The semantic system is involved in mathematical problem solving

Single-trial interindividual correlation shows semantic and visuospatial networks are fundamental for advanced mathematical learning

Mathematical learning and ability are crucial for individual and national economic and technological development, but the neural mechanisms underlying advanced mathematical learning remain unclear. The current study used functional magnetic resonance imaging (fMRI) to investigate how brain networks were involved in advanced mathematical learning and transfer. We recorded fMRI data from 24 undergraduate students as they learned the advanced mathematical concept of a commutative mathematical group. After learning, participants were required to complete learning and transfer behavioural tests. Results of single-trial interindividual brain-behaviour correlation analysis found that brain activity in the semantic and visuospatial networks, and the functional connectivity within the semantic network during advanced mathematical learning were positively correlated with learning and transfer effects. Additionally, the functional connectivity between the semantic and visuospatial networks was negatively correlated with the learning and transfer effects. These findings suggest that advanced mathematical learning relies on both semantic and visuospatial networks.

Mathematical problem solving is modulated by word priming

This study aimed to explore the influence of word priming on mathematical problem solving. In two experiments, participants were required to finish multiplication estimation tasks with a specified estimation strategy under different word priming conditions (Experiment 1: concrete words vs. Experiment 2: abstract words). The results showed that: (1) under the concrete word priming condition, in comparison to neutral, positive word priming improved accuracies (ACCs) when using a down-up strategy (e.g., doing 40 × 80 = 3200 for 43 × 78), while both positive and negative word priming reduced reaction time (RT); (2) under the abstract word priming condition, both positive and negative (vs. neutral) abstract word priming reduced RTs, while individuals' ACCs of completing the estimation task were not influenced by valence. The present study showed that whether concrete words or abstract words were adopted as experimental stimuli, participants' performance of completing mathematical problems was modulated by the valence of the priming word, which led us to develop a better understanding of how arithmetic performance is influenced by word processing.

When intuitive Bayesians need to be good readers: The problem-wording effect on Bayesian reasoning

Are humans intuitive Bayesians? It depends. People seem to be Bayesians when updating probabilities from experience but not when acquiring probabilities from descriptions (i.e., Bayesian textbook problems). Decades of research on textbook problems have focused on how the format of the statistical information (e.g., the natural frequency effect) affects such reasoning. However, it pays much less attention to the wording of these problems. Mathematical problem-solving literature indicates that wording is critical for performance. Wording effects (the wording varied across the problems and manipulations) can also have far-reaching consequences. These may have confounded between-format comparisons and moderated within-format variability in prior research. Therefore, across seven experiments (N = 4909), we investigated the impact of the wording of medical screening problems and statistical formats on Bayesian reasoning in a general adult population. Participants generated more Bayesian answers with natural frequencies than with single-event probabilities, but only with the improved wording. The improved wording of the natural frequencies consistently led to more Bayesian answers than the natural frequencies with standard wording. The improved wording effect occurred mainly due to a more efficient description of the statistical information-cueing required mathematical operations, an unambiguous association of numbers with their reference class and verbal simplification. The wording effect extends the current theoretical explanations of Bayesian reasoning and bears methodological and practical implications. Ultimately, even intuitive Bayesians must be good readers when solving Bayesian textbook problems.

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.

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.

Early Gray Matter Structural Covariance Predicts Longitudinal Gain in Arithmetic Ability in Children

Previous neuroimaging studies on arithmetic development have mainly focused on functional activation or functional connectivity between brain regions. It remains largely unknown how brain structures support arithmetic development. The present study investigated whether early gray matter structural covariance contributes to later gain in arithmetic ability in children. We used a public longitudinal sample comprising 63 typically developing children. The participants received structural magnetic resonance imaging scanning when they were 11 years old and were tested with a multiplication task at 11 years old (time 1) and 13 years old (time 2), respectively. Mean gray matter volumes were extracted from eight brain regions of interest to anchor salience network (SN), frontal-parietal network (FPN), motor network (MN), and default mode network (DMN) at time 1. We found that longitudinal gain in arithmetic ability was associated with stronger structural covariance of the SN seed with frontal and parietal regions and stronger structural covariance of the FPN seed with insula, but weaker structural covariance of the FPN seed with motor and temporal regions, weaker structural covariance of the MN seed with frontal and motor regions, and weaker structural covariance of the DMN seed with temporal region. However, we did not detect correlation between longitudinal gain in arithmetic ability and behavioral measure or regional gray matter volume at time 1. Our study provides novel evidence for a specific contribution of gray matter structural covariance to longitudinal gain in arithmetic ability in childhood.

The involvement of the semantic neural network in rule identification of mathematical processing

The role of the visuospatial network in mathematical processing has been established, but the involvement of the semantic network in mathematical processing is still poorly understood. The current study utilized a number series completion paradigm with the event-related potential (ERP) technique to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. In total, 32 right-handed undergraduate students were recruited and asked to complete the number series completion as well as the arithmetical computation task in which numbers were presented in sequence. The event-related potential and multi-voxel pattern analysis showed that the rule identification process involves more semantic processing when compared with the arithmetical computation processes, and it elicited higher amplitudes for the late negative component (LNC) in left frontal and temporal lobes. These results demonstrated that the semantic network supports the rule identification in mathematical processing, with the LNC acting as the neural marker.

Traditional Mexican Food: Phenolic Content and Public Health Relationship

Phenolic compounds have a positive effect on obesity, diabetes, and cardiovascular diseases because of their antioxidant and anti-inflammatory capacity. The prevalence of these diseases has increased in the last years in the Mexican population. Therefore, the Mexican diet must be assessed as provider of phenolic compounds. To assess this, a survey of phenolic compound intake was validated and applicated to 973 adults (798 females) between 18 and 79 years old. We compared the phenolic compound intake of 324 participants with more diseases (239 females) and 649 participants with healthier condition (559 females). The groups differed in sex, age, and scholarship. Males, older participants, and those with lower schooling reported suffering from more diseases. Regarding phenolic compound intake analyses, the participants with healthier conditions displayed a higher phenolic compound intake than the other group in all foods assessed. In addition, the regression model showed that the phenolic compounds intake of Mexican dishes, such as arroz con frijol or enchiladas, positively affected health status, suggesting that this traditional food is beneficial for the participant’s health condition. However, the weight effect of PCI was different for each disease. We conclude that, although PCI of Mexican food positively affects health conditions, this effect depends on sex, age, and participants’ diseases.

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.

Quantitative modelling demonstrates format-invariant representations of mathematical problems in the brain

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra- and cross-format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format-invariant manner.

Arithmetic in the signing brain: Differences and similarities in arithmetic processing between deaf signers and hearing non-signers

Deaf signers and hearing non-signers have previously been shown to recruit partially different brain regions during simple arithmetic. In light of the triple code model, the differences were interpreted as relating to stronger recruitment of the verbal system of numerical processing, that is, left angular and inferior frontal gyrus, in hearing non-signers, and of the quantity system of numerical processing, that is, right horizontal intraparietal sulcus, for deaf signers. The main aim of the present study was to better understand similarities and differences in the neural correlates supporting arithmetic in deaf compared to hearing individuals. Twenty-nine adult deaf signers and 29 hearing non-signers were enrolled in an functional magnetic resonance imaging study of simple and difficult subtraction and multiplication. Brain imaging data were analyzed using whole-brain analysis, region of interest analysis, and functional connectivity analysis. Although the groups were matched on age, gender, and nonverbal intelligence, the deaf group performed generally poorer than the hearing group in arithmetic. Nevertheless, we found generally similar networks to be involved for both groups, the only exception being the involvement of the left inferior frontal gyrus. This region was activated significantly stronger for the hearing compared to the deaf group but showed stronger functional connectivity with the left superior temporal gyrus in the deaf, compared to the hearing, group. These results lend no support to increased recruitment of the quantity system in deaf signers. Perhaps the reason for performance differences is to be found in other brain regions not included in the original triple code model.

The underlying neural bases of the reversal error while solving algebraic word problems

Problem solving is a core element in mathematical learning. The reversal error in problem solving occurs when students are able to recognize the information in the statement of comparison word problems, but they reverse the relationship between two variables when building the equations. Functional magnetic resonance images were acquired to identify for the first time the neural bases associated with the reversal error. The neuronal bases linked to this error have been used as inputs in 13 classifiers to discriminate between reversal error and non-reversal error groups. We found brain activation in bilateral fronto-parietal areas in the participants who committed reversal errors, and only left fronto-parietal activation in those who did not, suggesting that the reversal error group needed a greater cognitive demand. Instead, the non-reversal error group seems to show that they have developed solid algebraic knowledge. Additionally, the results showed brain activation in the right middle temporal gyrus when comparing the reversal error vs non-reversal error groups. This activation would be associated with the semantic processing which is required to understand the statement and build the equation. Finally, the classifier results show that the brain areas activated could be considered good biomarkers to help us identify competent solvers.

An fMRI intervention study of creative mathematical reasoning: behavioral and brain effects across different levels of cognitive ability

BACKGROUND

Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR.

METHODS

We employed a within-subject intervention (N=72, M_Age=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high).

RESULTS

On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups.

CONCLUSIONS

Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.

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.

Common Neural Functions during Children's Learning from Naturalistic and Controlled Mathematics Paradigms

Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.

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.

The Neural Correlates of Computational Thinking: Collaboration of Distinct Cognitive Components Revealed by fMRI

Recent technical advance attracts great attention to the promotion of programming skills, in particular, and computational thinking (CT), in general, as a new intellectual competency. However, the understanding of its cognitive substrates is limited. The present study used functional magnetic resonance imaging to examine the neural correlates of programming to understand the cognitive substrates of CT. Specifically, magnetic resonance imaging signals were collected while the participants were mentally solving programming problems, and we found that CT recruited distributed cortical regions, including the posterior parietal cortex, the medial frontal cortex, and the left lateral frontal cortex. These regions showed extensive univariate and multivariate resemblance with arithmetic, reasoning, and spatial cognition tasks. Based on the resemblance, clustering analyses revealed that cortical regions involved in CT can be divided into Reasoning, Calculation, Visuospatial, and Shared components. Further, connectivity increased during programming within the CT network constructed by these four components and decreased between the CT network and other cortical regions. In sum, our study revealed the cognitive components underlying CT and their neural correlates and further suggests that CT is not a simple sum of parallel cognitive processes, but a composite cognitive process integrating a set of intellectual abilities, particularly those in the science, technology, engineering, and math domains.

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.

Operation-Specific Lexical Consistency Effect in Fronto-Insular-Parietal Network During Word Problem Solving

The practice of mathematical word problem is ubiquitous and thought to impact academic achievement. However, the underlying neural mechanisms are still poorly understood. In this study, we investigate how lexical consistency of word problem description is modulated in adults' brain responses during word problem solution. Using functional magnetic resonance imaging methods, we examined compare word problems that included relational statements, such as "A dumpling costs 9 dollars. A wonton is 2 dollars less than a dumpling. How much does a wonton cost?" and manipulated lexical consistency (consistent: the relational term consistent with the operation to be performed, e.g., more-addition/inconsistent: e.g., less-addition) and problem operation (addition/subtraction). We found a consistency by operation interaction in the widespread fronto-insular-parietal activations, including the anterior insula, dorsoanterior cingulate cortex, middle frontal gyrus, and intraparietal sulcus, such that inconsistent problems engaged stronger activations than consistent problems for addition, whereas the consistency effect was inverse for subtraction. Critically, these results were more salient in the less successful problem solvers than their more successful peers. Our study is the first to demonstrate that lexical consistency effects on arithmetic neural networks are modulated during reading word problem that required distinct arithmetic operations. More broadly, our study has strong potentials to add linkage between neuroscience and education by remediating deficits and enhance instruction design in the school curriculum.

The neurocognitive gains of diagnostic reasoning training using simulated interactive veterinary cases

The present longitudinal study ascertained training-associated transformations in the neural underpinnings of diagnostic reasoning, using a simulation game named “Equine Virtual Farm” (EVF). Twenty participants underwent structural, EVF/task-based and resting-state MRI and diffusion tensor imaging (DTI) before and after completing their training on diagnosing simulated veterinary cases. Comparing playing veterinarian versus seeing a colorful image across training sessions revealed the transition of brain activity from scientific creativity regions pre-training (left middle frontal and temporal gyrus) to insight problem-solving regions post-training (right cerebellum, middle cingulate and medial superior gyrus and left postcentral gyrus). Further, applying linear mixed-effects modelling on graph centrality metrics revealed the central roles of the creative semantic (inferior frontal, middle frontal and angular gyrus and parahippocampus) and reward systems (orbital gyrus, nucleus accumbens and putamen) in driving pre-training diagnostic reasoning; whereas, regions implicated in inductive reasoning (superior temporal and medial postcentral gyrus and parahippocampus) were the main post-training hubs. Lastly, resting-state and DTI analysis revealed post-training effects within the occipitotemporal semantic processing region. Altogether, these results suggest that simulation-based training transforms diagnostic reasoning in novices from regions implicated in creative semantic processing to regions implicated in improvised rule-based problem-solving.

Arithmetic in the adult deaf signing brain

We have previously shown that deaf signers recruit partially different brain regions during simple arithmetic compared to a group of hearing non-signers, despite similar performance. Specifically, hearing individuals show more widespread activation in brain areas that have been related to the verbal system of numerical processing, i.e., the left angular and inferior frontal gyrus, whereas deaf individuals engaged brain areas that have been related to the quantity system of numerical processing, i.e., the right horizontal intraparietal sulcus. This indicates that compared to hearing non-signers, deaf signers can successfully make use of processes located in partially different brain areas during simple arithmetic. In this study, which is a conceptual replication and extension of the above-presented study, the main aim is to understand similarities and differences in neural correlates supporting arithmetic in deaf compared to hearing individuals. The primary objective is to investigate the role of the right horizontal intraparietal gyrus, the left inferior frontal gyrus, the hippocampus, and the left angular gyrus during simple and difficult arithmetic and how these regions are connected to each other. A second objective is to explore what other brain regions support arithmetic in deaf signers. Up to 34 adult deaf signers and the same amount of hearing non-signers will be enrolled in an functional magnetic resonance imaging study that will include simple and difficult subtraction and multiplication. Brain imaging data will be analyzed using whole-brain analysis, region of interest analysis and connectivity analysis. This is the first study to investigate neural underpinnings of arithmetic of different difficulties in deaf individuals.

Causal Cortical Network for Arithmetic Problem-Solving Represents Brain's Planning Rather than Reasoning

Arithmetic problem-solving whose components mainly involve the calculation, planning and reasoning, is an important mathematical skill. To date, the neural mechanism underlying arithmetic problem-solving remains unclear. In this study, a scheme that combined a novel 24 points game paradigm, conditional Granger causality analysis, and near-infrared spectroscopy (fNIRS) neuroimaging technique was developed to examine the differences in brain activation and effective connectivity between the calculation, planning, and reasoning. We discovered that the performance of planning was correlated with the activation in frontal cortex, whereas the performance of reasoning showed the relationship with the activation in parietal cortex. In addition, we also discovered that the directional effective connectivity between the anterior frontal and posterior parietal cortex was more closely related to planning rather than reasoning. It is expected that this work will pave a new avenue for an improved understanding of the neural underpinnings underlying arithmetic problem-solving, which also provides a novel indicator to evaluate the efficacy of mathematical education.

Fronto-insular-parietal network engagement underlying arithmetic word problem solving

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real-world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one-step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto-insular-parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task-dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out-of-scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto-insular-parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.

Age Effects on Spatiotemporal Dynamics of Response Inhibition: An MEG Study

Inhibition, the ability to suppress irrelevant information, thoughts or movements, is crucial for humans to perform context-appropriate behaviors. It was suggested that declined cognitive performance in older adults might be attributed to inhibitory deficiencies. Although previous studies have shown an age-associated reduction in inhibitory ability, the understanding regarding its cortical spatiotemporal maps remained limited. Thus, we used a whole-head magnetoencephalography (MEG) to elucidate the age effects on response inhibition, and to explore the brain activation differences in high- and low-performing seniors. We recruited 22 younger and 22 older adults to participate in the visual Go/No-go task. Both behavioral performance and neuromagnetic responses to No-go stimuli were analyzed. The behavioral results showed that the older adults made more false alarm (FA) errors than the younger adults did. The MEG results showed that the seniors exhibited declined cortical activities in middle temporal gyrus (MTG) and delayed activation in MTG, prefrontal cortex (PFC) and pre-supplementary motor area (pre-SMA). Furthermore, among the older adults, more recruitment of the left PFC was found in the high-performers than in the lower-performers. In conclusion, age-related deficiencies in response inhibition were observed in both behavioral performance and neurophysiological measurement. Our results also suggested that frontal recruitment plays a compensatory role in successful inhibition.