Numerical ordering and symbolic arithmetic share frontal and parietal circuits in the right hemisphere

The brain under pressure: Exploring neurophysiological responses to cognitive stress

Stress is an increasingly dominating part of our daily lives and higher performance requirements at work or to ourselves influence the physiological reaction of our body. Elevated stress levels can be reliably identified through electroencephalogram (EEG) and heart rate (HR) measurements. In this study, we examined how an arithmetic stress-inducing task impacted EEG and HR, establishing meaningful correlations between behavioral data and physiological recordings. Thirty-one healthy participants (15 females, 16 males, aged 20 to 37) willingly participated. Under time pressure, participants completed arithmetic calculations and filled out stress questionnaires before and after the task. Linear mixed effects (LME) allowed us to generate topographical association maps showing significant relations between EEG features (delta, theta, alpha, beta, and gamma power) and factors such as task difficulty, error rate, response time, stress scores, and HR. With task difficulty, we observed left centroparietal and parieto-occipital theta power decreases, and alpha power increases. Furthermore, frontal alpha, delta and theta activity increased with error rate and relative response time, while parieto-temporo-occipital alpha power decreased. Practice effects on EEG power included increases in temporal, parietal, and parieto-occipital theta and alpha activity. HR was positively associated with frontal delta, theta and alpha power whereas frontal gamma power decreases. Significant alpha laterality scores were observed for all factors except task difficulty and relative response time, showing overall increases in left parietal regions. Significant frontal alpha asymmetries emerged with increases in error rate, sex, run number, and HR and occipital alpha asymmetries were also found with run number and HR. Additionally we explored practice effects and noted sex-related differences in EEG features, HR, and questionnaire scores. Overall, our study enhances the understanding of EEG/ECG-based mental stress detection, crucial for early interventions, personalized treatment and objective stress assessment towards the development of a neuroadaptive system.

Connectome-based predictive modeling indicates dissociable neurocognitive mechanisms for numerical order and magnitude processing in children

Symbolic numbers contain information about their relative numerical cardinal magnitude (e.g., 2 < 3) and ordinal placement in the count-list (e.g., 1, 2, 3). Previous research has primarily investigated magnitude discrimination skills and their predictive capacity for math achievement, whereas numerical ordering has been less systematically explored. At approximately 10-12 years of age, numerical order processing skills have been observed to surpass cardinal magnitude discrimination skills as the key predictor of arithmetic ability. The neurocognitive mechanisms underlying this shift remain unclear. To this end, we investigated children's (ages 10-12) neural correlates of numerical order and magnitude discrimination, as well as task-based functional connectomes and their predictive capacity for numeracy-related behavioral outcomes. Results indicated that number discrimination uniquely relied on bilateral temporoparietal correlates, whereas order processing recruited the bilateral IPS, cerebellum, and left premotor cortex. Connectome-based models were not cross-predictive for numerical order and magnitude, suggesting two dissociable mechanisms jointly supported by visuospatial working memory. Neural correlates of learning and memory were predictive of age and arithmetic ability, only for the ordinal task-connectome, indicating that the numerical order mechanism may undergo a developmental shift, dissociating it from mechanisms supporting cardinal number processing.

Muscimol-induced inactivation of the ventral prefrontal cortex impairs counting performance in rhesus monkeys

Numbers are one of the three basic concepts of human abstract thinking. When human beings count, they often point to things, one by one, and read numbers in a positive integer column. The prefrontal cortex plays a wide range of roles in executive functions, including active maintenance and achievement of goals, adaptive coding and exertion of general intelligence, and completion of time complexity events. Nonhuman animals do not use number names, such as "one, two, three," or numerals, such as "1, 2, 3" to "count" in the same way as humans do. Our previous study established an animal model of counting in monkeys. Here, we used this model to determine whether the prefrontal cortex participates in counting in monkeys. Two 5-year-old female rhesus monkeys (macaques), weighing 5.0 kg and 5.5 kg, were selected to train in a counting task, counting from 1 to 5. When their counting task performance stabilized, we performed surgery on the prefrontal cortex to implant drug delivery tubes. After allowing the monkeys' physical condition and counting performance to recover, we injected either muscimol or normal saline into their dorsal and ventral prefrontal cortex. Thereafter, we observed their counting task performance and analyzed the error types and reaction time during the counting task. The monkeys' performance in the counting task decreased significantly after muscimol injection into the ventral prefrontal cortex; however, it was not affected after saline injection into the ventral prefrontal cortex, or after muscimol or saline injection into the dorsal prefrontal cortex. The ventral prefrontal cortex of the monkey is necessary for counting performance.

The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis

Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that different types of arithmetic problems are solved using different strategies. We used activation likelihood estimation (ALE) to conduct quantitative meta-analyses of mental arithmetic neuroimaging (n = 31) studies, and subsequently grouped contrasts from the 31 studies into problems that are typically solved using retrieval strategies (retrieval problems) (n = 18) and problems that are typically solved using procedural strategies (procedural problems) (n = 19). Foci were compiled to generate probabilistic maps of activation for mental arithmetic (i.e., all problem types), retrieval problems, and procedural problems. Conjunction and contrast analyses were conducted to examine overlapping and distinct activation for retrieval and procedural problems. The conjunction analysis revealed overlapping activation for retrieval and procedural problems in the bilateral inferior parietal lobules, regions typically associated with magnitude processing. Contrast analyses revealed specific activation in the left angular gyrus for retrieval problems and specific activation in the inferior frontal gyrus and cingulate gyrus for procedural problems. These findings indicate that the neural bases of arithmetic systematically differs according to problem type, providing new insights into the dynamic and task-dependent neural underpinnings of the calculating brain.

The Neural Representation of Ordinal Information: Domain-Specific or Domain-General?

Ordinal processing allows for the representation of the sequential relations between stimuli and is a fundamental aspect of different cognitive domains such as verbal working memory (WM), language and numerical cognition. Several studies suggest common ordinal coding mechanisms across these different domains but direct between-domain comparisons of ordinal coding are rare and have led to contradictory evidence. This fMRI study examined the commonality of ordinal representations across the WM, the number, and the letter domains by using a multivoxel pattern analysis approach and by focusing on triplet stimuli associated with robust ordinal distance effects. Neural patterns in fronto-parietal cortices distinguished ordinal distance in all domains. Critically, between-task predictions of ordinal distance in fronto-parietal cortices were robust between serial order WM, alphabetical order judgment but not when involving the numerical order judgment tasks. Moreover, frontal ROIs further supported between-task prediction of distance for the luminance judgment control task, the serial order WM, and the alphabetical tasks. These results suggest that common neural substrates characterize processing of ordinal information in WM and alphabetical but not numerical domains. This commonality, particularly in frontal cortices, may however reflect attentional control processes involved in judging ordinal distances rather than the intervention of domain-general ordinal codes.

The neural basis of counting sequences

Sequence processing is critical for complex behavior, and counting sequences hold a unique place underlying human numerical development. Despite this, the neural bases of counting sequences remain unstudied. We hypothesized that counting sequences in adults would involve representations in sensory, order, magnitude, and linguistic codes that implicate regions in auditory, supplementary motor, posterior parietal, and inferior frontal areas, respectively. In an fMRI scanner, participants heard four-number sequences in a 2 × 2 × 2 design. The sequences were adjacent or not (e.g., 5, 6, 7, 8 vs. 5, 6, 7, 9), ordered or not (e.g., 5, 6, 7, 8 vs. 8, 5, 7, 6), and were spoken by a voice of consistent or variable identity. Then, neural substrates of counting sequences were identified by testing for the effect of consecutiveness (ordered nonadjacent versus ordered adjacent, e.g., 5, 6, 7, 9 > 5, 6, 7, 8) in the hypothesized brain regions. Violations to consecutiveness elicited brain activity in the right inferior frontal gyrus (IFG) and the supplementary motor area (SMA). In contrast, no such activation was observed in the auditory cortex, despite violations in voice identity recruiting strong activity in that region. Also, no activation was observed in the inferior parietal lobule, despite a robust effect of orderedness observed in that brain region. These findings indicate that listening to counting sequences do not automatically elicit sensory or magnitude codes but suggest that the precise increments in the sequence are tracked by the mechanism for processing ordered associations in the SMA and by the mechanism for binding individual lexical items into a cohesive whole in the IFG.

EEG correlation during the solving of simple and complex logical-mathematical problems

Solving logical-mathematical word problems is a complex task that requires numerous cognitive operations, including comprehension, reasoning, and calculation. These abilities have been associated with activation of the parietal, temporal, and prefrontal cortices. It has been suggested that the reasoning involved in solving logical-mathematical problems requires the coordinated functionality of all these cortical areas. In this study was evaluated the activation and electroencephalographic (EEG) correlation of the prefrontal, temporal, and parietal regions in young men while solving logical-mathematical word problems with two degrees of difficulty: simple and complex. During the solving of complex problems, higher absolute power and EEG correlation of the alpha and fast bands between the left frontal and parietal cortices were observed. A temporal deactivation and functional decoupling of the right parietal-temporal cortices also were obtained. Solving complex problems probably require activation of a left prefrontal-parietal circuit to maintain and manipulate multiple pieces of information. The temporal deactivation and decreased parietal-temporal correlation could be associated to text processing and suppression of the content-dependent reasoning to focus cognitive resources on the mathematical reasoning. Together, these findings support a pivotal role for the left prefrontal and parietal cortices in mathematical reasoning and of the temporal regions in text processing required to understand and solve written mathematical problems.

Dissociating Arithmetic Operations in the Parietal Cortex Using 1 Hz Repetitive Transcranial Magnetic Stimulation: The Importance of Strategy Use

The triple-code model (TCM) of number processing suggests the involvement of distinct parietal cortex areas in arithmetic operations: the bilateral horizontal segment of the intraparietal sulcus (hIPS) for arithmetic operations that require the manipulation of numerical quantities (e.g., subtraction) and the left angular gyrus (AG) for arithmetic operations that require the retrieval of answers from long-term memory (e.g., multiplication). Although neuropsychological, neuroimaging, and brain stimulation studies suggest the dissociation of these operations into distinct parietal cortex areas, the role of strategy (online calculation vs. retrieval) is not yet fully established. In the present study, we further explored the causal involvement of the left AG for multiplication and left hIPS for subtraction using a neuronavigated repetitive transcranial magnetic stimulation (rTMS) paradigm. Stimulation sites were determined based on an fMRI experiment using the same tasks. To account for the effect of strategy, participants were asked whether they used retrieval or calculation for each individual problem. We predicted that the stimulation of the left AG would selectively disrupt the retrieval of the solution to multiplication problems. On the other hand, stimulation of the left hIPS should selectively disrupt subtraction. Our results revealed that left AG stimulation was detrimental to the retrieval and online calculation of solutions for multiplication problems, as well as, the retrieval (but not online calculation) of the solutions to subtraction problems. In contrast, left hIPS stimulation had no detrimental effect on both operations regardless of strategy.

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

Numerical working memory alters alpha-beta oscillations and connectivity in the parietal cortices

Although the neural bases of numerical processing and memory have been extensively studied, much remains to be elucidated concerning the spectral and temporal dynamics surrounding these important cognitive processes. To further this understanding, we employed a novel numerical working memory paradigm in 28 young, healthy adults who underwent magnetoencephalography (MEG). The resulting data were examined in the time-frequency domain prior to image reconstruction using a beamformer. Whole-brain, spectrally-constrained coherence was also employed to determine network connectivity. In response to the numerical task, participants exhibited robust alpha/beta oscillations in the bilateral parietal cortices. Whole-brain statistical comparisons examining the effect of numerical manipulation during memory-item maintenance revealed a difference centered in the right superior parietal cortex, such that oscillatory responses during numerical manipulation were significantly stronger than when no manipulation was necessary. Additionally, there was significantly reduced cortico-cortical coherence between the right and left superior parietal regions during the manipulation compared to the maintenance trials, indicating that these regions were functioning more independently when the numerical information had to be actively processed. In sum, these results support previous studies that have implicated the importance of parietal regions in numerical processing, but also provide new knowledge on the spectral, temporal, and network dynamics that serve this critical cognitive function during active working memory maintenance.

Neural representations of transitive relations predict current and future math calculation skills in children

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T₁), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T₁ and again 1.5 years later (T₂). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T₁ and T₂. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

Parametric Representation of Tactile Numerosity in Working Memory

Estimated numerosity perception is processed in an approximate number system (ANS) that resembles the perception of a continuous magnitude. The ANS consists of a right lateralized frontoparietal network comprising the lateral prefrontal cortex (LPFC) and the intraparietal sulcus. Although the ANS has been extensively investigated, only a few studies have focused on the mental representation of retained numerosity estimates. Specifically, the underlying mechanisms of estimated numerosity working memory (WM) is unclear. Besides numerosities, as another form of abstract quantity, vibrotactile WM studies provide initial evidence that the right LPFC takes a central role in maintaining magnitudes. In the present fMRI multivariate pattern analysis study, we designed a delayed match-to-numerosity paradigm to test what brain regions retain approximate numerosity memoranda. In line with parametric WM results, our study found numerosity-specific WM representations in the right LPFC as well as in the supplementary motor area and the left premotor cortex extending into the superior frontal gyrus, thus bridging the gap in abstract quantity WM literature.

The brain-structural correlates of mathematical expertise

Studies in several domains of expertise have established that experience-dependent plasticity brings about both functional and anatomical changes. However, little is known about how such changes come to shape the brain in the case of expertise acquired by professional mathematicians. Here, we aimed to identify cognitive and brain-structural (grey and white matter) characteristics of mathematicians as compared to non-mathematicians. Mathematicians and non-mathematician academics from the University of Oxford underwent structural and diffusion MRI scans, and were tested on a cognitive battery assessing working memory, attention, IQ, numerical and social skills. At the behavioural level, mathematical expertise was associated with better performance in domain-general and domain-specific dimensions. At the grey matter level, in a whole-brain analysis, behavioural performance correlated with grey matter density in left superior frontal gyrus - positively for mathematicians but negatively for non-mathematicians; in a region of interest analysis, we found in mathematicians higher grey matter density in the right superior parietal lobule, but lower grey matter density in the right intraparietal sulcus and in the left inferior frontal gyrus. In terms of white matter, there were no significant group differences in fractional anisotropy or mean diffusivity. These results reveal new insights into the relationship between mathematical expertise and grey matter metrics in brain regions previously implicated in numerical cognition, as well as in regions that have so far received less attention in this field. Further studies, based on longitudinal designs and cognitive training, could examine the conjecture that such cross-sectional findings arise from a bidirectional link between experience and structural brain changes that is itself subject to change across the lifespan.

Functionally distinct contributions of parietal cortex to a numerical landmark task: An fMRI study

This study aimed at establishing the neural basis of magnitude processing of multiple numbers from working memory. We designed a numerical landmark task and embedded it in a fragmented trial event-related fMRI design, allowing to separate encoding from decision processing. An attentional localiser task not involving numbers allowed further functional specification. The results show that in a numerical landmark task the right anterior intraparietal sulcus is involved in number encoding while more posterior parietal regions, bilateral superior parietal lobule and right inferior parietal lobule, provide domain-general support in the form of constructing a working memory representation or orienting spatial attention within that mental representation during number comparison. The results are in line with earlier studies reporting a functional distinction between anterior and posterior parietal contributions to number processing and further specify their role at a functional level.

The strength of alpha and gamma oscillations predicts behavioral switch costs

Cognitive flexibility is often examined using task-switch paradigms, whereby individuals either switch between tasks or repeat the same task on successive trials. The behavioral costs of switching in terms of accuracy and reaction time are well-known, but the oscillatory dynamics underlying such costs are poorly understood. Herein, we examined 25 healthy adults who performed a task-switching paradigm during magnetoencephalography (MEG). All MEG data were transformed into the time-frequency domain and significant oscillatory responses were imaged separately per condition (i.e., switch, repeat) using a beamformer. To determine the impact of task-switching on the neural dynamics, the resulting images were examined using paired-samples t-tests. Whole-brain correlations were also computed using the switch-related difference images (switch - repeat) and the switch-related behavioral data (i.e., switch costs). Our key results indicated stronger decreases in alpha and beta activity, and greater increases in gamma activity in nodes of the cingulo-opercular and fronto-parietal networks during switch relative to repeat trials. In addition, behavioral switch costs were positively correlated with switch-related differences in right frontal and inferior parietal alpha activity, and negatively correlated with switch effects in anterior cingulate and right temporoparietal gamma activity. In other words, participants who had a greater decrease in alpha or increase in gamma in these respective regions had smaller behavioral switch costs, which suggests that these oscillations are critical to supporting cognitive flexibility. In sum, we provide novel data linking switch effects and gamma oscillations, and employed a whole-brain approach to directly link switch-related oscillatory differences with switch-related performance differences.

Specialization of the Right Intraparietal Sulcus for Processing Mathematics During Development

Mathematical ability, especially perception of numbers and performance of arithmetics, is known to rely on the activation of intraparietal sulcus (IPS). However, reasoning ability and working memory, 2 highly associated abilities also activate partly overlapping regions. Most studies aimed at localizing mathematical function have used group averages, where individual variability is averaged out, thus confounding the anatomical specificity when localizing cognitive functions. Here, we analyze the functional anatomy of the intraparietal cortex by using individual analysis of subregions of IPS based on how they are structurally connected to frontal, parietal, and occipital cortex. Analysis of cortical thickness showed that the right anterior IPS, defined by its connections to the frontal lobe, was associated with both visuospatial working memory, and mathematics in 6-year-old children. This region specialized during development to be specifically related to mathematics, but not visuospatial working memory in adolescents and adults. This could be an example of interactive specialization, where interacting with the environment in combination with interactions between cortical regions leads from a more general role of right anterior IPS in spatial processing, to a specialization of this region for mathematics.

How do individual differences in children's domain specific and domain general abilities relate to brain activity within the intraparietal sulcus during arithmetic? An fMRI study

Previous research has demonstrated that children recruit the intraparietal sulcus (IPS) during arithmetic, which has largely been attributed to domain-specific processes such as quantity manipulations. However, the IPS has also been found to be important for domain-general abilities, such as visuo-spatial working memory (VSWM). Based on the current literature it is unclear whether individual differences in domain-specific skills, domain-general skills, or a combination of the two, are related to the recruitment of the IPS during arithmetic. This study examines how individual differences in both domain general and domain specific competencies relate to brain activity in the IPS during arithmetic, and whether the relationships are related to how brain activity is measured. In a sample of 44 school-aged children, we found that VSWM was only weakly related to a neural index of arithmetic complexity (neural problem size effect), whereas symbolic number processing skills (symbolic comparison and ordering) were related to overall arithmetic activity (both small and large problems). By simultaneously examining multiple domain-general and domain specific measures, we were also able to determine that symbolic skills were a stronger predictor of brain activity within the IPS than domain general skills such as VSWM and domain specific skills such as non-symbolic number processing. Together, these findings highlight that neural problem size effect may reflect different cognitive processes than brain activity across both small and large arithmetic problems, and that symbolic number processing skills are a critical predictor of variability in IPS activity during arithmetic. Hum Brain Mapp 38:3941-3956, 2017. © 2017 Wiley Periodicals, Inc.

Causal role of the posterior parietal cortex for two-digit mental subtraction and addition: A repetitive TMS study

Although parietal areas of the left hemisphere are known to be involved in simple mental calculation, the possible role of the homologue areas of the right hemisphere in mental complex calculation remains debated. In the present study, we tested the causal role of the posterior parietal cortex of both hemispheres in two-digit mental addition and subtraction by means of neuronavigated repetitive TMS (rTMS), investigating possible hemispheric asymmetries in specific parietal areas. In particular, we performed two rTMS experiments, which differed only for the target sites stimulated, on independent samples of participants. rTMS was delivered over the horizontal and ventral portions of the intraparietal sulcus (HIPS and VIPS, respectively) of each hemisphere in Experiment 1, and over the angular and supramarginal gyri (ANG and SMG, respectively) of each hemisphere in Experiment 2. First, we found that each cerebral area of the posterior parietal cortex is involved to some degree in the two-digit addition and subtraction. Second, in Experiment 1, we found a stronger pattern of hemispheric asymmetry for the involvement of HIPS in addition compared to subtraction. In particular, results showed a greater involvement of the right HIPS than the left one for addition. Moreover, we found less asymmetry for the VIPS. Taken together, these results suggest that two-digit mental addition is more strongly associated with the use of a spatial mapping compared to subtraction. In support of this view, in Experiment 2, a greater role of left and right ANG was found for addition needed in verbal processing of numbers and in visuospatial attention processes, respectively. We also revealed a greater involvement of the bilateral SMG in two-digit mental subtraction, in response to greater working memory load required to solve this latter operation compared to addition.

Comparing diffuse optical tomography and functional magnetic resonance imaging signals during a cognitive task: pilot study

Diffuse optical tomography (DOT) measures concentration changes in both oxy- and deoxyhemoglobin providing three-dimensional images of local brain activations. A pilot study, which compares both DOT and functional magnetic resonance imaging (fMRI) volumes through t-maps given by canonical statistical parametric mapping (SPM) processing for both data modalities, is presented. The DOT series were processed using a method that is based on a Bayesian filter application on raw DOT data to remove physiological changes and minimum description length application index to select a number of singular values, which reduce the data dimensionality during image reconstruction and adaptation of DOT volume series to normalized standard space. Therefore, statistical analysis is performed with canonical SPM software in the same way as fMRI analysis is done, accepting DOT volumes as if they were fMRI volumes. The results show the reproducibility and ruggedness of the method to process DOT series on group analysis using cognitive paradigms on the prefrontal cortex. Difficulties such as the fact that scalp-brain distances vary between subjects or cerebral activations are difficult to reproduce due to strategies used by the subjects to solve arithmetic problems are considered. T-images given by fMRI and DOT volume series analyzed in SPM show that at the functional level, both DOT and fMRI measures detect the same areas, although DOT provides complementary information to fMRI signals about cerebral activity.

The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol-Symbol Associations

Recently, a lot of studies in the domain of numerical cognition have been published demonstrating a robust association between numerical symbol processing and individual differences in mathematics achievement. Because numerical symbols are so important for mathematics achievement, many researchers want to provide an answer on the ‘symbol grounding problem,’ i.e., how does a symbol acquires its numerical meaning? The most popular account, the approximate number system (ANS) mapping account, assumes that a symbol acquires its numerical meaning by being mapped on a non-verbal and ANS. Here, we critically evaluate four arguments that are supposed to support this account, i.e., (1) there is an evolutionary system for approximate number processing, (2) non-symbolic and symbolic number processing show the same behavioral effects, (3) non-symbolic and symbolic numbers activate the same brain regions which are also involved in more advanced calculation and (4) non-symbolic comparison is related to the performance on symbolic mathematics achievement tasks. Based on this evaluation, we conclude that all of these arguments and consequently also the mapping account are questionable. Next we explored less popular alternative, where small numerical symbols are initially mapped on a precise representation and then, in combination with increasing knowledge of the counting list result in an independent and exact symbolic system based on order relations between symbols. We evaluate this account by reviewing evidence on order judgment tasks following the same four arguments. Although further research is necessary, the available evidence so far suggests that this symbol–symbol association account should be considered as a worthy alternative of how symbols acquire their meaning.

Probing the Neural Correlates of Number Processing

The cognitive and neural mechanisms that enable humans to encode and manipulate numerical information have been subject to an increasing number of experimental studies over the past 25 years or so. Here, I highlight recent findings about how numerical information is neurally coded, focusing on the theoretical implications derived from the most influential theoretical framework in numerical cognition—the Triple Code Model. At the core of this model is the assumption that bilateral parietal cortex hosts an approximate number system that codes for the cardinal value of perceived numerals. I will review studies that ask whether or not the numerical coding within this system is invariant to varying input notation, format, or modality, and whether or not the observed parietal activity is number-specific over and above the parietal involvement in response-related processes. Extant computational models of numerosity (the number of objects in a set) perception are summarized and related to empirical data from human neuroimaging and monkey neurophysiology.

Perceiving fingers in single-digit arithmetic problems

In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.

How number line estimation skills relate to neural activations in single digit subtraction problems

The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated with differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved in numerical magnitude and spatial processes.

Right-hemisphere (spatial?) acalculia and the influence of neglect

The present study aimed at exploring basic number and calculation abilities in right-hemisphere damaged patients (RHD), focusing primarily on one-digit orally presented tasks, which do not require explicit visuo-spatial abilities. Twenty-four non mentally-deteriorated RHD patients [12 with clinical neglect (RHDN+), 12 without clinical neglect (RHDN-)], and 12 healthy controls were included in the study. Participants were administered an ad hoc numerical battery assessing abilities such as counting, number magnitude comparison, writing and reading Arabic numerals and mental calculation, among others. Significant differences emerged among healthy controls and both the RHDN+ group and the RHDN- group, suggesting that the mathematical impairment of RHD patients does not necessarily correspond to the presence of left-neglect. A detailed analysis of the sub-tests of the battery evidenced expected differences among RHDN+ patients, RHDN- patients, and controls in writing and reading Arabic numerals. Crucially, differences between RHDN+ patients and controls were also found in tasks such as mental subtraction and mental multiplication, which do not require written visuo-spatial abilities. The present findings thus suggest that unilateral right hemisphere lesions may produce specific representational deficits that affect simple mental calculation, and not only the spatial arrangement of multi-digit written numbers as previously thought.

The role of ANS acuity and numeracy for the calibration and the coherence of subjective probability judgments

The purpose of the study was to investigate how numeracy and acuity of the approximate number system (ANS) relate to the calibration and coherence of probability judgments. Based on the literature on number cognition, a first hypothesis was that those with lower numeracy would maintain a less linear use of the probability scale, contributing to overconfidence and nonlinear calibration curves. A second hypothesis was that also poorer acuity of the ANS would be associated with overconfidence and non-linearity. A third hypothesis, in line with dual-systems theory (e.g., Kahneman and Frederick, 2002) was that people higher in numeracy should have better access to the normative probability rules, allowing them to decrease the rate of conjunction fallacies. Data from 213 participants sampled from the Swedish population showed that: (i) in line with the first hypothesis, overconfidence and the linearity of the calibration curves were related to numeracy, where people higher in numeracy were well calibrated with zero overconfidence. (ii) ANS was not associated with overconfidence and non-linearity, disconfirming the second hypothesis. (iii) The rate of conjunction fallacies was slightly, but to a statistically significant degree decreased by numeracy, but still high at all numeracy levels. An unexpected finding was that participants with better ANS acuity gave more realistic estimates of their performance relative to others.

Tones and numbers: a combined EEG-MEG study on the effects of musical expertise in magnitude comparisons of audiovisual stimuli

This study investigated the cortical responses underlying magnitude comparisons of multisensory stimuli and examined the effect that musical expertise has in this process. The comparative judgments were based on a newly learned rule binding the auditory and visual stimuli within the context of magnitude comparisons: "the higher the pitch of the tone, the larger the number presented." The cortical responses were measured by simultaneous MEG\EEG recordings and a combined source analysis with individualized realistic head models was performed. Musical expertise effects were investigated by comparing musicians to non-musicians. Congruent audiovisual stimuli, corresponding to the newly learned rule, elicited activity in frontotemporal and occipital areas. In contrast, incongruent stimuli activated temporal and parietal regions. Musicians when compared with nonmusicians showed increased differences between congruent and incongruent stimuli in a prefrontal region, thereby indicating that music expertise may affect multisensory comparative judgments within a generalized representation of analog magnitude.

Association between resting-state coactivation in the parieto-frontal network and intelligence during late childhood and adolescence

BACKGROUND AND PURPOSE

A number of studies have associated the adult intelligence quotient with the structure and function of the bilateral parieto-frontal networks, whereas the relationship between intelligence quotient and parieto-frontal network function has been found to be relatively weak in early childhood. Because both human intelligence and brain function undergo protracted development into adulthood, the purpose of the present study was to provide a better understanding of the development of the parieto-frontal network-intelligence quotient relationship.

MATERIALS AND METHODS

We performed independent component analysis of resting-state fMRI data of 84 children and 50 adolescents separately and then correlated full-scale intelligence quotient with the spatial maps of the bilateral parieto-frontal networks of each group.

RESULTS

In children, significant positive spatial-map versus intelligence quotient correlations were detected in the right angular gyrus and inferior frontal gyrus in the right parieto-frontal network, and no significant correlation was observed in the left parieto-frontal network. In adolescents, significant positive correlation was detected in the left inferior frontal gyrus in the left parieto-frontal network, and the correlations in the frontal pole in the 2 parieto-frontal networks were only marginally significant.

CONCLUSIONS

The present findings not only support the critical role of the parieto-frontal networks for intelligence but indicate that the relationship between intelligence quotient and the parieto-frontal network in the right hemisphere has been well established in late childhood, and that the relationship in the left hemisphere was also established in adolescence.

Common neural substrates for ordinal representation in short-term memory, numerical and alphabetical cognition

The representation and maintenance of serial order information is one of the main functions of verbal short-term memory (STM) but its neural correlates remain poorly understood. We show here that the neural substrates allowing for coding of order information in STM are shared with those supporting ordinal processing in the numerical and alphabetical domains. We designed an fMRI experiment determining the neural substrates sensitive to ordinal distance effects in numerical judgment, alphabetical judgment and serial order STM tasks. Null conjunction analyses for parametric ordinal distance effects showed a common involvement of the horizontal segment of the left intraparietal sulcus over the three tasks; in addition, right intraparietal sulcus involvement was also observed for ordinal distance effects in the STM and numerical judgment tasks. These findings demonstrate that shared neural correlates in the intraparietal cortex support processing of order information in verbal STM, number and alphabetical domains, and suggest the existence of domain general, potentially ordinal, comparison processes supported by the left intraparietal sulcus.