Visual perception can account for the close relation between numerosity processing and computational fluency

The interconnection of orthographic, phonetic, and semantic skills with arithmetic fluency

Arithmetic fluency is considered considers highly rely on language processing, encompassing essential skills. However, the independent predictive power of phonetic, semantic, or orthographic skills in relation to arithmetic fluency remains an unresolved query. This study introduces the common component hypothesis to elucidate the inconsistent findings in previous research. The hypothesis posits that significant correlations between language and mathematics hinge on whether the language and mathematics utilized in a given task share a common component. According to this hypothesis, processing skills for each of the three fundamental language elements (i.e., phonetic, semantic, orthographic) should correlate with arithmetic fluency, as these elements are also integral to simple arithmetic processing. A cohort of one hundred and ninety-eight primary school students participated in the study, undertaking a battery of tests assessing general cognitive abilities, psycholinguistic elements, and arithmetic fluency. The results showed that orthographic, phonetic, and semantic abilities independently predicted arithmetic fluency, even after accounting for all other cognitive predictors. These findings substantiate the common component hypothesis, providing empirical support for explaining the association between language and mathematics. This evidence contributes to addressing the interplay between language and mathematics in educational contexts.

Factors influencing the role of inhibitory control in non-symbolic numerical processing

Previous studies have found that inhibitory control plays an important role in non-symbolic numerical processing. However, this role may be influenced by the visual cue control method or the stimulus' presentation time. We investigated these questions by conducting three experiments using a priming paradigm to compare the level of inhibitory control in a sequential dot comparison task with single-dimensional and multi-dimensional control of visual cues under two presentation time conditions (300 ms and 1500 ms). We found that neither the method of visual cue control nor the presentation time of dot arrays affected the level of inhibitory control in the dot comparison task. These results reveal a stable role of inhibitory control in non-symbolic numerical processing, providing further evidence for integrating numerical and visual information during non-symbolic numerical processing.

Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency

BACKGROUND

Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'.

AIMS

The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels.

SAMPLE

Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later).

METHODS

Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured.

RESULTS

Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2.

CONCLUSION

Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.

Form perception is a cognitive correlate of the relation between subitizing ability and math performance

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).

Verbalized arithmetic principles correlate with mathematics achievement

BACKGROUND

When mathematical knowledge is expressed in general language, it is called verbalized mathematics. Previous studies on verbalized mathematics typically paid attention to mathematical vocabulary or educational practice. However, these studies did not exclude the role of symbolic mathematics ability, and almost no research has focused on verbalized mathematical principles.

AIMS

This study is aimed to investigate whether verbalized mathematics ability independently predicts mathematics achievement. The current study hypothesized that verbalized mathematics ability supports mathematics achievement independent of general language, related cognitive abilities and even symbolic mathematical ability.

SAMPLE

A sample of 241 undergraduates (136 males, 105 females, mean age = 21.95, SD = 2.38) in Beijing, China.

METHODS

A total of 12 tests were used, including a verbalized arithmetic principle test, a mathematics achievement test, and tests on general language (sentence completion test), symbolic mathematical ability (including symbolic arithmetic principles test, simple arithmetic computation and complex arithmetic computation), approximate number sense ability (numerosity comparison test) and several related cognitive covariates (including the non-verbal matrix reasoning, the syllogism reasoning, mental rotation, figure matching and choice reaction time).

RESULTS

Results showed that the processing of verbalized arithmetic principles displayed a significant role in mathematics achievement after controlling for general language, related cognitive abilities, approximate number sense ability and symbolic mathematics ability.

CONCLUSIONS

The results suggest that verbalized mathematics ability was an independent predictor and provided empirical evidence supporting the verbalized mathematics role on achievement as an independent component in three-component mathematics model.

Verbal but not visual-spatial working memory contributes to complex arithmetic calculation

The contribution of working memory to mathematics has been extensively studied. It has been proposed that verbal working memory (VWM) and visual-spatial working memory (VSWM) have distinct contributions, but results have been inconclusive. Here, we hypothesized that VWM and VSWM contribute differentially to separate sub-domains of mathematics. To test this hypothesis, we enrolled 199 primary school students and measured their VWM and VSWM with number/letter/matrix backward span tasks, and tested mathematics performance with simple subtraction, complex subtraction, multi-step calculation and number series completion, while controlling for several aspects of cognition. We found that while letter backward span had a significant contribution to complex subtraction, multi-step computation and number series completion, number backward span only had a significant contribution to multi-step computation, and matrix span had no effect on any math task. These results suggest that only VWM associated with complex mathematics, which might reflect verbal rehearsal. In contrast, VSWM does not appear to associated with mathematics.

Achievement in Fundamental Movement Skills, Spatial Abilities, and Mathematics among Lower Key Stage 2 Children

Research has demonstrated links between sport and mathematics learning, and their relationship with spatial abilities in children. This study explored the association between the development of fundamental movement skills (FMS) and mathematics achievement, and whether the understanding of specific spatial concepts mediated these relationships. Overall, 154 Year 3 children (69 males, 85 females, aged 7-8 years) from four schools in England completed an FMS assessment involving six skills; four spatial tasks assessing intrinsic-static, intrinsic-dynamic, extrinsic-static, and extrinsic-dynamic spatial abilities; and a mathematics test assessing numerical, geometrical, and arithmetical abilities. Overall FMS ability (a combined score across the six skills) was significantly positively correlated to overall mathematics achievement. This relationship was mediated by children's performance on the intrinsic-static spatial ability test. These findings suggest that children who have more mature FMS perform better in mathematics tasks, and this could be due to more developed intrinsic-static spatial ability. However, further research is necessary to determine the mediation effects of intrinsic-dynamic and extrinsic-static spatial ability.

Early neural markers for individual difference in mathematical achievement determined from rational number processing

The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.

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.

The database for extracting numerical and visual properties of numerosity processing in the Chinese population

The ability to handle non-symbolic numerosity has been recurrently linked to mathematical abilities. The accumulated data provide a rich resource that can reflect the underlying properties (i.e., dot ratio, area, convex hull, perimeters, distance, and hash) of numerosity processing. This article reports a database of numerosity processing in the Chinese population. The database contains five independent datasets with 7459, 4902, 415, 671, 414 participants respectively. For each dataset, all data were collected in the same online computerized test, examination room, professorial tester, and using the same protocols. Computational modeling method could be used to extract the dot ratio and visual properties of numerosity from five types of dot stimuli. This database enables researchers to test the theoretical hypotheses regarding numerosity processing using a large sample population. The database can also indicate the individual difference of non-symbolic numerosity in mathematical abilities.

Language Ability Accounts for Ethnic Difference in Mathematics Achievement

The mathematics achievement of minority students has always been a focal point of educators in China. This study investigated the differences in mathematics achievement between Han and minority pupils to determine if there is any cognitive mechanism that can account for the discrepancy. We recruited 236 Han students and 272 minority students (including Uygur and Kazak) from the same primary schools. They were tested on mathematics achievement, language abilities, and general cognitive abilities. The results showed that Han pupils had better mathematics achievement scores and better Chinese language ability than minority students. After controlling for age, gender, and general cognitive abilities, there were still significant differences in mathematics achievement between Han and minority students. However, these differences disappeared after controlling for language ability. These results suggest that the relatively poor levels of mathematics achievement observed in minority students is related to poor Chinese language skills.

Normative Values of the Groffman Visual Tracing Test for the Assessment of Oculomotor Performance in the Adult Population

The Groffman visual tracing (GVT) test is an indirect psychometric measure of oculomotor performance, used for the clinical assessment of eye movements. The test consists of two cards with five contorted lines of increasing overlap, crowding, and difficulty. The task starts from each of the letters at the top of the page, follows the line from the letter to the corresponding number at the bottom of the page, and the number is named. Although the GVT test was developed for the evaluation of children, it has also been applied to adults with visual and cognitive deficits. However, it lacks reference values. Therefore, the aim of the study was to assess oculomotor behavior across the typical human lifespan and to define normative data in an adult population. A total of 526 adults aged between 20 and 79 years, all without neurological or psychiatric deficits, were enrolled in the study. The results were analyzed by considering the accuracy and execution times separately. An influence of age, education and sex for accuracy was found, and age for the execution times was found. Norms for adults were developed considering the specific structure of the test and the accuracy and the execution time separately. The GVT test can now be applied in healthy and neurological adult populations for the evaluation of oculomotor performance.

What Skills Could Distinguish Developmental Dyscalculia and Typically Developing Children: Evidence From a 2-Year Longitudinal Screening

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

School-aged children diagnosed with an FASD exhibit visuo-cortical network disturbance: A magnetoencephalography (MEG) study

Children with prenatal alcohol exposure (PAE) often suffer from cognitive and neurobehavioral dysfunction throughout their lives, which may rise to a level of concern such that children receive a diagnosis under the fetal alcohol spectrum disorders (FASD) umbrella. Magnetoencephalography (MEG) contributes direct insight into neural processing and functional connectivity measures with temporal precision to understand cortical processing disorders that manifest during development. The impairment of perception may become more consequential among school-aged children with an FASD in the process of intellectual functioning and behavioral maturation. Fifty participants with the age range of 8-13 years participated in our study following parental informed consent and child assent. For each participant, visual responses were recorded using magnetoencephalography (MEG) while performing a prosaccade task with central stimuli (fovea centralis) and peripheral stimuli (left and right of central) presented on a screen, requiring participants to shift their gaze to the stimuli. After source analysis using minimum norm estimation (MNE), we investigated visual responses from each participant by measuring the latency and amplitude of visual evoked fields. Delayed peak latency of the visual response was identified in the primary visual area (calcarine fissure) and visual association areas (v2, v3) in young children with an FASD for both stimulus types (central and peripheral). But the difference in visual response latency was only statistically significant (p ≤ 0.01) for the peripheral (right) stimulus. We also observed reduced amplitude (p ≤ 0.006) of visual evoked response in children with an FASD for the central stimulus type in both primary and visual association areas. Multiple visual areas show impairment in children with an FASD, with visual delay and conduction disturbance more prominent in response to peripheral stimuli. Children with an FASD also exhibit significantly reduced amplitude of neural activation to central stimuli. These sensory deficits may lead to slow cognitive processing speed through continued intra-cortical network disturbance in children with an FASD.

Bidirectional relationship between visual perception and mathematics performance in Chinese kindergartners

In this longitudinal study, 64 kindergartners (mean age at T1 = 4.69 ± 0.33 years; 34 girls) were tested on visual perception skills (T2 and T3) and mathematics performance (T1 to T3) with 6-month intervals between the three testing waves. Cross-lagged path analysis showed a bidirectional relationship between visual perception and mathematics performance from T2 to T3. Specifically, children's visual perception at T2 significantly predicted their mathematics performance at T3 (B = 0.30, SE = 0.14, p = 0.03, β = 0.19). Children's mathematics performance at T1 accounted for unique variance in visual perception at T2 (B = 0.79, SE = 0.11, p < 0.001, β = 0.68) and visual perception at T3 (B = 0.27, SE = 0.12, p = 0.02, β = 0.32). Their mathematics performance at T2 also significantly predicted visual perception at T3 (B = 0.21, SE = 0.10, p = 0.04, β = 0.28). Totally, they explained 61% of the variance in mathematics performance and 39% of the variance in visual perception at T3. The results highlight the developmental courses as well as the reciprocal facilitations between visual perception and mathematics performance in the kindergarten period.

Mathematics anxiety and mathematical calculation in deaf children: A moderated mediation model of mathematics self-efficacy and intelligence

BACKGROUND

Previous studies have shown the relationship between mathematics anxiety and math performance in deaf students, but their inner influencing mechanism remains unclear.

AIM

To examine a moderated mediation model between mathematics anxiety and mathematical calculation, with intelligence as a moderator, and mathematics self-efficacy as a mediator.

METHODS

A sample of 247 deaf children from 2 special education schools and 247 hearing children (matched in intelligence) from one mainstream school in China completed computerized tests of intelligence and mathematical calculation and self-report questionnaires of mathematics anxiety and mathematics self-efficacy. Simple mediation analyses and moderated mediation analyses were conducted using PROCESS, and a simple slopes method was employed to plot the conditional indirect effects.

RESULTS

There was a significant negative correlation between mathematics anxiety and mathematical calculation, and between mathematics anxiety and mathematics self-efficacy in deaf children and hearing children. However, mathematics self-efficacy was positively associated with mathematical calculation in deaf children but not in hearing children, and the significantly negative relationship between mathematics anxiety and intelligence was observed only in deaf children but not in hearing children. Mathematics self-efficacy partially mediated the association between mathematics anxiety and mathematical calculation in deaf children; and the indirect effect between mathematics anxiety and mathematical calculation via mathematics self-efficacy was moderated by intelligence in deaf children but not in hearing children.

CONCLUSIONS

The results were discussed to illuminate the mechanism in relation to the practical implication for the intervention and early development of mathematics performance in deaf children.

Examining the Differential Role of General and Specific Processing Speed in Predicting Mathematical Achievement in Junior High School

Processing speed is divided into general (including perceptual speed and decision speed) and specific processing speed (including reading fluency and arithmetic fluency). Despite several study findings reporting the association between processing speed and children's mathematical achievement, it is still unclear whether general or specific processing speed differentially predicts mathematical achievement. The current study aimed to examine the role of general and specific processing speed in predicting mathematical achievements of junior high school students. Cognitive testing was performed in 212 junior school students at the beginning of the 7th grade year, along with assessment of general and specific processing speed. Relevant academic achievement scores were also recorded at the end of the 7th and 9th grade years. Hierarchical regression analyses showed that specific processing speed made a significant unique contribution in mathematical achievement by the end of the 7th grade and could significantly predict mathematical achievements in the high school entrance examinations by end of the 9th grade after controlling for age, gender, and general cognitive abilities. However, general processing speed could not predict mathematical achievements. Moreover, specific processing speed could significantly predict all academic achievements for both the 7th and 9th grade. These results demonstrated that specific processing speed, rather than general processing speed, was able to predict mathematical achievement and made a generalised contribution to all academic achievements in junior school. These findings suggest that specific processing speed could be a reflection of academic fluency and is therefore critical for long-term academic development.

Visual Perception Supports Adults in Numerosity Processing and Arithmetical Performance

Previous studies have found a correlation between numerosity processing and arithmetical performance. Visual perception has already been indicated as the shared cognitive mechanism between these two; however, these studies mostly focused on children. It is not clear whether the association between numerosity processing and arithmetical performance still existed following the development of individual arithmetical performance. Consequently, the underlying role of visual perception in numerosity processing and arithmetical performance has not been sufficiently studied in adults. For this study, researchers selected a total of 205 adult participants with an average age of 22years. The adults were administered arithmetic tests, numerosity comparison, and visual figure matching. Mental rotation, choice reaction time, and nonverbal intelligence were used as cognitive covariates. Results showed that numerosity comparison of adults correlated with their arithmetical performance, even after controlling for age and gender differences as well as general cognitive processing. However, after controlled for visual figure matching, the well-established association between numerosity comparison and arithmetic performance disappeared. These results supported the visual perception hypothesis, that visual perception measured by visual figure matching can account for the correlation between numerosity comparison and arithmetic performance. This indicated that even for adult populations, visual perceptual ability was the underlying component of numerosity processing and arithmetic performance.

Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.

Non-symbolic and symbolic number lines are dissociated

People use mental number lines for both symbolic numerals and numerosity, but little is known about how these two mental number lines are related. The current study investigated the association in effect size, directionality of the mental number line, and development between symbolic and non-symbolic mental number lines to determine if they were related to or independent from each other. We collected data from numerosity- and digit-matching tasks that used the following numbers: 11, 14, 17, 20, 23, 26, and 29. Tasks were performed by college undergraduates and the fifth-grade primary school students. The results showed that none of the effects for non-symbolic numbers was related to any of the effects for symbolic numbers, and vice versa, in both adults and children. Another notable finding was that the correlation between the SNARC (spatial-numerical association of response code) effect size and mathematical ability was negative in the adult group. These results are consistent with the dissociated processes hypothesis and suggest that mental number lines are notation-dependent. As shown by the SNARC effect, the mental number line might result in interference in the current task by an automatically activated spatial notation-dependent representation of numbers.

Neural association between non-verbal number sense and arithmetic fluency

Non‐verbal number sense has been shown to significantly correlate with arithmetic fluency. Accumulated behavioral evidence indicates that the cognitive mechanism relies on visual perception. However, few studies have investigated the neural mechanism underlying this association. Following the visual perception account, we hypothesized that there would be a neural association in occipital areas of the brain between non‐verbal number sense, arithmetic fluency, and visual perception. We analyzed event‐related potentials that are sensitive to neural responses while participants performed five cognitive tasks: simple addition, simple subtraction, numerosity comparison, figure matching, and character rhyming. The single‐trial ERP‐behavior correlation approach was used to enhance the statistical power. The results showed that the N1 component significantly correlated with reaction time at occipital electrodes on all tasks except for character rhyming. The N1 component for arithmetic fluency (simple addition and subtraction) and character rhyming correlated with the reaction time for numerosity comparison and figure matching. The results suggest that there are neural associations between arithmetic fluency, non‐verbal number sense, and visual perception in the occipital cortex, and that visual perception is the shared mechanism for both non‐verbal number sense and arithmetic fluency.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.

Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability

Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children's visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children's precision in a visual ANS task related to their math performance - replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.

Characteristics of cognitive impairment in adult asymptomatic moyamoya disease

Background

Cognitive impairment in adult moyamoya disease (MMD) is thought to be the result of ischemic stroke; however, the presence and extent of cognitive decline in asymptomatic patients is unclear.

Methods

After classification using T2-weighted fluid attenuated inversion recovery (FLAIR) magnetic resonance imaging (MRI), a total of 19 MMD patients with a history of cerebral infarction, 21 asymptomatic MMD patients, and 20 healthy controls matched for age, sex, and years of education were prospectively included in this study. A detailed neuropsychological evaluation of two moyamoya subgroups and normal controls was conducted.

Results

Asymptomatic patients showed varying degrees of decline in intelligence (Raven’s Standard Progressive Matrices, P = 0.001), spatial imagination (mental rotation, P = 0.014), working memory (verbal working memory-backward digit span, P = 0.011), and computational ability (simple subtraction, P = 0.014; complex subtraction, P < 0.001) compared with normal controls. MMD patients with cerebral infarction had more severe impairment in complex arithmetic (P = 0.027) and word short-term memory (P = 0.01) than those without symptoms.

Conclusion

In asymptomatic MMD patients, a variety of cognitive impairment precedes the onset of clinical symptoms such as cerebral infarction, which may be a long-term complication of conservative treatment.

Association between white matter impairment and cognitive dysfunction in patients with ischemic Moyamoya disease

Background

Ischemic Moyamoya disease is one of the important causes of stroke, which leads to severe impairment in cognitive functions. This cognitive impairment occurs prior to stroke. However, the cognitive functions that are impaired and the mechanisms of these impairments have not been determined.

Methods

We analyzed 12 patients with Moyamoya disease and 12 controls. All participants underwent cognitive tests and magnetic resonance imaging (MRI) scans. The diffusion tensor imaging (DTI) data was processed using Tract-Based Spatial Statistics (TBSS). Significantly different white matter areas were correlated with different cognitive functions.

Results

There were significant differences in intelligence and subtraction between the patients and controls (p < 0.05). The parameters of DTI such as fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) have different changes in anterior thalamic radiation, inferior fronto-occipital fasciculus (IFO), superior longitudinal fasciculus (SLF), uncinate fasciculus (UF), inferior longitudinal fasciculus, forceps minor, and other regions between the two groups.

Conclusion

Left UF and IFO may be the key brain regions affecting arithmetic function, while bilateral IFO has an effect on intelligence. RD and AD may be better indicators for early prediction of chronic white matter damage than FA, while MD tends to have a comprehensive indirect change. There is cognitive impairment in ischemic MMD, which is closely related to white matter impairment.

Trial registration

Clinical Trial Registration, Unique identifier: ChiCTR1900023610. Registered 4 June 2019 – Prospective study registered.

The effect of interictal epileptiform discharges on cognitive and academic performance in children with idiopathic epilepsy

Background

Interictal epileptiform discharges (IEDs) have been proven to impair cognitive function. However, it is not clear whether IEDs disrupt academic performance in children with idiopathic epilepsy, and the contribution of cognitive function deficits to impaired academic performance has not been clarified. This study aimed to examine the cognitive deficits and academic impairment in childhood idiopathic epilepsy with IEDs.

Methods

Ninety-seven childhood idiopathic epilepsy with IEDs, 77 childhood idiopathic epilepsy without IEDs, and 71 healthy controls completed a series of cognitive tests. We analyzed the cognitive performance in several domains including language, mathematics, psychomotor speed, spatial ability, memory, general intelligence, attention and executive functioning. Analysis of variance was conducted to compare the performance on all tests between the three groups.

Results

Childhood idiopathic epilepsy with IEDs exhibited not only general cognitive deficits in processing speed, spatial ability, and attention, but also arithmetic impairment. Furthermore, general cognitive deficits could account for the impaired arithmetic performance in childhood idiopathic epilepsy with IEDs.

Conclusions

Our study suggested that IEDs in children with idiopathic epilepsy affected both cognitive function and academic performance, and that the cognitive deficits may be responsible for arithmetic performance impairment.

A gifted SNARC? Directional spatial-numerical associations in gifted children with high-level math skills do not differ from controls

The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small/large magnitude numbers with the left/right hand side) is prevalent across the whole lifespan. Because the ability to relate numbers to space has been viewed as a cornerstone in the development of mathematical skills, the relationship between the SNARC effect and math skills has been frequently examined. The results remain largely inconsistent. Studies testing groups of people with very low or very high skill levels in math sometimes found relationships between SNARC and math skills. So far, however, studies testing such extreme math skills level groups were mostly investigating the SNARC effect in individuals revealing math difficulties. Groups with above average math skills remain understudied, especially in regard to children. Here, we investigate the SNARC effect in gifted children, as compared to normally developing children (overall n = 165). Frequentist and Bayesian analysis suggested that the groups did not differ from each other in the SNARC effect. These results are the first to provide evidence for the SNARC effect in a relatively large sample of gifted (and mathematically highly skilled) children. In sum, our study provides another piece of evidence for no direct link between the SNARC effect and mathematical ability in childhood.

Visual Processing Matters in Chinese Reading Acquisition and Early Mathematics

The main purpose of the present study was to investigate whether visual processing uniquely contributed to character reading and early mathematics in Chinese children. Eighty-two Chinese kindergarteners at K3 (mean age = 68 months, SD = 0.30) were followed up to grade one (mean age = 82 months, SD = 0.35) with an interval of 14 months. Nonverbal intelligence, inhibitory control, sustained attention, character reading, and mathematics were measured at kindergarten. Character reading and mathematics were assessed again at grade one. Results showed visual processing at kindergarten significantly predicted character reading at grade one after controlling for prior reading performance, inhibitory control, sustained attention, age, gender, and nonverbal IQ. Similarly, visual processing at kindergarten explained unique variance in early mathematics at grade one when prior mathematics performance and other covariates at kindergarten were controlled. These findings suggest that visual processing should serve as a domain-general precursor of children's performance in character reading and early mathematics and an important cognitive factor for later academic learning.

Visual form perception is fundamental for both reading comprehension and arithmetic computation

Visual perception has been found to be a critical factor for reading comprehension and arithmetic computation in separate lines of research with different measures of visual form perception. The current study of 1099 Chinese elementary school students investigated whether the same visual form perception (assessed by a geometric figure matching task) underlies both reading comprehension and arithmetic computation. The results showed that visual form perception had close relations with both reading comprehension and arithmetic computation, even after controlling for age, gender, and cognitive factors such as processing speed, attention, working memory, visuo-spatial processing, and general intelligence. Results also showed that numerosity comparison's relations with reading comprehension and arithmetic computation were fully accounted for by visual form perception. These results suggest that reading comprehension and arithmetic computation might share a similar visual form processing mechanism.

Differences in Counting Skills Between Chinese and German Children Are Accompanied by Differences in Processing of Approximate Numerical Magnitude Information

Human beings are supposed to possess an approximate number system (ANS) dedicated to extracting and representing approximate numerical magnitude information as well as an object tracking system (OTS) for the rapid and accurate enumeration of small sets. It is assumed that the OTS and the ANS independently contribute to the acquisition of more elaborate numerical concepts. Chinese children have been shown to exhibit more elaborate numerical concepts than their non-Chinese peers, but it is still an open question whether similar cross-national differences exist with regard to the underlying systems, namely the ANS and the OTS. In the present study, we investigated this question by comparing Chinese and German preschool children with regard to their performance in a non-symbolic numerical magnitude comparison task (assessing the ANS) and in an enumeration task (assessing the OTS). In addition, we compared children’s counting skills. To ensure that possible between-group differences could not be explained by differences in more general performance factors, we also assessed children’s reasoning ability and processing speed. Chinese children showed a better counting performance and a more accurate performance in the non-symbolic numerical magnitude comparison task. These differences in performance could not be ascribed to differences in reasoning abilities and processing speed. In contrast, Chinese and German children did not differ significantly in the enumeration of small sets. The superior counting performance of Chinese children was thus found to be reflected in the ANS but not in the OTS.

The influence of visual-spatial skills on the association between processing of nonsymbolic numerical magnitude and number word sequence skills

Nonsymbolic numerical magnitude processing skills are assumed to be fundamental to mathematical learning. Recent findings suggest that visual-spatial skills account for associations between children's performance in visually presented nonsymbolic numerical magnitude comparison tasks and their performance in visually presented arithmetic tasks. The aim of the current study was to examine whether associations between children's performance in visually presented tasks assessing nonsymbolic numerical magnitude processing skills and their performance in tasks assessing early mathematical skills, which do not involve visual stimulation, may also be mediated by visual-spatial skills. This line of reasoning is based on the assumption that children make use of mental visualization processes when working on tasks assessing early mathematical skills, such as knowledge of the sequence of number words, even when these tasks do not involve visual stimulation. We assessed 4- to 6-year-old children's performance in a nonsymbolic numerical magnitude comparison task, in tasks concerning knowledge of the sequence of number words, and in a developmental test to assess visual-spatial skills. Children's nonsymbolic numerical magnitude processing skills were found to be associated with their number word sequence skills. This association was fully mediated by interindividual differences in visual-spatial skills. The effect size of this mediation effect was small. We assume that the ability to construct mental visualizations constitutes the key factor underlying this mediation effect.

Numerical cognition is resilient to dramatic changes in early sensory experience

Humans and non-human animals can approximate large visual quantities without counting. The approximate number representations underlying this ability are noisy, with the amount of noise proportional to the quantity being represented. Numerate humans also have access to a separate system for representing exact quantities using number symbols and words; it is this second, exact system that supports most of formal mathematics. Although numerical approximation abilities and symbolic number abilities are distinct in representational format and in their phylogenetic and ontogenetic histories, they appear to be linked throughout development--individuals who can more precisely discriminate quantities without counting are better at math. The origins of this relationship are debated. On the one hand, symbolic number abilities may be directly linked to, perhaps even rooted in, numerical approximation abilities. On the other hand, the relationship between the two systems may simply reflect their independent relationships with visual abilities. To test this possibility, we asked whether approximate number and symbolic math abilities are linked in congenitally blind individuals who have never experienced visual sets or used visual strategies to learn math. Congenitally blind and blind-folded sighted participants completed an auditory numerical approximation task, as well as a symbolic arithmetic task and non-math control tasks. We found that the precision of approximate number representations was identical across congenitally blind and sighted groups, suggesting that the development of the Approximate Number System (ANS) does not depend on visual experience. Crucially, the relationship between numerical approximation and symbolic math abilities is preserved in congenitally blind individuals. These data support the idea that the Approximate Number System and symbolic number abilities are intrinsically linked, rather than indirectly linked through visual abilities.

Dyslexia and dyscalculia are characterized by common visual perception deficits

A number of studies have investigated the cognitive deficits underlying dyslexia and dyscalculia. Yet, it remains unclear as to whether dyslexia and dyscalculia are associated with the common visual perception deficits. The current investigation analyzed cognitive performance in children with dyslexia, dyscalculia, comorbidity, and typically developing subjects. The results showed that children with dyslexia, dyscalculia and comorbidity exhibited common deficits in numerosity processing and visual perception. Furthermore, visual perception deficits accounted for deficits in numerosity processing in all three groups. The results suggest that visual perception deficits are a common cognitive deficit underlying both developmental dyslexia and dyscalculia.

Bogdanova O, Kovas Y. Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation

The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations.

Attention Contributes to Arithmetic Deficits in New-Onset Childhood Absence Epilepsy

Neuropsychological studies indicate that new-onset childhood absence epilepsy (CAE) is associated with deficits in attention and executive functioning. However, the contribution of these deficits to impaired academic performance remains unclear. We aimed to examine whether attention and executive functioning deficits account for the academic difficulties prevalent in patients with new-onset CAE. We analyzed cognitive performance in several domains, including language, mathematics, psychomotor speed, spatial ability, memory, general intelligence, attention, and executive functioning, in 35 children with new-onset CAE and 33 control participants. Patients with new-onset CAE exhibited deficits in mathematics, general intelligence, attention, and executive functioning. Furthermore, attention deficits, as measured by a visual tracing task, accounted for impaired arithmetic performance in the new-onset CAE group. Therefore, attention deficits, rather than impaired general intelligence or executive functioning, may be responsible for arithmetic performance deficits in patients with new-onset CAE.