Notation-dependent and -independent representations of numbers in the parietal lobes

Numerical cognition across the lifespan: A selective review of key developmental stages and neural, cognitive, and affective underpinnings

Numerical cognition constitutes a set of hierarchically related skills and abilities that develop-and may subsequently begin to decline-over developmental time. An innate "number sense" has long been argued to provide a foundation for the development of increasingly complex and applied numerical cognition, such as symbolic numerical reference, arithmetic, and financial literacy. However, evidence for a direct link between basic perceptual mechanisms that allow us to determine numerical magnitude (e.g., "how many" objects are in front of us and whether some of these are of a "greater" or "lesser" quantity), and later symbolic applications for counting and mathematics, has recently been challenged. Understanding how one develops an increasingly precise sense of number and which neurocognitive mechanisms support arithmetic development and achievement is crucial for developing successful mathematics curricula, supporting individual financial literacy and decision-making, and designing appropriate intervention and remediation programs for mathematical learning disabilities as well as mathematics anxiety. The purpose of this review is to provide a broad overview of the cognitive, neural, and affective underpinnings of numerical cognition-spanning the earliest hours of infancy to senior adulthood-and highlight gaps in our knowledge that remain to be addressed.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Number, size, and space associated in a common system by distinct mechanisms

The spatial numerical association of response codes (SNARC) effect demonstrates that people respond faster to small numbers with their left hand and faster to large numbers with their right hand. The size congruity effect (SCE) refers to the fact that congruent trials between numerical values and physical sizes are faster than incongruent trials. Previous studies have found that the SNARC effect and SCE are independent when magnitudes or sizes are processed explicitly. This study aimed to explore whether number, size, and space are common and distinct mechanisms using an implicit parity judgment task. The results showed that the SNARC effect, SCE, and SNARC-like effect all co-existed. Furthermore, there was a significant interaction between the SNARC effect and SCE, in which the SNARC effect in the SCE-congruent condition was larger than in the SCE-incongruent condition, whereas SCE merely emerged in the SNARC-compatible trials. However, participants responded to small numbers in large size faster than to large numbers in small size with the left hand in SCE-incongruent trials, which reflected that number-space mapping (SNARC effect) was stronger than size-space mapping (SNARC-like effect). These findings provide new evidence for A Theory of Magnitude (ATOM), which suggests that number, size, and space are associated with a common generalized magnitude system through distinct mechanisms.

Identifying conceptual neural responses to symbolic numerals

The goal of measuring conceptual processing in numerical cognition is distanced by the possibility that neural responses to symbolic numerals are influenced by physical stimulus confounds. Here, we targeted conceptual responses to parity (even versus odd), using electroencephalogram (EEG) frequency-tagging with a symmetry/asymmetry design. Arabic numerals (2-9) were presented at 7.5 Hz in 50 s sequences; odd and even numbers were alternated to target differential, 'asymmetry' responses to parity at 3.75 Hz (7.5 Hz/2). Parity responses were probed with four different stimulus sets, increasing in intra-numeral stimulus variability, and with two control conditions composed of non-conceptual numeral alternations. Significant asymmetry responses were found over the occipitotemporal cortex to all conditions, even for the arbitrary controls. The large physical-differences control condition elicited the largest response in the stimulus set with the lowest variability (one font). Only in the stimulus set with the highest variability (20 drawn, coloured exemplars/numeral) did the response to parity surpass both control conditions. These findings show that physical differences across small sets of Arabic numerals can strongly influence, and even account for, automatic brain responses. However, carefully designed control conditions and highly variable stimulus sets may be used towards identifying truly conceptual neural responses.

Inter-individual, hemispheric and sex variability of brain activations during numerosity processing

Numerosity perception is a fundamental and innate cognitive function shared by both humans and many animal species. Previous research has primarily focused on exploring the spatial and functional consistency of neural activations that were associated with the processing of numerosity information. However, the inter-individual variability of brain activations of numerosity perception remains unclear. In the present study, with a large-sample functional magnetic resonance imaging (fMRI) dataset (n = 460), we aimed to localize the functional regions related to numerosity perceptions and explore the inter-individual, hemispheric, and sex differences within these brain regions. Fifteen subject-specific activated regions, including the anterior intraparietal sulcus (aIPS), posterior intraparietal sulcus (pIPS), insula, inferior frontal gyrus (IFG), inferior temporal gyrus (ITG), premotor area (PM), middle occipital gyrus (MOG) and anterior cingulate cortex (ACC), were delineated in each individual and then used to create a functional probabilistic atlas to quantify individual variability in brain activations of numerosity processing. Though the activation percentages of most regions were higher than 60%, the intersections of most regions across individuals were considerably lower, falling below 50%, indicating substantial variations in brain activations related to numerosity processing among individuals. Furthermore, significant hemispheric and sex differences in activation location, extent, and magnitude were also found in these regions. Most activated regions in the right hemisphere had larger activation volumes and activation magnitudes, and were located more lateral and anterior than their counterparts in the left hemisphere. In addition, in most of these regions, males displayed stronger activations than females. Our findings demonstrate large inter-individual, hemispheric, and sex differences in brain activations related to numerosity processing, and our probabilistic atlas can serve as a robust functional and spatial reference for mapping the numerosity-related neural networks.

A single tDCS session can enhance numerical competence

While numerical skills are increasingly important in modern life, few interventions have been developed to support those with numeracy skills difficulties. Previous studies have demonstrated that applying transcranial Direct Current Stimulation (tDCS) can improve numerical skills. However, tDCS interventions designed to induce lasting changes typically involve reapplying brain-stimulation over several days. Repeated tDCS application can increase the risks associated with the procedure, as well as restricts the transferability of the method to a wider population, particularly those who may experience mobility issues, such as stroke survivors with acalculia. The current study investigated whether a single session of tDCS (anodal to right parietal lobe and cathodal to left parietal lobe), followed by four self-practice sessions without tDCS, could result in enhancement of numerical skills. Nineteen healthy adults (n = 10 tDCS, n = 9 sham control) implicitly learnt the magnitude association of nine arbitrary symbols, previously used by Cohen Kadosh et al. (2010). Numerical proficiency was assessed using number-to-space task, while automaticity was assessed with numerical Stroop. Results revealed that single-session tDCS had a significant effect on participants' accuracy on the number-to-space tasks, but not on the numerical Stroop task's congruity effect, implying automaticity may require longer practice. We conclude that a single session of tDCS should be considered as an avenue for interventions.

The brain lateralization and development of math functions: progress since Sperry, 1974

In 1974, Roger Sperry, based on his seminal studies on the split-brain condition, concluded that math was almost exclusively sustained by the language dominant left hemisphere. The right hemisphere could perform additions up to sums less than 20, the only exception to a complete left hemisphere dominance. Studies on lateralized focal lesions came to a similar conclusion, except for written complex calculation, where spatial abilities are needed to display digits in the right location according to the specific requirements of calculation procedures. Fifty years later, the contribution of new theoretical and instrumental tools lead to a much more complex picture, whereby, while left hemisphere dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out in the right hemisphere. The developmental trajectory in the lateralization of math functions has also been clarified. This corpus of knowledge is reviewed here. The right hemisphere does not simply offer its support when calculation requires generic space processing, but its role can be very specific. For example, the right parietal lobe seems to store the operation-specific spatial layout required for complex arithmetical procedures and areas like the right insula are necessary in parsing complex numbers containing zero. Evidence is found for a complex orchestration between the two hemispheres even for simple tasks: each hemisphere has its specific role, concurring to the correct result. As for development, data point to right dominance for basic numerical processes. The picture that emerges at school age is a bilateral pattern with a significantly greater involvement of the right-hemisphere, particularly in non-symbolic tasks. The intraparietal sulcus shows a left hemisphere preponderance in response to symbolic stimuli at this age.

Contrasting symbolic and non-symbolic numerical representations in a joint classification task

Both symbolic (digits) and non-symbolic (dots) numerals are spatially coded, with relatively small numbers being responded faster with a left key and large numbers being responded faster with a right key (spatial-numerical association of response codes [SNARC]). The idea of format independent SNARC seems to support the existence of a common system for symbolic and non-symbolic numerical representations, although evidence in the field is still mixed. The aim of the present study is to investigate whether symbolic and non-symbolic numerals interact in the SNARC effect when both information is simultaneously displayed. To do so, participants were presented with dice-like patterns, with digits being used instead of dots. In two separate magnitude classification tasks, participants had to respond either to the number of digits presented on the screen or to their numerical size. In the non-symbolic task, they had to judge whether the digits on the screen were more or less than three, irrespective of the numerical value of the digits. In the symbolic task, participants had to judge whether the digits on the screen were numerically smaller or larger than three, irrespective of the number of digits being present. The results show a consistent SNARC effect in the symbolic task and no effect in the non-symbolic one. Furthermore, congruency between symbolic and non-symbolic numerals did not modulate the response patterns, thus supporting the idea of independent representations and questioning some propositions of current theoretical accounts.

Effect of Music Based Therapy Rhythmic Auditory Stimulation (RAS) Using Wearable Device in Rehabilitation of Neurological Patients: A Systematic Review

(1) Background: Even though music therapy is acknowledged to have positive benefits in neurology, there is still a lack of knowledge in the literature about the applicability of music treatments in clinical practice with a neurological population using wearable devices. (2) Methods: a systematic review was conducted following PRISMA 2020 guidelines on the 29 October 2022, searching in five databases: PubMed, PEDro, Medline, Web of Science, and Science Direct. (3) Results: A total of 2964 articles were found, including 413 from PubMed, 248 from Web of Science, 2110 from Science Direct, 163 from Medline, and none from PEDro. Duplicate entries, of which there were 1262, were eliminated. In the first screening phase, 1702 papers were screened for title and abstract. Subsequently, 1667 papers were removed, based on population, duplicate, outcome, and poor study design. Only 15 studies were considered after 35 papers had their full texts verified. Results showed significant values of spatiotemporal gait parameters in music-based therapy rhythmic auditory stimulation (RAS), including speed, stride length, cadence, and ROM. (4) Conclusions: The current findings confirm the value of music-based therapy RAS as a favorable and effective tool to implement in the health care system for the rehabilitation of patients with movement disorders.

Representations within the Intraparietal Sulcus Distinguish Numerical Tasks and Formats

How does our brain understand the number five when it is written as an Arabic numeral, and when presented as five fingers held up? Four facets have been implicated in adult numerical processing: semantic, visual, manual, and phonological/verbal. Here, we ask how the brain represents each, using a combination of tasks and stimuli. We collected fMRI data from adult participants while they completed our novel "four number code" paradigm. In this paradigm, participants viewed one of two stimulus types to tap into the visual and manual number codes, respectively. Concurrently, they completed one of two tasks to tap into the semantic and phonological/verbal number codes, respectively. Classification analyses revealed that neural codes representing distinctions between the number comparison and phonological tasks were generalizable across format (e.g., Arabic numerals to hands) within intraparietal sulcus (IPS), angular gyrus, and precentral gyrus. Neural codes representing distinctions between formats were generalizable across tasks within visual areas such as fusiform gyrus and calcarine sulcus, as well as within IPS. Our results identify the neural facets of numerical processing within a single paradigm and suggest that IPS is sensitive to distinctions between semantic and phonological/verbal, as well as visual and manual, facets of number representations.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (N_Study1 = 80, N_Study2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

Toward a unified account of nonsymbolic and symbolic representations of number: Insights from a combined psychophysical-computational approach

There is an ongoing, vibrant debate about whether numerical information in both nonsymbolic and symbolic notations would be supported by different neurocognitive systems or rather by a common preverbal approximate number system, which is ratio dependent and follows Weber's law. Here, we propose that the similarities between nonsymbolic and symbolic number processing can be explained based on the principle of efficient coding. To probe this hypothesis we employed a new empirical approach, by predicting the behavioural performance in number comparison tasks with symbolic (i.e., number words) and nonsymbolic (i.e., arrays of dots) information not only from numerical ratio, but for the first time also from natural language data. That is, we used data extracted from vector-space models that are informative about the distributional pattern of number-words usage in natural language. Results showed that linguistic estimates predicted the behavioural performance in both symbolic and nonsymbolic tasks. However, and critically, our results also showed a task-dependent dissociation: linguistic data better predicted the performance in the symbolic task, whereas real numerical ratio better predicted the performance in the nonsymbolic task. These findings indicate that efficient coding of environmental regularities is an explanatory principle of human behavior in tasks involving numerical information. They also suggest that the ability to discriminate a stimulus from similar ones varies as a function of the specific statistical structure of the considered learning environment.

Foundational Number Sense Training Gains Are Predicted by Hippocampal-Parietal Circuits

The development of mathematical skills in early childhood relies on number sense, the foundational ability to discriminate among quantities. Number sense in early childhood is predictive of academic and professional success, and deficits in number sense are thought to underlie lifelong impairments in mathematical abilities. Despite its importance, the brain circuit mechanisms that support number sense learning remain poorly understood. Here, we designed a theoretically motivated training program to determine brain circuit mechanisms underlying foundational number sense learning in female and male elementary school-age children (7-10 years). Our 4 week integrative number sense training program gradually strengthened the understanding of the relations between symbolic (Arabic numerals) and nonsymbolic (sets of items) representations of quantity. We found that our number sense training program improved symbolic quantity discrimination ability in children across a wide range of math abilities including children with learning difficulties. Crucially, the strength of pretraining functional connectivity between the hippocampus and intraparietal sulcus, brain regions implicated in associative learning and quantity discrimination, respectively, predicted individual differences in number sense learning across typically developing children and children with learning difficulties. Reverse meta-analysis of interregional coactivations across 14,371 fMRI studies and 89 cognitive functions confirmed a reliable role for hippocampal-intraparietal sulcus circuits in learning. Our study identifies a canonical hippocampal-parietal circuit for learning that plays a foundational role in children's cognitive skill acquisition. Findings provide important insights into neurobiological circuit markers of individual differences in children's learning and delineate a robust target for effective cognitive interventions.SIGNIFICANCE STATEMENT Mathematical skill development relies on number sense, the ability to discriminate among quantities. Here, we develop a theoretically motivated training program and investigate brain circuits that predict number sense learning in children during a period important for acquisition of foundational cognitive skills. Our integrated number sense training program was effective in children across a wide a range of math abilities, including children with learning difficulties. We identify hippocampal-parietal circuits that predict individual differences in learning gains. Our study identifies a brain circuit critical for the acquisition of foundational cognitive skills, which will be useful for developing effective interventions to remediate learning disabilities.

The impact of musical training in symbolic and non-symbolic audiovisual judgements of magnitude

Quantity estimation can be represented in either an analog or symbolic manner and recent evidence now suggests that analog and symbolic representation of quantities interact. Nonetheless, those two representational forms of quantities may be enhanced by convergent multisensory information. Here, we elucidate those interactions using high-density electroencephalography (EEG) and an audiovisual oddball paradigm. Participants were presented simultaneous audiovisual tokens in which the co-varying pitch of tones was combined with the embedded cardinality of dot patterns. Incongruencies were elicited independently from symbolic and non-symbolic modality within the audio-visual percept, violating the newly acquired rule that “the higher the pitch of the tone, the larger the cardinality of the figure.” The effect of neural plasticity in symbolic and non-symbolic numerical representations of quantities was investigated through a cross-sectional design, comparing musicians to musically naïve controls. Individual’s cortical activity was reconstructed and statistically modeled for a predefined time-window of the evoked response (130–170 ms). To summarize, we show that symbolic and non-symbolic processing of magnitudes is re-organized in cortical space, with professional musicians showing altered activity in motor and temporal areas. Thus, we argue that the symbolic representation of quantities is altered through musical training.

Number Stroop Effects in Arabic Digits and ASL Number Signs: The Impact of Age and Setting of Language Acquisition

Multiple studies have reported mathematics underachievement for students who are deaf, but the onset, scope, and causes of this phenomenon remain understudied. Early language deprivation might be one factor influencing the acquisition of numbers. In this study, we investigated a basic and fundamental mathematical skill, automatic magnitude processing, in two formats (Arabic digits and American Sign Language number signs) and the influence of age of first language exposure on both formats by using two versions of the Number Stroop Test. We compared the performance of individuals born deaf who experienced early language deprivation to that of individuals born deaf who experienced sign language in early life and hearing second language learners of ASL. In both formats of magnitude representation, late first language learners demonstrated overall slower reaction times. They were also less accurate on incongruent trials but performed no differently from early signers and second language learners on other trials. When magnitude was represented by Arabic digits, late first language learners exhibited robust Number Stroop Effects, suggesting automatic magnitude processing, but they also demonstrated a large speed difference between size and number judgments not observed in the other groups. In a task with ASL number signs, the Number Stroop Effect was not found in any group, suggesting that magnitude representation might be format-specific, in line with the results from several other languages. Late first language learners also demonstrate unusual patterns of slower reaction time for neutral rather than incongruent stimuli. Together, the results show that early language deprivation affects the ability to automatically judge quantities expressed both linguistically and by Arabic digits, but that it can be acquired later in life when language is available. Contrary to previous studies that find differences in speed of number processing between deaf and hearing participants, we find that when language is acquired early in life, deaf signers perform identically to hearing participants.

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.

Causal dynamics and information flow in parietal-temporal-hippocampal circuits during mental arithmetic revealed by high-temporal resolution human intracranial EEG

Mental arithmetic involves distributed brain regions spanning parietal and temporal cortices, yet little is known about the neural dynamics of causal functional circuits that link them. Here we use high-temporal resolution (1000 Hz sampling rate) intracranial EEG from 35 participants, 362 electrodes, and 1727 electrode pairs, to investigate dynamic causal circuits linking posterior parietal cortex (PPC) with ventral temporal-occipital cortex and hippocampal regions which constitute the perceptual, visuospatial, and mnemonic building blocks of mental arithmetic. Nonlinear phase transfer entropy measures capable of capturing information flow identified dorsal PPC as a causal inflow hub during mental arithmetic, with strong causal influences from fusiform gyrus in ventral temporal-occipital cortex as well as the hippocampus. Net causal inflow into dorsal PPC was significantly higher during mental arithmetic, compared to both resting-state and verbal memory recall. Our analysis also revealed functional heterogeneity of casual signaling in the PPC, with greater net causal inflow into the dorsal PCC, compared to ventral PPC. Additionally, the strength of causal influences was significantly higher on dorsal, compared to ventral, PPC from the hippocampus, and ventral temporal-occipital cortex during mental arithmetic, when compared to both resting-state and verbal memory recall. Our findings provide novel insights into dynamic neural circuits and hubs underlying numerical problem solving and reveal neurophysiological circuit mechanisms by which both the visual number form processing and declarative memory systems dynamically engage the PPC during mental arithmetic.

The neural signatures of social hierarchy-related learning and interaction: A coordinate- and connectivity-based meta-analysis

Numerous neuroimaging studies have investigated the neural mechanisms of two mutually independent yet closely related cognitive processes aiding humans to navigate complex societies: social hierarchy-related learning (SH-RL) and social hierarchy-related interaction (SH-RI). To integrate these heterogeneous results into a more fine-grained and reliable characterization of the neural basis of social hierarchy, we combined coordinate-based meta-analyses with connectivity and functional decoding analyses to understand the underlying neuropsychological mechanism of SH-RL and SH-RI. We identified the anterior insula and temporoparietal junction (dominance detection), medial prefrontal cortex (information updating and computation), and intraparietal sulcus region, amygdala, and hippocampus (social hierarchy representation) as consistent activated brain regions for SH-RL, but the striatum, amygdala, and hippocampus associated with reward processing for SH-RI. Our results provide an overview of the neural architecture of the neuropsychological processes underlying how we understand, and interact within, social hierarchy.

Automatic integration of numerical formats examined with frequency-tagged EEG

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (< 5) depicted in single (digits, dots, number words) or mixed notation (dots-digits, number words-dots, digits-number words), presented at 10 Hz. Periodically, a deviant stimulus (> 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits-number words and number words-dots, but not for digits-dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.

The neural basis of number word processing in children and adults

The ability to map number words to their corresponding quantity representations is a gatekeeper for children's future math success (Spaepen et al., 2018). Without number word knowledge at school entry, children are at greater risk for developing math learning difficulties (Chu et al., 2019). In the present study, we used functional magnetic resonance imaging (fMRI) to examine the neural basis for processing the meaning of spoken number words and its developmental trajectory in 4- to 10-year-old children, and in adults. In a number word-quantity mapping paradigm, participants listened to number words while simultaneously viewing quantities that were congruent or incongruent to the number word they heard. Whole brain analyses revealed that adults showed a neural congruity effect with greater neural activation for incongruent relative to congruent trials in anterior cingulate cortex (ACC) and left intraparietal sulcus (LIPS). In contrast, children did not show a significant neural congruity effect. However, a region of interest analysis in the child sample demonstrated age-related increases in the neural congruity effect, specifically in the LIPS. The positive correlation between neural congruity in LIPS and age was stronger in children who were already attending school, suggesting that developmental changes in LIPS function are experience-dependent.

Symbols Are Special: An fMRI Adaptation Study of Symbolic, Nonsymbolic, and Non-Numerical Magnitude Processing in the Human Brain

How are different formats of magnitudes represented in the human brain? We used functional magnetic resonance imaging adaptation to isolate representations of symbols, quantities, and physical size in 45 adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physical size, anatomically and representationally. Anatomically, passive processing of quantities and size correlate with activation in the right intraparietal sulcus, whereas symbolic number processing, compared with quantity processing, correlates with activation in the left inferior parietal lobule. Representationally, neural patterns of activation supporting symbols are dissimilar from neural activation patterns supporting quantity and size in the bilateral parietal lobes. These findings challenge the longstanding notion that the culturally acquired ability to conceptualize symbolic numbers is represented using entirely the same brain systems that support the evolutionarily ancient system used to process quantities. Moreover, these data reveal that regions that support numerical magnitude processing are also important for the processing of non-numerical magnitudes. This discovery compels future investigations of the neural consequences of acquiring knowledge of symbolic numbers.

Order processing of number symbols is influenced by direction, but not format

This study probed the cognitive mechanisms that underlie order processing for number symbols, specifically the extent to which the direction and format in which number symbols are presented influence the processing of numerical order, as well as the extent to which the relationship between numerical order processing and mathematical achievement is specific to Arabic numerals or generalisable to other notational formats. Seventy adults who were bilingual in English and Chinese completed a Numerical Ordinality Task, using number sequences of various directional conditions (i.e., ascending, descending, mixed) and notational formats (i.e., Arabic numerals, English number words, and Chinese number words). Order processing was found to occur for ascending and descending number sequences (i.e., ordered but not non-ordered trials), with the overall pattern of data supporting the theoretical perspective that the strength and closeness of associations between items in the number sequence could underlie numerical order processing. However, order processing was found to be independent of the notational format in which the numerical stimuli were presented, suggesting that the psychological representations and processes associated with numerical order are abstract across different formats of number symbols. In addition, a relationship between the processing speed for numerical order judgements and mathematical achievement was observed for Arabic numerals and Chinese number words, and to a weaker extent, English number words. Together, our findings have started to uncover the cognitive mechanisms that could underlie order processing for different formats of number symbols, and raise new questions about the generalisability of these findings to other notational formats.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Neurocognitive modeling of latent memory processes reveals reorganization of hippocampal-cortical circuits underlying learning and efficient strategies

Efficient memory-based problem-solving strategies are a cardinal feature of expertise across a wide range of cognitive domains in childhood. However, little is known about the neurocognitive mechanisms that underlie the acquisition of efficient memory-based problem-solving strategies. Here we develop, to the best of our knowledge, a novel neurocognitive process model of latent memory processes to investigate how cognitive training designed to improve children's problem-solving skills alters brain network organization and leads to increased use and efficiency of memory retrieval-based strategies. We found that training increased both the use and efficiency of memory retrieval. Functional brain network analysis revealed training-induced changes in modular network organization, characterized by increase in network modules and reorganization of hippocampal-cortical circuits. Critically, training-related changes in modular network organization predicted performance gains, with emergent hippocampal, rather than parietal cortex, circuitry driving gains in efficiency of memory retrieval. Our findings elucidate a neurocognitive process model of brain network mechanisms that drive learning and gains in children's efficient problem-solving strategies.

The averaging of numerosities: A psychometric investigation of the mental line

Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes—the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.

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).

Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison

Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

Neural Processing Mechanism of Mental Calculation Based on Cerebral Oscillatory Changes: A Comparison Between Abacus Experts and Novices

Background: Abacus experts could mentally calculate fast some mathematical operations using multi-digit numbers. The temporal dynamics of abacus mental calculation are still unknown although some behavioral and neuroimaging studies have suggested a visuospatial and visuomotor neural process during abacus mental calculation. Therefore, this contribution aims to clarify the significant similarities and the differences between experts and novices by investigating calculation-induced neuromagnetic responses based on cerebral oscillatory changes.

Methods: Twelve to 13 healthy abacus experts and 17 non-experts participated in two experimental paradigms using non-invasive neuromagnetic measurements. In experiments 1 and 2, the spatial distribution of oscillatory changes presented mental calculations and temporal frequency profiles during addition while examining multiplication tasks. The MEG data were analyzed using synthetic aperture magnetometry (SAM) with an adaptive beamformer to calculate the group average of the spatial distribution of oscillatory changes and their temporal frequency profiles in source-level analyses.

Results: Using a group average of the spatial distribution of oscillatory changes, we observed some common brain activities in both right-handed abacus experts and non-experts. In non-experts, we detected the right dorsolateral prefrontal cortex (DLPFC) and bilateral Intraparietal sulcus (IPS); whereas in experts, detected the bilateral parieto-occipital sulcus (POS), right inferior frontal gyrus (IFG), and left sensorimotor areas mainly. Based on the findings generated, we could propose calculation processing models for both abacus experts and non- experts conveniently.

Conclusion: The proposed model of calculation processing in abacus experts and novices revealed that the novices could calculate logically depending on numerical processing in the left IPS. In contrast, abacus experts are utilizing spatial processing using a memorized imaginary abacus, which distributed over the bilateral hemispheres in the IFG and sensorimotor areas.

Numerical cognition: A meta-analysis of neuroimaging, transcranial magnetic stimulation and brain-damaged patients studies

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We review neuroimaging, TMS, and patients studies on numerical cognition.

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We focused on the predictions derived from the Triple Code Model (TCM).

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Our findings generally agree with TCM predictions.

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Our results open avenues for the study of the neural bases of numerical cognition.

This article offers the first comprehensive review examining the neurocognitive bases of numerical cognition from neuroimaging, Transcranial Magnetic Stimulation (TMS) and brain-damaged patients studies. We focused on the predictions derived from the Triple Code Model (TCM), particularly the assumption that the representation of numerical quantities rests on a single format-independent representation (i.e., the analogical code) involving both intraparietal sulci (IPS). To do so, we conducted a meta-analysis based on 28 neuroimaging, 12 TMS and 12 brain-damaged patients studies, including arithmetic and magnitude tasks in symbolic and non-symbolic formats. Our findings generally agree with the TCM predictions indicating that both IPS are engaged in all tasks. Nonetheless, the results of brain-damaged patients studies conflicted with neuroimaging and TMS studies, suggesting a right hemisphere lateralization for non-symbolic formats. Our findings also led us to discuss the involvement of brain regions other than IPS in the processing of the analogical code as well as the neural substrate of other codes underlying numerical cognition (i.e., the auditory-verbal code).

Factoring in the spatial effects of symbolic number representation

Spatial constituents of adult symbolic number representation produce effects of size-value congruity, Spatial Numerical Association of Response Codes (SNARC), and numerical distance. According to behavioral experiments, these effects belong to distinct processing stages. Yet, these effects evoke overlapping responses in both early and late Event Related Potentials (ERPs). To probe whether these overlaps indicate sharing of resources, all relevant stimulus and response conditions were factorially combined in a numerical value comparison task. To secure ERP validity, same numbers were compared against variable reference values. This design resulted in previously unobserved interactions in behavior but inhibited late ERP effects. All effects arose early in the P1 component (around 100 ms) and most showed hemispheric specificity. Independency of congruity and SNARC effects was observed, whereas SNARC and numerical distance were closely intertwined. Differences in hemispheric specificity, rather than stage-wise separation, were key to independence.

P300 amplitude and latency reflect arithmetic skill: An ERP study of the problem size effect

The effect of arithmetic problem size is widespread in behavior (e.g., slower responses to 8 × 7 than 2 × 2). Here, we measure event related potentials (ERPs) to determine how the problem size effect unfolds under different conditions. Adults judged the correctness of simple multiplication problems (2 × 4 = 8 versus 9) that varied in size and operand number format (written digits versus spoken number words). The P300, an ERP component associated with stimulus categorization, was measured from solution onset. P300 amplitude was greatest for small and correct solutions, as expected for easily categorized stimuli. Large incorrect solutions elicited a disproportionately reduced P300, an interaction not measurable in verification behavior. Additionally, ERP measures revealed effects of operand format preceding, but not following, solution onset. The significance of these findings for theories of mathematical cognition are addressed.

Spatial-numerical associations: Shared symbolic and non-symbolic numerical representations

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial-numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

Tactile enumeration: A case study of acalculia

Enumeration is one of the building blocks of arithmetic and fingers are used as a counting tool in early steps. Subitizing-fast and accurate enumeration of small quantities-has been vastly studied in the visual modality, but less in the tactile modality. We explored tactile enumeration using fingers, and gray matter (GM) changes using voxel-based morphometry (VBM), in acalculia. We examined JD, a 22-year-old female with acalculia following a stroke to the left inferior parietal cortex. JD and a neurologically healthy normal comparison (NC) group reported how many fingers were stimulated. JD was tested at several time points, including at acute and chronic phases. Using the sensory intact hand for tactile enumeration, JD showed deficit in the acute phase, compared to the NC group, and improvement in the chronic phase of (1) the RT slope of enumerating up to four stimuli, (2) enumerating neighboring fingers, and (3) arithmetic fluency performance. Moreover, VBM analysis showed a larger GM volume for JD relative to the NC group in the right middle occipital cortex, most profoundly in the chronic phase. JD's performance serves as a first glance of tactile enumeration in acalculia. Pattern-recognition-based results support the suggestion of subitizing being the enumeration process when using one hand. Moreover, the increase in GM in the occipital cortex lays the groundwork for studying the innate and primitive ability to perceive and evaluate sizes or amounts-"sense of magnitude"- as a multisensory magnitude area and as part of a recovery path for deficits in basic numerical abilities.

Distinct neural mechanisms for reading Arabic vs. verbal numbers: An ERP study

In this electroencephalogram/event-related potential (EEG/ERP) study, 16 volunteers were asked to compare the numerical equality of 360 pairs of multidigit numbers presented in Arabic or verbal format. Behavioural data showed faster and more accurate responses for digit targets, with a right hand/left hemisphere advantage only for verbal numerals. Occipito-temporal N1, peaking at approximately 180 ms, was strongly left-lateralized during verbal number processing and bilateral during digit processing. A LORETA (low-resolution electromagnetic tomography) source reconstruction performed at the N1 latency stage (155-185 ms) revealed greater brain activation during coding of Arabic than of verbal stimuli. Digit perceptual coding was associated with the activation of the right angular gyrus (rAG), the left fusiform gyrus (FG,BA37), and left and right superior and medial frontal areas. N1 sources for verbal numerals included the left FG (BA37), the precuneus (BA31), the parahippocampal area and a small right prefrontal activation. In addition, verbal numerals elicited a late frontocentral negativity, possibly reflecting stimulus unfamiliarity or complexity. Overall, the data suggest distinct mechanisms for number reading through ciphers (digits) or words. Information about quantity was accessed earlier and more accurately if numbers were in a nonlinguistic code. Indeed, it can be speculated that numerosity processing would involve circuits originally involved in processing space (i.e., rAG/rIPS).

The neural bases of price estimation: Effects of size and precision of the estimate

People are often confronted with the need of estimating the market price of goods. An important question is how people estimate prices, given the variability of products and prices available. Using event-related fMRI, we investigated how numerical processing modulates the neural bases of retail price estimation by focusing on two numerical dimensions: the size and precision of the estimates. Participants were presented with several product labels and made market price estimates for those products. Measures of product buying frequency and market price variability were also collected. The estimation of higher prices required longer response times, was associated with greater variation in responses across participants, and correlated with increasing medial and lateral prefrontal cortex (PFC) activity. Moreover, price estimates followed Weber's law, a hallmark feature of numerical processing. Increasing accuracy in price estimation, indexed by decreasing Weber fraction, engaged the intraparietal sulcus (IPS), a critical region in numerical processing. Our findings provide evidence for distinguishable neural mechanisms associated with the size and the precision of price estimates.

Spatial Arrangement and Set Size Influence the Coding of Non-symbolic Quantities in the Intraparietal Sulcus

Performance in visual quantification tasks shows two characteristic patterns as a function of set size. A precise subitizing process for small sets (up to four) was contrasted with an approximate estimation process for larger sets. The spatial arrangement of elements in a set also influences visual quantification performance, with frequently perceived arrangements (e.g., dice patterns) being faster enumerated than random arrangements. Neuropsychological and imaging studies identified the intraparietal sulcus (IPS), as key brain area for quantification, both within and above the subitizing range. However, it is not yet clear if and how set size and spatial arrangement of elements in a set modulate IPS activity during quantification. In an fMRI study, participants enumerated briefly presented dot patterns with random, canonical or dice arrangement within and above the subitizing range. We evaluated how activity amplitude and pattern in the IPS were influenced by size and spatial arrangement of a set. We found a discontinuity in the amplitude of IPS response between subitizing and estimation range, with steep activity increase for sets exceeding four elements. In the estimation range, random dot arrangements elicited stronger IPS response than canonical arrangements which in turn elicited stronger response than dice arrangements. Furthermore, IPS activity patterns differed systematically between arrangements. We found a signature in the IPS response for a transition between subitizing and estimation processes during quantification. Differences in amplitude and pattern of IPS activity for different spatial arrangements indicated a more precise representation of non-symbolic numerical magnitude for dice and canonical than for random arrangements. These findings challenge the idea of an abstract coding of numerosity in the IPS even within a single notation.

Representation of numerical magnitude in math-anxious individuals

Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

Mechanisms of interactive specialization and emergence of functional brain circuits supporting cognitive development in children

Cognitive development is thought to depend on the refinement and specialization of functional circuits over time, yet little is known about how this process unfolds over the course of childhood. Here we investigated growth trajectories of functional brain circuits and tested an interactive specialization model of neurocognitive development which posits that the refinement of task-related functional networks is driven by a shared history of co-activation between cortical regions. We tested this model in a longitudinal cohort of 30 children with behavioral and task-related functional brain imaging data at multiple time points spanning childhood and adolescence, focusing on the maturation of parietal circuits associated with numerical problem solving and learning. Hierarchical linear modeling revealed selective strengthening as well as weakening of functional brain circuits. Connectivity between parietal and prefrontal cortex decreased over time, while connectivity within posterior brain regions, including intra-hemispheric and inter-hemispheric parietal connectivity, as well as parietal connectivity with ventral temporal occipital cortex regions implicated in quantity manipulation and numerical symbol recognition, increased over time. Our study provides insights into the longitudinal maturation of functional circuits in the human brain and the mechanisms by which interactive specialization shapes children's cognitive development and learning.

Neural correlates of quantity processing of Chinese numeral classifiers

Linguistic analysis suggests that numeral classifiers carry quantity information. However, previous neuroimaging studies have shown that classifiers did not elicit higher activation in the intraparietal sulcus (IPS), associated with representation of numerical magnitude, than tool nouns did. This study aimed to control the semantic attributes of classifiers and reexamine the underlying neural correlates. Participants performed a semantic distance comparison task in which they judged which one of the two items was semantically closer to the target. Processing classifiers elicited higher activation than tool nouns in the bilateral inferior parietal lobules (IPL), middle frontal gyri (MFG), right superior frontal gyrus (SFG), and left lingual gyrus. Conjunction analysis showed that the IPS was commonly activated for classifiers, numbers, dots, and number words. The results support that classifiers activate quantity representations, implicating that the system of classifiers is part of magnitude cognition. Furthermore, the results suggest that the IPS represents magnitude independent of notations.

Influence of biases in numerical magnitude allocation on human prosocial decision making

Over the past decade neuroscientific research has attempted to probe the neurobiological underpinnings of human prosocial decision making. Such research has almost ubiquitously employed tasks such as the dictator game or similar variations (i.e., ultimatum game). Considering the explicit numerical nature of such tasks, it is surprising that the influence of numerical cognition on decision making during task performance remains unknown. While performing these tasks, participants typically tend to anchor on a 50:50 split that necessitates an explicit numerical judgement (i.e., number-pair bisection). Accordingly, we hypothesize that the decision-making process during the dictator game recruits overlapping cognitive processes to those known to be engaged during number-pair bisection. We observed that biases in numerical magnitude allocation correlated with the formulation of decisions during the dictator game. That is, intrinsic biases toward smaller numerical magnitudes were associated with the formulation of less favorable decisions, whereas biases toward larger magnitudes were associated with more favorable choices. We proceeded to corroborate this relationship by subliminally and systematically inducing biases in numerical magnitude toward either higher or lower numbers using a visuo-vestibular stimulation paradigm. Such subliminal alterations in numerical magnitude allocation led to proportional and corresponding changes to an individual's decision making during the dictator game. Critically, no relationship was observed between neither intrinsic nor induced biases in numerical magnitude on decision making when assessed using a nonnumerical-based prosocial questionnaire. Our findings demonstrate numerical influences on decisions formulated during the dictator game and highlight the necessity to control for confounds associated with numerical cognition in human decision-making paradigms.NEW & NOTEWORTHY We demonstrate that intrinsic biases in numerical magnitude can directly predict the amount of money donated by an individual to an anonymous stranger during the dictator game. Furthermore, subliminally inducing perceptual biases in numerical-magnitude allocation can actively drive prosocial choices in the corresponding direction. Our findings provide evidence for numerical influences on decision making during performance of the dictator game. Accordingly, without the implementation of an adequate control for numerical influences, the dictator game and other tasks with an inherent numerical component (i.e., ultimatum game) should be employed with caution in the assessment of human behavior.

Repetition suppression: a means to index neural representations using BOLD?

Understanding how the human brain gives rise to complex cognitive processes remains one of the biggest challenges of contemporary neuroscience. While invasive recording in animal models can provide insight into neural processes that are conserved across species, our understanding of cognition more broadly relies upon investigation of the human brain itself. There is therefore an imperative to establish non-invasive tools that allow human brain activity to be measured at high spatial and temporal resolution. In recent years, various attempts have been made to refine the coarse signal available in functional magnetic resonance imaging (fMRI), providing a means to investigate neural activity at the meso-scale, i.e. at the level of neural populations. The most widely used techniques include repetition suppression and multivariate pattern analysis. Human neuroscience can now use these techniques to investigate how representations are encoded across neural populations and transformed by relevant computations. Here, we review the physiological basis, applications and limitations of fMRI repetition suppression with a brief comparison to multivariate techniques. By doing so, we show how fMRI repetition suppression holds promise as a tool to reveal complex neural mechanisms that underlie human cognitive function.

This article is part of the themed issue ‘Interpreting BOLD: a dialogue between cognitive and cellular neuroscience’.

Flexible Verbal–Spatial Mapping in the Horizontal and Vertical SNARC Effects of Mainland Chinese Readers

Traditionally, the spatial–numerical association of response codes (SNARC) effect was explained by assuming that the processing of numbers automatically activates internal visuospatial codes. In contrast, Gevers et al. (2010) suggested that the SNARC effect can result from both visuospatial and verbal–spatial processing, with verbal–spatial being the dominant processing mechanism. The current study tested this assumption in two experiments with the SNARC effects obtained from the horizontal and the vertical directions. Consistent with the assumption of Gevers et al., the horizontal SNARC effect is dominantly driven by verbal–spatial coding in Arabic numerals and simplified and complex Chinese numbers. More specifically, in the horizontal direction, mainland Chinese participants more dominantly associate small numbers with the verbal–spatial “left” and large numbers with the verbal–spatial “right.” But inconsistent with key predictions of Gevers et al., a remarkable association was found between small numbers with the visuospatial “top” and large numbers with the visuospatial “bottom” in the vertical SNARC effect for numbers in Arabic numerals and simplified Chinese numbers and a dominant association between small numbers with the verbal–spatial coding “bottom” and large numbers with the verbal–spatial coding “top” for complex Chinese numbers, also in the vertical SNARC effect. These findings demonstrate that verbal–spatial coding of numbers is flexible, which is plausible because of the direction-dissociative and notation-specific nature of number–space mapping.