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In this article, we present the results of an 11-month longitudinal study (beginning when children were 6 years old) focusing on measures of the approximate number sense (ANS) and knowledge of the Arabic numeral system as possible influences on the development of arithmetic skills. Multiple measures of symbolic and nonsymbolic magnitude judgment were shown to define a unitary factor that appears to index the efficiency of an ANS system, which is a strong longitudinal correlate of arithmetic skills. However, path models revealed that knowledge of Arabic numerals at 6 years was a powerful longitudinal predictor of the growth in arithmetic skills, whereas variations in magnitude-comparison ability played no additional role in predicting variations in arithmetic skills. These results suggest that verbal processes concerned with learning the labels for Arabic numerals, and the ability to translate between Arabic numerals and verbal codes, place critical constraints on arithmetic development.

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were presented either in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format.

Continuous dimensions, such as time, space, and numerosity, have been suggested to be subserved by common neurocognitive mechanisms. Neuroimaging studies that have investigated either one or two dimensions simultaneously have consistently identified neural correlates in the parietal cortex of the brain. However, studies investigating the degree of neural overlap across several dimensions are inconclusive, and it remains an open question whether a potential overlap can be conceptualized as a neurocognitive magnitude processing system. The current functional magnetic resonance imaging study investigated the potential neurocognitive overlap across three dimensions. A sample of adults ( = 24) performed three different magnitude processing tasks: a temporal discrimination task, a number discrimination task, and a line length discrimination task. A conjunction analysis revealed several overlapping neural substrates across multiple magnitude dimensions, and we argue that these cortical nodes comprise a distributed magnitude processing system. Key components of this predominantly right-lateralized system include the intraparietal sulcus, insula, premotor cortex/SMA, and inferior frontal gyrus. Together with previous research highlighting intraparietal sulcus, our results suggest that the insula also is a core component of the magnitude processing system. We discuss the functional role of each of these components in the magnitude processing system and suggest that further research of this system may provide insight into the etiology of neurodevelopmental disorders where cognitive deficits in magnitude processing are manifest.

•The human IPS is recruited for diverse types of numerical processing.•We used high-resolution 7T fMRI to test for functional heterogeneity of its subparts.•Medial IPS subparts preferentially respond to non-symbolic sets of items vs digits.•Operating on numbers (comparison and calculation) recruits lateral IPS subparts.•The latter activations are likely distinct from the human equivalent of VIP. Human functional imaging has identified the middle part of the intraparietal sulcus (IPS) as an important brain substrate for different types of numerical tasks. This area is often equated with the macaque ventral intraparietal area (VIP) where neuronal selectivity for non-symbolic numerical stimuli (sets of items) is found. However, the low spatial resolution and whole-brain averaging analysis performed in most fMRI studies limit the extent to which an exact correspondence of activations in different numerical tasks with specific sub-regions of the IPS can be established. Here we acquired high-resolution 7T fMRI data in a group of human adults and related the activations in several numerical contrasts (implying different numerical stimuli and tasks) to anatomical and functional landmarks on the cortical surface. Our results reveal a functional heterogeneity within human intraparietal cortex where the retinotopic visual field maps in superior/medial parts of the IPS and superior parietal gyrus respond preferentially to the visual processing of concrete sets of items (over single Arabic numerals), whereas lateral/inferior parts of the IPS are predominantly recruited during numerical operations such as calculation and quantitative comparison. Since calculation and comparison-related activity fell mainly outside the retinotopic visual field maps considered the human functional equivalent of the monkey VIP/LIP complex, the areas most activated during such numerical operations in humans are likely different from VIP.

•Cognitive control in two-digit number processing is primarily associated with the inferior frontal gyrus (IFG).•Functional near-infrared spectroscopy (fNIRS) reveals that cognitive control operates as a domain-general process in the frontal cortex.•Behavioral and neuroimaging evidence support the decomposed representation of multi-digit numbers.•The study contributes to understanding the neural mechanisms underlying cognitive control in numerical tasks. Cognitive control plays an indispensable role in multi-digit number processing. The place-value structure of multi-digit numbers is apparent when comparing numbers. If the comparison of units yields a different result from the comparison of decades, the process takes longer than comparing compatible number pairs. Behavioral and eye-tracking studies have shown that this unit-decade compatibility effect was larger under high as compared to low cognitive control demands. However, the question arises whether cognitive control operates mainly as a domain-general effect in the frontal cortex, or if it directly affects domain-specific number magnitude processes in the parietal cortex. In the current fNIRS study, cognitive control demands were manipulated by adjusting the proportion of within-decade fillers in two-digit number comparison tasks (N = 80). The compatibility effect was replicated, and the fNIRS results showed that cognitive control is associated with the inferior frontal gyrus in two-digit number comparison. Thus, cognitive control operates mainly in the frontal cortex and does not directly affect domain-specific number magnitude processes in the parietal cortex. Methodological and linguistic limitations are discussed. Overall, this neurocognitive evidence supports that domain-general cognitive processes are relevant for multi-digit number processing.

Humans and other animals base important decisions on estimates of number, and intraparietal cortex is thought to provide a crucial substrate of this ability. However, it remains debated whether an independent neuronal processing mechanism underlies this ‘number sense’, or whether number is instead judged indirectly on the basis of other quantitative features. We performed high-resolution 7 Tesla fMRI while adult human volunteers attended either to the numerosity or an orthogonal dimension (average item size) of visual dot arrays. Along the dorsal visual stream, numerosity explained a significant amount of variance in activation patterns, above and beyond non-numerical dimensions. Its representation was selectively amplified and progressively enhanced across the hierarchy when task relevant. Our results reveal a sensory extraction mechanism yielding information on numerosity separable from other dimensions already at early visual stages and suggest that later regions along the dorsal stream are most important for explicit manipulation of numerical quantity. Numbers and the ability to count and calculate are an essential part of human culture. They are part of everyday life, featuring in calendars, computers or the weekly shop, but also in some of humanity’s biggest achievements: without them the pyramids or space travel would not exist. A precursor of sophisticated mathematical skill could reside in a simpler mental ability: the capacity to assess numerical quantities at a glance. This ‘number sense’ appears in humans in early childhood and it is also present in other animals, but it is still poorly understood. Brain imaging techniques have identified the parts of the brain that are active when perceiving numbers or making calculations. As techniques have advanced, it has become possible to resolve fine differences in brain activity that occur when people switch their attention between different visual tasks. But how exactly does the human brain process visual information to make sense of numbers? One theory suggests that humans use visual cues, such as the size of a group of objects or how densely packed objects are, to estimate numbers. On the other hand, it is also possible that humans can sense number directly, without reference to other properties of the group being observed. Castaldi et al. presented twenty adult volunteers with groups of dots and asked them to focus either on the number of dots or on the size of the dots during a brain scan. This approach allowed the separation of brain signals specific to number from signals corresponding to other visual cues, such as size or density of the group. The experiment revealed that brain activity changed depending on the number of dots displayed. The signal related to number became stronger when people focused on the number of dots, while signals related to other properties of the group remained unchanged. Moreover, brain signals for number were observed at the very early stages of visual processing, in the parts of the brain that receive input from the eyes first. These results suggest that the human visual system perceives number directly, and not by processing information about the size or density of a group of objects. This finding provides insights into how human brains encode numbers, which could be important to understand disorders where number sense can be impaired leading to difficulties learning math and operating with numbers.

Numerical skills are essential in our everyday life, and impairments in the development of number processing and calculation have a negative impact on schooling and professional careers. Approximately 3 to 6 % of children are affected from specific disorders of numerical understanding (developmental dyscalculia (DD)). Impaired development of number processing skills in these children is characterized by problems in various aspects of numeracy as well as alterations of brain activation and brain structure. Moreover, DD is assumed to be a very heterogeneous disorder putting special challenges to define homogeneous diagnostic criteria. Finally, interdisciplinary perspectives from psychology, neuroscience and education can contribute to the design for interventions, and although results are still sparse, they are promising and have shown positive effects on behaviour as well as brain function. Conclusion: In the current review, we are going to give an overview about typical and atypical development of numerical abilities at the behavioural and neuronal level. Furthermore, current status and obstacles in the definition and diagnostics of DD are discussed, and finally, relevant points that should be considered to make an intervention as successful as possible are summarized. (Orig.).

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

Arabic digits (e.g., “6”) and number words (e.g., “六”, “six”, “ ”) are the two main formats in which numbers can be represented. Although phonology plays a crucial role in the semantic accessing of alphabetic words and Chinese characters, whether it is involved in the processing of different numerical notations, which have been shown to be dissociable from characters, is still unknown. Using a parity judgment task, two experiments were performed by manipulating the phonological relationship between a prime and a target. The primes were Tibetan or Chinese characters and the targets were presented either as number words (Experiment 1 ) or as Arabic digits (Experiment 2 ). The results revealed that phonology affected semantic access for both number words and Arabic digits. Additionally, semantic access for Tibetan number words was more susceptible to phonological information. The results for Arabic digits followed the same pattern for Tibetan primes. Further, language proficiency also affected the role of phonology in number processing. Participants with low language proficiency relied more on phonological encoding when processing the numbers. The results suggest that phonology is crucial for semantic access of different numerical notations.

Functional neuroimaging serves as a tool to better understand the cerebral correlates of atypical behaviors, such as learning difficulties. While significant advances have been made in characterizing the neural correlates of reading difficulties (developmental dyslexia), comparatively little is known about the neurobiological correlates of mathematical learning difficulties, such as developmental dyscalculia (DD). Furthermore, the available neuroimaging studies of DD are characterized by small sample sizes and variable inclusion criteria, which make it problematic to compare across studies. In addition, studies to date have focused on identifying single deficits in neuronal processing among children with DD (e.g., mental arithmetic), rather than probing differences in brain function across different processing domains that are known to be affected in children with DD. Here, we seek to address the limitations of prior investigations. Specifically, we used functional magnetic resonance imaging (fMRI) to probe brain differences between children with and without persistent DD; 68 children (8‐10 years old, 30 with DD) participated in an fMRI study designed to investigate group differences in the functional neuroanatomy associated with commonly reported behavioral deficits in children with DD: basic number processing, mental arithmetic and visuo‐spatial working memory (VSWM). Behavioral data revealed that children with DD were less accurate than their typically achieving (TA) peers for the basic number processing and arithmetic tasks. No behavioral differences were found for the tasks measuring VSWM. A pre‐registered, whole‐brain, voxelwise univariate analysis of the fMRI data from the entire sample of children (DD and TA) revealed areas commonly associated with the three tasks (basic number processing, mental arithmetic, and VSWM). However, the examination of differences in brain activation between children with and without DD revealed no consistent group differences in brain activation. In view of these null results, we ran exploratory, Bayesian analyses on the data to quantify the amount of evidence for no group differences. This analysis provides supporting evidence for no group differences across all three tasks. We present the largest fMRI study comparing children with and without persistent DD to date. We found no group differences in brain activation using univariate, frequentist analyses. Moreover, Bayesian analyses revealed evidence for the null hypothesis of no group differences. These findings contradict previous literature and reveal the need to investigate the neural basis of DD using multivariate and network‐based approaches to brain imaging. Bayesian achievement group contrasts for all three fMRI task contrasts.