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.

Crows recognize geometric regularity

The perception of geometric regularity in shapes, a form of elementary Euclidean geometry, is a fundamental mathematical intuition in humans. We demonstrate this geometric understanding in an animal, the carrion crow. Crows were trained to detect a visually distinct intruder shape among six concurrent arbitrary shapes. The crows were able to immediately apply this intruder concept to quadrilaterals, identifying the one that exhibited differing geometric properties compared to the others in the set. The crows exhibited a geometric regularity effect, showing better performance with shapes featuring right angles, parallel lines, or symmetry over more irregular shapes. This performance advantage did not require learning. Our findings suggest that geometric intuitions are not specific to humans but are deeply rooted in biological evolution.

Money counts: effects of monetary vs. purely numerical values on the mental representation of quantities

It has been established that humans use different cognitive models to represent and process numerical quantities. In this study, we investigated whether the representation of monetary values fundamentally differs from the representation of numbers. We also examined the influence of both socio/economic factors and mathematical ability on such representation. A group of adults (N = 272) were tested anonymously with a variant of the number-to-position task (Siegler & Opfer, 2003). They were asked to position on a horizontal line quantities expressed either in numerical format (e.g., 50) in the "Number" conditions or as monetary values (e.g., 50€) in the "Money" conditions. The extremes of the line consisted either of specific values (i.e. "2 or 2€" and "503 or 503€") in the "Fixed" conditions or of unspecific concepts of quantity (e.g., "little" and "a lot") in the "Fuzzy" conditions. A linear model, as opposed to a logarithmic one, provided the best fit of group average data in all experimental conditions except for the "Money-Fuzzy" condition. The percentages of absolute error were significantly larger for Money stimuli than Number stimuli in both Fixed and Fuzzy conditions. This is consistent with the law of diminishing marginal utility, which entails that the value of monetary quantities is described by a concave curve rather than a linear relationship. As expected from previous research, participants who were more used to spending large quantities of money were closer to the linear representation model. Participants with higher mathematical abilities represented numerical values more closely to a linear model, but no such effect was found for monetary quantities.

What the Science of Learning Teaches Us About Arithmetic Fluency

High-quality mathematics education not only improves life outcomes for individuals but also drives innovation and progress across society. But what exactly constitutes high-quality mathematics education? In this article, we contribute to this discussion by focusing on arithmetic fluency. The debate over how best to teach arithmetic has been long and fierce. Should we emphasize memorization techniques such as flashcards and timed drills or promote "thinking strategies" via play and authentic problem solving? Too often, recommendations for a "balanced" approach lack the depth and specificity needed to effectively guide educators or inform public understanding. Here, we draw on developmental cognitive science, particularly Sfard's process-object duality and Karmiloff-Smith's implicit-explicit knowledge continuum, to present memorization and thinking strategies not as opposing methods but as complementary forces. This framework enables us to offer specific recommendations for fostering arithmetic fluency based on the science of learning. We define arithmetic fluency, provide evidence on its importance, describe the cognitive structures and processes supporting it, and share evidence-based guidance for promoting it. Our recommendations include progress monitoring for early numeracy, providing explicit instruction to teach important strategies and concepts, implementing well-structured retrieval practice, introducing time-limited practice only after students demonstrate accuracy, and allocating sufficient time for discussion and cognitive reflection. By blending theory, evidence, and practical advice, we equip educators and policymakers with the knowledge needed to ensure all children have access to the opportunities needed to achieve arithmetic fluency.

Brood-parasitic female cowbirds have better numerical abilities than males on a task resembling nest prospecting behaviour

Selection can act in a sex-specific manner on cognitive abilities, including numerosity, especially when ecological roles differ between sexes. However, few systems exist in which numerical abilities would be expected to differ between the sexes, and even fewer focus on systems in which females are predicted to outperform males. In obligate brood-parasitic brown-headed cowbirds (Molothrus ater), only females select and parasitize host nests, and would benefit from enhanced numerical abilities to distinguish suitable host nests in the process of egg laying from unsuitable nests that have begun incubation. To test this hypothesis, we trained cowbirds to use touchscreens and discriminate between sets of images differing in number. Cowbirds distinguished images based on number alone (i.e. without using non-numerical cues), and females outperformed males across combinations of objects ranging from one to six (range in host egg numbers), but this difference disappeared across higher numbered combinations. In addition, males spent less time deciding on the correct stimulus than females, but made less accurate decisions overall, suggesting they 'guessed' correct answers more than females. We add to the growing evidence for complex numerical abilities in diverse taxa, and show these abilities can be shaped by ecology in a sex-specific way.

Working Memory Deficits in School-Age Children With Cochlear Implants Are Primarily Explained by Deficits in the Processing of Auditory and Lexical Information

PURPOSE

Prelingual deaf children with cochlear implants show lower digit span test scores compared to normal-hearing peers, suggesting a working memory impairment. To pinpoint more precisely the subprocesses responsible for this impairment, we designed a sequence reproduction task with varying length (two to six stimuli), modality (auditory or visual), and compressibility (sequences with more or less regular patterns). Results on 22 school-age children with cochlear implants and 21 normal-hearing children revealed a deficit of children with cochlear implants only in the auditory modality. We observed no deficit in the visual modality and no deficit in the ability to detect and use regular patterns to improve memorization.

CONCLUSION

These results suggest that the working memory deficit of children with cochlear implants is explained by an impairment in the processing, encoding, and/or storage of the auditory and lexical information, as opposed to a global storage deficit or an inability to use compressibility strategies to improve memorization.

SUPPLEMENTAL MATERIAL

https://doi.org/10.23641/asha.28216088.

Neural representation of action symbols in primate frontal cortex

At the core of intelligence is proficiency in solving new problems, including those that differ dramatically from problems seen before. Problem-solving, in turn, depends on goal-directed generation of novel thoughts and behaviors1, which has been proposed to rely on internal representations of discrete units, or symbols, and processes that can recombine them into a large set of possible composite representations1-11. Although this view has been influential in formulating cognitive-level explanations of behavior, definitive evidence for a neuronal substrate of symbols has remained elusive. Here, we identify a neural population encoding action symbols-internal, recombinable representations of discrete units of motor behavior-localized to a specific area of frontal cortex. In macaque monkeys performing a drawing-like task designed to assess recombination of learned action symbols into novel sequences, we found behavioral evidence for three critical features that indicate actions have an underlying symbolic representation: (i) invariance over low-level motor parameters; (ii) categorical structure, reflecting discrete classes of action; and (iii) recombination into novel sequences. In simultaneous neural recordings across motor, premotor, and prefrontal cortex, we found that planning-related population activity in ventral premotor cortex encodes actions in a manner that, like behavior, reflects motor invariance, categorical structure, and recombination, three properties indicating a symbolic representation. Activity in no other recorded area exhibited this combination of properties. These findings reveal a neural representation of action symbols localized to PMv, and therefore identify a putative neural substrate for symbolic cognitive operations.

Children's Understanding of Topological Relations

A core aim of developmental cognitive science is to uncover the basic building blocks of human thought. For instance, work revealing that even young children, adults without formal education, and distant animal species are sensitive to basic Euclidean properties indicates that humans may be endowed with some primitive understanding of Euclidean geometry. But what about other forms of geometry? Here, we explore children's sensitivity to topological spatial forms. We show that children, like adults, spontaneously distinguish and match items in accordance with their topological relations. As well, we show that children's judgments about object similarity are remarkably consistent with adults', indicating stability in object concepts throughout the lifespan. Finally, we compare children's sensitivity to various topological forms with their sensitivity to geometric properties like curvature, perpendicularity, and symmetry, and find that while there is some variability in performance across all the features tested, overall performance for geometric vs. topological is comparable. Collectively, these findings suggest that even young children have an intuitive understanding of topological relations and suggest that topological relations may be among the building blocks of human visuospatial representation.

Children's arithmetic skills do not transfer between applied and academic mathematics

Many children from low-income backgrounds worldwide fail to master school mathematics1; however, some children extensively use mental arithmetic outside school2,3. Here we surveyed children in Kolkata and Delhi, India, who work in markets (n = 1,436), to investigate whether maths skills acquired in real-world settings transfer to the classroom and vice versa. Nearly all these children used complex arithmetic calculations effectively at work. They were also proficient in solving hypothetical market maths problems and verbal maths problems that were anchored to concrete contexts. However, they were unable to solve arithmetic problems of equal or lesser complexity when presented in the abstract format typically used in school. The children's performance in market maths problems was not explained by memorization, access to help, reduced stress with more familiar formats or high incentives for correct performance. By contrast, children with no market-selling experience (n = 471), enrolled in nearby schools, showed the opposite pattern. These children performed more accurately on simple abstract problems, but only 1% could correctly answer an applied market maths problem that more than one third of working children solved (β = 0.35, s.e.m. = 0.03; 95% confidence interval = 0.30-0.40, P < 0.001). School children used highly inefficient written calculations, could not combine different operations and arrived at answers too slowly to be useful in real-life or in higher maths. These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal maths.

The counting principle makes number words unique

Following Ariel (2021. Why it's hard to construct ad hoc number concepts. In Caterina Mauri, Ilaria Fiorentini, & Eugenio Goria (eds.), Building categories in interaction: Linguistic resources at work, 439-462. Amsterdam: John Benjamins), we argue that number words manifest distinct distributional patterns from open-class lexical items. When modified, open-class words typically take selectors (as in kinda table), which select a subset of their potential denotations (e.g., "nonprototypical table"). They are typically not modified by loosening operators (e.g., approximately), since even if bare, typical lexemes can broaden their interpretation (e.g., table referring to a rock used as a table). Number words, on the other hand, have a single, precise meaning and denotation and cannot take a selector, which would need to select a subset of their (single) denotation (??kinda seven). However, they are often overtly broadened (approximately seven), creating a range of values around N. First, we extend Ariel's empirical examination to the larger COCA and to Hebrew (HeTenTen). Second, we propose that open-class and number words belong to sparse versus dense lexical domains, respectively, because the former exhibit prototypicality effects, but the latter do not. Third, we further support the contrast between sparse and dense domains by reference to: synchronic word2vec models of sparse and dense lexemes, which testify to their differential distributions, numeral use in noncounting communities, and different renewal rates for the two lexical types.

Perceiving Topological Relations

There are many ways to describe and represent the visuospatial world. A space can be described by its euclidean properties-the size of objects, the angles of boundaries, the distances between them. A space can also be described in nonspatial terms: One could explain the layout of a city by the order of its streets. Somewhere in between, topological representations-such as those commonly depicted in public-transit maps-capture coarse relational structure without precise euclidean detail, offering a relatively efficient, low-dimensional way of capturing spatial content. Here, we ask whether human adults quickly and automatically perceive such relations. In six experiments, we show that differences in simple topological features influence a range of visual tasks from object matching to number estimation to visual search. We discuss the possibility that topological relations are a kind of visual primitive that supports visuospatial representation.

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.

Mapping and modeling the semantic space of math concepts

Mathematics is an underexplored domain of human cognition. While many studies have focused on subsets of math concepts such as numbers, fractions, or geometric shapes, few have ventured beyond these elementary domains. Here, we attempted to map out the full space of math concepts and to answer two specific questions: can distributed semantic models, such a GloVe, provide a satisfactory fit to human semantic judgements in mathematics? And how does this fit vary with education? We first analyzed all of the French and English Wikipedia pages with math contents, and used a semi-automatic procedure to extract the 1000 most frequent math terms in both languages. In a second step, we collected extensive behavioral judgements of familiarity and semantic similarity between them. About half of the variance in human similarity judgements was explained by vector embeddings that attempt to capture latent semantic structures based on cooccurence statistics. Participants' self-reported level of education modulated familiarity and similarity, allowing us to create a partial hierarchy among high-level math concepts. Our results converge onto the proposal of a map of math space, organized as a database of math terms with information about their frequency, familiarity, grade of acquisition, and entanglement with other concepts.

Investigating frontoparietal networks and activation in children with mathematics learning difficulties: Cases with different deficit profiles

Approximately 15%-20% of school-aged children suffer from mathematics learning difficulties (MLD). Most children with developmental dyscalculia (DD) or MLD also have comorbid cognitive deficits. Recent literature suggests that research should focus on uncovering the neural underpinnings of MLD across more inclusive samples, rather than limiting studies to pure cases of DD or MLD with highly stringent inclusion criteria. Therefore, this study aims to identify neural aberrancies that may be common across multiple MLD cases with different deficit profiles. Nine MLD cases and 45 typically developing (TD) children, all around 7 years old (27 boys), were recruited. Using functional near-infrared spectroscopy (fNIRS), brain data were collected during an approximate resting state and a mathematical computation task (addition). Graph theory was then applied to assess global and nodal network indicators of brain function. When comparing the network indicators and brain activation of the MLD cases to those of TD children, no unified neural aberrancy was found across all cases. However, three MLD cases did show distinct neural aberrancies compared to TD children. The study discusses the implications of these findings, considering both the neural aberrancies in the three MLD cases and the neural similarities found in the other six cases, which were comparable to those of the TD children. This raises important questions about the presence and nature of aberrant neural indicators in MLD across large cohorts and highlights the need for further research in this area.

Feature-selective adaptation of numerosity perception

Perceptual adaptation has been widely used to infer the existence of numerosity detectors, enabling animals to quickly estimate the number of objects in a scene. Here, we investigated, in humans, whether numerosity adaptation is influenced by stimulus feature changes as previous research suggested that adaptation is reduced when the colour of adapting and test stimuli did not match. We tested whether such adaptation reduction is due to unspecific novelty effects or changes of stimuli identity. Numerosity adaptation was measured for stimuli matched or unmatched for low-level (colour, luminance, shape and motion) or high-level (letters' identity and face emotions) features. Robust numerosity adaptation occurred in all conditions, but it was reduced when adapting and test stimuli differed for colour, luminance and shape. However, no reduction was observed between moving and still stimuli, a readable change that did not affect the item's identity. Similarly, changes in letters' spatial rotations or face features did not affect adaptation magnitude. Overall, changes in stimulus identity defined by low-level features, rather than novelty in general, determined the strength of the adaptation effects, provided these changes were readily noticeable. These findings suggest that numerosity mechanisms operate on categorized items in addition to the total quantity of the set.

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.

Application of Navigated Transcranial Magnetic Stimulation (nTMS) to Study the Visual-Spatial Network and Prevent Neglect in Brain Tumour Surgery

Objective: Navigated transcranial magnetic stimulation (nTMS) has seldom been used to study visuospatial (VS) circuits so far. Our work studied (I) VS functions in neurosurgical oncological patients by using repetitive nTMS (rnTMS), (II) the possible subcortical circuits underneath, and (III) the correspondence between nTMS and direct cortical stimulation (DCS) during awake procedures. Methods: We designed a monocentric prospective study, adopting a protocol to use rnTMS for preoperative planning, including VS functions for lesions potentially involving the VS network, including neurosurgical awake and asleep procedures. nTMS-based-DTI tractography allowed the visualization of subcortical circuits. Statistical analyses on nTMS/DCS points were performed. Clinical results were collected pre- and postoperatively. Results: Finally, 27 patients with primitive intra-axial brain lesions were enrolled between April 2023 and March 2024. Specific tests and an experimental integrated VS test (VISA) were used. The clinical evaluation (at 5 ± 7, 30 ± 10, 90 ± 10 days after surgery) documented 33% of patients with neglect in the left hemisphere four days after surgery and, during the 3-month follow-up, preservation of visuospatial function/clinical recovery (90.62% in MMSE, 98.86% in the bell test, 80% in the clock test, and 98% in the OCS test). The surgical strategy was modulated according to the nTMS map. Subcortical bundles were traced to identify those most involved in these functions: SFLII > SLFII > SLFI. A comparison of the nTMS and DCS points in awake surgery (n = 10 patients) documented a sensitivity (Se) of 12%, a specificity (Sp) of 91.21%, a positive predictive value (PPV) of 42%, a negative predictive value (NPV) of 66%, and an accuracy of ~63.7%. Conclusions: Based on our preliminary results, nTMS is advantageous for studying cognitive functions, minimising neurological impairment. Further analyses are needed to validate our data.

Going Round in Circles: A Cognitive Bias in Geometric Reasoning

Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got "locked" on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations into the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.

A longitudinal study of math skills in heritage bilingual children: profiles of strengths and weaknesses

Many children are exposed to a heritage language in the home context, and they learn mathematics in the school context in the societal language (Italian in the present study). More evidence is needed on how Heritage Bilinguals (HBs) perform in different subtypes of numeracy and mathematics skills in a longitudinal perspective. This longitudinal study aimed to analyze the mathematical skills of heritage bilingual children. 220 HBs (50.5% female, from different linguistic/ethnic groups, including Indo-Iranian, Arabic, Chinese, Romanian, Albanian and Slavic languages) and 440 monolinguals (46.8% female, mostly Italian) were followed from second to third grade (aged between 7 and 9 years). The following tasks were administered: dictation, symbolic comparison, number line, mental calculation, multiplication tables, approximate calculation, problem-solving and written calculations. The results showed an advantage for HBs in approximate calculation, but they underperformed in problem-solving, multiplication tables, and mental calculations. A profile analysis highlighted the percentages of children at risk for math impairment. The study provides a longitudinal profile of strengths and weaknesses in the mathematics profile of children with HBs, with developmental trajectories that vary according to verbal load. The discussion focuses on the role of verbal load in math tasks in the assessment of HBs, and implications for clinical and educational contexts.

Cognitive Maps for a Non-Euclidean Environment: Path Integration and Spatial Memory on a Sphere

Humans build mental models of the world and utilize them for various cognitive tasks. The exact form of cognitive maps is not fully understood, especially for novel and complex environments beyond the flat Euclidean environment. To address this gap, we investigated path integration-a critical process underlying cognitive mapping-and spatial-memory capacity on the spherical (non-Euclidean) and planar (Euclidean) environments in young healthy adults (N = 20) using immersive virtual reality. We observed a strong Euclidean bias during the path-integration task on the spherical surface, even among participants who possessed knowledge of non-Euclidean geometry. Notably, despite this bias, participants demonstrated reasonable navigation ability on the sphere. This observation and simulation suggest that humans navigate nonflat surfaces by constructing locally confined Euclidean maps and flexibly combining them. This insight sheds light on potential neural mechanisms and behavioral strategies for solving complex cognitive tasks.

The left digit effect in an unbounded number line task

The left digit effect in number line estimation refers to the phenomenon where numerals with similar magnitudes but different leftmost digits (e.g., 19 and 22) are estimated to be farther apart on a number line than is warranted. The effect has been studied using a bounded number line task, a task in which a line is bounded by two endpoints (e.g., 0 and 100), and where one must indicate the correct location of a target numeral on the line. The goal of the present work is to investigate the left digit effect in an unbounded number line task, a task that involves using the size of one unit to determine a target numeral's location, and that elicits strategies different from those used in the bounded number line task. In a preregistered study, participants (N = 58 college students) completed four blocks of 38 trials each of an unbounded number line task, with target numerals ranging between 0 and 100. We found a medium and statistically reliable left digit effect (d = 0.70). The study offers further evidence that the effect is not driven by response strategies specific to the bounded number line task. We discuss other possible sources of the effect including conversion of symbols to magnitudes in these and other contexts.

Does instructional intervention reduce the left digit effect in number line estimation?

A robust left digit effect arises in number line estimation, whereby the leftmost digits of numerals have an undue influence on placements such that, for example, numbers like 298 are placed far to the left of numbers like 302. Past efforts to motivate more accurate performance using trial-by-trial and summary feedback have not led to a reduction in the left digit effect. In two experiments, we asked whether it is possible to reduce or eliminate the left digit effect in number line estimation through an instructional intervention in which one is explicitly taught about the left digit effect. In Experiment 1 (N = 134), participants completed two blocks (60 trials per block) of a self-paced 0-1,000 number line estimation task and were randomly assigned to either an instruction or a control condition. In Experiment 2 (N = 143), the procedure was enhanced with a learning check, and with additional measures to assess changes in behaviour as a result of instruction. In both experiments, a left digit effect was found in each block of each condition. Although there was evidence that instruction changed behaviour, these changes did not result in any reduction in the left digit effect relative to the control condition. These findings demonstrate that the left digit effect cannot be easily reduced by making people aware of it.

Experience of Euclidean geometry sculpts the development and dynamics of rodent hippocampal sequential cell assemblies

Euclidean space is the fabric of the world we live in. Whether and how geometric experience shapes our spatial-temporal representations of the world remained unknown. We deprived male rats of experience with crucial features of Euclidean geometry by rearing them inside spheres, and compared activity of large hippocampal neuronal ensembles during navigation and sleep with that of cuboid cage-reared controls. Sphere-rearing from birth permitted emergence of accurate neuronal ensemble spatial codes and preconfigured and plastic time-compressed neuronal sequences. However, sphere-rearing led to diminished individual place cell tuning, more similar neuronal mapping of different track ends/corners, and impaired pattern separation and plasticity of multiple linear tracks, coupled with reduced preconfigured sleep network repertoires. Subsequent experience with multiple linear environments over four days largely reversed these effects. Thus, early-life experience with Euclidean geometry enriches the hippocampal repertoire of preconfigured neuronal patterns selected toward unique representation and discrimination of multiple linear environments.

Dedicated comparatives aid comparisons of magnitude: a study with Pitjantjatjara-English bilinguals

When expressing comparisons of magnitude, Pitjantjatjara, a language indigenous to the land now known as Australia, employs contextually driven comparators (e.g., Anyupa is tall. Uma is short) rather than a dedicated morphological or syntactic comparative construction (e.g., Anyupa is taller than Uma). Pitjantjatjara also has a small number of lexicalized numerals, employing 'one', 'two', 'three', then 'many'. It is hypothesized that having dedicated comparatives in language and elaborated number systems aid comparisons of magnitudes. Fluent Pitjantjatjara-English bilinguals participated in tasks assessing their accuracy and reaction times when comparing two types of magnitude: numerosity (quantities of dots), and extent (line lengths). They repeated the comparisons in both languages on different days, allowing for the effect of language being spoken on responses to be assessed. No differences were found for numerosity; however, participants were less accurate when making comparisons of extent using Pitjantjatjara. Accuracy when using Pitjantjatjara decreased as the magnitude of the comparison increased and as differences between the comparators decreased. This result suggests a potential influence of linguistic comparison strategy on comparison behavior.

Why concepts are (probably) vectors

For decades, cognitive scientists have debated what kind of representation might characterize human concepts. Whatever the format of the representation, it must allow for the computation of varied properties, including similarities, features, categories, definitions, and relations. It must also support the development of theories, ad hoc categories, and knowledge of procedures. Here, we discuss why vector-based representations provide a compelling account that can meet all these needs while being plausibly encoded into neural architectures. This view has become especially promising with recent advances in both large language models and vector symbolic architectures. These innovations show how vectors can handle many properties traditionally thought to be out of reach for neural models, including compositionality, definitions, structures, and symbolic computational processes.

New measures of number line estimation performance reveal children's ordinal understanding of numbers

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance.

Recruitment of magnitude representations to understand graded words

Language understanding and mathematics understanding are two fundamental forms of human thinking. Prior research has largely focused on the question of how language shapes mathematical thinking. The current study considers the converse question. Specifically, it investigates whether the magnitude representations that are thought to anchor understanding of number are also recruited to understand the meanings of graded words. These are words that come in scales (e.g., Anger) whose members can be ordered by the degree to which they possess the defining property (e.g., calm, annoyed, angry, furious). Experiment 1 uses the comparison paradigm to find evidence that the distance, ratio, and boundary effects that are taken as evidence of the recruitment of magnitude representations extend from numbers to words. Experiment 2 uses a similarity rating paradigm and multi-dimensional scaling to find converging evidence for these effects in graded word understanding. Experiment 3 evaluates an alternative hypothesis - that these effects for graded words simply reflect the statistical structure of the linguistic environment - by using machine learning models of distributional word semantics: LSA, word2vec, GloVe, counterfitted word vectors, BERT, RoBERTa, and GPT-2. These models fail to show the full pattern of effects observed of humans in Experiment 2, suggesting that more is needed than mere statistics. This research paves the way for further investigations of the role of magnitude representations in sentence and text comprehension, and of the question of whether language understanding and number understanding draw on shared or independent magnitude representations. It also informs the role of machine learning models in cognitive psychology research.

Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency

BACKGROUND

Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'.

AIMS

The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels.

SAMPLE

Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later).

METHODS

Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured.

RESULTS

Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2.

CONCLUSION

Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.

Exploring Early Number Abilities With Multimodal Transformers

Early number skills represent critical milestones in children's cognitive development and are shaped over years of interacting with quantities and numerals in various contexts. Several connectionist computational models have attempted to emulate how certain number concepts may be learned, represented, and processed in the brain. However, these models mainly used highly simplified inputs and focused on limited tasks. We expand on previous work in two directions: First, we train a model end-to-end on video demonstrations in a synthetic environment with multimodal visual and language inputs. Second, we use a more holistic dataset of 35 tasks, covering enumeration, set comparisons, symbolic digits, and seriation. The order in which the model acquires tasks reflects input length and variability, and the resulting trajectories mostly fit with findings from educational psychology. The trained model also displays symbolic and non-symbolic size and distance effects. Using techniques from interpretability research, we investigate how our attention-based model integrates cross-modal representations and binds them into context-specific associative networks to solve different tasks. We compare models trained with and without symbolic inputs and find that the purely non-symbolic model employs more processing-intensive strategies to determine set size.

Rational number representation by the approximate number system

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

Symbolic metaprogram search improves learning efficiency and explains rule learning in humans

Throughout their lives, humans seem to learn a variety of rules for things like applying category labels, following procedures, and explaining causal relationships. These rules are often algorithmically rich but are nonetheless acquired with minimal data and computation. Symbolic models based on program learning successfully explain rule-learning in many domains, but performance degrades quickly as program complexity increases. It remains unclear how to scale symbolic rule-learning methods to model human performance in challenging domains. Here we show that symbolic search over the space of metaprograms-programs that revise programs-dramatically improves learning efficiency. On a behavioral benchmark of 100 algorithmically rich rules, this approach fits human learning more accurately than alternative models while also using orders of magnitude less search. The computation required to match median human performance is consistent with conservative estimates of human thinking time. Our results suggest that metaprogram-like representations may help human learners to efficiently acquire rules.

The relationship between numerical magnitude processing and math anxiety, and their joint effect on adult math performance, varied by indicators of numerical tasks

According to the hypothesis of Maloney et al. (Cognition 114(2):293-297, 2010. https://doi.org/10.1016/j.cognition.2009.09.013), math anxiety is related to deficits in numerical magnitude processing, which in turn compromises the development of advanced math skills. Because previous studies on this topic are contradictory, which may be due to methodological differences in the measurement of numerical magnitude processing, we tested Maloney et al.'s hypothesis using different tasks and their indicators: numerical magnitude processing (symbolic and non-symbolic comparison tasks: accuracy, reaction time, numerical ratio, distance and size effects, and Weber fraction; number line estimation task: estimation error), math anxiety (combined scores of learning, testing, math problem solving, and general math anxiety), and math performance. The results of our study conducted on 119 young adults mostly support the hypothesis proposed by Maloney et al. that deficiency in symbolic magnitude processing is related to math anxiety, but the relationship between non-symbolic processes and math anxiety was opposite to the assumptions. Moreover, the results indicate that estimation processes (but not comparison processes) and math anxiety are related to math performance in adults. Finally, high math anxiety moderated the relationship between reaction time in the symbolic comparison task, reaction time in the non-symbolic comparison task, numerical ratio effect in the symbolic comparison task, and math performance. Because the results of the joint effect of numerical magnitude processing and math anxiety on math performance were inconsistent, this part of the hypothesis is called into question.

Caricaturing Shapes in Visual Memory

When representing high-level stimuli, such as faces and animals, we tend to emphasize salient features-such as a face's prominent cheekbones or a bird's pointed beak. Such mental caricaturing leaves traces in memory, which exaggerates these distinctive qualities. How broadly does this phenomenon extend? Here, in six experiments (N = 700 adults), we explored how memory automatically caricatures basic units of visual processing-simple geometric shapes-even without task-related demands to do so. Participants saw a novel shape and then immediately adjusted a copy of that shape to match what they had seen. Surprisingly, participants reconstructed shapes in exaggerated form, amplifying curvature, enlarging salient parts, and so on. Follow-up experiments generalized this bias to new parameters, ruled out strategic responding, and amplified the effects in serial transmission. Thus, even the most basic stimuli we encounter are remembered as caricatures of themselves.

What curves are parallel? The core feature of preschoolers' intuitive parallel category

Existing evidence has revealed that humans can spontaneously categorize many geometric shapes without formal education. Children around 4 years could distinguish between intersecting lines and parallel lines. Three features can be used to identify parallel lines, namely "translational congruence," "never meet," and "constant distance." This study separated them by using pairs of curves that possess only one of these features. Two experiments across 2021-2023, respectively, compared the relative priority of "translational congruence" with "constant distance," and "never meet" with "constant distance" among 3- to 5-year-old Chinese preschoolers (Ntotal = 314, 48% female). The results showed that preschoolers consistently grouped "constant distance" curves with parallel lines. This suggests that the core feature of intuitive parallel category is "constant distance" at this age.

Is core knowledge a natural subdivision of infant cognition?

We examine Spelke's core knowledge taxonomy and test its boundaries. We ask whether Spelke's core knowledge is a distinct type of cognition in the sense that the cognitive processes it includes and excludes are biologically and mechanically coherent.

Divisive language

What language devises, it might divide. By exploring the relations among the core geometries of the physical world, the abstract geometry of Euclid, and language, I give new insight into both the persistence of core knowledge into adulthood and our access to it through language. My extension of Spelke's language argument has implications for pedagogy, philosophy, and artificial intelligence.

Geometry in the brain optimized for sign language - A unique role of the anterior superior parietal lobule in deaf signers

Geometry has been identified as a cognitive domain where deaf individuals exhibit relative strength, yet the neural mechanisms underlying geometry processing in this population remain poorly understood. This fMRI study aimed to investigate the neural correlates of geometry processing in deaf and hearing individuals. Twenty-two adult deaf signers and 25 hearing non-signers completed a geometry decision task. We found no group differences in performance, while there were some differences in parietal activation. As expected, the posterior superior parietal lobule (SPL) was recruited for both groups. The anterior SPL was significantly more activated in the deaf group, and the inferior parietal lobule was significantly more deactivated in the hearing group. In conclusion, despite similar performance across groups, there were differences in the recruitment of parietal regions. These differences may reflect inherent differences in brain organization due to different early sensory and linguistic experiences.

Auditory time perception impairment in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.

Young children intuitively organize numbers on straight, horizontal lines from left to right before the onset of formal instruction

The number line estimation task is frequently used to measure children's numerical magnitude understanding. It is unclear whether the resulting straight, horizontal, left-to-right-oriented estimate patterns indicate task constraints or children's intuitive number-space mapping. Three- to six-year-old children (N = 72, Mage = 4.89, 56% girls, 94% German citizenship) were asked to explain the meaning of numbers to a teddy by laying out a rope and attaching cards showing non-symbolic numerosities (dots) to it. Most children intuitively created straight, horizontal, and left-to-right-oriented representations. Characteristics of the line correlated with age, mathematical competencies, and home numeracy. This demonstrates the usefulness of the number line estimation task for assessing how children intuitively map numbers onto space.

Diversity of spatial activities and parents' spatial talk complexity predict preschoolers' gains in spatial skills

Children's spatial activities and parental spatial talk were measured to examine their associations with variability in preschoolers' spatial skills (N = 113, Mage = 4 years, 4 months; 51% female; 80% White, 11% Black, and 9% other). Parents who reported more diversity in daily spatial activities and used longer spatial talk utterances during a spatial activity had children with greater gains in spatial skills from ages 4 to 5 (β = .17 and β = .40, respectively). Importantly, this study is the first to move beyond frequency counts of spatial input and investigate the links among the diversity of children's daily spatial activities, as well as the complexity of parents' spatial language across different contexts, and preschoolers' gains in spatial skills, an important predictor of later STEM success.

Developmental changes of the impact of visual cues on ANS acuity across grades 1-5: Different patterns of visual cues on numerosity processing

Numerous studies have consistently demonstrated the presence of the approximate number system (ANS) throughout development. Research has also revealed that visual cues may influence the ANS acuity, which may change with age. However, most studies have drawn conclusions based on performance differences between incongruent and congruent trials, which may be confounded by an individual's ability to inhibit interference. Therefore, to examine the developmental changes of the impact of visual cues on ANS acuity, we utilized congruent trials with varying visual cues. Our sample comprised Chinese children from grade one to grade five. We manipulated the salience of numerical cues (numerical ratio) and visual cues (dot size) in a non-symbolic numerosity comparison task. The results revealed a discernible leap in development from first to third grade and first to fifth grade; however, this upward trajectory did not persist into the transition from third to fifth grade, where no appreciable advancement was observed. Moreover, we observed different effects of visual cues on the dot-comparison task depending on the numerical cues and age. Specifically, visual cues (i.e., dot size) only facilitated ANS acuity in older school-aged children when numerical cues were weakened. The results indicate the presence of two distinct magnitude representational systems-one for the numerical dimension and another for the non-numerical dimension-during development.

Human-level few-shot concept induction through minimax entropy learning

Humans learn concepts both from labeled supervision and by unsupervised observation of patterns, a process machines are being taught to mimic by training on large annotated datasets-a method quite different from the human pathway, wherein few examples with no supervision suffice to induce an unfamiliar relational concept. We introduce a computational model designed to emulate human inductive reasoning on abstract reasoning tasks, such as those in IQ tests, using a minimax entropy approach. This method combines identifying the most effective constraints on data via minimum entropy with determining the best combination of them via maximum entropy. Our model, which applies this unsupervised technique, induces concepts from just one instance, reaching human-level performance on tasks of Raven's Progressive Matrices (RPM), Machine Number Sense (MNS), and Odd-One-Out (O3). These results demonstrate the potential of minimax entropy learning for enabling machines to learn relational concepts efficiently with minimal input.

What Makes Us Smart?

How did humans become clever enough to live in nearly every major ecosystem on earth, create vaccines against deadly plagues, explore the oceans depths, and routinely traverse the globe at 30,000 feet in aluminum tubes while nibbling on roasted almonds? Drawing on recent developments in our understanding of human evolution, we consider what makes us distinctively smarter than other animals. Contrary to conventional wisdom, human brilliance emerges not from our innate brainpower or raw computational capacities, but from the sharing of information in communities and networks over generations. We review how larger, more diverse, and more optimally interconnected networks of minds give rise to faster innovation and how the cognitive products of this cumulative cultural evolutionary process feedback to make us individually "smarter"-in the sense of being better at meeting the challenges and problems posed by our societies and socioecologies. Here, we consider not only how cultural evolution supplies us with "thinking tools" (like counting systems and fractions) but also how it has shaped our ontologies (e.g., do germs and witches exist?) and epistemologies, including our notions of what constitutes a "good reason" or "good evidence" (e.g., are dreams a source of evidence?). Building on this, we consider how cultural evolution has organized and distributed cultural knowledge and cognitive tasks among subpopulations, effectively shifting both thinking and production to the level of the community, population, or network, resulting in collective information processing and group decisions. Cultural evolution can turn mindless mobs into wise crowds by facilitating and constraining cognition through a wide variety of epistemic institutions-political, legal, and scientific. These institutions process information and aid better decision-making by suppressing or encouraging the use of different cultural epistemologies and ontologies.

Magnitude representation of preschool children with autism spectrum condition

LAY ABSTRACT

The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation (e.g. presenting the number of a collection of objects) is a fundamental numerical ability presented since early infancy and is correlated with children's later learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in precision of magnitude representations. This study compared preschool children with and without autism spectrum condition in their precision of magnitude representation with an approximate number comparison task, in which children compared two sets of dots without counting and chose the set with more dots. Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition. This difference existed even when multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities were statistically controlled. Moreover, the individual difference of the numerical comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. In addition, the large variance in the precision of their magnitude representation suggests that individualized mathematics interventions are needed for children with autism spectrum condition.

Recruitment of the premotor cortex during arithmetic operations by the monkey

Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.

Exploring the Importance of Environmental Complexity for Newly Hatched Zebrafish

The effects of an early impoverished social or physical environment on vertebrate neural development and cognition has been known for decades. While existing studies have focused on the long-term effects, measuring adult cognitive phenotypes, studies on the effects of environmental complexity on the early stages of development are lacking. Zebrafish (Danio rerio) hatchlings are assumed to have minimal interaction with their environment and are routinely reared in small, bare containers. To investigate the effects of being raised under such conditions on development of behaviour and cognition, hatchlings housed for 10 days in either an enriched or a standard environment underwent two cognitive tasks. The results were mixed. Subjects of the two treatments did not differ in performance when required to discriminate two areas. Conversely, we found a significant effect in a number discrimination task, with subjects from impoverished condition performing significantly worse. In both experiments, larvae reared in impoverished environment showed a reduced locomotor activity. Given the effects that enrichment appears to exert on larvae, a third experiment explored whether hatchlings exhibit a spontaneous preference for more complex environments. When offered a choice between a bare setting and one with objects of different shapes and colors, larvae spent over 70% of time in the enriched sector. Deepening these effects of an early impoverished environment on cognitive development is crucial for the welfare of captive zebrafish populations and for enhancing the quality and reliability of studies on larval zebrafish.

A number sense as an emergent property of the manipulating brain

The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. We explore this question through a model, assuming that the learner is able to pick up and place small objects from, and to, locations of its choosing, and will spontaneously engage in such undirected manipulation. We further assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with a supervisory signal from the motor system. We model perception using standard deep networks for feature extraction and classification. Our main finding is that, from learning the task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers and quantity. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned with supervision from a simple pre-training task. Our observations suggest that cross-modal learning is a powerful learning mechanism that may be harnessed in artificial intelligence.

Examining Profiles of U.S. Children's Screen Time and Associations with Academic Skills

Children's screen time (ST) increased in recent years, but investigations of the content and context (e.g., parental presence, and device type) of ST in predicting early academic skills remains understudied. In this study of 127 four- and five-year-olds, we examined whether the educational content and contextual information about children's ST from time diary interviews at age 4 predicted direct assessments of academic skills at age five. Cluster analyses detected three unique groups: Cluster One was "lowest ST and highest non-educational TV, with little parental presence," Cluster Two was "moderate ST and highest educational mobile devices, with moderate parental presence," and Cluster Three was "highest total ST and moderate educational ST and high parental presence." Children in Cluster Two scored significantly higher in literacy skills at age five than peers in Cluster One and Cluster Three. Children in Cluster One scored significantly higher in spatial skills compared to those in Cluster Three. No significant associations were detected between children's ST and number skills. Findings suggest that educational content and contextual features of ST combine in meaningful ways and appear to better predict children's literacy and spatial skills compared to variable-centered approaches. Methodological implications of this research and future directions are discussed.

Understanding the social-emotional components of our "number sense": insights from a novel non-symbolic numerical comparison task

Introduction

A large body of work has identified a core sense of number supported by the Approximate Number System (ANS) that is present in infancy and across species. Although it is commonly assumed that the ANS directly processes perceptual input and is relatively independent from affective factors, some evidence points at a correlation between ANS performance and math anxiety. However, the evidence is mixed. We tested whether giving participants active control in completing a numerical task would change the relationship between math anxiety on performance.

Methods

Adult participants (N = 103) completed a novel four-alternative-forced-choice non-symbolic numerical comparison task. In a repeated-measures design, participants either passively viewed different dot arrays or actively chose to view each array (i.e., active information-seeking) before deciding on the largest quantity. Participants also provided confidence judgments during the passive version of the task.

Results

We replicated the ratio-dependent signature in participants' accuracy in both the passive and active versions of the task using this novel paradigm, as well as in trial-level confidence judgments and information-seeking behavior. Participants' self-reported math anxiety significantly correlated with their accuracy on the passive version of the task. Critically, the correlation disappeared in the active version of the task. Gender also emerged as a predictor of confidence judgments and a moderator of the effect of task on overall accuracy and the effect of active information seeking on accuracy in the active version of the task. Exploratory analysis of estimated Weber Fraction suggests that these results may be driven by auxiliary factors instead of changes in ANS acuity.

Conclusion

These findings have implications for understanding the relationship between math anxiety and performance on numerical tasks.