Large scale studies have documented socioeconomic (SES) and racial/ethnic disparities in children's standardized math achievement at kindergarten entry. These early math skills predict future mathematics achievement and career success. However, limited research has been conducted using large sample sizes to understand how SES and race/ethnicity are related to children's numerical skills at even younger ages. The current study aims to investigate sociodemographic variability in three fundamental areas of early numeracy: nonverbal numerosity discrimination, rote counting, and cardinal number word knowledge. In addition, we will examine if the relations between numerical skills might be explained by their shared correlations to sociodemographic factors and if differences in numerical skills between sociodemographic groups can be explained by variability in working memory. Finally, we also investigate whether childcare attendance moderates early sociodemographic differences in numerical abilities. To achieve these goals, data from children aged 2; 6-6; 0 will be gathered from ∼ 45 US sites, drawn from a larger multi-lab international project (ManyNumbers project). The findings of this research will enhance our understanding of early emerging variability in numerical skills and provide insights into developing responsive and inclusive educational practices that support diverse learning needs in the early years. SUMMARY: Early mathematical skills are crucial for long-term academic and career achievement. SES and race/ethnicity-related disparities in math achievement emerge as early as preschool. Most studies use standardized math assessments that combine different numerical skills to assess achievement gaps, leaving uncertain which specific skills vary with demographic variables. We explore disparities in developmentally significant numerical skills and their relation to demographic variables. We also report relations between WM, childcare attendance and numerical skills. Data from approximately N = 1080 children aged 2;6-6;0 will be collected from ∼ 45 US labs, including demographic information and numeracy measures.

Abstract One of the most astonishing abilities documented in human newborns is that they can abstract numerosity – the number of items in sets - across sensory modalities. Its underlying neural mechanisms remain unknown. Using high-density EEG and a frequency-tagging paradigm, we measured neural entrainment to periodically presented visual arrays that were either numerically congruent or incongruent with previously familiarized and concurrently presented auditory sequences in 21 newborns (0–3 days old). The amplitude of neural entrainment to the visual arrays provided a robust index of cross-modal numerical congruency: it was significantly reduced for numerically congruent relative to incongruent stimuli, consistent with a cross-modal numerosity repetition-suppression mechanism. These findings identify a candidate neural mechanism supporting newborns’ ability to encode numerosity in an abstract supramodal format, and reinforce the view that number constitutes a foundational dimension of human perception since birth.

"Core knowledge" refers to a set of cognitive systems that underwrite early representations of the physical and social world, appear universally across cultures, and likely result from our genetic endowment. Although this framework is canonically considered as a hypothesis about early-emerging conception - how we think and reason about the world - here we present an alternative view: that many such representations are inherently perceptual in nature. This "core perception" view explains an intriguing (and otherwise mysterious) aspect of core-knowledge processes and representations: that they also operate in adults, where they display key empirical signatures of perceptual processing. We first illustrate this overlap using recent work on "core physics", the domain of core knowledge concerned with physical objects, representing properties such as persistence through time, cohesion, solidity, and causal interactions. We review evidence that adult vision incorporates exactly these representations of core physics, while also displaying empirical signatures of genuinely perceptual mechanisms, such as rapid and automatic operation on the basis of specific sensory inputs, informational encapsulation, and interaction with other perceptual processes. We further argue that the same pattern holds for other areas of core knowledge, including geometrical, numerical, and social domains. In light of this evidence, we conclude that many infant results appealing to precocious reasoning abilities are better explained by sophisticated perceptual mechanisms shared by infants and adults. Our core-perception view elevates the status of perception in accounting for the origins of conceptual knowledge, and generates a range of ready-to-test hypotheses in developmental psychology, vision science, and more.

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such “Eureka” moments when learning science concepts, and how do these episodes relate to learning mechanisms? To address these questions, we developed a new paradigm where participants learned a mathematical concept in the lab, in a single experimental session. Participants were given 1 to 7 lessons introducing the concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. They were then tested on their understanding of geodesics in several tasks requiring increasing levels of generalization from the information taught in the lessons. Our findings indicate that insight experiences are common when learning mathematics, as such experiences were reported by about 61% of our participants. Moreover, the participants who experienced insights performed better in a generalization test where they needed to identify a type of geodesic that had not been presented in the lessons, and this, even after controlling for their confidence in their own understanding. Based on these findings, we suggest that concept learning involves mechanisms that generally are not accessible to introspection, except when the process reaches key computational steps and insights are triggered.

Sensitivity to numbers is a crucial and evolutionarily conserved cognitive ability. The lack of experimental models amenable to systematic genetic and neural manipulation has precluded discovering circuits required for numerical cognition. Here, we demonstrate that in a two-choice task Drosophila fruit flies spontaneously prefer sets containing more objects. This preference is determined by the ratio between the two numerical quantities tested, a characteristic signature of numerical cognition across species. Individual flies maintained their numerical choice over consecutive days. Using a numerical visual conditioning paradigm, we found that flies are capable of associating sucrose with numerical quantities and can be trained to reverse their spontaneous preference for large quantities. Finally, we show that silencing LC11 neurons reduces the preference for more objects, thus identifying a neuronal substrate for numerical cognition in invertebrates. This discovery paves the way for the systematic analysis of the behavioral and neural mechanisms underlying sensitivity to numerosity.

Raw data and analysis codes corresponding to the article of Bengochea et al 2023 : Numerical discrimination in Drosophila melanogaster.

From the very first days of life, newborns are not tied to represent narrow, modality- and object-specific aspects of their environment. Rather, they sometimes react to abstract properties shared by stimuli of very different nature, such as approximate numerosity or magnitude. As of now, however, there is no evidence that newborns possess abstract representations that apply to small sets: in particular, while newborns can match large approximate numerosities across senses, this ability does not extend to small numerosities. In two experiments, we presented newborn infants (N = 64, age 17 to 98 hours) with patterned sets AB or ABB simultaneously in the auditory and visual modalities. Auditory patterns were presented as periodic sequences of sounds (AB: triangle-drum-triangle-drum-triangle-drum …; ABB: triangle-drum-drum-triangle-drum-drum-triangle-drum-drum …), and visual patterns as arrays of 2 or 3 shapes (AB: circle-diamond; ABB: circle-diamond-diamond). In both experiments, we found that participants reacted and looked longer when the patterns matched across the auditory and visual modalities – provided that the first stimulus they received was congruent. These findings uncover the existence of yet another type of abstract representations at birth, applying to small sets. As such, they bolster the hypothesis that newborns are endowed with the capacity to represent their environment in broad strokes, in terms of its most abstract properties. This capacity for abstraction could later serve as a scaffold for infants to learn about the particular entities surrounding them.

Inter-individual differences in infants' numerosity processing have been assessed using a change detection paradigm, where participants were presented with two concurrent streams of images, one alternating between two numerosities and the other showing one constant numerosity. While most infants look longer at the changing stream in this paradigm, the reasons underlying these preferences have remained unclear. We suggest that, besides being attracted by numerosity changes, infants perhaps also respond to the alternating pattern of the changing stream. We conducted two experiments (N = 32) with 6-month-old infants to assess this hypothesis. In the first experiment, infants responded to changes in numerosity even when the changing stream showed numerosities in an unpredictable random order. In the second experiment, infants did not display any preference when an alternating stream was pitted against a random stream. These findings do not provide evidence that the alternating pattern of the changing stream contributes to drive infants' preferences. Instead, around the age of 6 months, infants' responses in the numerosity change detection paradigm appear to be mainly driven by changes in numerosity, with different levels of preference reflecting inter-individual difference in the acuity of numerosity perception.

In order to reach human performance on complex visual tasks, artificial systems need to incorporate a significant amount of understanding of the world in terms of macroscopic objects, movements, forces, etc. Inspired by work on intuitive physics in infants, we propose an evaluation benchmark which diagnoses how much a given system understands about physics by testing whether it can tell apart well matched videos of possible versus impossible events constructed with a game engine. The test requires systems to compute a physical plausibility score over an entire video. To prevent perceptual biases, the dataset is made of pixel matched quadruplets of videos, enforcing systems to focus on high level temporal dependencies between frames rather than pixel-level details. We then describe two Deep Neural Networks systems aimed at learning intuitive physics in an unsupervised way, using only physically possible videos. The systems are trained with a future semantic mask prediction objective and tested on the possible versus impossible discrimination task. The analysis of their results compared to human data gives novel insights in the potentials and limitations of next frame prediction architectures.

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3-34 years), and 25 participants from the Amazon (age 5-67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded.

From a very young age, humans are able to recognize objects or living beings while they move and assume different postures. This ability to recognize object identities through flexible aspects could be based on invariant properties of shapes, such as for example the properties put forward by the formalism of the medial axis theory (also called skeleton theory). This formalism, which was originally designed to describe organic shapes such as bodies or plants, can indeed easily capture “natural” invariances, such as the shape of an animal’s body as it moves. Several behavioral or brain imaging studies have started to highlight the role of the medial axis parameters in human vision, including in categorization. However, all these studies used different characterizations of the medial axis properties, making it hard to compare their results. In particular, across studies the authors manipulated different aspects of the shapes and their medial axes and used different measures to quantify skeletal similarities. Our work had two aims. First, we created a formal mathematical space providing a full description of shapes in the language of the medial axis formalism, which can be used as a unifying framework for cognitive research. For this purpose, we defined three families of parameters: topological parameters describing the structure of the skeleton in the format of a non-measured graph; skeleton parameters specifying the details of the shape’s skeleton; and growth parameters describing how the shape can be grown from its skeleton. Second, we also implemented a Matlab toolbox generating shapes specified in the vocabulary of these medial-axis parameters, and selectively manipulating each skeleton and growth parameter in isolation. In conclusion, our work introduces both a unifying parametric language and a methodological tool paving the way for future systematic investigations of the role of the medial-axis parameters in human vision.

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex spatial transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry.

From an early age, humans intuitively expect physical objects to obey core principles, including continuity (objects follow spatiotemporally continuous paths) and solidity (two solid objects cannot occupy the same space at the same time). These two principles are sometimes viewed as deriving from a single overarching “persistence” principle. Indeed, violations of solidity where one solid object seemingly passes through another could theoretically be interpreted as a violation of continuity, with an object “teleporting” to switch places rather than passing through a solid obstacle. However, it is an empirical issue whether the two principles are processed distinctly or identically to one another. Here, adult participants tracked objects during dynamic events in a novel location detection task, which sometimes involved violations of the principles of continuity or solidity. While participants explicitly noticed both types of violations and reported being equally surprised at both, they made more errors and answered more slowly after continuity violations than after solidity violations. Our results demonstrate that the two principles show different signature patterns, and are thus represented distinctly in the mind.

Research in developmental cognitive science reveals that human infants perceive shape changes in 2D visual forms that are repeatedly presented over long durations. Nevertheless, infants’ sensitivity to shape under the brief conditions of natural viewing has been little studied. Three experiments tested for this sensitivity by presenting 128 seven-month-old infants with shapes for the briefer durations under which they might see them in dynamic scenes. The experiments probed infants’ sensitivity to two fundamental geometric properties of scale- and orientation-invariant shape: relative length and angle. Infants detected shape changes in closed figures, which presented changes in both geometric properties. Infants also detected shape changes in open figures differing in angle when figures were presented at limited orientations. In contrast, when open figures were presented at unlimited orientations, infants detected changes in relative length but not in angle. The present research therefore suggests that, as infants look around at the cluttered and changing visual world, relative length is the primary geometric property by which they perceive scale- and orientation-invariant shape.

Euclidean geometry defines objects that can be realized in space, and may therefore be founded in spatial perception. We investigated whether the perception of small, 2-dimen- sional visual forms could provide cognitive foundations for Euclidean knowledge, by asking two questions. First, are humans sensitive to form variations that are relevant to Eu- clidean geometry (e.g. changes in angle)? Second, can ob- servers easily disregard variations that are irrelevant to Eu- clidean geometry (e.g., changes in scale)? Participants from the U.S. (age 3-34 years) and from the Amazon (age 5-67) were asked to locate deviants in panels of 6 forms of vari- able orientation. Results indicate that perception of forms aligns with a restricted version of Euclidean geometry, where forms are defined in terms of metric proportions and global size, but mirror images are assimilated. Moreo- ver, children below 6 did not clearly analyze forms in terms of the shape property of angle.

In order to reach human performance on complex visual tasks, artificial systems need to incorporate a significant amount of understanding of the world in terms of macroscopic objects, movements, forces, etc. Inspired by work on intuitive physics in infants, we propose an evaluation framework which diagnoses how much a given system understands about physics by testing whether it can tell apart well matched videos of possible versus impossible events. The test requires systems to compute a physical plausibility score over an entire video. It is free of bias and can test a range of specific physical reasoning skills. We then describe the first release of a benchmark dataset aimed at learning intuitive physics in an unsupervised way, using videos constructed with a game engine. We describe two Deep Neural Network baseline systems trained with a future frame prediction objective and tested on the possible versus impossible discrimination task. The analysis of their results compared to human data gives novel insights in the potentials and limitations of next frame prediction architectures.

At the scale in which we live, space is continuous. Nevertheless, our perception and cognition parse the world into categories, whether physical, like scene or object. or abstract, like infinitesimal point or 7. The present study focuses on 2 categories of special angles in planar geometry. parallels and perpendiculars, and we evaluate how these categories might be reflected in adults' basic angle discrimination. In the first experiment, participants were most precise when detecting 2 parallel or perpendicular lines among other pairs of lines at different relative orientations. Detection was also enhanced for 2 connected lines whose angle approached 90 degrees, with precision peaking at 90 degrees. These patterns emerged despite large variations in the scales and orientations of the angle exemplars. In the second experiment, the enhanced detection of perpendiculars persisted when stimuli were rotated in depth. indicating a capacity to discriminate shapes based on perpendicularity in 3 dimensions despite large variation in angles' 2-dimensional projections. The results suggest that 2 categorical concepts which lie at the foundation of Euclidean geometry, parallelism and perpendicularity, are reflected in our discrimination of simple visual forms. and they pave the way for future studies exploring the developmental and evolutionary origins of these cognitive categories.

Leibovich et al. opened up an important discussion on the nature and origins of numerosity perception. The authors rightly point out that non-numerical features of stimuli influence this ability. Despite these biases, there is evidence that from birth, humans perceive and represent numerosities, and not just non-numerical quantitative features such as item size, density, and convex hull.

Numerous studies have shown that many animal species can be trained to discriminate between stimuli differing in numerosity. However, in the absence of generalization tests with untrained numerosities, what decision criterion was used by subjects remains unclear: the subjects may succeed by selecting a specific number of items (a criterion over absolute numerosities), or by applying a more general relative numerosity rule, for example, selecting the larger/smaller quantity of items. The latter case may require more powerful representations, supporting judgments of order ("more/less") beyond simple "same/different" judgments, but a relative numerosity rule may also be more adaptive. In previous research, we showed that guppies (Poecilia reticulata) spontaneously prefer relative numerosity rules. To date it is unclear whether this preference is shared by other fish and, more broadly, other species. Here we compared the performance of angelfish (Pterophyllum scalare) with that of human adults (Homo sapiens) in a task in which subjects were initially trained to select arrays containing 10 dots (either in 5 vs. 10 or 10 vs. 20 comparisons). Subsequently they were tested with the previously trained numerosity and a novel numerosity (respectively, 20 or 5). In the absence of explicit instructions, both species spontaneously favored a relative rule, selecting the novel numerosity. These similarities demonstrate that, beyond shared representations for numerical quantities, vertebrate species may also share a system for taking decisions about quantities. (PsycINFO Database Record