Observers Efficiently Extract the Minimal and Maximal Element in Perceptual Magnitude Sets: Evidence for a Bipartite Format.

The mind represents abstract magnitude information, including time, space, and number, but in what format is this information stored? We show support for the bipartite format of perceptual magnitudes, in which the measured value on a dimension is scaled to the dynamic range of the input, leading to a privileged status for values at the lowest and highest end of the range. In six experiments with college undergraduates, we show that observers are faster and more accurate to find the endpoints (i.e.

Effects of spatial frequency cross-adaptation on the visual number sense.

When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? We investigate the role of specific spatial frequencies to the encoding of number through cross-adaptation. In two experiments, observers were peripherally adapted to six randomly generated sinusoidal gratings varying from relatively low-spatial frequency (M = 0.

Children dynamically update and extend the interface between number words and perceptual magnitudes.

As adults, we represent and think about number, space, and time in at least two ways: our intuitive-but imprecise-perceptual representations, and the slowly learned-but precise-number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test two accounts of this developmental milestone.

Effects of Robotics Education on Young Children's Cognitive Development: a Pilot Study with Eye-Tracking.

The emerging field of robotics education (RE) is a new and rapidly growing subject area worldwide. It may provide a playful and novel learning environment for children to engage with all aspects of science, technology, engineering, and mathematics (STEM) learning. The purpose of this research is to examine how robotics learning activities may affect the cognitive abilities and cognitive processes of 6-8 years old children.

Visual numerosity perception shows no advantage in real-world scenes compared to artificial displays.

While the human visual system is sensitive to numerosity, the mechanisms that allow perception to extract and represent the number of objects in a scene remains unknown. Prominent theoretical approaches posit that numerosity perception emerges from passive experience with visual scenes throughout development, and that unsupervised deep neural network models mirror all characteristic behavioral features observed in participants. Here, we derive and test a novel prediction: if the visual number sense emerges from exposure to real-world scenes, then the closer a stimulus aligns with the natural statistics of the real world, the better number perception should be.

The malleable impact of non-numeric features in visual number perception.

Non-numeric stimulus features frequently influence observers' number judgments: when judging the number of items in a display, we will often (mis)perceive the set with a larger cumulative surface area as more numerous. These "congruency effects" are often used as evidence for how vision extracts numeric information and have been invoked in arguments surrounding whether non-numeric cues (e.g.

Real models: The limits of behavioural evidence for understanding the ANS.

Clarke and Beck use behavioural evidence to argue that (1) approximate ratio computations are sufficient for claiming that the approximate number system (ANS) represents the rationals, and (2) the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.

Are children's judgments of another's accuracy linked to their metacognitive confidence judgments?

Unlabelled: The world can be a confusing place, which leads to a significant challenge: how do we figure out what is true? To accomplish this, children possess two relevant skills: reasoning about the likelihood of their own accuracy (metacognitive confidence) and reasoning about the likelihood of others' accuracy (mindreading). Guided by Signal Detection Theory and Simulation Theory, we examine whether these two self- and other-oriented skills are one in the same, relying on a single cognitive process. Specifically, Signal Detection Theory proposes that confidence in a decision is purely derived from the imprecision of that decision, predicting a tight correlation between decision accuracy and confidence.

The effect of gender stereotypes on young girls' intuitive number sense.

Despite the global importance of science, engineering, and math-related fields, women are consistently underrepresented in these areas. One source of this disparity is likely the prevalence of gender stereotypes that constrain girls' and women's math performance and interest. The current research explores the developmental roots of these effects by examining the impact of stereotypes on young girls' intuitive number sense, a universal skill that predicts later math ability.

Mini managers: Children strategically divide cognitive labor among collaborators, but with a self-serving bias.

Strategic collaboration according to the law of comparative advantage involves dividing tasks based on the relative capabilities of group members. Three experiments (N = 405, primarily White and Asian, 45% female, collected 2016-2019 in Canada) examined how this strategy develops in children when dividing cognitive labor. Children divided questions about numbers between two partners.

Linguistic meanings as cognitive instructions.

Natural languages like English connect pronunciations with meanings. Linguistic pronunciations can be described in ways that relate them to our motor system (e.g.

Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability.

Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study.

Children flexibly compare their confidence within and across perceptual domains.

How does a person make decisions across perceptual boundaries? Here, we test the account that confidence constitutes a common currency for perceptual decisions even in childhood by examining whether confidence can be compared across distinct perceptual dimensions. We conducted a strict test of domain-generality in confidence reasoning by asking 6- to 7-year-olds to compare their confidence in 2 decisions, either from the same perceptual dimension (e.g.

The intuitive number sense contributes to symbolic equation error detection abilities.

Research over the past 20 years has suggested that our intuitive sense of number-the Approximate Number System (ANS)-is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the and of symbolic math equation errors.

The publication gender gap in psychology.

Women are notably underrepresented in the academic sciences. Psychology is a pertinent case study of gender inequality in science, because women make up over three quarters of undergraduate and graduate students but only a third of all full professors. Here, publication records from 125 high-impact, peer-reviewed psychology journals are analyzed to describe nuanced patterns about how men and women contribute to research psychology.

Visual illusions help reveal the primitives of number perception.

The human perceptual system is responsive to numerical information within visual and auditory scenes. For example, when shown 2 displays of dots, observers can instantly, albeit approximately, identify the set that is more numerous. Theories in perceptual and cognitive psychology have focused on 2 mechanisms for how vision accomplishes such a feat: Under the domain-specific encoding theory, number is represented as a primary visual feature of perception, much like motion or color, while under the domain-general theory, the visual system represents number indirectly, through a complex combination of features such as the size of the dots, their total cluster, and so forth.

An Introduction to the Approximate Number System.

What are young children's first intuitions about numbers and what role do these play in their later understanding of mathematics? Traditionally, has been viewed as a culturally derived breakthrough occurring relatively recently in human history that requires years of education to master. Contrary to this view, research in cognitive development indicates that our minds come equipped with a rich and flexible sense of number-the Approximate Number System (ANS). Recently, several major challenges have been mounted to the existence of the ANS and its value as a domain-specific system for representing number.

The contributions of non-numeric dimensions to number encoding, representations, and decision-making factors.

Leibovich et al. suggest that congruency effects in number perception (biases towards smaller, denser, etc., dots) are evidence for the number's dependence on these dimensions.

Children's intuitive sense of number develops independently of their perception of area, density, length, and time.

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS - indexed as the most difficult ratio of two numbers that children can reliably discriminate - is well known to improve with development: whereas infants require relatively large ratios to discriminate number, children can discriminate finer and finer changes in number between toddlerhood and early adulthood. Which factors drive the developmental improvements in ANS precision? Here, we investigate the influence of four non-numeric dimensions - area, density, line length, and time - on ANS development, exploring the degree to which the ANS develops independently from these other dimensions, from inhibitory control, and from domain-general factors such as attention and working memory that are shared between these tasks.

Better together: Multiple lines of evidence for a link between approximate and exact number representations: A reply to Merkley, Matejko, and Ansari.

The results of our recent experiments suggest that temporarily modulating children's approximate number system (ANS) precision leads to a domain-specific change in their symbolic math performance (Journal of Experimental Child Psychology, 2016, Vol. 147, pp. 82-99).

The precision of mapping between number words and the approximate number system predicts children's formal math abilities.

Children can represent number in at least two ways: by using their non-verbal, intuitive approximate number system (ANS) and by using words and symbols to count and represent numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children's math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons.

Acquisition of the Cardinal Principle Coincides with Improvement in Approximate Number System Acuity in Preschoolers.

Human mathematical abilities comprise both learned, symbolic representations of number and unlearned, non-symbolic evolutionarily primitive cognitive systems for representing quantities. However, the mechanisms by which our symbolic (verbal) number system becomes integrated with the non-symbolic (non-verbal) representations of approximate magnitude (supported by the Approximate Number System, or ANS) are not well understood. To explore this connection, forty-six children participated in a 6-month longitudinal study assessing verbal number knowledge and non-verbal numerical acuity.

Changing the precision of preschoolers' approximate number system representations changes their symbolic math performance.

From early in life, humans have access to an approximate number system (ANS) that supports an intuitive sense of numerical quantity. Previous work in both children and adults suggests that individual differences in the precision of ANS representations correlate with symbolic math performance. However, this work has been almost entirely correlational in nature.

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.

Eye movements reveal distinct encoding patterns for number and cumulative surface area in random dot arrays.

Humans can quickly and intuitively represent the number of objects in a scene using visual evidence through the Approximate Number System (ANS). But the computations that support the encoding of visual number-the transformation from the retinal input into ANS representations-remain controversial. Two types of number encoding theories have been proposed: those arguing that number is encoded through a dedicated, enumeration computation, and those arguing that visual number is inferred from nonnumber specific visual features, such as surface area, density, convex hull, etc.