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.

The traditional view of cognition as detached from emotions is recently being questioned. This study aimed to investigate the influence of emotional valence on the accuracy and bias in the representation of numbers on the mental number line (MNL). The study included 164 participants who were randomly assigned into two groups with induced positive and negative emotional valence using matched arousal film clips. Participants performed a computerised number-to-position (CNP) task to estimate the position of numbers on a horizontal line. The results showed that participants in the positive valence group exhibited a rightward bias, while those in the negative valence group showed an opposite pattern. The analysis of mean absolute error revealed that the negative valence group had higher error rates compared to the positive valence group. Furthermore, the MNL estimation pattern analysis indicated that a two-cycle cyclic power model (CPM) best explained the data for both groups. These findings suggest that emotional valence influences the spatial representation of numbers on the MNL and affects accuracy in numerical estimations. Our findings are finally discussed in terms of body-specificity and the Brain\'s Asymmetric Frequency Tuning (BAFT) theories. The study provides new insights into the interplay between emotions and numerical cognition.

To determine how young children use and execute finger-based strategies, 5- to 8-year-olds were asked to solve simple addition problems under a choice condition (i.e., they could choose finger-based or non-finger strategies on each problem) and under two no-choice conditions (one in which they needed to use finger-based strategies on all problems and one in which they could not use finger-based strategies). Results showed that children (a) used both finger-based and non-finger strategies to solve simple addition problems in all age groups, (b) used fingers less and less often as they grew older, especially while solving smaller problems, (c) calibrated their use of finger-based strategies to both problem features and strategy performance, and (d) improved efficiency of both finger-based and non-finger strategy execution. Moreover, (e) strategy performance was the best predictor of strategy selection in all age groups, and (f) when they had the possibility to use fingers, children of all age groups obtained better performance relative to when they could not use fingers, especially on larger problems.

Numerical cognition is a field that investigates the sociocultural, developmental, cognitive, and biological aspects of mathematical abilities. Recent findings in cognitive neuroscience suggest that cognitive skills are facilitated by distributed, transient, and dynamic networks in the brain, rather than isolated functional modules. Further, research on the bodily and evolutionary bases of cognition reveals that our cognitive skills harness capacities originally evolved for action and that cognition is best understood in conjunction with perceptuomotor capacities. Despite these insights, neural models of numerical cognition struggle to capture the relation between mathematical skills and perceptuomotor systems. One front to addressing this issue is to identify building block sensorimotor processes (BBPs) in the brain that support numerical skills and develop a new ontology connecting the sensorimotor system with mathematical cognition. BBPs here are identified as sensorimotor functions, associated with distributed networks in the brain, and are consistently identified as supporting different cognitive abilities. BBPs can be identified with new approaches to neuroimaging; by examining an array of sensorimotor and cognitive tasks in experimental designs, employing data-driven informatics approaches to identify sensorimotor networks supporting cognitive processes, and interpreting the results considering the evolutionary and bodily foundations of mathematical abilities. New empirical insights on the BBPs can eventually lead to a revamped embodied cognitive ontology in numerical cognition. Among other mathematical skills, numerical magnitude processing and its sensorimotor origins are discussed to substantiate the arguments presented. Additionally, an fMRI study design is provided to illustrate the application of the arguments presented in empirical research.

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.

Representing the quantity zero as a symbolic concept is considered a unique achievement of abstract human thought.1,2 To conceptualize zero, one must abstract away from the (absence of) sensory evidence to construct a representation of numerical absence: creating \"something\" out of \"nothing.\"2,3,4 Previous investigations of the neural representation of natural numbers reveal distinct numerosity-selective neural populations that overlap in their tuning curves with adjacent numerosities.5,6 Importantly, a component of this neural code is thought to be invariant across non-symbolic and symbolic numerical formats.7,8,9,10,11 Although behavioral evidence indicates that zero occupies a place at the beginning of this mental number line,12,13,14 in humans zero is also associated with unique behavioral and developmental profiles compared to natural numbers,4,15,16,17 suggestive of a distinct neural basis for zero. We characterized the neural representation of zero in the human brain by employing two qualitatively different numerical tasks18,19 in concert with magnetoencephalography (MEG) recordings. We assay both neural representations of non-symbolic numerosities (dot patterns), including zero (empty sets), and symbolic numerals, including symbolic zero. Our results reveal that neural representations of zero are situated along a graded neural number line shared with other natural numbers. Notably, symbolic representations of zero generalized to predict non-symbolic empty sets. We go on to localize abstract representations of numerical zero to posterior association cortex, extending the purview of parietal cortex in human numerical cognition to encompass representations of zero.10,20.

In the present study, we conducted a Stroop-like task in which the participants were required to decide whether the presented stimulus, which could be either a colored digit or a colored rectangle, consisted of more or less than five colors. Like other Stroop-like tasks, the stimuli could be congruent (the stimulus was a digit that was equal to the presented number of colors), incongruent (the stimulus was a digit that was different than the presented number of colors), or neutral (a colored rectangle). We utilized a two-to-one response setting so that in some incongruent trials the digit and the number of colors would elicit the same response (e.g., the digit 3 containing two colors; both are smaller than 5), while in some incongruent trials, the digit and the number of colors would elicit different responses (e.g., the digit 3 containing 6 colors). This enabled us to measure both conflicts arising from stimulus-stimulus and stimulus-response compatibilities. Our results indicated the existence of stimulus-stimulus compatibility (SSC), stimulus-response compatibility (SRC), and task conflict. Interestingly, these effects were in interaction with the number of colors, so that in small numbers, SSC and SRC were found, and in large numbers, SRC and task conflict were found. Moreover, the results suggest that our task includes two types of task conflict that are raised due to three different tasks: processing the meaning of the digit vs. estimating the number of colors and counting the number of colors vs. estimating the number of colors.

Previous research described different cognitive processes on how individuals process distributional information. Based on these processes, the current research uncovered a novel phenomenon in distribution perception: the Endpoint Leverage Effect. Subjective endpoints influence distribution estimations not only locally around the endpoint but also influence estimations across the whole value range of the distribution. The influence is largest close to the respective endpoint and decreases in size toward the opposite end of the value range. Three experiments investigate this phenomenon: Experiment 1 provides correlational evidence for the Endpoint Leverage Effect after presenting participants with a numerical distribution. Experiment 2 demonstrates the Endpoint Leverage Effect by manipulating the subjective endpoints of a numerical distribution directly. Experiment 3 generalizes the phenomenon by investigating a general population sample and estimations regarding a real-world income distribution. In addition, quantitative model analysis examines the cognitive processes underlying the effect. Overall, the novel Endpoint Leverage Effect is found in all three experiments, inspiring further research in a wide area of contexts.

Impaired numerosity perception in developmental dyscalculia (low \"number acuity\") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.

The aim of this study was to explore a number sense deficits in children with developmental dyscalculia, dyslexia, co-occurring disorder and their typically developing peers. A non-symbolic quantity comparison task was used in this study to examine whether children with dyscalculia have number sense deficits. Children aged 10-11 years old from nine primary schools in Taif city, Saudi Arabia, were selected to participate in this study. The children were divided into the dyscalculia group (n = 62), the dyslexia group (n = 60), and co-occurring disorder group (n = 65), and the typically developing peers group (n = 100).4 groups (dyscalculia, dyslexia, co-occurring disorder and typically developing peers group) × 2 stimulus ratio (6:7; 8:12). There were significant differences in non-symbolic quantity comparison tasks between children with dyslexia, co-occurring disorder, and typically developing peers. These results indicate that children with dyscalculia do have number sense deficiencies, but number sense deficiencies are not specific to children with dyscalculia.