Behavior-related potentials from single-trial interindividual correlation between event related potentials and behavioral performance reveals right lateralized processing of numerosity.

Accumulated functional magnetic resonance imaging (fMRI) and electroencephalography evidence indicate that numerosity is first processed in the occipito-parietal cortex. fMRI evidence also indicates right-lateralized processing of numerosity, but there is no consistent evidence from event-related potential (ERP) studies. This study investigated the ERP of numerosity processing in the left, right, and bilateral visual fields. The single-trial ERP-behavioral correlation was applied to show how the ERP was associated with behavioral responses. The results showed a significant early behavioral-ERP correlation on the right N1 component when stimuli were presented in the left visual field rather than in the right visual field. The behavioral ERP correlation was termed BN1. There was bilateral BN1 based on the reaction time or error rate, but the right BN1 was larger than that the left BN1 when the stimulus was present in the bilateral visual field. Therefore, this study provided a new neural marker for individual differences in processing numerosity and suggested that processing numerosity was supported by the right occipito-parietal cortex.

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).

High-definition transcranial direct current stimulation (HD-tDCS) of the left middle temporal gyrus (LMTG) improves mathematical reasoning.

The role of the visuospatial network in mathematical processing has been established, but the role of the semantic neural network in mathematical processing is still poorly understood. The current study used high-definition transcranial direct current stimulation (HD-tDCS) to examine whether the semantic network supports mathematical processing. Using a single-blind, randomized, sham-controlled experimental design, 48 participants were randomly assigned to receive either anodal or sham HD-tDCS on the left middle temporal gyrus (LMTG), a core region of the semantic network. A number series completion task was used to measure mathematical reasoning and an arithmetical computation task was used as a control condition. Both tasks were administered before and after the 20 min HD-tDCS. The results showed that anodal HD-tDCS on the LMTG enhanced performance on the number series completion task, but not on the arithmetical computation task. Trial-level analysis further showed greater improvement at the more difficult problems of the number series completion task. These results demonstrate that the semantic network plays an important role in mathematical processing.

The developmental relationship between nonsymbolic and symbolic fraction abilities.

A fundamental research question in quantitative cognition concerns the developmental relationship between nonsymbolic and symbolic quantitative abilities. This study examined this developmental relationship in abilities to process nonsymbolic and symbolic fractions. There were 99 6th graders (Mage = 11.86 years), 101 10th graders (Mage = 15.71 years), and 102 undergraduate and graduate students (Mage = 21.97 years) participating in this study, and their nonsymbolic and symbolic fraction abilities were measured with nonsymbolic and symbolic fraction comparison tasks, respectively. Nonsymbolic and symbolic fraction abilities were significantly correlated in all age groups even after controlling for the ability to process nonsymbolic absolute quantity and general cognitive abilities, including working memory and inhibitory control. Moreover, the strength of nonsymbolic-symbolic correlations was higher in 6th graders than in 10th graders and adults. These findings suggest a weakened association between nonsymbolic and symbolic fraction abilities during development, and this developmental pattern may be related with participants' increasing proficiency in symbolic fractions.

Phonological activation improves semantic access provided by Arabic digits and number words.

Arabic digits (e.g., "6") and number words (e.g., "", "six", " ") are the two main formats in which numbers can be represented. Although phonology plays a crucial role in the semantic accessing of alphabetic words and Chinese characters, whether it is involved in the processing of different numerical notations, which have been shown to be dissociable from characters, is still unknown. Using a parity judgment task, two experiments were performed by manipulating the phonological relationship between a prime and a target. The primes were Tibetan or Chinese characters and the targets were presented either as number words (Experiment 1) or as Arabic digits (Experiment 2). The results revealed that phonology affected semantic access for both number words and Arabic digits. Additionally, semantic access for Tibetan number words was more susceptible to phonological information. The results for Arabic digits followed the same pattern for Tibetan primes. Further, language proficiency also affected the role of phonology in number processing. Participants with low language proficiency relied more on phonological encoding when processing the numbers. The results suggest that phonology is crucial for semantic access of different numerical notations.

Altered resting-state functional connectivity in the prefrontal cortex is related to the development of dyscalculia in patients with Turner syndrome.

AIM: Patients with Turner syndrome have a high rate of developmental dyscalculia, but the underlying neurocognitive mechanisms are not well-understood. Some studies have implicated visuospatial impairments in patients with Turner syndrome, but others have focused on poor procedural skills in patients with Turner syndrome. This study used brain imaging data to test these two alternative views. METHODS: This study recruited 44 girls with Turner syndrome (mean age, 12.91 years; SD, 2.02), with 13 (29.5%) of them meeting the criterion for developmental dyscalculia, and 14 normally developing girls (mean age, 14.26 years; SD, 2.18) as a comparison group. All participants were given basic mathematical ability tests and an intelligence test and were scanned using magnetic resonance imaging. We compared patients with Turner syndrome who had dyscalculia, patients with Turner syndrome who did not have dyscalculia, and the normal controls in terms of brain structures and resting-state functional activity. RESULTS: Compared with normal controls, both groups of patients with Turner syndrome (with or without dyscalculia) showed similarly altered functional connectivity in the occipitoparietal dorsal stream. Importantly, compared with patients with Turner syndrome without dyscalculia and normal controls, patients with Turner syndrome with dyscalculia showed decreased functional connectivity between the prefrontal and the lateral occipital cortex. CONCLUSION: We concluded that both groups of patients with Turner syndrome shared visual deficits, and patients with Turner syndrome with dyscalculia had a deficit in frontal cortex-based higher cognitive processing. It is not their visuospatial deficits but rather their deficits in higher cognitive processing that are responsible for the development of dyscalculia in patients with Turner syndrome.

The structure correspondence hypothesis predicts how word and sentence in language correlate with term and principle in mathematics.

The association between language and mathematics is an important debated topic. Here, we proposed a structure correspondence hypothesis to explain under what conditions language and mathematics are closely related. According to the hypothesis, there would be an association when they have equivalent structure. One hundred and fifty high school students were recruited to finish mathematical and language tests at the element level (i.e., geometric term processing and word analogy) and at the low-dimensional combination level (i.e., geometric principle processing and sentence completion) as well as the tests to measure cognitive covariates (general intelligence and spatial processing). After controlling for age, gender and cognitive covariates, geometric term processing and word analogy were closely correlated, and geometric principle processing and sentence completion were significantly correlated. No other correlations were found. The results support the structure correspondence hypothesis and provide a new perspective of structure of language and verbalized mathematics for the relation between language and mathematics.

Different cognitive mechanisms used for solving open and closed math problems.

Problem-solving skills are very important in our daily life. Almost all problem-solving studies have addressed the cognitive correlates of solving closed problems, but only limited studies have investigated the cognitive mechanisms of solving open problems. The current study aimed to systematically examine differences between the cognitive mechanisms used for solving open and closed problems. In total, the abilities of 142 high school students to solve open and closed problems were assessed, as were a series of general cognitive abilities as controlled variates. Analogical reasoning uniquely contributed to solving both open and closed math problems, after controlling for age, gender, and inductive reasoning. Reactive cognitive flexibility (measured using the Wisconsin card sorting test) and spatial working memory uniquely correlated only with solving open and closed math problems, respectively. These findings suggest that the cognitive processes used to solve open and closed math problems differ. Open and closed math problems appear to require more reactive cognitive flexibility for generation and more memory for retrieval, respectively.

Algebra dissociates from arithmetic in the brain semantic network.

BACKGROUND: Mathematical expressions mainly include arithmetic (such as 8 - (1 + 3)) and algebra (such as a - (b + c)). Previous studies have shown that both algebraic processing and arithmetic involved the bilateral parietal brain regions. Although previous studies have revealed that algebra was dissociated from arithmetic, the neural bases of the dissociation between algebraic processing and arithmetic is still unclear. The present study uses functional magnetic resonance imaging (fMRI) to identify the specific brain networks for algebraic and arithmetic processing. METHODS: Using fMRI, this study scanned 30 undergraduates and directly compared the brain activation during algebra and arithmetic. Brain activations, single-trial (item-wise) interindividual correlation and mean-trial interindividual correlation related to algebra processing were compared with those related to arithmetic. The functional connectivity was analyzed by a seed-based region of interest (ROI)-to-ROI analysis. RESULTS: Brain activation analyses showed that algebra elicited greater activation in the angular gyrus and arithmetic elicited greater activation in the bilateral supplementary motor area, left insula, and left inferior parietal lobule. Interindividual single-trial brain-behavior correlation revealed significant brain-behavior correlations in the semantic network, including the middle temporal gyri, inferior frontal gyri, dorsomedial prefrontal cortices, and left angular gyrus, for algebra. For arithmetic, the significant brain-behavior correlations were located in the phonological network, including the precentral gyrus and supplementary motor area, and in the visuospatial network, including the bilateral superior parietal lobules. For algebra, significant positive functional connectivity was observed between the visuospatial network and semantic network, whereas for arithmetic, significant positive functional connectivity was observed only between the visuospatial network and phonological network. CONCLUSION: These findings suggest that algebra relies on the semantic network and conversely, arithmetic relies on the phonological and visuospatial networks.

Mathematics Meets Science in the Brain.

Mathematics and science are highly integrated disciplines, but the brain association between mathematics and science remains unclear. The current study used functional magnetic resonance imaging (fMRI) scans of 34 undergraduates (17 males, mean age = 20.3±1.64 years old) while they completed mathematical, physical and chemical principles, arithmetic computation, and sentence comprehension. We examined neural activation level, neural activation pattern, and neural connectivity to investigate the neural associations between mathematics and science (including physics and chemistry). The results showed that mathematical, physical, and chemical principles elicited similar neural activation level and neural activation pattern in the visuospatial network (mainly in the middle frontal gyrus and inferior parietal lobule), which were different from those elicited by sentence comprehension; those three principles also elicited similar neural activation level and neural activation pattern in the semantic network (mainly in the middle temporal gyrus, angular gyrus, inferior frontal gyrus, and dorsomedial prefrontal cortex), in contrast to that elicited by arithmetic computation. Effective connectivity analyses showed stronger connectivity between the middle temporal gyrus and inferior parietal lobule for mathematical, physical, and chemical principles than for sentence comprehension. The results suggest that visuospatial and semantic networks were critical for processing both mathematics and science.

The association between non-symbolic number comparison and mathematical abilities depends on fluency.

Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.

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.

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.

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.

Short-term numerosity training promotes symbolic arithmetic in children with developmental dyscalculia: The mediating role of visual form perception.

Studies have shown that numerosity-based arithmetic training can promote arithmetic learning in typically developing children as well as children with developmental dyscalculia (DD), but the cognitive mechanism underlying this training effect remains unclear. The main aim of the current study was to examine the role of visual form perception in arithmetic improvement through an 8-day numerosity training for DD children. Eighty DD children were selected from four Chinese primary schools. They were randomly divided into the intervention and control groups. The intervention group received training on an apple-collecting game, whereas the control group received an English dictation task. Children's cognitive and arithmetic performances were assessed before and after training. The results showed that the intervention group showed a significant improvement in arithmetic performance, approximate number system (ANS) acuity, and visual form perception, but not in spatial processing and sentence comprehension. The control group showed no significant improvement in any cognitive ability. Mediation analysis further showed that training-related improvement in arithmetic performance was fully mediated by the improvement in visual form perception. The results suggest that short-term numerosity training enhances the arithmetic performance of DD children by improving their visual form perception.

Visual form perception predicts 3-year longitudinal development of mathematical achievement.

Numerous studies have demonstrated an association between approximate number system (ANS) acuity and mathematical performance. Studies have also shown that ANS acuity can predict the longitudinal development of mathematical achievement. Visual form perception in the current investigation was proposed to account for the predictive role of ANS acuity in the development of mathematical achievement. One hundred and eighty-eight school children (100 males, 88 females; mean age = 12.2 ± 0.3 years) participated in the study by completing five tests: numerosity comparison, figure matching, mental rotation, nonverbal matrix reasoning, and choice reaction time. Three years later, they took a mathematical achievement test. We assessed whether the early tests predicted mathematical achievement at the later date. Analysis showed that the ANS acuity measured via numerosity comparison significantly predicted mathematical achievement 3 years later, even when controlling for individual differences in mental rotation, nonverbal matrix reasoning, and choice reaction time, as well as age and gender differences. Hierarchical regression and mediation analyses further showed that the longitudinal predictive role of ANS acuity in mathematical achievement was interpreted by visual form perception measured with a figure-matching test. Together, these results indicate that visual form perception may be the underlying cognitive mechanism that links ANS acuity to mathematical achievement in terms of longitudinal development.

The semantic system is involved in mathematical problem solving.

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving.

The neural circuits for arithmetic principles.

Arithmetic principles are the regularities underlying arithmetic computation. Little is known about how the brain supports the processing of arithmetic principles. The current fMRI study examined neural activation and functional connectivity during the processing of verbalized arithmetic principles, as compared to numerical computation and general language processing. As expected, arithmetic principles elicited stronger activation in bilateral horizontal intraparietal sulcus and right supramarginal gyrus than did language processing, and stronger activation in left middle temporal lobe and left orbital part of inferior frontal gyrus than did computation. In contrast, computation elicited greater activation in bilateral horizontal intraparietal sulcus (extending to posterior superior parietal lobule) than did either arithmetic principles or language processing. Functional connectivity analysis with the psychophysiological interaction approach (PPI) showed that left temporal-parietal (MTG-HIPS) connectivity was stronger during the processing of arithmetic principle and language than during computation, whereas parietal-occipital connectivities were stronger during computation than during the processing of arithmetic principles and language. Additionally, the left fronto-parietal (orbital IFG-HIPS) connectivity was stronger during the processing of arithmetic principles than during computation. The results suggest that verbalized arithmetic principles engage a neural network that overlaps but is distinct from the networks for computation and language processing.

Modality-Dependent or Modality-Independent Processing in Mental Arithmetic: Evidence From Unimpaired Auditory Multiplication for a Patient With Left Frontotemporal Stroke.

OBJECTIVES: Mental arithmetic is essential to daily life. Researchers have explored the mechanisms that underlie mental arithmetic. Whether mental arithmetic fact retrieval is dependent on surface modality or knowledge format is still highly debated. Chinese individuals typically use a procedure strategy for addition; and they typically use a rote verbal strategy for multiplication. This provides a way to examine the effect of surface modality on different arithmetic operations. METHODS: We used a series of neuropsychological tests (i.e., general cognitive, language processing, numerical processing, addition, and multiplication in visual and auditory conditions) for a patient who had experienced a left frontotemporal stroke. RESULTS: The patient had language production impairment; but preserved verbal processing concerning basic numerical abilities. Moreover, the patient had preserved multiplication in the auditory presentation rather than in the visual presentation. The patient suffered from impairments in an addition task, regardless of visual or auditory presentation. CONCLUSIONS: The findings suggest that mental multiplication could be characterized as a form of modality-dependent processing, which was accessed through auditory input. The learning strategy of multiplication table recitation could shape the verbal memory of multiplication leading to persistence of the auditory module. (JINS, 2017, 23, 692-699).