psychotic disorders including schizophrenia. VCFS may offer a model of the relationship between ID and risk of major mental health difficulties. This paper reviews literature on the cognitive phenotype and its relationship with a polymorphism of the gene coding for catechol O-methyltransferase (COMT), a gene haploinsufficient in VCFS which modulates prefrontal dopamine levels. Principal features of the variable cognitive phenotype of VCFS in young people are ID, superiority of verbal over performance I.Q. and verbal over visuospatial memory, and difficulties with number and object magnitude comparisons, time perception and memory for serial order, and orienting of attention. Despite some improvements with age, problems with higher order attentional tasks involving planning persist, possibly modulated by COMT activity levels. Candidate cognitive endophenotypes include problems with retrieval of contextual information from memory and in executive control and focussing of attention. Longitudinal research using common core batteries of psychometric assessments, and experimental measures of cognitive function capable of direct translation for use with animal models, will further advance understanding of the developmental dynamics of VCFS.

Current tests and trends in single-case neuropsychology

In this issue of Cortex, Crawford, Garthwaite and Ryan publish bayesian statistical tests that will enable researchers to take account of covariates when comparing single patients to control samples. In this article, we provide some context for this development, from an audit of the Cortex archives. We suggest that single-case research is alive and well, and more rigorous than ever, and that current practice has been shaped considerably by Crawford and colleagues' statistical refinements over the past 12 years. However, there is scope for further tightening and standardisation of statistical methods and reporting standards. The advantages offered by the new bayesian tests should promote the even wider use of appropriate statistical methods, with benefits for the validity of individual studies, and for cross-comparability in the single-case literature.

Nonverbal learning disabilities: a critical review

This article presents a critical review of the term and concept of nonverbal learning disability (NLD). After a brief historical introduction, the article focuses on the apparent rarity of NLD; the hypothesis of the frequent co-occurrence of emotional disorder, depression, and suicide in NLD; the white matter hypothesis as an explanation of the origin of NLD; and the question of NLD as part of a variety of other disorders. It is argued that NLD presents a broad hypothesis, but that there is little evidence to support its use in clinical practice.

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.

Single-digit arithmetic in children with dyslexia

It has been suggested that individuals with dyslexia show poorer performance on those aspects of arithmetic that involve the manipulation of verbal representations, such as the use of fact retrieval strategies. The present study examined this in 13 children with dyslexia who showed normal general mathematics achievement and 16 matched controls. All children completed a multiplication and a subtraction task, which were specifically designed to elicit the use of retrieval and procedural strategies, respectively. Our findings revealed that despite normal mathematics achievement, children with dyslexia were less accurate and slower in single-digit arithmetic, particularly in multiplication. The reaction time data revealed an interesting group by operation interaction. Control children were significantly faster in multiplication than in subtraction, whereas no such operation effect was found in children with dyslexia. This suggests that in multiplication children with dyslexia used less retrieval or less efficient retrieval (or both). This is in line with the hypothesis that children with dyslexia may have difficulties with the verbal aspects of number and arithmetic, as retrieval strategies depend upon phonological representations in long-term memory.

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.

Working memory and individual differences in mathematics achievement: a longitudinal study from first grade to second grade

This longitudinal study examined the relationship between working memory and individual differences in mathematics. Working memory measures, comprising the phonological loop, the visuospatial sketchpad, and the central executive, were administered at the start of first grade. Mathematics achievement was assessed 4 months later (at the middle of first grade) and 1 year later (at the start of second grade). Working memory was significantly related to mathematics achievement in both grades, showing that working memory clearly predicts later mathematics achievement. The central executive was a unique predictor of both first- and second-grade mathematics achievement. There were age-related differences with regard to the contribution of the slave systems to mathematics performance; the visuospatial sketchpad was a unique predictor of first-grade, but not second-grade, mathematics achievement, whereas the phonological loop emerged as a unique predictor of second-grade, but not first-grade, mathematics achievement.

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.