Geometry as a Universal Mental Construction

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.

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.

Developmental differences in children's and adults' use of geometric information in map-reading tasks

Using maps effectively requires the ability to scale distances while preserving angle and orientation, the three properties of Euclidean geometry. The aim of the current study was twofold: first, to examine how the ability to represent and use these Euclidean properties changes with development when scaling maps in object-to-object relationships and, second, to explore the effects on the scaling performance of two variables of the array of objects, type of angular configuration and relative vector length. To this end, we tested seventy-five 4-, 6-, and 8-year-old children, as well as twenty-five adults, in a simple completion task with different linear and triangular configurations of objects. This study revealed important developmental changes between 4 and 6 years of age and between 8 years of age and adulthood for both distance and angle representation, while it also showed that the configuration variables affected younger and older children's performances in different ways when scaling distances and preserving angles and orientation. This study was instrumental in showing that, from an early age, children are able to exploit an intrinsic system of reference to scale geometrical configurations of objects.

What makes a landmark effective in adolescent and adult rats? Sex and age differences in a navigation task

In three experiments, rats of different ages were trained in a circular pool to find a hidden platform whose location was defined in terms of a single landmark, a cylinder outside the pool. Following training, two main components of the landmark, its shape and pattern, were tested individually. Experiment 1 was performed by adolescent and adult rats (Exp. 1a, males; Exp. 1b, females). Adult rats always learned faster than the adolescent animals. On test trials, interesting tendencies were found-mainly, one favoring males on the shape test trial, and another favoring females on the pattern test trial. Experiment 2 was conducted only with adolescent rats, and these males and females did not differ when learning the task. However, on test trials the males learned more about the landmark shape component than about the landmark pattern component, while the females learned equally about the two components of the landmark. Finally, Experiment 3 was conducted only with adult rats, and again the males and females did not differ when learning the task. However, on test trials the males learned equally about the two components of the landmark (shape and pattern), but the females learned more about the landmark pattern component than about the landmark shape component. This set of experiments supports the claim that male and female rats can learn rather different things about a landmark that signals the location of the platform, with age being a critical variable.

Bayesian validation of grammar productions for the language of thought

Probabilistic proposals of Language of Thoughts (LoTs) can explain learning across different domains as statistical inference over a compositionally structured hypothesis space. While frameworks may differ on how a LoT may be implemented computationally, they all share the property that they are built from a set of atomic symbols and rules by which these symbols can be combined. In this work we propose an extra validation step for the set of atomic productions defined by the experimenter. It starts by expanding the defined LoT grammar for the cognitive domain with a broader set of arbitrary productions and then uses Bayesian inference to prune the productions from the experimental data. The result allows the researcher to validate that the resulting grammar still matches the intuitive grammar chosen for the domain. We then test this method in the language of geometry, a specific LoT model for geometrical sequence learning. Finally, despite the fact of the geometrical LoT not being a universal (i.e. Turing-complete) language, we show an empirical relation between a sequence’s probability and its complexity consistent with the theoretical relationship for universal languages described by Levin’s Coding Theorem.

Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics

Many poor children are underprepared for demanding primary school curricula. Research in cognitive science suggests that school achievement could be improved by preschool pedagogy in which numerate adults engage children's spontaneous, nonsymbolic mathematical concepts. To test this suggestion, we designed and evaluated a game-based preschool curriculum intended to exercise children's emerging skills in number and geometry. In a randomized field experiment with 1540 children (average age 4.9 years) in 214 Indian preschools, 4 months of math game play yielded marked and enduring improvement on the exercised intuitive abilities, relative to no-treatment and active control conditions. Math-trained children also showed immediate gains on symbolic mathematical skills but displayed no advantage in subsequent learning of the language and concepts of school mathematics.

Core knowledge and the emergence of symbols: The case of maps

Map reading is unique to humans but present in people of diverse cultures, at ages as young as 4 years. Here we explore the nature and sources of this ability, asking both what geometric information young children use in maps and what non-symbolic systems are associated with their map-reading performance. Four-year-old children were given two tests of map-based navigation (placing an object within a small 3D surface layout at a position indicated on a 2D map), one focused on distance relations and the other on angle relations. Children also were given two non-symbolic tasks, testing their use of geometry for navigation (a reorientation task) and for visual form analysis (a deviant-detection task). Although children successfully performed both map tasks, their performance on the two map tasks was uncorrelated, providing evidence for distinct abilities to represent distance and angle on 2D maps of 3D surface layouts. In contrast, performance on each map task was associated with performance on one of the two non-symbolic tasks: map-based navigation by distance correlated with sensitivity to the shape of the environment in the reorientation task, whereas map-based navigation by angle correlated with sensitivity to the shapes of 2D forms and patterns in the deviant detection task. These findings suggest links between one uniquely human, emerging symbolic ability, geometric map use, and two core systems of geometry.

Two randomized trials provide no consistent evidence for nonmusical cognitive benefits of brief preschool music enrichment

Young children regularly engage in musical activities, but the effects of early music education on children's cognitive development are unknown. While some studies have found associations between musical training in childhood and later nonmusical cognitive outcomes, few randomized controlled trials (RCTs) have been employed to assess causal effects of music lessons on child cognition and no clear pattern of results has emerged. We conducted two RCTs with preschool children investigating the cognitive effects of a brief series of music classes, as compared to a similar but non-musical form of arts instruction (visual arts classes, Experiment 1) or to a no-treatment control (Experiment 2). Consistent with typical preschool arts enrichment programs, parents attended classes with their children, participating in a variety of developmentally appropriate arts activities. After six weeks of class, we assessed children's skills in four distinct cognitive areas in which older arts-trained students have been reported to excel: spatial-navigational reasoning, visual form analysis, numerical discrimination, and receptive vocabulary. We initially found that children from the music class showed greater spatial-navigational ability than did children from the visual arts class, while children from the visual arts class showed greater visual form analysis ability than children from the music class (Experiment 1). However, a partial replication attempt comparing music training to a no-treatment control failed to confirm these findings (Experiment 2), and the combined results of the two experiments were negative: overall, children provided with music classes performed no better than those with visual arts or no classes on any assessment. Our findings underscore the need for replication in RCTs, and suggest caution in interpreting the positive findings from past studies of cognitive effects of music instruction.

Core foundations of abstract geometry

Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.

Core systems of geometry in animal minds

Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds.