Deciphering Cortical Number Coding from Human Brain Activity Patterns

Origins of numbers: a shared language-of-thought for arithmetic and geometry?

Concepts of exact number are often thought to originate from counting and the successor function, or from a refinement of the approximate number system (ANS). We argue here for a third origin: a shared language-of-thought (LoT) for geometry and arithmetic that involves primitives of repetition, concatenation, and recursive embedding. Applied to sets, those primitives engender concepts of exact integers through recursive applications of additions and multiplications. Links between geometry and arithmetic also explain the emergence of higher-level notions (squares, primes, etc.). Under our hypothesis, understanding a number means having one or several mental expressions for it, and their minimal description length (MDL) determines how easily they can be mentally manipulated. Several historical, developmental, linguistic, and brain imaging phenomena provide preliminary support for our proposal.

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.

Hierarchical representations of relative numerical magnitudes in the human frontoparietal cortex

The ability to estimate numerical magnitude is essential for decision-making and is thought to underlie arithmetic skills. In humans, neural populations in the frontoparietal regions are tuned to represent numerosity. However, it remains unclear whether their response properties are fixed to a specific numerosity (i.e., absolute code) or dynamically scaled according to the range of numerosities relevant to the context (i.e., relative code). Here, using functional magnetic resonance imaging combined with multivariate pattern analysis, we uncover evidence that representations of relative numerosity coding emerge gradually as visual information processing advances in the frontoparietal regions. In contrast, the early sensory areas predominantly exhibit absolute coding. These findings indicate a hierarchical organization of relative numerosity representations that adapt their response properties according to the context. Our results highlight the existence of a context-dependent optimization mechanism in numerosity representation, enabling the efficient processing of infinite magnitude information with finite neural resources.

Anodal High-definition Transcranial Direct Current Stimulation Over the Left (but not Right) Parietal Cortex Facilitates Mental Arithmetic

Non-invasive brain stimulation (NIBS) techniques such as transcranial direct current stimulation (tDCS) allow for investigating the functional involvement of specific brain areas in mental arithmetic. In this study, we employed for the first time high-definition (HD)-tDCS, which offers enhanced spatial precision, to explore the functional roles of the left and right intraparietal sulcus (IPS) in mental arithmetic. A total of 25 participants underwent anodal left IPS, anodal right IPS, and sham stimulation in separate sessions in counterbalanced order while solving single- and multi-step addition and subtraction problems. We found that stimulation of the left IPS, but not the right IPS or sham stimulation, improved arithmetic performance speed. These results provide further evidence for the functional involvement of the left IPS in a broad range of arithmetic tasks and highlight the potential of NIBS for cognitive enhancement.

Supplementary Information

The online version contains supplementary material available at 10.1007/s41465-024-00314-0.

Single-neuron representation of nonsymbolic and symbolic number zero in the human medial temporal lobe

The number zero holds a special status among numbers, indispensable for developing a comprehensive number theory.1,2,3,4 Despite its importance in mathematics, the neuronal foundation of zero in the human brain is unknown. We conducted single-neuron recordings in neurosurgical patients5,6,7 while they made judgments involving nonsymbolic number representations (dot numerosity), including the empty set, and symbolic numbers (Arabic numerals), including numeral zero. Neurons showed responsiveness to either the empty set or numeral zero, but not both. Neuronal activity to zero in both nonsymbolic and symbolic formats exhibited a numerical distance effect, indicating that zero representations are integrated together with countable numerosities and positive integers at the low end of the number line.8,9 A boundary in neuronal coding existed between the nonsymbolic empty set and small numerosities, correlating with the relative difficulty in discriminating numerosity zero behaviorally. Conversely, no such boundary was found for symbolic zero activity, suggesting that symbolic representations integrate zero with other numerals along the number line, reconciling its outlier role. The status of zero as a special nonsymbolic numerical quantity is reflected in the activity of neurons in the human brain, which seems to serve as a scaffold for more advanced representations of zero as a symbolic number.

Symbolic and non-symbolic representations of numerical zero in the human brain

Representing the quantity zero as a symbolic concept is considered a unique achievement of abstract human thought.1,2 To conceptualize zero, one must abstract away from the (absence of) sensory evidence to construct a representation of numerical absence: creating "something" out of "nothing."2,3,4 Previous investigations of the neural representation of natural numbers reveal distinct numerosity-selective neural populations that overlap in their tuning curves with adjacent numerosities.5,6 Importantly, a component of this neural code is thought to be invariant across non-symbolic and symbolic numerical formats.7,8,9,10,11 Although behavioral evidence indicates that zero occupies a place at the beginning of this mental number line,12,13,14 in humans zero is also associated with unique behavioral and developmental profiles compared to natural numbers,4,15,16,17 suggestive of a distinct neural basis for zero. We characterized the neural representation of zero in the human brain by employing two qualitatively different numerical tasks18,19 in concert with magnetoencephalography (MEG) recordings. We assay both neural representations of non-symbolic numerosities (dot patterns), including zero (empty sets), and symbolic numerals, including symbolic zero. Our results reveal that neural representations of zero are situated along a graded neural number line shared with other natural numbers. Notably, symbolic representations of zero generalized to predict non-symbolic empty sets. We go on to localize abstract representations of numerical zero to posterior association cortex, extending the purview of parietal cortex in human numerical cognition to encompass representations of zero.10,20.

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.

Magnitude shifts spatial attention from left to right in rhesus monkeys as in the human mental number line

Humans typically represent numbers and quantities along a left-to-right continuum. Early perspectives attributed number-space association to culture; however, recent evidence in newborns and animals challenges this hypothesis. We investigate whether the length of an array of dots influences spatial bias in rhesus macaques. We designed a touch-screen task that required monkeys to remember the location of a target. At test, monkeys maintained high performance with arrays of 2, 4, 6, or 10 dots, regardless of changes in the array's location, spacing, and length. Monkeys remembered better left targets with 2-dot arrays and right targets with 6- or 10-dot arrays. Replacing the 10-dot array with a long bar, yielded more accurate performance with rightward locations, consistent with an underlying left-to-right oriented magnitude code. Our study supports the hypothesis of a spatially oriented mental magnitude line common to humans and animals, countering the idea that this code arises from uniquely human cultural learning.

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging

Much of human culture's advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.

Brain-imaging evidence for compression of binary sound sequences in human memory

According to the language-of-thought hypothesis, regular sequences are compressed in human memory using recursive loops akin to a mental program that predicts future items. We tested this theory by probing memory for 16-item sequences made of two sounds. We recorded brain activity with functional MRI and magneto-encephalography (MEG) while participants listened to a hierarchy of sequences of variable complexity, whose minimal description required transition probabilities, chunking, or nested structures. Occasional deviant sounds probed the participants' knowledge of the sequence. We predicted that task difficulty and brain activity would be proportional to the complexity derived from the minimal description length in our formal language. Furthermore, activity should increase with complexity for learned sequences, and decrease with complexity for deviants. These predictions were upheld in both fMRI and MEG, indicating that sequence predictions are highly dependent on sequence structure and become weaker and delayed as complexity increases. The proposed language recruited bilateral superior temporal, precentral, anterior intraparietal, and cerebellar cortices. These regions overlapped extensively with a localizer for mathematical calculation, and much less with spoken or written language processing. We propose that these areas collectively encode regular sequences as repetitions with variations and their recursive composition into nested structures.

Structural brain changes in emotion recognition across the adult lifespan

Emotion recognition (ER) declines with increasing age, yet little is known whether this observation is based on structural brain changes conveyed by differential atrophy. To investigate whether age-related ER decline correlates with reduced grey matter (GM) volume in emotion-related brain regions, we conducted a voxel-based morphometry analysis using data of the Human Connectome Project-Aging (N = 238, aged 36-87) in which facial ER was tested. We expected to find brain regions that show an additive or super-additive age-related change in GM volume indicating atrophic processes that reduce ER in older adults. The data did not support our hypotheses after correction for multiple comparisons. Exploratory analyses with a threshold of P < 0.001 (uncorrected), however, suggested that relationships between GM volume and age-related general ER may be widely distributed across the cortex. Yet, small effect sizes imply that only a small fraction of the decline of ER in older adults can be attributed to local GM volume changes in single voxels or their multivariate patterns.

Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain

One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.

Frequency of adapting events affects face aftereffects but not blur aftereffects

The dynamics of visual adaptation remain poorly understood. Recent studies have found that the strength of adaptation aftereffects in the perception of numerosity depends more strongly on the number of adaptation events than on the duration of the adaptation. We investigated whether such effects can be observed for other visual attributes. We measured blur (perceived focus-sharp vs blurred adapt) and face (perceived race- Asian vs. White adapt) aftereffects by varying the number of adaptation events (4 or 16) and the duration of each adaptation event (0.25 s or 1 s). We found evidence for an effect of event number on face but not on blur adaptation, though the effect for faces was significant for only one of the two face adapt conditions (Asian). Our results suggest that different perceptual dimensions may vary in how adaptation effects accrue, potentially because of differences in factors such as the sites (early or late) of the sensitivity changes or nature of the stimulus. These differences may impact how and how rapidly the visual system can adjust to different visual properties.

The neural correlates of individual differences in numerosity perception: A voxel-based morphometry study

Numerosity perception is a fundamental cognitive function in humans and animals. Using an individual difference approach with a comprehensive dataset (N = 249), we performed a voxel-based morphometry analysis to unravel the neuroanatomical substrates associated with individual differences in numerosity perception sensitivity, measured by a classical non-symbolic numerical judgment task. Results showed that greater gray matter volume (GMV) in the left cerebellum, right temporal pole, and right parahippocampal was positively correlated to higher perceptual sensitivity to numerosity. In contrast, the GMV in the left intraparietal sulcus, and bilateral precentral/postcentral gyrus was negatively correlated to the sensitivity of numerosity perception. These findings indicate that a wide range of brain structures, rather than a specific anatomical structure or circuit, forms the neuroanatomical basis of numerosity perception, lending support to the emerging network view of the neural representation of numerosity. This work contributes to a more comprehensive understanding of how the brain processes numerical information.

•Unveils neuroanatomical basis of numerosity perception •Discovers positive and negative greater GMV correlations •Links GMV in a wide range of brain regions to numerical sensitivity •Supports the network view of the neural representation of numerosity perception

Overlapping but separate number representations in the intraparietal sulcus-Probing format- and modality-independence in sighted Braille readers

The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.

Neural Basis of Social Influence of Observing Other's Perception in Dot-Number Estimation

Our perceptions and decisions are often implicitly influenced by observing another's actions. However, it is unclear how observing other people's perceptual decisions without interacting with them can engage the processing of self-other discrepancies and change the observer's decisions. In this study, we employed functional magnetic resonance imaging and a computational model to investigate the neural basis of how unilaterally observing the other's perceptual decisions modulated one's own decisions. The experimental task was to discriminate whether the number of presented dots was higher or lower than a reference number. The participants performed the task solely while unilaterally observing the performance of another "participant," who produced overestimations and underestimations in the same task in separate sessions. Results of the behavioral analysis showed that the participants' decisions were modulated to resemble those of the other. Image analysis based on computational model revealed that the activation in the medial prefrontal cortex was associated with the discrepancy between the inferred participant's and the presented other's decisions. In addition, the number-sensitive region in the superior parietal region showed altered activation patterns after observing the other's overestimations and underestimations. The activity of the superior parietal region was not involved in assessing the observation of other's perceptual decisions, but it was engaged in plain numerosity perception. These results suggest that computational modeling can capture the neuro-behavioral processing of self-other discrepancies in perception followed by the activity modulation in the number-sensitive region in the task of dot-number estimation.

Longitudinal relationship between number line estimation and other mathematical abilities in Chinese preschool children

Many cross-sectional studies have shown that number line estimation is associated with other mathematical skills, but there has been limited longitudinal research. To systematically examine such associations longitudinally at the earliest stage of mathematical learning, the current study tested 40 Chinese preschoolers (mean age = 4.97 years, SD = 0.18) and followed them up 8 months later. For both waves of data collection, children were administered six tasks: number line estimation, dot counting, comparison of two dot arrays, comparison of triple dot arrays, symbolic number comparison, and simple addition. Results of two-wave cross-lagged panel analysis showed that (a) dot counting and non-symbolic numerical comparison at Time 1 had significant longitudinal associations with number line estimation at Time 2, (b) number line estimation had bidirectional associations with symbolic number comparison, and (c) number line estimation at Time 1 had a marginally significant longitudinal association with simple addition at Time 2. These results extend the small but accumulating literature on the longitudinal relations between number line estimation and other mathematical skills and specify the important role of number line estimation in the early development of mathematical skills.

Omit needless words: Sentence length perception

Short sentences improve readability. Short sentences also promote social justice through accessibility and inclusiveness. Despite this, much remains unknown about sentence length perception-an important factor in producing readable writing. Accordingly, we conducted a psychophysical study using procedures from Signal Detection Theory to examine sentence length perception in naive adults. Participants viewed real-world full-page text samples and judged whether a bolded target sentence contained more or fewer than 17 words. The experiment yielded four findings. First, naïve adults perceived sentence length in real-world text samples quickly (median = 300-400 ms) and precisely (median = ~90% correct). Second, flipping real-world text samples upside-down generated no reaction-time cost and nearly no loss in the precision of sentence length perception. This differs from the large inversion effects that characterize other highly practiced, real-world perceptual tasks involving canonically oriented stimuli, most notably face perception and reading. Third, participants significantly underestimated the length of mirror-reversed sentences-but not upside-down, nor standard sentences. This finding parallels participants' familiarity with commonly occurring left-justified right-ragged text, and suggests a novel demonstration of left-lateralized anchoring in scene syntax. Fourth, error patterns demonstrated that participants achieved their high speed, high precision sentence-length judgments by heuristically counting text lines, not by explicitly counting words. This suggests practical advice for writing instructors to offer students. When copy editing, students can quickly and precisely identify their long sentences via a line-counting heuristic, e.g., "a 17-word sentence spans about 1.5 text lines". Students can subsequently improve a long sentence's readability and inclusiveness by omitting needless words.

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.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

A shared numerical magnitude representation evidenced by the distance effect in frequency-tagging EEG

Humans can effortlessly abstract numerical information from various codes and contexts. However, whether the access to the underlying magnitude information relies on common or distinct brain representations remains highly debated. Here, we recorded electrophysiological responses to periodic variation of numerosity (every five items) occurring in rapid streams of numbers presented at 6 Hz in randomly varying codes—Arabic digits, number words, canonical dot patterns and finger configurations. Results demonstrated that numerical information was abstracted and generalized over the different representation codes by revealing clear discrimination responses (at 1.2 Hz) of the deviant numerosity from the base numerosity, recorded over parieto-occipital electrodes. Crucially, and supporting the claim that discrimination responses reflected magnitude processing, the presentation of a deviant numerosity distant from the base (e.g., base “2” and deviant “8”) elicited larger right-hemispheric responses than the presentation of a close deviant numerosity (e.g., base “2” and deviant “3”). This finding nicely represents the neural signature of the distance effect, an interpretation further reinforced by the clear correlation with individuals’ behavioral performance in an independent numerical comparison task. Our results therefore provide for the first time unambiguously a reliable and specific neural marker of a magnitude representation that is shared among several numerical codes.

Intracranial recordings show evidence of numerosity tuning in human parietal cortex

Numerosity is the set size of a group of items. Numerosity perception is a trait shared across numerous species. Numerosity-selective neural populations are thought to underlie numerosity perception. These neurons have been identified primarily using electrical recordings in animal models and blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) in humans. Here we use electrical intracranial recordings to investigate numerosity tuning in humans, focusing on high-frequency transient activations. These recordings combine a high spatial and temporal resolution and can bridge the gap between animal models and human recordings. In line with previous studies, we find numerosity-tuned responses at parietal sites in two out of three participants. Neuronal populations at these locations did not respond to other visual stimuli, i.e. faces, houses, and letters, in contrast to several occipital sites. Our findings further corroborate the specificity of numerosity tuning of in parietal cortex, and further link fMRI results and electrophysiological recordings.

Attention drives human numerosity-selective responses

Numerosity, the set size of a group of items, helps guide behavior and decisions. Previous studies have shown that neural populations respond selectively to numerosities. How numerosity is extracted from the visual scene is a longstanding debate, often contrasting low-level visual with high-level cognitive processes. Here, we investigate how attention influences numerosity-selective responses. The stimuli consisted of black and white dots within the same display. Participants' attention was focused on either black or white dots, while we systematically changed the numerosity of black, white, and total dots. Using 7 T fMRI, we show that the numerosity-tuned neural populations respond only when attention is focused on their preferred numerosity, irrespective of the unattended or total numerosities. Without attention, responses to preferred numerosity are suppressed. Unlike traditional effects of attention in the visual cortex, where attention enhances already existing responses, these results suggest that attention is required to drive numerosity-selective responses.

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

Electrophysiological Signatures of Numerosity Encoding in a Delayed Match-to-Sample Task

The number of elements in a small set of items is appraised in a fast and exact manner, a phenomenon called subitizing. In contrast, humans provide imprecise responses when comparing larger numerosities, with decreasing precision as the number of elements increases. Estimation is thought to rely on a dedicated system for the approximate representation of numerosity. While previous behavioral and neuroimaging studies associate subitizing to a domain-general system related to object tracking and identification, the nature of small numerosity processing is still debated. We investigated the neural processing of numerosity across subitizing and estimation ranges by examining electrophysiological activity during the memory retention period in a delayed numerical match-to-sample task. We also assessed potential differences in the neural signature of numerical magnitude in a fully non-symbolic or cross-format comparison. In line with behavioral performance, we observed modulation of parietal-occipital neural activity as a function of numerosity that differed in two ranges, with distinctive neural signatures of small numerosities showing clear similarities with those observed in visuospatial working memory tasks. We also found differences in neural activity related to numerical information in anticipation of single vs. cross-format comparison, suggesting a top-down modulation of numerical processing. Finally, behavioral results revealed enhanced performance in the mixed-format conditions and a significant correlation between task performance and symbolic mathematical skills. Overall, we provide evidence for distinct mechanisms related to small and large numerosity and differences in numerical encoding based on task demands.

The role of neural tuning in quantity perception

Perception of quantities, such as numerosity, timing, and size, is essential for behavior and cognition. Accumulating evidence demonstrates neurons processing quantities are tuned, that is, have a preferred quantity amount, not only for numerosity, but also other quantity dimensions and sensory modalities. We argue that quantity-tuned neurons are fundamental to understanding quantity perception. We illustrate how the properties of quantity-tuned neurons can underlie a range of perceptual phenomena. Furthermore, quantity-tuned neurons are organized in distinct but overlapping topographic maps. We suggest that this overlap in tuning provides the neural basis for perceptual interactions between different quantities, without the need for a common neural representational code.

Laminar processing of numerosity supports a canonical cortical microcircuit in human parietal cortex

As neural signals travel through the visual hierarchy, spatial precision decreases and specificity for stimulus features increases.^1-4 A similar hierarchy has been found for laminar processing in V1, where information from the thalamus predominantly targets the central layers, while spatial precision decreases and feature specificity increases toward superficial and deeper layers.^5-17 This laminar processing scheme is proposed to represent a canonical cortical microcircuit that is similar across the cortex.^11,18-21 Here, we go beyond early visual cortex and investigate whether processing of numerosity (the set size of a group of items) across cortical depth in the parietal association cortex follows this hypothesis. Numerosity processing is implicated in many tasks such as multiple object tracking,²² mathematics,^23-25 decision making,²⁶ and dividing attention.²⁷ Neurons in the parietal association cortex are tuned to numerosity, with both a preferred numerosity tuning and tuning width (i.e., specificity).^28-30 We quantified preferred numerosity responses across cortical depth in the parietal association cortex with ultra-high field fMRI and population receptive field-based numerosity modeling.^1,28,31 We find that numerosity responses sharpen, i.e., become increasingly specific, moving away from the central layers. This suggests that the laminar processing scheme for numerosity processing in the parietal cortex is similar to primary visual cortex, providing support for the canonical cortical microcircuit hypothesis beyond primary visual cortex.

Suggested visual blockade during hypnosis: Top-down modulation of stimulus processing in a visual oddball task

Several theories of hypnosis assume that responses to hypnotic suggestions are implemented through top-down modulations via a frontoparietal network that is involved in monitoring and cognitive control. The current study addressed this issue re-analyzing previously published event-related-potentials (ERP) (N1, P2, and P3b amplitudes) and combined it with source reconstruction and connectivity analysis methods. ERP data were obtained from participants engaged in a visual oddball paradigm composed of target, standard, and distractor stimuli during a hypnosis (HYP) and a control (CON) condition. In both conditions, participants were asked to count the rare targets presented on a video screen. During HYP participants received suggestions that a wooden board in front of their eyes would obstruct their view of the screen. The results showed that participants’ counting accuracy was significantly impaired during HYP compared to CON. ERP components in the N1 and P2 window revealed no amplitude differences between CON and HYP at sensor-level. In contrast, P3b amplitudes in response to target stimuli were significantly reduced during HYP compared to CON. Source analysis of the P3b amplitudes in response to targets indicated that HYP was associated with reduced source activities in occipital and parietal brain areas related to stimulus categorization and attention. We further explored how these brain sources interacted by computing time-frequency effective connectivity between electrodes that best represented frontal, parietal, and occipital sources. This analysis revealed reduced directed information flow from parietal attentional to frontal executive sources during processing of target stimuli. These results provide preliminary evidence that hypnotic suggestions of a visual blockade are associated with a disruption of the coupling within the frontoparietal network implicated in top-down control.

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.

Population Models, Not Analyses, of Human Neuroscience Measurements

Selectivity for many basic properties of visual stimuli, such as orientation, is thought to be organized at the scale of cortical columns, making it difficult or impossible to measure directly with noninvasive human neuroscience measurement. However, computational analyses of neuroimaging data have shown that selectivity for orientation can be recovered by considering the pattern of response across a region of cortex. This suggests that computational analyses can reveal representation encoded at a finer spatial scale than is implied by the spatial resolution limits of measurement techniques. This potentially opens up the possibility to study a much wider range of neural phenomena that are otherwise inaccessible through noninvasive measurement. However, as we review in this article, a large body of evidence suggests an alternative hypothesis to this superresolution account: that orientation information is available at the spatial scale of cortical maps and thus easily measurable at the spatial resolution of standard techniques. In fact, a population model shows that this orientation information need not even come from single-unit selectivity for orientation tuning, but instead can result from population selectivity for spatial frequency. Thus, a categorical error of interpretation can result whereby orientation selectivity can be confused with spatial frequency selectivity. This is similarly problematic for the interpretation of results from numerous studies of more complex representations and cognitive functions that have built upon the computational techniques used to reveal stimulus orientation. We suggest in this review that these interpretational ambiguities can be avoided by treating computational analyses as models of the neural processes that give rise to measurement. Building upon the modeling tradition in vision science using considerations of whether population models meet a set of core criteria is important for creating the foundation for a cumulative and replicable approach to making valid inferences from human neuroscience measurements. Expected final online publication date for the Annual Review of Vision Science, Volume 7 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Decoding location-specific and location-invariant stages of numerosity processing in subitizing

Extracting the number of objects in perceived scenes is a fundamental cognitive ability. Number processing is proposed to rely on two consecutive stages: an early object location map that captures individuated objects in a location‐specific way and a subsequent location‐invariant representation that captures numerosity at an abstract level. However, it is unclear whether this framework applies to small numerosities that can be individuated at once (“subitized”). Here, we reanalyzed data from two electroencephalography (EEG) experiments using multivariate pattern decoding to identify location‐specific and location‐invariant stages of numerosity processing in the subitizing range. In these experiments, one to three targets were presented in the left or right hemifield, which allowed for decoding target numerosity within each hemifield separately (location specific) or across hemifields (location invariant). Experiment 1 indicated the presence of a location‐specific stage (180–200 ms after stimulus), followed by a location‐invariant stage (300 ms after stimulus). A time‐by‐channel searchlight analysis revealed that the early location‐specific stage is most evident at occipital channels, whereas the late location‐invariant stage is most evident at parietal channels. Experiment 2 showed that both location‐specific and location‐invariant components are engaged only during tasks that explicitly require numerosity processing, ruling out automatic, and passive recording of numerosity. These results suggest that numerosity coding in subitizing is strongly grounded on an attention‐based, location‐specific stage. This stage overlaps with the subsequent activation of a location‐invariant stage, where a full representation of numerosity is finalized. Taken together, our findings provide clear evidence for a temporal and spatial segregation of location‐specific and location‐invariant numerosity coding of small object numerosities.

Neural basis of approximate number in congenital blindness

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.

Automatic Processing of Numerosity in Human Neocortex Evidenced by Occipital and Parietal Neuromagnetic Responses

Humans and other animal species are endowed with the ability to sense, represent, and mentally manipulate the number of items in a set without needing to count them. One central hypothesis is that this ability relies on an automated functional system dedicated to numerosity, the perception of the discrete numerical magnitude of a set of items. This system has classically been associated with intraparietal regions, however accumulating evidence in favor of an early visual number sense calls into question the functional role of parietal regions in numerosity processing. Targeting specifically numerosity among other visual features in the earliest stages of processing requires high temporal and spatial resolution. We used frequency-tagged magnetoencephalography to investigate the early automatic processing of numerical magnitudes and measured the steady-state brain responses specifically evoked by numerical and other visual changes in the visual scene. The neuromagnetic responses showed implicit discrimination of numerosity, total occupied area, and convex hull. The source reconstruction corresponding to the implicit discrimination responses showed common and separate sources along the ventral and dorsal visual pathways. Occipital sources attested the perceptual salience of numerosity similarly to both other implicitly discriminable visual features. Crucially, we found parietal responses uniquely associated with numerosity discrimination, showing automatic processing of numerosity in the parietal cortex, even when not relevant to the task. Taken together, these results provide further insights into the functional roles of parietal and occipital regions in numerosity encoding along the visual hierarchy.

The future of neuromodulation: smart neuromodulation

Introduction: The International Neuromodulation Society defines neuromodulation as the alteration of nerve activity through targeted delivery of a stimulus, such as electrical stimulation or chemical agents, to specific neurological sites in the body.Areas covered: In the near future (<5 years) increasingly complex implantable neuromodulation systems will enter the market. These devices are capable of closed-loop stimulation and the delivery of novel stimulation designs, pushing the need for upgradability. But what about the near-to-far future, meaning 5-10 years from now?Expert opinion: We propose that neuromodulation in the near to far future (5-10 years) will involve integration of adaptive network neuromodulation with predictive artificial intelligence, automatically adjusted by brain and external sensors, and controlled via cloud-based applications. The components will be introduced in a phased approach, culminating in a fully autonomous brain-stimulator-cloud interface. This may, in the long future (>10 years), lead to the brain of the future, a brain with integrated artificial intelligence.

Symbolic categorization of novel multisensory stimuli in the human brain

When primates (both human and non-human) learn to categorize simple visual or acoustic stimuli by means of non-verbal matching tasks, two types of changes occur in their brain: early sensory cortices increase the precision with which they encode sensory information, and parietal and lateral prefrontal cortices develop a categorical response to the stimuli. Contrary to non-human animals, however, our species mostly constructs categories using linguistic labels. Moreover, we naturally tend to define categories by means of multiple sensory features of the stimuli. Here we trained adult subjects to parse a novel audiovisual stimulus space into 4 orthogonal categories, by associating each category to a specific symbol. We then used multi-voxel pattern analysis (MVPA) to show that during a cross-format category repetition detection task three neural representational changes were detectable. First, visual and acoustic cortices increased both precision and selectivity to their preferred sensory feature, displaying increased sensory segregation. Second, a frontoparietal network developed a multisensory object-specific response. Third, the right hippocampus and, at least to some extent, the left angular gyrus, developed a shared representational code common to symbols and objects. In particular, the right hippocampus displayed the highest level of abstraction and generalization from a format to the other, and also predicted symbolic categorization performance outside the scanner. Taken together, these results indicate that when humans categorize multisensory objects by means of language the set of changes occurring in the brain only partially overlaps with that described by classical models of non-verbal unisensory categorization in primates.

Space, time and number: common coding mechanisms and interactions between domains

Space, time and number are key dimensions that underlie how we perceive, identify and act within the environment. They are interconnected in our behaviour and brain. In this study, we examined interdependencies between these dimensions. To this end, left- and right-handed participants performed an object collision task that required space–time processing and arithmetic tests that involved number processing. Handedness of the participants influenced collision detection with left-handers being more accurate than right-handers, which is in line with the premise that hand preference guides individual differences as a result of sensorimotor experiences and distinct interhemispheric integration patterns. The data further showed that successful collision detection was a predictor for arithmetic achievement, at least in right-handers. These findings suggest that handedness plays a mediating role in binding information processing across domains, likely due to selective connectivity properties within the sensorimotor system that is guided by hemispheric lateralisation patterns.

Representation of visual numerosity information during working memory in humans: An fMRI decoding study

Both animal and human studies on numerosity have shown the importance of the parietal cortex for numerosity processing. However, most studies have focused on the perceptual processing of numerosity. Still, it is unclear how and where numerosity information is coded when this information is retained during a working memory delay phase. Such temporal storage could be realized by the same structures as perceptual processes, or be transformed to a more abstract representation, potentially involving prefrontal regions. FMRI decoding studies allow the identification of brain areas that exhibit multi‐voxel activation patterns specific to the content of working memory. Here, we used an assumption‐free searchlight‐decoding approach to test where numerosity‐specific codes can be found during a 12 s retention period. Participants (n = 24) performed a retro‐cue delayed match‐to‐sample task, in which numerosity information was presented as visual dot arrays. We found mnemonic numerosity‐specific activation in the right lateral portion of the intraparietal sulcus; an area well‐known for perceptual processing of numerosity. The applied retro‐cue design dissociated working memory delay activity from perceptual processes and showed that the intraparietal sulcus also maintained working memory representation independent of perception.

Computer code comprehension shares neural resources with formal logical inference in the fronto-parietal network

Despite the importance of programming to modern society, the cognitive and neural bases of code comprehension are largely unknown. Programming languages might 'recycle' neurocognitive mechanisms originally developed for natural languages. Alternatively, comprehension of code could depend on fronto-parietal networks shared with other culturally-invented symbol systems, such as formal logic and symbolic math such as algebra. Expert programmers (average 11 years of programming experience) performed code comprehension and memory control tasks while undergoing fMRI. The same participants also performed formal logic, symbolic math, executive control, and language localizer tasks. A left-lateralized fronto-parietal network was recruited for code comprehension. Patterns of activity within this network distinguish between 'for' loops and 'if' conditional code functions. In terms of the underlying neural basis, code comprehension overlapped extensively with formal logic and to a lesser degree math. Overlap with executive processes and language was low, but laterality of language and code covaried across individuals. Cultural symbol systems, including code, depend on a distinctive fronto-parietal cortical network.

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).

Functional magnetic resonance imaging multivoxel pattern analysis reveals neuronal substrates for collaboration and competition with myopic and predictive strategic reasoning

Competition and collaboration are strategies that can be used to optimize the outcomes of social interactions. Research into the neuronal substrates underlying these aspects of social behavior has been limited due to the difficulty in distinguishing complex activation via univariate analysis. Therefore, we employed multivoxel pattern analysis of functional magnetic resonance imaging to reveal the neuronal activations underlying competitive and collaborative processes when the collaborator/opponent used myopic/predictive reasoning. Twenty‐four healthy subjects participated in 2 × 2 matrix‐based sequential‐move games. Searchlight‐based multivoxel patterns were used as input for a support vector machine using nested cross‐validation to distinguish game conditions, and identified voxels were validated via the regression of the behavioral data with bootstrapping. The left anterior insula (accuracy = 78.5%) was associated with competition, and middle frontal gyrus (75.1%) was associated with predictive reasoning. The inferior/superior parietal lobules (84.8%) and middle frontal gyrus (84.7%) were associated with competition, particularly in trials with a predictive opponent. The visual/motor areas were related to response time as a proxy for visual attention and task difficulty. Our results suggest that multivoxel patterns better represent the neuronal substrates underlying the social cognition of collaboration and competition intermixed with myopic and predictive reasoning than do univariate features.

A parietal region processing numerosity of observed actions: An FMRI study

When observing others' behavior, it is important to perceive not only the identity of the observed actions (OAs), but also the number of times they were performed. Given the mounting evidence implicating posterior parietal cortex in action observation, and in particular that of manipulative actions, the aim of this study was to identify the parietal region, if any, that contributes to the processing of observed manipulative action (OMA) numerosity, using the functional magnetic resonance imaging technique. Twenty‐one right‐handed healthy volunteers performed two discrimination tasks while in the scanner, responding to video stimuli in which an actor performed manipulative actions on colored target balls that appeared four times consecutively. The subjects discriminated between two small numerosities of either OMAs (“Action” condition) or colors of balls (“Ball” condition). A significant difference between the “Action” and “Ball” conditions was observed in occipito‐temporal cortex and the putative human anterior intraparietal sulcus (phAIP) area as well as the third topographic map of numerosity‐selective neurons at the post‐central sulcus (NPC3) of the left parietal cortex. A further region of interest analysis of the group‐average data showed that at the single voxel level the latter area, more than any other parietal or occipito‐temporal numerosity map, favored numerosity of OAs. These results suggest that phAIP processes the identity of OMAs, while neighboring NPC3 likely processes the numerosity of the identified OAs.

Shared Numerosity Representations Across Formats and Tasks Revealed with 7 Tesla fMRI: Decoding, Generalization, and Individual Differences in Behavior

Debate continues on whether encoding of symbolic number is grounded in nonsymbolic numerical magnitudes. Nevertheless, fluency of perceiving both number formats, and translating between them, predicts math skills across the life span. Therefore, this study asked if numbers share cortical activation patterns across formats and tasks, and whether neural response to number predicts math-related behaviors. We analyzed patterns of neural activation using 7 Tesla functional magnetic resonance imaging in a sample of 39 healthy adults. Discrimination was successful between numerosities 2, 4, 6, and 8 dots and generalized to activation patterns of the same numerosities represented as Arabic digits in the bilateral parietal lobes and left inferior frontal gyrus (IFG) (and vice versa). This indicates that numerosity-specific neural resources are shared between formats. Generalization was also successful across tasks where participants either identified or compared numerosities in bilateral parietal lobes and IFG. Individual differences in decoding did not relate to performance on a number comparison task completed outside of the scanner, but generalization between formats and across tasks negatively related to math achievement in the parietal lobes. Together, these findings suggest that individual differences in representational specificity within format and task contexts relate to mathematical expertise.

Are differences between social classes reduced by non-symbolic numerical tasks? Evidence from the ELFE cohort

BACKGROUND

Young children's mathematics abilities may be divided between symbolic and non-symbolic skills. Lower performance of SES disadvantaged versus advantaged children has already been established in symbolic math.

AIM

This study aimed to verify the effect of children's SES category on non-symbolic mathematical (numerical) performance.

SAMPLE

The main sample comprises 4,955 children from the French longitudinal study, ELFE, tested when they were in the nursery school (4- to 5-year-olds).

METHOD

The distinction between symbolic and non-symbolic math skills based on the specific math assessment items used in the present study was verified on a larger sample. The SES-related difference in non-symbolic math skills was then examined in the ELFE sample only.

RESULTS

The children's performance in non-symbolic maths is significantly and almost as strongly correlated with their family's income and their mother's level of education as their performances in symbolic maths. Linear regression mixed-effects modelling shows that the score in non-symbolic maths (out of 100) of children from families with below median income is 3.8 points lower than that of their peers from families with above median income.

CONCLUSION

Children from disadvantaged SES backgrounds perform significantly lower than those from advantaged backgrounds in non-symbolic maths. Even if non-symbolic math skills retain an educational interest, they should not reduce the importance of symbolic math skills in young children.

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

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

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.