Arithmetic and the brain

Updating functional brain units: Insights far beyond Luria

This paper reviews Luria's model of the three functional units of the brain. To meet this objective, several issues were reviewed: the theory of functional systems and the contributions of phylogenesis and embryogenesis to the brain's functional organization. This review revealed several facts. In the first place, the relationship/integration of basic homeostatic needs with complex forms of behavior. Secondly, the multi-scale hierarchical and distributed organization of the brain and interactions between cells and systems. Thirdly, the phylogenetic role of exaptation, especially in basal ganglia and cerebellum expansion. Finally, the tripartite embryogenetic organization of the brain: rhinic, limbic/paralimbic, and supralimbic zones. Obviously, these principles of brain organization are in contradiction with attempts to establish separate functional brain units. The proposed new model is made up of two large integrated complexes: a primordial-limbic complex (Luria's Unit I) and a telencephalic-cortical complex (Luria's Units II and III). As a result, five functional units were delineated: Unit I. Primordial or preferential (brainstem), for life-support, behavioral modulation, and waking regulation; Unit II. Limbic and paralimbic systems, for emotions and hedonic evaluation (danger and relevance detection and contribution to reward/motivational processing) and the creation of cognitive maps (contextual memory, navigation, and generativity [imagination]); Unit III. Telencephalic-cortical, for sensorimotor and cognitive processing (gnosis, praxis, language, calculation, etc.), semantic and episodic (contextual) memory processing, and multimodal conscious agency; Unit IV. Basal ganglia systems, for behavior selection and reinforcement (reward-oriented behavior); Unit V. Cerebellar systems, for the prediction/anticipation (orthometric supervision) of the outcome of an action. The proposed brain units are nothing more than abstractions within the brain's simultaneous and distributed physiological processes. As function transcends anatomy, the model necessarily involves transition and overlap between structures. Beyond the classic approaches, this review includes information on recent systemic perspectives on functional brain organization. The limitations of this review are discussed.

A number sense as an emergent property of the manipulating brain

The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. We explore this question through a model, assuming that the learner is able to pick up and place small objects from, and to, locations of its choosing, and will spontaneously engage in such undirected manipulation. We further assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with a supervisory signal from the motor system. We model perception using standard deep networks for feature extraction and classification. Our main finding is that, from learning the task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers and quantity. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned with supervision from a simple pre-training task. Our observations suggest that cross-modal learning is a powerful learning mechanism that may be harnessed in artificial intelligence.

From functional neuroimaging to neurostimulation: fNIRS devices as cognitive enhancers

Functional near-infrared spectroscopy (fNIRS) relies on near-infrared (NIR) light for changes in tissue oxygenation. For decades, this technique has been used in neuroscience to measure cortical activity. However, recent research suggests that NIR light directed to neural populations can modulate their activity through "photobiomodulation" (PBM). Yet, fNIRS is being used exclusively as a measurement tool. By adopting cognitive tests sensitive to prefrontal functioning, we show that a 'classical' fNIRS device, placed in correspondence of the prefrontal cortices of healthy participants, induces faster RTs and better accuracy in some of the indexes considered. A well-matched control group, wearing the same but inactive device, did not show any improvement. Hence, our findings indicate that the 'standard' use of fNIRS devices generates PBM impacting cognition. The neuromodulatory power intrinsic in that technique has been so far completely overlooked, and future studies will need to take this into account.

The longitudinal contribution of mapping to arithmetic: Do numeral knowledge, inhibition or analogical reasoning matter?

BACKGROUND

Recent studies have revealed the association between mapping and arithmetic (Ferres-Forga et al., J. Numer. Cogn., 8, 2022, 123; LeFevre et al., J. Numer. Cogn., 8, 2022, 1).

AIM

The underlying mechanism remains unclear.

MATERIALS & METHODS

The current study recruited 118 kindergarten children and followed up on them three times at 6-month intervals. They completed measures to assess mapping skills (T1), non-verbal IQ (T1), numeral knowledge (T2), inhibitory control (T2), analogical reasoning (T2) and arithmetic (T3).

RESULTS

The results showed that mapping accounted for significant variance in arithmetic ability over and above age, gender and non-verbal IQ. Furthermore, analogical reasoning played an important role in the relationship between mapping and mathematics ability.

DISCUSSION

The findings suggest the association between mapping and mathematics ability prior to formal schooling.

CONCLUSION

Analogical reasoning, rather than numeral knowledge or inhibitory control, may drive that association in young children.

Distinct Contributions of the Cerebellum and Basal Ganglia to Arithmetic Procedures

Humans exhibit complex mathematical skills attributed to the exceptional enlargement of neocortical regions throughout evolution. In the current work, we initiated a novel exploration of the ancient subcortical neural network essential for mathematical cognition. Using a neuropsychological approach, we report that degeneration of two subcortical structures, the cerebellum and basal ganglia, impairs performance in symbolic arithmetic. We identify distinct computational impairments in male and female participants with cerebellar degeneration (CD) or Parkinson's disease (PD). The CD group exhibited a disproportionate cost when the arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group showed a disproportionate cost for equations with increasing addends, suggesting that the basal ganglia are critical for chaining multiple operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Notably, we discuss how the counting and chaining operations relate to cerebellar and basal ganglia function in other task domains (e.g., motor processes). Overall, we provide a novel perspective on how the cerebellum and basal ganglia contribute to symbolic arithmetic. Our studies demonstrate the constraints on the computational role of two subcortical regions in higher cognition.

Benefits of a targeted rehabilitation of number transcoding in secondary acalculia: A single-case experimental design

BACKGROUND

Despite its potentially significant functional and emotional impact, acalculia is still too rarely assessed and managed by speech and language therapists. Research on the rehabilitation of numerical transcoding remains scarce in the literature and, despite positive results, presents a low level of evidence.

AIMS

The present study aims to evaluate the effectiveness of a targeted rehabilitation of numerical transcoding in two patients suffering from a chronic secondary acalculia.

METHODS & PROCEDURES

Two post-brain injury females with secondary acalculia took part in a single-case experimental design with multiple baseline across subjects according to a three-phase experimental protocol: baseline involving global cognitive rehabilitation (5-7 measurements with randomized sequential introduction); targeted intervention (10 measurements); follow-up (2 immediate measurements and 1 month after the end of the intervention). Repeated outcome measures consisted of six lists composed of numbers of equivalent difficulty that were used alternately to assess numerical transcoding. We used a reverse digit span as a control measure to assess the specificity of the intervention. Rehabilitation lasted 5 weeks and consisted of errorless learning with colour cues, tables and number-words cards.

OUTCOMES & RESULTS

During baseline period involving global cognitive rehabilitation, transcoding scores remained unchanged. In contrast, there was a significant improvement in scores for both patients during the intervention phase targeting transcoding and maintenance of benefits 1-month post-intervention.

CONCLUSIONS & IMPLICATIONS

This study demonstrates that a specific rehabilitation targeting numerical transcoding following chronic secondary acalculia can be effective in improving transcoding skills.

WHAT THIS PAPER ADDS

What is already known on the subject Transcoding difficulties in patients with acalculia can cause a significant disability in everyday life activities. In secondary acalculia, rehabilitation of cognitive functions associated with number processing (attention, working memory, language) is not sufficient for improvement of transcoding. What this paper adds to existing knowledge An intervention specifically targeting numerical transcoding significantly and durably improves the skills of patients with chronic secondary acalculia. What are the potential or actual clinical implications of this work? Procedural error-free intervention using colour cueing, tables, cards with number-words, copy and repetition seems effective to improve transcoding skills in chronic acalculia.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Contributions of Lower Structures to Higher Cognition: Towards a Dynamic Network Model

Researchers often attribute higher cognition to the enlargement of cortical regions throughout evolution, reflecting the belief that humans sit at the top of the cognitive pyramid. Implicitly, this approach assumes that the subcortex is of secondary importance for higher-order cognition. While it is now recognized that subcortical regions can be involved in various cognitive domains, it remains unclear how they contribute to computations essential for higher-level cognitive processes such as endogenous attention and numerical cognition. Herein, we identify three models of subcortical-cortical relations in these cognitive processes: (i) subcortical regions are not involved in higher cognition; (ii) subcortical computations support elemental forms of higher cognition mainly in species without a developed cortex; and (iii) higher cognition depends on a whole-brain dynamic network, requiring integrated cortical and subcortical computations. Based on evolutionary theories and recent data, we propose the SEED hypothesis: the Subcortex is Essential for the Early Development of higher cognition. According to the five principles of the SEED hypothesis, subcortical computations are essential for the emergence of cognitive abilities that enable organisms to adapt to an ever-changing environment. We examine the implications of the SEED hypothesis from a multidisciplinary perspective to understand how the subcortex contributes to various forms of higher cognition.

Recurrence quantification analysis during a mental calculation task

The identification of brain dynamical changes under different cognitive conditions with noninvasive techniques such as electroencephalography (EEG) is relevant for the understanding of their underlying neural mechanisms. The comprehension of these mechanisms has applications in the early diagnosis of neurological disorders and asynchronous brain computer interfaces. In both cases, there are no reported features that could describe intersubject and intra subject dynamics behavior accurately enough to be applied on a daily basis. The present work proposes the use of three nonlinear features (recurrence rate, determinism, and recurrence times) extracted from recurrence quantification analysis (RQA) to describe central and parietal EEG power series complexity in continuous alternating episodes of mental calculation and rest state. Our results demonstrate a consistent mean directional change of determinism, recurrence rate, and recurrence times between conditions. Increasing values of determinism and recurrence rate were present from the rest state to mental calculation, whereas recurrence times showed the opposite pattern. The analyzed features in the present study showed statistically significant changes between rest and mental calculation states in both individual and population analysis. In general, our study described mental calculation EEG power series as less complex systems in comparison to the rest state. Moreover, ANOVA showed stability of RQA features along time.

Research progress of neonatal hypoxic-ischemic encephalopathy in nonhuman primate models

Neonatal hypoxic-ischemic encephalopathy (HIE) is one of the important complications of neonatal asphyxia, which not only leads to neurological disability but also seriously threatens the life of neonates. Over the years, animal models of HIE have been a research hotspot to find ways to cope with HIE and thereby reduce the risk of neonatal death or disability in moderate-to-severe HIE. By reviewing the literature related to HIE over the years, it was found that nonhuman primates share a high degree of homology with human gross neural anatomy. The basic data on nonhuman primates are not yet complete, so it is urgent to mine and develop new nonhuman primate model data. In recent years, the research on nonhuman primate HIE models has been gradually enriched and the content is more novel. Therefore, the purpose of this review is to further summarize the methods for establishing the nonhuman primate HIE model and to better elucidate the relevance of the nonhuman primate model to humans by observing the behavioral manifestations, neuropathology, and a series of biomarkers of HIE in primates HIE. Finally, the most popular and desirable treatments studied in nonhuman primate models in the past 5 years are summarized.

Late dominance of the right hemisphere during narrative comprehension

PET and fMRI studies suggest that auditory narrative comprehension is supported by a bilateral multilobar cortical network. The superior temporal resolution of magnetoencephalography (MEG) makes it an attractive tool to investigate the dynamics of how different neuroanatomic substrates engage during narrative comprehension. Using beta-band power changes as a marker of cortical engagement, we studied MEG responses during an auditory story comprehension task in 31 healthy adults. The protocol consisted of two runs, each interleaving 7 blocks of the story comprehension task with 15 blocks of an auditorily presented math task as a control for phonological processing, working memory, and attention processes. Sources at the cortical surface were estimated with a frequency-resolved beamformer. Beta-band power was estimated in the frequency range of 16-24 Hz over 1-sec epochs starting from 400 msec after stimulus onset until the end of a story or math problem presentation. These power estimates were compared to 1-second epochs of data before the stimulus block onset. The task-related cortical engagement was inferred from beta-band power decrements. Group-level source activations were statistically compared using non-parametric permutation testing. A story-math contrast of beta-band power changes showed greater bilateral cortical engagement within the fusiform gyrus, inferior and middle temporal gyri, parahippocampal gyrus, and left inferior frontal gyrus (IFG) during story comprehension. A math-story contrast of beta power decrements showed greater bilateral but left-lateralized engagement of the middle frontal gyrus and superior parietal lobule. The evolution of cortical engagement during five temporal windows across the presentation of stories showed significant involvement during the first interval of the narrative of bilateral opercular and insular regions as well as the ventral and lateral temporal cortex, extending more posteriorly on the left and medially on the right. Over time, there continued to be sustained right anterior ventral temporal engagement, with increasing involvement of the right anterior parahippocampal gyrus, STG, MTG, posterior superior temporal sulcus, inferior parietal lobule, frontal operculum, and insula, while left hemisphere engagement decreased. Our findings are consistent with prior imaging studies of narrative comprehension, but in addition, they demonstrate increasing right-lateralized engagement over the course of narratives, suggesting an important role for these right-hemispheric regions in semantic integration as well as social and pragmatic inference processing.

Exceptional abilities in autism: Theories and open questions

The vast majority of research on autism spectrum disorder (ASD) focuses on characterizing and addressing the social communication deficits and restricted, repetitive patterns of behavior that constitute the diagnostic criteria for the disorder. Yet, a small but significant portion of individuals diagnosed with ASD exhibit exceptional cognitive abilities in one or more domains. These "twice-exceptional" individuals often have unique skills that enable them to make significant contributions to the workforce, while at the same time facing unique challenges during the transition to independent living due to a lack of services and broad public misperceptions regarding their condition. Here we review the current literature on cognitive divergence in ASD, focusing on cognitive theories, neural substrates, and clinical and societal implications for increasing understanding of this phenomenon.

Phonological Processing, Visuospatial Skills, and Pattern Understanding in Chinese Developmental Dyscalculia

A number of previous studies have identified cognitive deficits in developmental dyscalculia (DD). Yet, most of these studies were in alphabetic languages, whereas few of them examined Chinese DD. Here, we conducted a study aiming to determine the cognitive factors associated with DD in Chinese children. Five candidate cognitive factors of DD-phonological retrieval, phonological awareness, visual-spatial attention, spatial thinking, and pattern understanding-were examined in the present study. A total of 904 Chinese children ages 8 to 11 years participated in this study. From the sample, 97 children were identified with DD through tests of arithmetic ability, and 93 age- and IQ-matched typically developing children were selected as controls. Logistic regression analysis revealed that phonological retrieval, pattern understanding, visual-spatial attention, and phonological awareness significantly predicted DD, whereas spatial thinking failed to do so. Results of logistic relative weights analysis showed that all five factors explained statistically significant amounts of variance in arithmetic scores. Phonological retrieval had the most influence on DD, followed by pattern understanding, visual-spatial attention, phonological awareness, and spatial thinking. These findings have important clinical implications for diagnosis and intervention of Chinese DD.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (M_age = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

Underestimation in temporal numerosity judgments computationally explained by population coding model

The ability to judge numerosity is essential to an animal’s survival. Nevertheless, the number of signals presented in a sequence is often underestimated. We attempted to elucidate the mechanism for the underestimation by means of computational modeling based on population coding. In the model, the population of neurons which were selective to the logarithmic number of signals responded to sequential signals and the population activity was integrated by a temporal window. The total number of signals was decoded by a weighted average of the integrated activity. The model predicted well the general trends in the human data while the prediction was not fully sufficient for the novel aging effect wherein underestimation was significantly greater for the elderly than for the young in specific stimulus conditions. Barring the aging effect, we can conclude that humans judge the number of signals in sequence by temporally integrating the neural representations of numerosity.

The presence of adjacent others facilitates interpersonal neural synchronization in the left prefrontal cortex during a simple addition task

The hyperscanning technique, that is, simultaneous measurement of neural signals in more than one person, is a powerful research tool for understanding humans' social interactions. In recent years, many studies have investigated interpersonal neural synchronization during various types of communication processes. However, there has been little focus on the impact of the presence of others without explicit social interaction, despite the mere presence of others having been suggested as influencing behavior. In this study, we clarify whether neural signals during a self-paced, repeated, addition task are synchronized when another individual is adjacent without direct interaction. Twenty pairs of participants were measured using a hyperscanning approach with near-infrared spectroscopy. The results show that interpersonal neural synchronization of the task-related signal in the left forehead region was enhanced under the condition of being adjacent to another participant. By contrast, a significant decrease in neural synchronization in the center of the forehead region, where increased neural synchronization is often reported in explicit communication, was observed. Thus, the results indicate that the adjacency of others modulates interpersonal neural synchronization in the task-related signal, and the effect on cognitive processing is different from that of explicit social interaction.

Effectiveness of a Serious Game Design and Game Mechanic Factors for Attention and Executive Function Improvement in the Elderly: A Pretest-Posttest Study

Attention allows us to focus and process information from our environment, and executive function enables us to plan, work, and manage our daily lives. As individuals become older, both of these cognitive abilities decline. It is essential for the elderly to perform more cognitive exercises. Previous studies have shown that arithmetic calculations require attention span and that playing video games requires executive function. Therefore, we developed a serious game involving mental arithmetic calculations specifically for improving attention span and executive functions. Our objective was to analyze the effectiveness of the game and the efficacy of the game’s mechanic factors affecting attention span and executive function in the elderly. Forty elderly volunteers who are over 60 years of age were invited to join an eight-week cognitive training program through an elderly social welfare center. Four assessment tests were used in pre-test and post-test before and after the training period. D-CAT and SAT are used for screening attention span; TMT-A and TMT-B are used for screening executive function. They were instructed to play the game for at least 15 min per day, 5 days per week, for a total of 8 weeks. There were three independent variables (difficulty, pressure, and competition) with two parameters that could be selected. A paired-sample t-test showed the effective results by comparing the pre-test scores and post-test scores of the cognitive training. There were significant improvements in attention span and executive functions. The mixed repeated-measure ANOVA and MANCOVA results showed that two game mechanic factors (difficulty and pressure) had a significant effect and an interaction effect, but the other factor (competition) had a non-significant effect. In conclusion, the game showed a significant enhancement in both attention span and executive functions after training, and the difficulty factor and the pressure factor were shown to have an effect, but the competition factor was shown to have no effect.

Math Skills: a New Look from Functional Data Analysis

Mental calculations involve various areas of the brain. The frontal, parietal and temporal lobes of the left hemisphere have a principal role in the completion of this typology of tasks. Their level of activation varies based on the mathematical competence and attentiveness of the subject under examination and the perceived difficulty of the task. Recent literature often investigates patterns of cerebral activity through fMRI, which is an expensive technique. In this scenario, EEGs represent a more straightforward and cheaper way to collect information regarding brain activity. In this work, we propose an EEG based method to detect differences in the cerebral activation level of people characterized by different abilities in carrying out the same arithmetical task. Our approach consists in the extraction of the activation level of a given region starting from the EEG acquired during resting state and during the completion of a subtraction task. We then analyze these data through Functional Data Analysis, a statistical technique that allows operating on biomedical signals as if they were functions. The application of this technique allowed for the detection of distinct cerebral patterns among the two groups and, more specifically, highlighted the presence of higher levels of activation in the parietal lobe in the population characterized by a lower performance.

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.

Cognitive profiles in the acute phase of traumatic brain injury according to injury severity

Although several studies have documented the chronic phase of traumatic brain injury (TBI), few verified the nature and severity of cognitive impairments during the acute phase. Among the studies carried out during the acute phase, instrumental functions were rarely examined compared to attention, memory, and executive functions. This study aimed to compare the nature and intensity of cognitive problems in the acute phase according to TBI severity and age. It was hypothesized that cognitive impairments would increase in line with TBI severity and age, and that instrumental functions would be less affected in victims of mild or moderate TBI than in those with severe TBI. The Brief Cognitive Exam in Traumatology (EXACT), a new and reliable test specifically designed and validated to briefly assess global cognitive functioning during the acute phase, was administered to 319 mild to severe TBI victims (aged 16 to 96 years), within three months post-accident. The EXACT evaluates five domains: Language, Instrumental functions (other than language), Attention and working memory, Episodic memory, and Executive functions and behavioral regulation. Results confirmed the negative influence of TBI severity and age on global cognitive functioning. Also, compared to victims with a mild or moderate TBI, a higher proportion of those with a severe TBI presented impaired instrumental functions (calculation, praxis, and gnosis). Thus, during the acute phase, the nature and severity of cognitive impairments vary according to TBI severity.

Mathematical Abilities in School-Aged Children: A Structural Magnetic Resonance Imaging Analysis With Radiomics

Structural magnetic resonance imaging (sMRI) studies have shown that children that differ in some mathematical abilities show differences in gray matter volume mainly in parietal and frontal regions that are involved in number processing, attentional control, and memory. In the present study, a structural neuroimaging analysis based on radiomics and machine learning models is presented with the aim of identifying the brain areas that better predict children’s performance in a variety of mathematical tests. A sample of 77 school-aged children from third to sixth grade were administered four mathematical tests: Math fluency, Calculation, Applied problems and Quantitative concepts as well as a structural brain imaging scan. By extracting radiomics related to the shape, intensity, and texture of specific brain areas, we observed that areas from the frontal, parietal, temporal, and occipital lobes, basal ganglia, and limbic system, were differentially related to children’s performance in the mathematical tests. sMRI-based analyses in the context of mathematical performance have been mainly focused on volumetric measures. However, the results for radiomics-based analysis showed that for these areas, texture features were the most important for the regression models, while volume accounted for less than 15% of the shape importance. These findings highlight the potential of radiomics for more in-depth analysis of medical images for the identification of brain areas related to mathematical abilities.

Subcortical Cognition: The Fruit Below the Rind

Cognitive neuroscience has highlighted the cerebral cortex while often overlooking subcortical structures. This cortical proclivity is found in basic and translational research on many aspects of cognition, especially higher cognitive domains such as language, reading, music, and math. We suggest that, for both anatomical and evolutionary reasons, multiple subcortical structures play substantial roles across higher and lower cognition. We present a comprehensive review of existing evidence, which indeed reveals extensive subcortical contributions in multiple cognitive domains. We argue that the findings are overall both real and important. Next, we advance a theoretical framework to capture the nature of (sub)cortical contributions to cognition. Finally, we propose how new subcortical cognitive roles can be identified by leveraging anatomical and evolutionary principles, and we describe specific methods that can be used to reveal subcortical cognition. Altogether, this review aims to advance cognitive neuroscience by highlighting subcortical cognition and facilitating its future investigation. Expected final online publication date for the Annual Review of Neuroscience, Volume 45 is July 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Bilateral intraparietal activation for number tasks in studies using an adaptation paradigm: A meta-analysis

Mathematical processing is important for professional successes. The Adaptation Paradigm has been widely used to study the brain underpinnings of mathematical processing. In this study, we aim at shedding light on an important component of mathematical processing, namely numerical cognition. To do so, we performed a meta-analysis using the Activation Likelihood Estimation method on studies that have employed the Adaptation Paradigm for examining numerical cognition. We found a bilateral Intraparietal Sulcus (IPS) activation in studies using both symbolic and non-symbolic stimuli formats. We also found a right lateralized brain activation for the non-symbolic condition and a left lateralized brain activation for the symbolic condition. These results imply that the Adaptation Paradigm likely targets numeric magnitude processing and confirms the potency of this paradigm to activate the Intraparietal Sulcus.

The link between number and action in human infants

Humans' inborn ability to represent and manipulate numerical quantities is supported by the parietal cortex, which is also involved in a variety of spatial and motor abilities. While the behavioral links between numerical and spatial information have been extensively studied, little is known about the connection between number and action. Some studies in adults have shown a series of interference effects when simultaneously processing numerical and action information. We investigated the origins of this link by testing forty infants (7- to 9-month-old) in one of two experimental conditions: one group was habituated to congruent number-hand pairings, where the larger the number, the more open the hand-shape associated; the second group was habituated to incongruent number-hand pairings, where the larger the number, the more close the hand-shape associated. In test trials, both groups of infants were presented with congruent and incongruent pairings. We found that only infants habituated to congruency showed a significantly higher looking time to the test trial depicting incongruent pairings. These findings show for the first time that infants spontaneously associate magnitude-related changes across the dimensions of number and action-related information, thus offering support to the existence of an early, preverbal number-action link in the human mind.

What Ability Can Predict Mathematics Performance in Typically Developing Preschoolers and Those with Autism Spectrum Disorder?

Research evaluating predictors of mathematics ability in preschoolers with autism spectrum disorder (ASD) is scarce and inconclusive. The present study first compared the mathematics ability and cognitive abilities of preschoolers with ASD and age-matched typically developing (TD) peers. Then, we examined the relative contributions of cognitive abilities to the mathematics ability of preschoolers with ASD and TD. The results show that compared to those of their age-matched TD peers, the mathematics and cognitive abilities of preschoolers with ASD were impaired. The predictors of mathematics ability were found to differ among preschoolers with ASD and their age-matched TD peers. For TD preschoolers, the domain-specific approximate number system (ANS) was the key predictor of mathematics ability. For preschoolers with ASD, domain-general working memory (WM) was most important.

Cognitive and brain correlates of acquired number-colour synaesthetic-like associations

Synaesthesia is a condition in which one sensory dimension triggers another sensation. The exact contribution of genetic and environmental factors in synaesthesia is not yet fully understood. Most synaesthesia phenotypes involve associations in which the synaesthetic inducer constitutes some form of linguistic/conceptual information acquired during the course of development (e.g., digits, letters, and names of months). To study the role of learning in synaesthesia, we induced synaesthesia by training and examined the behavioural and brain correlates of number-colour associations. We took advantage of the well-known behavioural and neural signature of numbers and used number symbols as inducers. Short (2 weeks) and long (4 weeks) training protocols were conducted with two different groups. Task-related BOLD response was acquired while participants performed Stroop tasks requiring naming colours while ignoring the stimuli (i.e., number symbols, dots, words). If the arbitrary association involving number-colour is automatic, the irrelevant dimension (i.e., numbers) would interfere with the colour response. In addition, if number-colour associations are transferred to linguistic and non-symbolic representations, the passive viewing of stimuli (i.e., words and dots) would disrupt colour naming. Behavioural findings showed automatic associations as both training protocols elicited reliable congruency effects for all stimulus dimensions. Congruency effects following both training protocols produced reliable brain activations in various cortical sites involved in number and in cognitive control. The behavioural and brain patterns reported here support the role of learning in the brain correlates of developmental synaesthesia and provide the first evidence that automatic associations involving different magnitude dimensions can be acquired.

What do neuropsychological tests assess?

Background. Contemporary neuroimaging techniques, particularly fMRI and PET, have demonstrated that cognitive abilities do not strictly depend on specific brain areas, but rather on complex brain circuits or systems.Methods. Using PubMed and Google Scholar databases, a search for functional studies (fMRI and PET) during the performance of several neuropsychological tests was done. The pattern of brain activity found during the solution of some executive functions, language, memory, calculation, and visuospatial/visuoconstructive abilities is reviewed.Results. Brain activity supporting the performance in these tests is usually quite extended, and involves not only those brain areas traditionally assumed in neuropsychology, but also other cortical and sometimes subcortical regions.Conclusions. Most neuropsychological tests are simultaneously evaluating different cognitive abilities associated with the activity of diverse brain areas. "Cognitive/anatomical" correlations could only be established for some relatively simple functions. This change in the understanding about the brain organization of cognition has not been reflected in the interpretation of the neuropsychological tests yet. The interpretation of neuropsychological tests should be based not only in clinical observations but also in functional studies. This is a necessary further step in clinical neuropsychology.

Increased structural covariance in brain regions for number processing and memory in children with developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Several studies demonstrated functional network alterations in DD. Yet, there are no studies, which examined the structural network integrity in DD. We compared whole‐brain maps of volume based structural covariance between 19 (4 males) children with DD and 18 (4 males) typically developing children. We found elevated structural covariance in the DD group between the anterior intraparietal sulcus to the middle temporal and frontal gyrus (p < 0.05, corrected). A hippocampus subfield analysis showed higher structural covariance in the DD group for area CA3 to the parahippocampal and calcarine sulcus, angular gyrus and anterior part of the intraparietal sulcus as well as to the lingual gyrus. Lower structural covariance in this group was seen for the subiculum to orbitofrontal gyrus, anterior insula and middle frontal gyrus. In contrast, the primary motor cortex (control region) revealed no difference in structural covariance between groups. Our results extend functional magnetic resonance studies by revealing abnormal gray matter integrity in children with DD. These findings thus indicate that the pathophysiology of DD is mediated by both structural and functional abnormalities in a network involved in number processing and memory function.

Ancient visual channels have a causal role in arithmetic calculations

Humans exhibit complex arithmetic skills, often attributed to our exceptionally large neocortex. However, the past decade has provided ample evidence that the functional domain of the subcortex extends well beyond basic functions. Using a sensitive behavioral method, for the first time, we explored the contributions of lower-order visual monocular channels to symbolic arithmetic operations, addition and subtraction. The pattern of results from 4 different experiments provides converging evidence for a causal relation between mental arithmetic and primitive subcortical regions. The results have major implications for our understanding of the neuroevolutionary development of general numerical abilities–subcortical regions, which are shared across different species, are essential to complex numerical operations. In a bigger conceptual framework, these findings and others call for a shift from the modal view of the exclusive role of the neocortex in high-level cognition to a view that emphasizes the interplay between subcortical and cortical brain networks.

Mathematics Disability vs. Learning Disability: A 360 Degree Analysis

A fundamental issue for research in mathematics disability (MD) and reading disability (RD) is: If these disabilities are clearly distinct, why is there so high a level of comorbidity, together with the converse; if these disabilities are so similar, why are there clear differences in underlying causes and aetiology? In order to address this puzzle, we introduce the “360 degree analysis” (360DA) framework and apply it to the overlap between RD and MD. The 360DA process starts by analyzing the issue from four perspectives: theoretical, developmental, affective, and pedagogical. Under 360DA, these analyses are then integrated to provide insights for theory, and for individual assessment and support, together with directions for future progress. The analyses confirm extensive similarities between arithmetic and reading development in terms of rote learning, executive function (EF), and affective trauma, but also major differences in terms of the conceptual needs, the motor coordination needs, and the methods of scaffolding. In terms of theory, commonalities are interpreted naturally in terms of initial general developmental delay followed by domain-independent affective trauma following school failure. Dissociations are interpreted in terms of cerebellar vs. hippocampal learning networks, sequential vs. spatial processing, and language vs. spatial scaffolding, with a further dimension of the need for accurate fixation for reading. The framework has significant theoretical and applied implications.

Operational momentum during children's approximate arithmetic relates to symbolic math skills and space-magnitude association

Operational momentum (OM) refers to the behavioral tendency to overestimate or underestimate the results of addition or subtraction, respectively. The cognitive mechanism of the OM effect and how it is related to the development of symbolic math abilities are not well understood. The current study examined whether individual differences in the OM effect are related to symbolic arithmetic abilities, number line estimation performance, and the space-magnitude association effect in young children. In this study, first-grade elementary school children manifested the OM effect during approximate addition and subtraction. Individual differences in the OM effect were not correlated with number line estimation error. Interestingly, children who showed a greater degree of the OM effect performed not worse, but better on the symbolic arithmetic task. In addition, the OM effect was correlated with the space-magnitude association (size congruity) effect measured with the Numerical Stroop task. More specifically, the OM bias was correlated with the ability to inhibit interference from competing information on the incongruent trials of the Numerical Stroop task. Our results suggest that the inaccuracy of numerical magnitude representations is not the source of the OM effect. Given that children with better math ability showed a greater OM bias, a stronger OM effect may reflect better intuition in arithmetic operations. Altogether, we carefully interpret these findings as suggesting that a greater OM effect reflects superior intuition or fundamental knowledge of arithmetic operations and a more adult-like maturation of the reorienting component of the attentional system.

Primitive visual channels have a causal role in cognitive transfer

Scientific investigations have long emphasized the cortex's role in cognitive transfer and arithmetic abilities. To date, however, this assumption has not been thoroughly empirically investigated. Here we demonstrated that primitive mechanisms-lower visual channels-have a causal role in cognitive transfer of complex skills such as symbolic arithmetic. We found that exposing only one monocular channel to a visuospatial training resulted in a larger transfer effect in the trained monocular channel compared to the untrained monocular channel. Such cognitive transfer was found for both novel figural-spatial problems (near transfer) and novel subtraction problems (far transfer). Importantly, the benefits of the trained eye were not observed in old problems and in other tasks that did not involve visuospatial abilities (the Stroop task, a multiplication task). These results challenge the exclusive role of the cortex in cognitive transfer and complex arithmetic. In addition, the results suggest a new mechanism for the emergence of cognitive skills, that could be shared across different species.

Visual-Spatial Ability Predicts Academic Achievement Through Arithmetic and Reading Abilities

This study aimed to investigate how visual–spatial ability predicted academic achievement through arithmetic and reading abilities. Four hundred and ninety-nine Chinese children aged from 10.1 to 11.2 years were recruited and measured visual–spatial, arithmetic, and reading abilities. Their mathematical and Chinese language academic achievements were collected for two consecutive school years, respectively, during the same year as cognitive tests and 1 year after the cognitive tests. Correlation analysis indicated that visual–spatial, arithmetic, and reading abilities and academic achievements were significantly correlated with each other. The structural equation modelling analyses showed that there were two paths from visual–spatial ability to academic achievement: a major path mediated by arithmetic ability and a minor serial mediation path from visual–spatial ability to arithmetic ability to reading ability, then to academic achievement. Results shed light on the importance of visual–spatial ability in education.

Gray Matter Atrophy in Amnestic Mild Cognitive Impairment: A Voxel-Based Meta-Analysis

Background: Voxel-based morphometry (VBM) has been widely used to investigate structural alterations in amnesia mild cognitive impairment (aMCI). However, inconsistent results have hindered our understanding of the exact neuropathology related to aMCI. Objectives: Our aim was to systematically review the literature reporting VBM on aMCI to elucidate consistent gray matter alterations, their functional characterization, and corresponding co-activation patterns. Methods: The PubMed, Web of Science, and EMBASE databases were searched for VBM studies on aMCI published from inception up to June 2020. Peak coordinates were extracted from clusters that showed significant gray matter differences between aMCI patients and healthy controls (HC). Meta-analysis was performed using seed-based d mapping with the permutation of subject images (SDM-PSI), a newly improved meta-analytic method. Functional characterization and task-based co-activation patterns using the BrainMap database were performed on significant clusters to explore their functional roles. Finally, VBM was performed based on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset to further support the findings. Results: A total of 31 studies with 681 aMCI patients and 837 HC were included in this systematic review. The aMCI group showed significant gray matter atrophy in the left amygdala and right hippocampus, which was consistent with results from the ADNI dataset. Functional characterization revealed that these regions were mainly associated with emotion, cognition, and perception. Further, meta-regression analysis demonstrated that gray matter atrophy in the left inferior frontal gyrus and the left angular gyrus was significantly associated with cognitive impairment in the aMCI group. Conclusions: The findings of gray matter atrophy in the left amygdala and right hippocampus are highly consistent and robust, and not only offer a better understanding of the underlying neuropathology but also provide accurate potential biomarkers for aMCI.

Neural alignment predicts learning outcomes in students taking an introduction to computer science course

Despite major advances in measuring human brain activity during and after educational experiences, it is unclear how learners internalize new content, especially in real-life and online settings. In this work, we introduce a neural approach to predicting and assessing learning outcomes in a real-life setting. Our approach hinges on the idea that successful learning involves forming the right set of neural representations, which are captured in canonical activity patterns shared across individuals. Specifically, we hypothesized that learning is mirrored in neural alignment: the degree to which an individual learner's neural representations match those of experts, as well as those of other learners. We tested this hypothesis in a longitudinal functional MRI study that regularly scanned college students enrolled in an introduction to computer science course. We additionally scanned graduate student experts in computer science. We show that alignment among students successfully predicts overall performance in a final exam. Furthermore, within individual students, we find better learning outcomes for concepts that evoke better alignment with experts and with other students, revealing neural patterns associated with specific learned concepts in individuals.

The Insula Is a Hub for Functional Brain Network in Patients With Anti-N-Methyl-D-Aspartate Receptor Encephalitis

BACKGROUND

In recent years, imaging technologies have been rapidly evolving, with an emphasis on the characterization of brain structure changes and functional imaging in patients with autoimmune encephalitis. However, the neural basis of anti-N-methyl-D-aspartate receptor (NMDAR) encephalitis and its linked cognitive decline is unclear. Our research aimed to assess changes in the functional brain network in patients with anti-NMDAR encephalitis and whether these changes lead to cognitive impairment.

METHODS

Twenty-one anti-NMDAR encephalitis patients and 22 age-, gender-, and education status-matched healthy controls were assessed using resting functional magnetic resonance imaging (fMRI) scanning and neuropsychological tests, including the Hamilton Depression Scale (HAMD24), the Montreal Cognitive Assessment (MoCA), and the Hamilton Anxiety Scale (HAMA). A functional brain network was constructed using fMRI, and the topology of the network parameters was analyzed using graph theory. Next, we extracted the aberrant topological parameters of the functional network as seeds and compared causal connectivity with the whole brain. Lastly, we explored the correlation of aberrant topological structures with deficits in cognitive performance.

RESULTS

Relative to healthy controls, anti-NMDAR encephalitis patients exhibited decreased MoCA scores and increased HAMA and HAMD24 scores (p < 0.05). The nodal clustering coefficient and nodal local efficiency of the left insula (Insula_L) were significantly decreased in anti-NMDAR encephalitis patients (p < 0.05 following Bonferroni correction). Moreover, anti-NMDAR encephalitis patients showed a weakened causal connectivity from the left insula to the left inferior parietal lobe (Parietal_Inf_L) compared to healthy controls. Conversely, the left superior parietal lobe (Parietal_sup_L) exhibited an enhanced causal connectivity to the left insula in anti-NMDAR encephalitis patients compared to controls. Unexpectedly, these alterations were not correlated with any neuropsychological test scores.

CONCLUSION

This research describes topological abnormalities in the functional brain network in anti-NMDAR encephalitis. These results will be conducive to understand the structure and function of the brain network of patients with anti-NMDAR encephalitis and further explore the neuropathophysiological mechanisms.

Frontal Functional Network Disruption Associated with Amyotrophic Lateral Sclerosis: An fNIRS-Based Minimum Spanning Tree Analysis

Recent evidence increasingly associates network disruption in brain organization with multiple neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS), a rare terminal disease. However, the comparability of brain network characteristics across different studies remains a challenge for conventional graph theoretical methods. One suggested method to address this issue is minimum spanning tree (MST) analysis, which provides a less biased comparison. Here, we assessed the novel application of MST network analysis to hemodynamic responses recorded by functional near-infrared spectroscopy (fNIRS) neuroimaging modality, during an activity-based paradigm to investigate hypothetical disruptions in frontal functional brain network topology as a marker of the executive dysfunction, one of the most prevalent cognitive deficit reported across ALS studies. We analyzed data recorded from nine participants with ALS and ten age-matched healthy controls by first estimating functional connectivity, using phase-locking value (PLV) analysis, and then constructing the corresponding individual and group MSTs. Our results showed significant between-group differences in several MST topological properties, including leaf fraction, maximum degree, diameter, eccentricity, and degree divergence. We further observed a global shift toward more centralized frontal network organizations in the ALS group, interpreted as a more random or dysregulated network in this cohort. Moreover, the similarity analysis demonstrated marginally significantly increased overlap in the individual MSTs from the control group, implying a reference network with lower topological variation in the healthy cohort. Our nodal analysis characterized the main local hubs in healthy controls as distributed more evenly over the frontal cortex, with slightly higher occurrence in the left prefrontal cortex (PFC), while in the ALS group, the most frequent hubs were asymmetrical, observed primarily in the right prefrontal cortex. Furthermore, it was demonstrated that the global PLV (gPLV) synchronization metric is associated with disease progression, and a few topological properties, including leaf fraction and tree hierarchy, are linked to disease duration. These results suggest that dysregulation, centralization, and asymmetry of the hemodynamic-based frontal functional network during activity are potential neuro-topological markers of ALS pathogenesis. Our findings can possibly support new bedside assessments of the functional status of ALS' brain network and could hypothetically extend to applications in other neurodegenerative diseases.

Tactile to visual number priming in the left intraparietal cortex of sighted Braille readers

Numbers can be presented in different notations and sensory modalities. It is currently debated to what extent these formats overlap onto a single representation. We asked whether such an overlap exists between symbolic numbers represented in two sensory modalities: Arabic digits and Braille numbers. A unique group of sighted Braille readers underwent extensive Braille reading training and was tested in an fMRI repetition-suppression paradigm with tactile Braille digit primes and visual Arabic digit targets. Our results reveal cross-modal priming: compared to repetition of two different quantities (e.g., Braille “5” and Arabic “2”), repetition of the same quantity presented in two modalities (e.g., Braille “5” and Arabic “5”) led to a reduction of activation in several sub-regions of the Intraparietal Sulcus (IPS), a key cortical region for magnitude processing. Thus, in sighted Braille readers, the representations of numbers read by sight and by touch overlap to a degree sufficient to cause repetition suppression. This effect was modulated by the numerical prime-probe distance. Altogether this indicates that the left parietal cortex hosts neural assemblies that are sensitive to numerical information from different notations (number words or Arabic digits) and modalities (tactile and visual).

Thalamus is a common locus of reading, arithmetic, and IQ: Analysis of local intrinsic functional properties

Neuroimaging studies of basic achievement skills - reading and arithmetic - often control for the effect of IQ to identify unique neural correlates of each skill. This may underestimate possible effects of common factors between achievement and IQ measures on neuroimaging results. Here, we simultaneously examined achievement (reading and arithmetic) and IQ measures in young adults, aiming to identify MRI correlates of their common factors. Resting-state fMRI (rs-fMRI) data were analyzed using two metrics assessing local intrinsic functional properties; regional homogeneity (ReHo) and fractional amplitude low frequency fluctuation (fALFF), measuring local intrinsic functional connectivity and intrinsic functional activity, respectively. ReHo highlighted the thalamus/pulvinar (a subcortical region implied for selective attention) as a common locus for both achievement skills and IQ. More specifically, the higher the ReHo values, the lower the achievement and IQ scores. For fALFF, the left superior parietal lobule, part of the dorsal attention network, was positively associated with reading and IQ. Collectively, our results highlight attention-related regions, particularly the thalamus/pulvinar as a key region related to individual differences in performance on all the three measures. ReHo in the thalamus/pulvinar may serve as a tool to examine brain mechanisms underlying a comorbidity of reading and arithmetic difficulties, which could co-occur with weakness in general intellectual abilities.

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.

The relationship between the height dimension and numerical processing

It is well documented that the ability to perceive numbers depends on perception of size. However, size consists of two different dimensions: height and width. In previous size-congruency experiments, the changes in the size dimension were confounded by changes in both the height and width dimensions. Hence, it is not clear if two digits that are equal in size but with different width and height produce a congruency effect and if so, which dimension (height or width) will be associated with quantity more prominently. In fact, different theories might predict different outcomes for the association of height versus width with numbers. To resolve this issue, this study included two experiments in which two equal-size digits that differed from each other in the height and width dimensions were presented and participants were asked to decide which digit is numerically larger. The results revealed a novel congruency effect in which larger numbers are associated more prominently with the height dimension when compared with the width dimension. This effect has important implications for understanding the relationship between number processing and the spatial perception system.

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.

Children's neural activity during number line estimations assessed by functional near-infrared spectroscopy (fNIRS)

Number line estimation (NLE) is an educational task in which children estimate the location of a value (e.g., 25) on a blank line that represents a numerical range (e.g., 0-100). NLE performance is a strong predictor of success in mathematics, and error patterns on this task help provide a glimpse into how children may represent number internally. However, a missing and fundamental element of this puzzle is the identification of neural correlates of NLE in children. That is, understanding possible neural signatures related to NLE performance will provide valuable insight into the cognitive processes that underlie children's development of NLE ability. Using functional near-infrared spectroscopy (fNIRS), we provide the first investigation of concurrent behavioral and cortical signatures of NLE performance in children. Specifically, our results highlight significant fronto-parietal changes in cortical activation in response to increases in NLE scale (e.g., 0-100 vs. 0-100,000). Furthermore, our results demonstrate that NLE performance feedback (auditory, visual, or audiovisual), as well as children's grade (2nd vs. 3rd) influence cortical responding during an NLE task.

Hemispheric asymmetries in processing numerical meaning in arithmetic

Hemispheric asymmetries in arithmetic have been hypothesized based on neuropsychological, developmental, and neuroimaging work. However, it has been challenging to separate asymmetries related to arithmetic specifically, from those associated general cognitive or linguistic processes. Here we attempt to experimentally isolate the processing of numerical meaning in arithmetic problems from language and memory retrieval by employing novel non-symbolic addition problems, where participants estimated the sum of two dot arrays and judged whether a probe dot array was the correct sum of the first two arrays. Furthermore, we experimentally manipulated which hemisphere receive the probe array first using a visual half-field paradigm while recording event-related potentials (ERP). We find that neural sensitivity to numerical meaning in arithmetic arises under left but not right visual field presentation during early and middle portions of the late positive complex (LPC, 400-800 ms). Furthermore, we find that subsequent accuracy for judgements of whether the probe is the correct sum is better under right visual field presentation than left, suggesting a left hemisphere advantage for integrating information for categorization or decision making related to arithmetic. Finally, neural signatures of operational momentum, or differential sensitivity to whether the probe was greater or less than the sum, occurred at a later portion of the LPC (800-1000 ms) and regardless of visual field of presentation, suggesting a temporal and functional dissociation between magnitude and ordinal processing in arithmetic. Together these results provide novel evidence for differences in timing and hemispheric lateralization for several cognitive processes involved in arithmetic thinking.

Distinct strategies for estimating the temporal average of numerical and perceptual information

Humans can estimate global trends in dynamic information presented either as perceptual features or as symbolic codes such as numbers. Previous studies on temporal statistics estimation have shown that observers judge the temporal average of visual attributes according to information from the last few frames of the presentation sequence (in what is referred to as the recency effect). Here, we investigated how humans estimate the temporal average of number vs. orientation using identical stimuli for the two tasks. In Experiment 1, a randomly-selected single-digit number was serially presented at orientations randomly varying over time. In Experiment 2, a texture comprising a random number of Gabor elements was shown at orientations randomly varying over time. In both experiments, observers judged the temporal averages of the numerical values and orientations in separate blocks. Results showed that observers judging the temporal average of orientation relied upon information from later frames as predicted by a typical model of perceptual decision making. By contrast, for the judgement of numerical values, we found that the impacts of each temporal frame were constant or varied little across temporal frames regardless of whether the numerical information was given as digits or by the number of texture elements. The results are interpreted as evidence that distinct computational strategies may be involved in estimating the temporal averages of perceptual features and numerical information.

Language-specific numerical estimation in bilingual children

We tested 5- to 7-year-old bilingual learners of French and English (N = 91) to investigate how language-specific knowledge of verbal numerals affects numerical estimation. Participants made verbal estimates for rapidly presented random dot arrays in each of their two languages. Estimation accuracy differed across children's two languages, an effect that remained when controlling for children's familiarity with number words across their two languages. In addition, children's estimates were equivalently well ordered in their two languages, suggesting that differences in accuracy were due to how children represented the relative distance between number words in each language. Overall, these results suggest that bilingual children have different mappings between their verbal and nonverbal counting systems across their two languages and that those differences in mappings are likely driven by an asymmetry in their knowledge of the structure of the count list across their languages. Implications for bilingual math education are discussed.

Combining neuropsychological tests to improve the assessment of arithmetic difficulties in children with ADHD

OBJECTIVE

To compare the ways of evaluating arithmetic skills in Brazilian children with ADHD by combining three validated neuropsychological tests and determining whether they are sensitive to the methylphenidate treatment.

METHODS

Forty-two children (9‒12 years old) participated in the present study: 20 were children with ADHD (DSM-IV) and 22 were age-matched controls. A classification criterion was used for each test separately and one, for their combination to detect the presence of arithmetic difficulties at two time points: baseline (time 1); and when children with ADHD were taking 0.3‒0.5 mg/kg of methylphenidate (time 2). The study also assessed children's subtraction performance, combining parts of these tests.

RESULTS

Separately, the tests were only sensitive to differences between groups without medication. However, by combining the three neuropsychological tests, we observed a difference and detected a reduction in arithmetic difficulties associated with the methylphenidate treatment. The same effects were found in subtraction exercises, which require a borrowing procedure.

CONCLUSIONS

The present study detected arithmetic difficulties in Brazilian children with ADHD and the effects of methylphenidate. Given this improvement in sensitivity, combining tests could be a promising alternative when working with limited samples.