Fast processing speed, enhanced mathematics: exploring the relation between approximate number system and arithmetic ability in athletes and video game players

Early math achievement predicts later outcomes. Individual differences in the precision of approximate representations of number and the mapping between nonsymbolic and symbolic number representations predict math achievement; honing these representations improves math skills. The goal of this registered report is to disentangle the potential mechanisms of transfer. Three hundred and nineteen 4- to 6-year-old children in 26 publicly funded classrooms in a non-urban county in the Northeastern United States were assigned to a tablet-based, teacher-facilitated training designed to target the approximate number system, symbolic number skills, or executive function. Executive function training improved math more than symbolic number training; the differences were attributable to improvement in symbolic number skills. There were no differences between executive function and approximate number training. The results suggest that supporting ancillary skills may bolster early mathematical skills.

Mathematical abilities are critical for the developmental outcomes of children with autism spectrum disorder (ASD). However, little is known about these abilities and their association with the approximate number system (ANS) in preschoolers with ASD beyond Western samples, including Chinese children. This cross-sectional study examined whether formal and informal mathematical abilities differed between children with and without ASD and assessed the extent to which these abilities were associated with ANS acuity. Participants included 47 children with ASD and 47 typically developing (TD) children aged 3-7 years. All children were assessed on measures of formal and informal mathematical abilities, ANS acuity, and non-verbal IQ. No significant group differences in mathematical abilities were found among children aged 3-5 years. However, among children aged 6-7 years, the ASD group showed significantly lower performance in mathematical abilities compared to their TD peers. ANS acuity was significantly correlated with both formal and informal mathematical abilities in the ASD group, but only with informal mathematical abilities in the TD group. Furthermore, ANS acuity accounted for 5.4% of the unique variance in formal mathematical abilities specifically within the ASD group. The patterns of mathematical abilities and their relationship with ANS acuity differ between preschoolers with and without ASD. These findings suggest a differential association between ANS and formal mathematics learning in children with ASD, highlighting implications for the design of early numeracy interventions.

Parental skills strongly predict children's cognitive development. This is the case even for abilities such as non-symbolic magnitude processing, which are evolutionary old and might be expected to show relatively invariant neural architecture. However, whether this behavioral similarity reflects similar neural representations between parents and children is unknown. Here we combined fMRI with dyadic representational similarity analysis to measure mother-child neural similarity during a numerosity adaptation task. Forty-four mother-child dyads (children's mean age = 8.55yr) viewed sequences of dot arrays where numerosity remained either constant or varied. We assessed whether neural patterns associated with the numerosity adaptation effect showed greater similarity in familial than non-familial dyads. Results revealed family-specific neural similarity in the right intraparietal sulcus, a core region for non-symbolic magnitude processing. Structural analyses revealed that cortical thickness in this region also showed family-specific similarity, suggesting that functional transmission may partly reflect shared anatomical properties. These findings indicate that even evolutionarily ancient cognitive systems like the approximate number system show intergenerational neural transmission. Together with prior evidence of familial transmission in regions associated with executive functions during mental arithmetic, the present study highlights multiple pathways through which math skills may be transmitted from parents to children.

Number sense is the intuitive, non-verbal ability to perceive and process numerical quantities without formal counting. This evolutionarily conserved trait, shared by different animal species, is supported by two mechanisms: the object tracking system (OTS) for small sets and the approximate number system (ANS) for larger quantities. Although historically viewed as distinct, these systems interact dynamically; their disruption is implicated in developmental dyscalculia and disorders such as Williams-Beuren syndrome (WBS), a chromosome microdeletion characterised by marked numerical and visuospatial deficits. Here, we synthesise neurobiological advances to provide an integrative perspective on the neural substrates of number sense. Field studies provide ecological validity, while laboratory procedures offer tighter precision; together, they illuminate the biological foundations of numerical cognition. Although number sense is conserved, human studies indicate only moderate heritability likely reflecting directional selection. Nonetheless, genetic findings converge on neurodevelopmental and synaptic mechanisms. Zebrafish (Danio rerio) offer a powerful platform to bridge genes, circuits and behaviour. For instance, manipulating zebrafish genes linked to WBS reveals gene-specific effects on quantity processing. At the neural level, numerical cognition is largely supported by specialised number-selective neurons. Whole-brain calcium imaging in larval zebrafish demonstrates that these neurons emerge by 3 days postfertilisation and follow a trajectory where representations of small numerosities precede larger ones. Altogether, integrating genetic, behavioural and circuit-level approaches provides a powerful framework for uncovering conserved mechanisms of numerosity supporting higher-level cognitive functions, including mathematics.

Mechanisms by which animals acquire, process, store, and use information from their environment (i.e., cognitive abilities), like other traits, evolve in response to selection pressures. Individuals with distinct intrinsic traits may benefit to varying degrees from different strategies when solving ecologically relevant cognitive tasks. This effect may be especially pronounced in social species, where group composition can shape the development of different cognitive strategies. In this study, we investigated the quantity discrimination abilities of two highly social New World primates using spontaneous choice tests. Our aim was to explore the effects of species-specific biology and intrinsic traits, such as sex and age, on cognitive performance. We tested 14 focal individuals using five quantity combinations with varying ratios (0.25, 0.5, 0.75): 1 vs. 2, 1 vs. 4, 3 vs. 4, 6 vs. 8, and 6 vs. 12. We found that performance was primarily driven by ratio-dependence rather than absolute differences between quantities. This, combined with the lack of significant differences in response time across quantity combinations, suggests that the Approximate Number System (ANS) is the primary cognitive mechanism underlying quantity discrimination in the studied species. Additionally, response time varied with intrinsic traits such as species, sex, and age; however, we did not detect differences in performance. Our results may reflect the unique social structure of these species, as well as differences in their biology, such as feeding behavior, providing valuable insights into the quantitative abilities of New World monkeys. These findings highlight the need for a deeper exploration of the evolutionary trade-offs and selective pressures shaping the complex interactions among behavior, intrinsic traits, and cognitive performance.

Human numerical cognition relies on two core systems: the Approximate Number System (ANS), supporting approximate magnitude estimation, and the Object Tracking System (OTS), enabling precise individuation of up to 3 or 4 items. This study tested 32 healthy, full-term newborns (0-3 days old; 18 females) recruited from a maternity ward serving a socioeconomically and ethnically diverse population. Newborns familiarized with 2 elements (OTS range) preferred 1 element on the left, whereas those familiarized with 4 elements (ANS range) preferred 12 elements on the right. This pattern (η²p = 0.462) indicates that both numerical systems exhibit a shared spatial signature from birth, suggesting that spatial organization is a fundamental property of early numerical cognition.

To uncover universal principles of vocal behavior, studies have examined whether linguistic laws apply across species. Menzerath’s law, for instance, posits that larger constructs have shorter constituent parts, reflecting an efficiency principle that reduces articulatory and energetic demands. Another proposed universal is final lengthening, where end-of-sequence vocalizations are extended to potentially signal sequence boundaries. While studies have examined these temporal patterns in ecological communicative contexts, it remains unclear whether they also emerge in more constrained, externally instructed vocal responses. This study examines temporal patterns in vocal sequences during a numerically cued production task in crows and humans. While both species performed the same task, they differ in their numerical representations: crows rely on an approximate number system, whereas humans possess a symbolic understanding of number. Crows showed a negative correlation between sequence length and vocalization duration—consistent with Menzerath’s law—and a positive correlation between sequence position and duration, consistent with final lengthening. In contrast, humans exhibited the opposite: vocalization duration increased with sequence size and decreased with position. These findings suggest that Menzerath’s law is not a universal principle but shaped by species-specific cognition, motor constraints, and task demands. This highlights the importance of considering context and cognitive capacities when interpreting temporal patterns in vocal behavior across species.

The role of Approximate Number System (ANS) in adult symbolic number processing remains controversial. Despite evidences for a linear and precise representation of symbolic numbers in adults, this study, based on Dual-Process Theory (DPT), proposes that ANS should still influence symbolic number processing in adults. To examine this possibility, we conducted two hand tracking experiments using a manual reaching numerical comparison task. In Experiment 1, we investigated differences in adults’ performances when comparing small numbers (#1–#9 vs. #5) and large numbers (91–99 vs. 95). The results showed that adults exhibited both higher response accuracy and greater deviation in movement trajectories when comparing small number pairs rather than large number pairs, indicating an implicit size effect in symbolic number representation. In Experiment 2, we ruled out the possibility that the results of Experiment 1 were driven by differences in visual format of stimuli (e.g., 9 vs. #9 vs. 09). Together, these findings provide consistent evidences for the implicit influence of ANS on adults’ symbolic number processing, unveiling the dual representations of symbolic numbers in adulthood and underscoring the potential of visuomotor tasks for probing implicit cognitive processing.

In non-symbolic numerical comparison tasks (Approximate Number System or ANS tasks) where participants determine which of two dot arrays is more numerous, judgments can be biased by irrelevant non-numerical dimensions of magnitude, such as dot size or the total occupied area. While inhibition may help overcome these conflicts, the mechanisms guiding attention toward relevant numerical information remain unclear. We hypothesized that modes of attentional processing - focusing on individual elements (local processing) versus the overall configuration (global processing) - may influence how participants resolve numerical conflicts. Fifty-four adults (Mage = 32.07 years, SD = 11.38) completed ANS trials preceded by prime items designed to activate either a local or global processing mode, or no prime in a control condition. Global priming did not significantly affect performance, while local priming modulated numerosity/magnitude conflicts across magnitude dimensions, notably reducing the impact of convex hull. These findings shed light on how perceptual modes impact adults’ ability to extract numerical information in the face of visual conflict.

The approximate number system (ANS) is thought to mediate symbolic and non-symbolic numerical magnitude comparison. Challenging this view, the dual system model stipulates that non-symbolic comparisons rely on the ANS while symbolic comparisons rely on a discrete semantic system (DSS). In three experiments, the current study tests whether symbolic and non-symbolic magnitude comparisons rely on a common ANS or a DSS by examining the correlation between the size and distance effects in numerical magnitude comparison. We replicated previous studies, which used one-digit numbers 1 to 9, but also aimed to increase variance by using less familiar number ranges. Experiment 1 used a fixed-reference paradigm (reference = 55) with two-digit integers (11-99). Experiments 2 and 3 extended the design to decimals (0.01-0.98) with variable (Experiment 2) or fixed reference (Experiment 3). All experiments additionally included non-symbolic dot comparison in which the expected negative correlation between size and distance effect emerged. Across experiments, size and distance effects in less familiar number ranges were uncorrelated when presented in symbolic format, corroborating the idea that symbolic number comparison relies on a DSS. These findings were moderated by the observation of a significant correlation between size and distance effects in a subsample of participants who showed significant size and distance effects at the individual level. Interpretation of the current results must take into account limitations concerning specificities of multi-digit number processing, the reliability of the effects, and the possible role of unmeasured external factors in shaping the observed correlations.

Abstract Relative to fractions, decimal numbers are thought to be easier for students to learn because they employ the same base-10 system as whole numbers. However, unlike whole numbers, larger decimals can have fewer digits, leading to worse performance when comparing Inconsistent decimal pairs, like 0.8 vs 0.26, than Consistent pairs like 0.86 vs 0.2. Students may be applying the whole number rule: “more digits = larger number” or they could be ignoring the decimal points and comparing 8 vs 26. This study used neuroimaging and our specially designed stimulus set to distinguish between these possibilities. We focused on the intraparietal sulcus (IPS), implicated in numerical magnitude processing, and the anterior cingulate cortex (ACC) and insula, implicated in inhibitory control. We found no neural differences between Consistent and Inconsistent comparisons, suggesting that the number of digits does not drive brain responses in skilled adults (n=21). Instead, for Consistent comparisons, we found that the IPS was sensitive to the actual distance between the decimals, while the ACC showed this pattern for Inconsistent comparisons. Crucially, we also examined the effect of the distance between the decimal pairs when ignoring the decimal point. Here, we found sensitivity to this distance among Inconsistent comparisons in the IPS and insula, suggesting that whole number referents are automatically processed during decimal comparison and require engagement of cognitive control regions to counteract. More broadly, our results underscore the unique challenges of decimal notation, revealing the need for educational practices that emphasize differences to whole numbers rather than highlighting similarities.

Understanding how cognitive abilities support mathematical learning across development remains a central question in psychology. Traditionally, scietific literature has distinguished between domain-specific abilities, referring to processes specifically involved in quantity/numerical processing and supported by systems such as the Approximate Number System (ANS) and the Object Tracking System (OTS), and domain-general abilities, which encompass broader cognitive resources such as working memory and executive functions. This paper proposes a developmental and dynamic framework that integrates previous theoretical perspectives and extends them to the earliest stages of life, suggesting that early learning may rely primarily on mechanisms dedicated to numerical understanding, whereas with age and schooling, broader cognitive resources gradually become more influential in supporting complex mathematical reasoning.

Studying numerical interferences has become a widely used method for investigating the representations that underlie numerical cognition. Here, we contrast the classic pure approximate number system (ANS) framework and a more recently proposed hybrid approximate number system-discrete semantic system framework with respect to their distinctive predictions for the nonsymbolic and symbolic spatial numerical associations of response codes (SNARC) effect (the most extensively studied interference between numbers and space). We compare the symbolic (Indo-Arabic numerals) to the nonsymbolic (arrays of dots) version of a SNARC paradigm (n = 77). In contrast to previous studies, in the present experiment, (a) the magnitude is irrelevant for solving the task (a color judgment task), and (b) the nonsymbolic stimuli contain arrays of dots outside the subitizing range, ensuring to activate the ANS. We found clear evidence for the SNARC effect in the symbolic color task. However, we found no indication of the SNARC effect in the nonsymbolic color task. This pattern of results supports the hybrid approximate number system-discrete semantic system framework, assuming that the SNARC interference is a symbolic effect while refuting the pure ANS view of the SNARC effect, which necessitates the presence of the SNARC interference using a nonsymbolic format, too. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

A robust finding in numerical cognition is that connecting items within an array leads to systematic underestimation of numerosity. This provides evidence that approximate numerosity perception relies on discrete objects rather than on continuous variables (e.g., total area, density, convex hull). While this connectedness effect is often attributed to perceptual grouping, an alternative interpretation is that connected items may capture covert attention, thereby biasing the sampling of visual information. We tested these competing accounts by combining a numerosity estimation task with a target-detection task modeled after Posner’s cueing paradigm. On each trial, participants viewed dot arrays (14–20 items) that included two red lines, either connecting a pair of dots or terminating near unconnected dots. A target diamond could appear either near (congruent) or far (incongruent) from the quadrant containing the red lines. Participants first performed a go/no-go detection task, then estimated the array numerosity. Replicating prior work, connected arrays were consistently underestimated relative to unconnected ones. Crucially, detection performance showed no evidence of attentional capture: reaction times and accuracy did not differ as a function of connectedness or target position. These findings demonstrate that the underestimation effect cannot be attributed to covert attentional allocation. Instead, they support the view that perceptual grouping—rather than attentional biases—drives the connectedness effect in the Approximate Number System. More broadly, our results strengthen the case for segmentation-based mechanisms as a critical foundation of visual number perception.

This systematic review examines the burgeoning field of investigating mathematical efficiency through electroencephalography (EEG), aiming to elucidate the neural substrates and temporal dynamics underlying efficient mathematical processing. Through comprehensive database searches and rigorous inclusion criteria, a total of 15 EEG studies were identified and synthesized. Findings reveal distinct neural oscillations and event-related potentials (ERPs) associated with various facets of mathematical cognition, including numerical magnitude processing, arithmetic operations, working memory engagement, and problem-solving strategies. Furthermore, the review highlights the impact of individual differences, developmental trajectories, and mathematical expertise on EEG-derived measures of mathematical efficiency. Methodological considerations, encompassing experimental design, data preprocessing, and analytical techniques, are critically evaluated to enhance methodological rigor and reproducibility within the field. By consolidating evidence from diverse studies, this systematic review advances our understanding of the neural mechanisms underpinning mathematical cognition and delineates avenues for future research aimed at optimizing mathematical learning and performance through EEG-based approaches.

The role of the approximate number system (ANS) in scaffolding symbolic mathematics remains unresolved. A prior neuroimaging study from our group (Suárez-Pellicioni & Booth, 2018) found no significant longitudinal effects of ANS acuity—indexed by intraparietal sulcus (IPS) activation—on gains in math fluency. However, the absence of age-specific analyses and exclusive focus on fluency, which emphasizes retrieval, may have contributed to these null findings. To address these limitations, the present study examined whether age moderates the relationship between inter-hemispheric IPS functional connectivity during a non-symbolic comparison task and math skill. Specifically, we tested: (1) baseline associations at Time 1 (T1); (2) whether T1 connectivity predicts gains in math skill over time (scaffolding hypothesis); and (3) whether changes in connectivity relate to longitudinal gains. Forty-eight children completed a dot comparison task in the scanner at T1 and again two years later. Standardized measures of subtraction skill and math fluency were collected at both time points. We measured general psychophysiological interaction (gPPI) between IPS seeds and contralateral IPS regions. For subtraction skill, we found no evidence of a concurrent association at T1 or predictive effects of T1 connectivity moderated by age. However, changes in connectivity over time revealed an age-dependent pattern: younger children showed gains linked to increased right-left parietal connectivity, while older children showed gains with decreased connectivity. This suggests a developmental shift from effortful integration to more efficient processing. Effects were specific to subtraction, not fluency.

How are cognitive abilities and mathematical abilities related in early childhood? Unraveling the mediation mechanism and age-related influences.

We investigated the effects of cognitive training with transcranial random noise stimulation (tRNS) applied to the intraparietal sulcus (IPS) or dorsolateral prefrontal cortex (DLPFC) on improving a multidirectional number line estimation task. We predicted that a single session of tRNS targeting IPS would enhance accuracy without affecting response speed, while a single session of tRNS targeting the DLPFC would improve response speed without influencing accuracy. Through a repeated measure within-between-subject design, 39 healthy participants (M = 21.39, SD = 2.64) were divided into either an IPS (n = 20) or DLPFC (n = 19) bilateral stimulation group, whereby in a counterbalanced order, the participants received a sham session and a session of tRNS separated by 1 week. Stimulation was paired with training tasks focused on the approximate number system. Participants were measured by their speed and accuracy on a multidirectional number line estimation task. Findings partially support predictions, tRNS to the IPS improved accuracy but not speed on the number line estimation task after a single session. Contrary to expectations on tRNS to the DLPFC, no effects were observed. Findings contribute to our understanding of using a single session tRNS as a tool in interventions aimed at maths low achievers.

The impact of mathematical anxiety and working memory on children's approximate number system and the n-back training effect.