Developmental specialization of the left intraparietal sulcus for symbolic ordinal processing

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.

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.

Are numerical abilities determined at early age? A brain morphology study in children and adolescents with and without developmental dyscalculia

The intraparietal sulcus (IPS) has been associated with numerical processing. A recent study reported that the IPS sulcal pattern was associated with arithmetic and symbolic number abilities in children and adults. In the present study, we evaluated the link between numerical abilities and the IPS sulcal pattern in children with Developmental Dyscalculia (DD) and typically developing children (TD), extending previous analyses considering other sulcal features and the postcentral sulcus (PoCS). First, we confirm the longitudinal sulcal pattern stability of the IPS and the PoCS. Second, we found a lower proportion of left sectioned IPS and a higher proportion of a double-horizontal IPS shape bilaterally in DD compared to TD. Third, our analyses revealed that arithmetic is the only aspect of numerical processing that is significantly related to the IPS sulcal pattern (sectioned vs not sectioned), and that this relationship is specific to the left hemisphere. And last, correlation analyses of age and arithmetic in children without a sectioned left IPS indicate that although they may have an inherent disadvantage in numerical abilities, these may improve with age. Thus, our results indicate that only the left IPS sulcal pattern is related to numerical abilities and that other factors co-determine numerical abilities.

Electrophysiological correlates of symbolic numerical order processing

Determining if a sequence of numbers is ordered or not is one of the fundamental aspects of numerical processing linked to concurrent and future arithmetic skills. While some studies have explored the neural underpinnings of order processing using functional magnetic resonance imaging, our understanding of electrophysiological correlates is comparatively limited. To address this gap, we used a three-item symbolic numerical order verification task (with Arabic numerals from 1 to 9) to study event-related potentials (ERPs) in 73 adult participants in an exploratory approach. We presented three-item sequences and manipulated their order (ordered vs. unordered) as well as their inter-item numerical distance (one vs. two). Participants had to determine if a presented sequence was ordered or not. They also completed a speeded arithmetic fluency test, which measured their arithmetic skills. Our results revealed a significant mean amplitude difference in the grand average ERP waveform between ordered and unordered sequences in a time window of 500-750 ms at left anterior-frontal, left parietal, and central electrodes. We also identified distance-related amplitude differences for both ordered and unordered sequences. While unordered sequences showed an effect in the time window of 500-750 ms at electrode clusters around anterior-frontal and right-frontal regions, ordered sequences differed in an earlier time window (190-275 ms) in frontal and right parieto-occipital regions. Only the mean amplitude difference between ordered and unordered sequences showed an association with arithmetic fluency at the left anterior-frontal electrode. While the earlier time window for ordered sequences is consistent with a more automated and efficient processing of ordered sequential items, distance-related differences in unordered sequences occur later in time.

Enhancing learning outcomes through multisensory integration: A fMRI study of audio-visual training in virtual reality

The integration of information from different sensory modalities is a fundamental process that enhances perception and performance in real and virtual environments (VR). Understanding these mechanisms, especially during learning tasks that exploit novel multisensory cue combinations provides opportunities for the development of new rehabilitative interventions. This study aimed to investigate how functional brain changes support behavioural performance improvements during an audio-visual (AV) learning task. Twenty healthy participants underwent a 30 min daily VR training for four weeks. The task was an AV adaptation of a 'scanning training' paradigm that is commonly used in hemianopia rehabilitation. Functional magnetic resonance imaging (fMRI) and performance data were collected at baseline, after two and four weeks of training, and four weeks post-training. We show that behavioural performance, operationalised as mean reaction time reduction in VR, significantly improves. In separate tests in a controlled laboratory environment, we showed that the behavioural performance gains in the VR training environment transferred to a significant mean RT reduction for the trained AV voluntary task on a computer screen. Enhancements were observed in both the visual-only and AV conditions, with the latter demonstrating a faster response time supported by the presence of audio cues. The behavioural learning effect also transfers to two additional tasks that were tested: a visual search task and an involuntary visual task. Our fMRI results reveal an increase in functional activation (BOLD signal) in multisensory brain regions involved in early-stage AV processing: the thalamus, the caudal inferior parietal lobe and cerebellum. These functional changes were only observed for the trained, multisensory, task and not for unimodal visual stimulation. Functional activation changes in the thalamus were significantly correlated to behavioural performance improvements. This study demonstrates that incorporating spatial auditory cues to voluntary visual training in VR leads to augmented brain activation changes in multisensory integration, resulting in measurable performance gains across tasks. The findings highlight the potential of VR-based multisensory training as an effective method for enhancing cognitive function and as a potentially valuable tool in rehabilitative programmes.

Connectome-based predictive modeling indicates dissociable neurocognitive mechanisms for numerical order and magnitude processing in children

Symbolic numbers contain information about their relative numerical cardinal magnitude (e.g., 2 < 3) and ordinal placement in the count-list (e.g., 1, 2, 3). Previous research has primarily investigated magnitude discrimination skills and their predictive capacity for math achievement, whereas numerical ordering has been less systematically explored. At approximately 10-12 years of age, numerical order processing skills have been observed to surpass cardinal magnitude discrimination skills as the key predictor of arithmetic ability. The neurocognitive mechanisms underlying this shift remain unclear. To this end, we investigated children's (ages 10-12) neural correlates of numerical order and magnitude discrimination, as well as task-based functional connectomes and their predictive capacity for numeracy-related behavioral outcomes. Results indicated that number discrimination uniquely relied on bilateral temporoparietal correlates, whereas order processing recruited the bilateral IPS, cerebellum, and left premotor cortex. Connectome-based models were not cross-predictive for numerical order and magnitude, suggesting two dissociable mechanisms jointly supported by visuospatial working memory. Neural correlates of learning and memory were predictive of age and arithmetic ability, only for the ordinal task-connectome, indicating that the numerical order mechanism may undergo a developmental shift, dissociating it from mechanisms supporting cardinal number processing.

The neural basis of number word processing in children and adults

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

Numeral order and the operationalization of the numerical system

Recent years have witnessed an increase in research on how numeral ordering skills relate to children's and adults' mathematics achievement both cross-sectionally and longitudinally. Nonetheless, it remains unknown which core competency numeral ordering tasks measure, which cognitive mechanisms underlie performance on these tasks, and why numeral ordering skills relate to arithmetic and math achievement. In the current study, we focused on the processes underlying decision-making in the numeral order judgement task with triplets to investigate these questions. A drift-diffusion model for two-choice decisions was fit to data from 97 undergraduates. Findings aligned with the hypothesis that numeral ordering skills reflected the operationalization of the numerical system, where small numbers provide more evidence of an ordered response than large numbers. Furthermore, the pattern of findings suggested that arithmetic achievement was associated with the accuracy of the ordinal representations of numbers.

The Neural Representation of Ordinal Information: Domain-Specific or Domain-General?

Ordinal processing allows for the representation of the sequential relations between stimuli and is a fundamental aspect of different cognitive domains such as verbal working memory (WM), language and numerical cognition. Several studies suggest common ordinal coding mechanisms across these different domains but direct between-domain comparisons of ordinal coding are rare and have led to contradictory evidence. This fMRI study examined the commonality of ordinal representations across the WM, the number, and the letter domains by using a multivoxel pattern analysis approach and by focusing on triplet stimuli associated with robust ordinal distance effects. Neural patterns in fronto-parietal cortices distinguished ordinal distance in all domains. Critically, between-task predictions of ordinal distance in fronto-parietal cortices were robust between serial order WM, alphabetical order judgment but not when involving the numerical order judgment tasks. Moreover, frontal ROIs further supported between-task prediction of distance for the luminance judgment control task, the serial order WM, and the alphabetical tasks. These results suggest that common neural substrates characterize processing of ordinal information in WM and alphabetical but not numerical domains. This commonality, particularly in frontal cortices, may however reflect attentional control processes involved in judging ordinal distances rather than the intervention of domain-general ordinal codes.

Sulcation of the intraparietal sulcus is related to symbolic but not non-symbolic number skills

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The horizontal segment of intraparietal sulcus (HIPS) is one of the key functional regions for processing numbers.

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Sulcal morphology is a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning.

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The HIPS sulcal pattern explains part of the variance in participant’s symbolic number comparison and math fluency abilities.

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Participant’s non-symbolic number comparison abilities was not explained by HIPS sulcal pattern.

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This association between HIPS sulcal pattern and symbolic number abilities was stable from childhood to young adulthood.

Understanding the constraints, including biological ones, that may influence mathematical development is of great importance because math ability is a key predictor of career success, income and even psychological well-being. While research in developmental cognitive neuroscience of mathematics has extensively studied the key functional regions for processing numbers, particularly the horizontal segment of intraparietal sulcus (HIPS), few studies have investigated the effects of early cerebral constraints on later mathematical abilities. In this pre-registered study, we investigated whether variability of the sulcal pattern of the HIPS, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounts for individual difference in symbolic and non-symbolic number abilities. Seventy-seven typically developing school-aged children and 21 young adults participated in our study. We found that the HIPS sulcal pattern, (a) explains part of the variance in participant’s symbolic number comparison and math fluency abilities, and (b) that this association between HIPS sulcal pattern and symbolic number abilities was found to be stable from childhood to young adulthood. However, (c) we did not find an association between participant’s non-symbolic number abilities and HIPS sulcal morphology. Our findings suggest that early cerebral constraints may influence individual difference in math abilities, in addition to the well-established neuroplastic factors.

Developmental brain dynamics of numerical and arithmetic abilities

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

What we count dictates how we count: A tale of two encodings

We argue that what we count has a crucial impact on how we count, to the extent that even adults may have difficulty using elementary mathematical notions in concrete situations. Specifically, we investigate how the use of certain types of quantities (durations, heights, number of floors) may emphasize the ordinality of the numbers featured in a problem, whereas other quantities (collections, weights, prices) may emphasize the cardinality of the depicted numerical situations. We suggest that this distinction leads to the construction of one of two possible encodings, either a cardinal or an ordinal representation. This difference should, in turn, constrain the way we approach problems, influencing our mathematical reasoning in multiple activities. This hypothesis is tested in six experiments (N = 916), using different versions of multiple-strategy arithmetic word problems. We show that the distinction between cardinal and ordinal quantities predicts problem sorting (Experiment 1), perception of similarity between problems (Experiment 2), direct problem comparison (Experiment 3), choice of a solving algorithm (Experiment 4), problem solvability estimation (Experiment 5) and solution validity assessment (Experiment 6). The results provide converging clues shedding light into the fundamental importance of the cardinal versus ordinal distinction on adults' reasoning about numerical situations. Overall, we report multiple evidence that general, non-mathematical knowledge associated with the use of different quantities shapes adults' encoding, recoding and solving of mathematical word problems. The implications regarding mathematical cognition and theories of arithmetic problem solving are discussed.

Shared Neural Circuits for Visuospatial Working Memory and Arithmetic in Children and Adults

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of frontoparietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

Neurodevelopmental differences in child and adult number processing: An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children's and 44 healthy adults' recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.