Damage to the Intraparietal Sulcus Impairs Magnitude Representations of Results of Complex Arithmetic Problems

The role of the intraparietal sulcus in numeracy: A review of parietal lesion cases

Prominent theories of numeracy link the intraparietal sulcus (IPS) to approximate representations of quantity that undergird basic math abilities. The goal of this review is to better understand the neural basis of mathematical cognition through the lens of acalculia, by identifying numeracy-focused single case studies of patients with parietal lesions and testing for causal relationships between numeracy impairments and the locus of parietal damage. A systematic literature review identified 27 single case studies with left parietal lesions and categorized administered tasks across four numeracy domains: Approximation, Calculation, Ordinality/Cardinality, and Transcoding. We compared published lesion images by drawing a sphere at the inferred center-of-mass and assigning each case to an anatomical group (IPS or Other Parietal damage) based on overlap with left IPS and original anatomical description. We performed Fisher's Exact Test to compare behavioral performance on each numeracy domain between the two groups. As an exploratory follow-up, we used Activation Likelihood Estimation (ALE) to identify sites of damage within parietal cortex preferentially associated with impairments in each domain. We found that Approximation impairments were significantly more frequent in the IPS group (p = .003). The exploratory ALE analysis revealed that only Approximation impairment cases significantly overlapped with the IPS, while impairments in other domains were localized to different regions of the parietal lobe. Based on the pattern of impairments shown across these cases, we conclude that damage to the left IPS is linked to impairments in approximation ability specifically. Our findings support theoretical claims linking IPS to magnitude representation, but do not provide evidence that IPS critically underpins performance across all numeracy tasks. Instead, our findings are more compatible with models of dissociable circuits of numerical processing within the parietal lobe.

Cognitive and Neural Differences in Exact and Approximate Arithmetic Using the Production Paradigm: An fNIRS Study

This study investigated the cognitive and neural mechanisms of exact and approximate arithmetic using fNIRS technology during natural calculation processes (i.e., the production paradigm). Behavioral results showed (1) a significantly longer reaction time for exact arithmetic compared to approximate arithmetic, and (2) both exact and approximate arithmetic exhibited a problem size effect, with larger operands requiring more time. The fNIRS results further revealed differences in the neural bases underlying these two arithmetic processes, with exact arithmetic showing greater activation in the L-SFG (left superior frontal gyrus, CH16), while approximate arithmetic exhibited problem size effect in the right hemisphere. Additionally, larger operands registered more brain activities in the R-DLPFC (right dorsolateral prefrontal cortex, CH4), R-SFG (right superior frontal gyrus, CH2), and PMC and SMA (pre- and supplementary motor cortexes, CH3) compared to smaller operands in approximate arithmetic. Moreover, correlation analysis found a significant correlation between approximate arithmetic and semantic processing in the R-PMC and R-SMA (right pre- and supplementary motor cortexes). These findings suggest a neural dissociation between exact and approximate arithmetic, with exact arithmetic processing showing a dominant role in the left hemisphere, while approximate arithmetic processing was more sensitive in the right hemisphere.

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.

The componential nature of arithmetical cognition: some important questions

Research on typically developing children and adults and people with developmental and acquired dyscalculia converges in indicating that arithmetical ability is not unitary but is made up of many different components. Categories of components include non-symbolic quantity representation and processing; symbolic quantity representation and processing; counting procedures and principles; arithmetic operations; arithmetical knowledge and understanding; multiple forms and applications of conceptual knowledge of arithmetic; and domain-general abilities such as attention, executive functions and working memory. There is much evidence that different components can and often do show considerable functional independence, not only in developmental and acquired dyscalculia, but in typically achieving children and adults. At the same time, it is possible to find complex interactions and bidirectional relationships between the different components, including between domain-specific and apparently domain-general abilities. There is a great deal that still needs to be discovered. In particular, we need to learn more about the origins in infancy of subitizing and approximate magnitude comparison, the extent to which these interact, the extent to which they may be further divisible, and the extent and ways in which they themselves may develop with age and the extent to which they may influence later-developing components. There also needs to be a lot more research on exactly how domain-general and domain-specific abilities contribute to mathematical development, and how they interact with one another.

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

Neural Correlates of Numerical Estimation: The Role of Strategy Use

Introduction: Computation estimation is the ability to provide an approximate answer to a complex arithmetic problem without calculating it exactly. Despite its importance in daily life, the neuronal network underlying computation estimation is largely unknown. Methods: We looked at the neuronal correlates of two computational estimation strategies: approximated calculation and sense of magnitude (SOM)–intuitive representation of magnitude, without calculation. During an fMRI scan, thirty-one college students judged whether the result of a two-digit multiplication problem was larger or smaller than a given reference number. In two different blocks, they were asked to use a specific strategy (AC or SOM). Results: The two strategies activated brain regions related to calculation, numerical cognition, decision-making, and working memory. AC more than SOM elicited activations in multiple, domain-specific brain regions in the parietal lobule, including the left SMG (BA 40), the bilateral superior parietal lobule (BA 7), and the right inferior parietal lobule (BA 7). The activation level of the IFG was positively correlated to individual accuracy, indicating that the IFG has an essential role in both strategies. Conclusions: These finding suggest that the analogic code of magnitude is more involved in the AC than the SOM strategy.

The relationship between mental rotation and arithmetic: do number line estimation, working memory, or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.