Navigation as a source of geometric knowledge: young children's use of length, angle, distance, and direction in a reorientation task

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.

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.

Wild Tibetan Macaques Use a Route-Based Mental Map to Navigate in Large-Scale Space

Many animals face significant challenges in locating and acquiring resources that are unevenly distributed in space and time. In the case of nonhuman primates, it remains unclear how individuals remember goal locations and whether they navigate using a route-based or a coordinate-based mental representation when moving between out-of-sight feeding and resting sites (i.e., large-scale space). Here, we examine spatial memory and mental map formation in wild Tibetan macaques (Macaca thibetana) inhabiting a mountainous, forested ecosystem characterized by steep terrain that limits direct vision to 25 meters. We used an instantaneous scan sampling technique at 10-min intervals to record the behavior and location of macaques on Mt. Huangshan, Anhui Province, China, from September 2020 to August 2023. Over 214 days, we obtained 7180 GPS points of the macaques' locations. Our study revealed that the macaques reused 1264 route segments (average length 204.26 m) at least four times each. The number of feeding and resting sites around the habitual route segment, terrain roughness, and dense vegetation areas significantly influenced the use of route segments by our study group. In addition, we found evidence that the monkeys reused 48 nodes to reorient their travel path. We found that monkeys approached a revisited foraging or resting site from the same limited set of directions, which is inconsistent with a coordinate-based spatial representation. In addition, the direction in which the macaques left a feeding or resting site was significantly different from the straight-line direction required to reach their next feeding or resting site, suggesting that the macaques frequently reoriented their direction of travel to reach their goal. Finally, on average, macaques traveled 24% (CI = 1.24) farther than the straight-line distance to reach revisited feeding and resting sites. From our robust data set, we conclude that Tibetan macaques navigate large spaces using a route-based mental representation that appears to help them locate food resources in dense, rugged montane forests and heterogeneous habitats.

A common format for representing spatial location in visual and motor working memory

Does the mind rely on similar systems of spatial representation for both perception and action? Here, we assessed the format of location representations in two simple spatial localization tasks. In one task, participants simply remembered the location of an item based solely on visual input. In another, participants remembered the location of a point in space based solely on kinesthetic input. Participants' recall errors were more consistent with the use of polar coordinates than Cartesian coordinates in both tasks. Moreover, measures of spatial bias and performance were correlated across modalities. In a subsequent study, we tested the flexibility with which people use polar coordinates to represent space; we show that the format in which the information is presented to participants influences how that information is encoded and the errors that are made as a result. We suggest that polar coordinates may be a common means of representing location information across visual and motor modalities, but that these representations are also flexible in form.

The developmental trajectories of children's reorientation to global and local properties of environmental geometry

The way in which organisms represent the shape of their environments during navigation has been debated in cognitive, comparative, and developmental psychology. While there is evidence that adult humans encode the entire boundary shape of an environment (a global-shape representation), there are also data demonstrating that organisms reorient using only segments of the boundary that signal a goal location (a local-shape representation). Developmental studies offer unique insights into this debate; however, most studies have used designs that cannot dissociate the type of boundary-shape representation that children use to guide reorientation. Thus, we examined the developmental trajectories of children's reorientation according to local and global boundary shape. Participants aged 6-12 years were trained to find a goal hidden in one corner of a virtual arena, after which they were required to reorient in a novel test arena. From 10.5 years, children performed above chance when the test arena permitted reorientation based only on local-shape (Experiment 2), or only global-shape (Experiment 3) information. Moreover, when these responses were placed into conflict, older children reoriented with respect to global-shape information (Experiment 4). These age-related findings were not due to older children being better able to reorient in virtual environments per se: when trained and tested within the same environment (Experiment 1), children performed above chance from 6 years. Together, our results suggest (a) the ability to reorient on the basis of global- and local-shape representations develops in parallel, and (b) shape-based information is weighted to determine which representation informs reorientation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

What have we learned from research on the "geometric module"?

This article is an overview of the research and controversy initiated by Cheng's (Cognition, 23(2), 149-178, 1986) article hypothesizing a purely geometric module in spatial representation. Hundreds of experiments later, we know much more about spatial behavior across a very wide array of species, ages, and kinds of conditions, but there is still no consensus model of the phenomena. I argue for an adaptive combination approach that entails several principles: (1) a focus on ecological niches and the spatial information they offer; (2) an approach to development that is experience-expectant: (3) continued plasticity as environmental conditions change; (4) language as one of many cognitive tools that can support spatial behavior.

Précis of What Babies Know

Where does human knowledge begin? Research on human infants, children, adults, and nonhuman animals, using diverse methods from the cognitive, brain, and computational sciences, provides evidence for six early emerging, domain-specific systems of core knowledge. These automatic, unconscious systems are situated between perceptual systems and systems of explicit concepts and beliefs. They emerge early in infancy, guide children's learning, and function throughout life.

Navigational roots of spatial and temporal memory structure

Our minds are constantly in transit, from the present to the past to the future, across places we have and have not directly experienced. Nevertheless, memories of our mental time travel are not organized continuously and are adaptively chunked into contexts and episodes. In this paper, I will review evidence that suggests that spatial boundary representations play a critical role in providing structure to both our spatial and temporal memories. I will illustrate the intimate connection between hippocampal spatial mapping and temporal sequencing of episodic memory to propose that high-level cognitive processes like mental time travel and conceptual mapping are rooted in basic navigational mechanisms that we humans and nonhuman animals share. Our neuroscientific understanding of hippocampal function across species may provide new insight into the origins of even the most uniquely human cognitive abilities.

Redundancy and Reducibility in the Formats of Spatial Representations

Mental representations are the essence of cognition. Yet to understand how the mind works, one must understand not just the content of mental representations (i.e., what information is stored) but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a "case study" of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly "redundant" formats may support the flexible spatial behavior observed in humans and that researchers should approach the study of all mental representations with this possibility in mind.

Effects of spatial boundaries on episodic memory development

Children's spatial mapping starts out particularly sensitive to 3D wall-like boundaries and develops over early childhood to flexibly include other boundary types. This study investigated whether spatial boundaries influence children's episodic memory, as in adults, and whether this effect is modulated by boundary type. Eighty-one Korean children (34 girls, 36-84 months old) re-enacted a sequence of three discrete hiding events within a space containing one of three boundaries: 3D wall, aligned objects, or 2D line. Children's memory of events occurring on one side of the boundary developed earlier than those that crossed the boundary. At first, this interaction only applied to the 3D wall and extended to other boundary types with age, suggesting that children's changing spatial representations influence their episodic memory development.

The Geometric World of Fishes: A Synthesis on Spatial Reorientation in Teleosts

Fishes navigate through underwater environments with remarkable spatial precision and memory. Freshwater and seawater species make use of several orientation strategies for adaptative behavior that is on par with terrestrial organisms, and research on cognitive mapping and landmark use in fish have shown that relational and associative spatial learning guide goal-directed navigation not only in terrestrial but also in aquatic habitats. In the past thirty years, researchers explored spatial cognition in fishes in relation to the use of environmental geometry, perhaps because of the scientific value to compare them with land-dwelling animals. Geometric navigation involves the encoding of macrostructural characteristics of space, which are based on the Euclidean concepts of "points", "surfaces", and "boundaries". The current review aims to inspect the extant literature on navigation by geometry in fishes, emphasizing both the recruitment of visual/extra-visual strategies and the nature of the behavioral task on orientation performance.

Blindfolded adults' use of geometric cues in haptic-based relocation

Non-visual information is important for navigation in limited visibility conditions. We designed a haptic-based relocation task to examine blindfolded adults' use of geometric cues. Forty-eight participants learned to locate a corner in a parallelogram frame. They were then tested in different transformed frames: (a) a reverse-parallelogram, in which locations predicted by original length information and angle information conflicted, (b) a rectangle, which retained only length information, and (c) a rhombus, which retained only angle information. Results show that access to the environment's geometry through haptic modality is sufficient for relocation. However, adults' performances in the current task were different from that in visual tasks in previous findings. First, compared to previous findings in visual-based tasks, length information lost its priority. Approximately half of the participants relied on angle information in the conflict test and the other half relied on length. Second, though participants encoded both length and angle information in the learning phase, only one cue was relied on after the conflict test. Finally, though participants encoded the target location successfully, they failed to represent the global shape of the environment. We attribute adults' different performances in haptic-based and visual-based tasks to the high cognitive demands in encoding and using haptic spatial cues, especially length information.

Separation of geometric and featural information in children's spatial representation: Evidence from a model selection task

Previous studies in spatial reorientation have found that young children rely mainly on geometric shapes for reorientation and sometimes ignore features in the environment. Theoretical interpretations of children's reorientation performance are usually attributed to children's spatial representation of their surrounding environments. The geometric module theory states that featural information is represented separately from geometric shape in young children's reorientation, whereas the adaptive combination model depicts an integral representation. Reorientation tasks, however, require the recognition of a specific location, and thus how the whole environment is represented remains unknown. The current study, using a model selection task, explored young children's representation of the whole surrounding environment. A total of 75 children aged 3-5 years participated in the study. In each trial, children observed a large enclosure and were then asked to choose the corresponding model from two small models. The geometric shapes of the enclosure (rectangle vs. rhombus) and the types of distractors (shape distraction vs. feature position distraction) varied. Results showed that all three age groups performed above the chance level in the shape distraction conditions. Children had more difficulty with the feature position distraction conditions than with the shape distraction conditions. When the distractor shared the feature but at an inappropriate position, children's performance was significantly poorer, especially in the rhombic enclosure. The results provide evidence that young children may represent featural cues separately from geometric shapes.

Learning by Doing: The Use of Distance, Corners and Length in Rewarded Geometric Tasks by Zebrafish (Danio rerio)

Simple Summary

Geometric navigation allows animals to efficiently move towards essential life-spaces by taking advantage of macrostructural information such as distance, angular magnitude, and length, in relation to left-right positional sense. In natural contexts, these cues can be referred to extensive three-dimensional surfaces such as a slope or a riverbed, thus becoming crucial to orient and find useful supplies. In controlled contexts, it is possible to set apart these components by handling the global shape of the experimental space (rectangular or square) as well, with the aim to specially probe the impact of each of them on navigation behavior of animals, including fishes. The present study aimed at investigating whether a well-known vertebrate, the zebrafish, could learn to encode and retain in memory such metric information (in terms of distances, corners, and lengths) in association with left–right directions, to gain rewards. Our results showed that zebrafish learned to use all these geometric attributes when repeatedly exposed to them, over a period of training, thereby giving strength to the ecological relevance of environmental geometry as a source of spatial knowledge. Generally, the engagement of zebrafish may consent to assess computations underlying large-scale-based navigation, also by drawing targeted comparisons, due to its behavioral, cognitive, and even emotional similarities with mammals.

Abstract

Zebrafish spontaneously use distance and directional relationships among three-dimensional extended surfaces to reorient within a rectangular arena. However, they fail to take advantage of either an array of freestanding corners or an array of unequal-length surfaces to search for a no-longer-present goal under a spontaneous cued memory procedure, being unable to use the information supplied by corners and length without some kind of rewarded training. The present study aimed to tease apart the geometric components characterizing a rectangular enclosure under a procedure recruiting the reference memory, thus training zebrafish in fragmented layouts that provided differences in surface distance, corners, and length. Results showed that fish, besides the distance, easily learned to use both corners and length if subjected to a rewarded exit task over time, suggesting that they can represent all the geometrically informative parts of a rectangular arena when consistently exposed to them. Altogether, these findings highlight crucially important issues apropos the employment of different behavioral protocols (spontaneous choice versus training over time) to assess spatial abilities of zebrafish, further paving the way to deepen the role of visual and nonvisual encodings of isolated geometric components in relation to macrostructural boundaries.

Navigating in a challenging semiarid environment: the use of a route-based mental map by a small-bodied neotropical primate

To increase efficiency in the search for resources, many animals rely on their spatial abilities. Specifically, primates have been reported to use mostly topological and rarely Euclidean maps when navigating in large-scale space. Here, we aimed to investigate if the navigation of wild common marmosets inhabiting a semiarid environment is consistent with a topological representation and how environmental factors affect navigation. We collected 497 h of direct behavioral and GPS information on a group of marmosets using a 2-min instantaneous focal animal sampling technique. We found that our study group reused not only long-route segments (mean of 1007 m) but entire daily routes, a pattern that is not commonly seen in primates. The most frequently reused route segments were the ones closer to feeding sites, distant to resting sites, and in areas sparse in tree vegetation. We also identified a total of 56 clustered direction change points indicating that the group modified their direction of travel. These changes in direction were influenced by their close proximity to resting and feeding sites. Despite our small sample size, the obtained results are important and consistent with the contention that common marmosets navigate using a topological map that seems to benefit these animals in response to the exploitation of clustered exudate trees. Based on our findings, we hypothesize that the Caatinga landscape imposes physical restrictions in our group's navigation such as gaps in vegetation, small trees and xerophytic plants. This study, based on preliminary evidence, raises the question of whether navigation patterns are an intrinsic characteristic of a species or are ecologically dependent and change according to the environment.

Uncertainty promotes information-seeking actions, but what information?

Navigating an unfamiliar city almost certainly brings out uncertainty about getting from place to place. This uncertainty, in turn, triggers information gathering. While navigational uncertainty is common, little is known about what type of information people seek when they are uncertain. The primary choices for information types with environments include landmarks (distal or local), landmark configurations (relation between two or more landmarks), and a distinct geometry, at least for some environments. Uncertainty could lead individuals to more likely seek one of these information types. Extant research informs both predictions about and empirical work exploring this question. This review covers relevant cognitive literature and then suggests empirical approaches to better understand information-seeking actions triggered by uncertainty. Notably, we propose that examining continuous navigation data can provide important insights into information seeking. Benefits of continuous data will be elaborated through one paradigm, spatial reorientation, which intentionally induces uncertainty through disorientation and cue conflict. While this and other methods have been used previously, data have primarily reflected only the final choice. Continuous behavior during a task can better reveal the cognition-action loop contributing to spatial learning and decision making.

Hierarchical Development of Early Visual-Spatial Abilities - A Taxonomy Based Assessment Using the MaGrid App

Visual-spatial abilities (VSA) are considered a building block of early numerical development. They are intuitively acquired in early childhood and differentiate in further development. However, when children enter school, there already are considerable individual differences in children's visual-spatial and numerical abilities. To better understand this diversity, it is necessary to empirically evaluate the development as well as the latent structure of early VSA as proposed by the 2 by 2 taxonomy of Newcombe and Shipley (2015). In the present study, we report on a tablet-based assessment of VSA using the digital application (app) MaGrid in kindergarten children aged 4-6 years. We investigated whether the visual-spatial tasks implemented in MaGrid are sensitive to replicate previously observed age differences in VSA and thus a hierarchical development of VSA. Additionally, we evaluated whether the selected tasks conform to the taxonomy of VSA by Newcombe and Shipley (2015) applying a confirmatory factor analysis (CFA) approach. Our results indicated that the hierarchical development of VSA can be measured using MaGrid. Furthermore, the CFA substantiated the hypothesized factor structure of VSA in line with the dimensions proposed in the taxonomy of Newcombe and Shipley (2015). Taken together, the present results advance our knowledge to the (hierarchical) development as well as the latent structure of early VSA in kindergarten children.

Path integration in large-scale space and with novel geometries: Comparing vector addition and encoding-error models

Path integration is thought to rely on vestibular and proprioceptive cues yet most studies in humans involve primarily visual input, providing limited insight into their respective contributions. We developed a paradigm involving walking in an omnidirectional treadmill in which participants were guided on two sides of a triangle and then found their back way to origin. In Experiment 1, we tested a range of different triangle types while keeping the distance of the unguided side constant to determine the influence of spatial geometry. Participants overshot the angle they needed to turn and undershot the distance they needed to walk, with no consistent effect of triangle type. In Experiment 2, we manipulated distance while keeping angle constant to determine how path integration operated over both shorter and longer distances. Participants underestimated the distance they needed to walk to the origin, with error increasing as a function of the walked distance. To attempt to account for our findings, we developed configural-based computational models involving vector addition, the second of which included terms for the influence of past trials on the current one. We compared against a previously developed configural model of human path integration, the Encoding-Error model. We found that the vector addition models captured the tendency of participants to under-encode guided sides of the triangles and an influence of past trials on current trials. Together, our findings expand our understanding of body-based contributions to human path integration, further suggesting the value of vector addition models in understanding these important components of human navigation.

How do we remember where we have been? One important mechanism for doing so is called path integration, which refers to the computation of one’s position in space with only self-motion cues. By tracking the direction and distance we have walked, we can create a mental arrow from the current location to the origin, termed the homing vector. Previous studies have shown that the homing vector is subject to systematic distortions depending on previously experienced paths, yet what influences these patterns of errors, particularly in humans, remains uncertain. In this study, we compare two models of path integration based on participants walking two sides of a triangle without vision and then completing the third side based on their estimate of the homing vector. We found no effect of triangle shape on systematic errors, while the systematic errors scaled with path length logarithmically, similar to Weber-Fechner law. While we show that both models captured participants’ behavior, a model based on vector addition best captured the patterns of error in the homing vector. Our study therefore has important implications for how humans track their location, suggesting that vector-based models provide a reasonable and simple explanation for how we do so.

Distinct and combined responses to environmental geometry and features in a working-memory reorientation task in rats and chicks

The original provocative formulation of the ‘geometric module’ hypothesis was based on a working-memory task in rats which suggested that spontaneous reorientation behavior is based solely on the environmental geometry and is impervious to featural cues. Here, we retested that claim by returning to a spontaneous navigation task with rats and domestic chicks, using a single prominent featural cue (a striped wall) within a rectangular arena. Experiments 1 and 2 tested the influence of geometry and features separately. In Experiment 1, we found that both rats and chicks used environmental geometry to compute locations in a plain rectangular arena. In Experiment 2, while chicks failed to spontaneously use a striped wall in a square arena, rats showed a modest influence of the featural cue as a local marker to the goal. The critical third experiment tested the striped wall inside the rectangular arena. We found that although chicks solely relied on geometry, rats navigated based on both environmental geometry and the featural cue. While our findings with rats are contrary to classic claims of an impervious geometric module, they are consistent with the hypothesis that navigation by boundaries and features may involve distinct underlying cognitive computations. We conclude by discussing the similarities and differences in feature-use across tasks and species.

On the transfer of spatial learning between geometrically different shaped environments in the terrestrial toad, Rhinella arenarum

When trained in a rectangular arena, some research has suggested that rats are guided by local features rather than overall boundary geometry. We explored this hypothesis using the terrestrial toad, Rhinella arenarum, as a comparative contrast. In two experiments, toads were trained to find a water-reward goal location in either a featureless rectangular arena (Experiment 1) or in a rectangular arena with a removable colored feature panel covering one short wall (Experiment 2). After learning to successfully locate the water reward, probe trials were carried out by changing the shape of the arena into a kite form with two 90°-angled corners, and in the case of Experiment 2, also shifting the location of the color panel. The results of Experiment 1 indicated that the toads, in contrast to rats, relied primarily on overall shape or boundary geometry to encode the location of a goal. Under the probe conditions of the altered environmental geometry in Experiment 2, the toads seemed to preferentially choose a corner that was generally correct relative to the feature panel experienced during training. Together, the data of the current study suggest that toads and rats differ in the strategies they employ to represent spatial information available in a rectangular arena. Further, the results support the hypothesis that amphibians and mammals engage different neural mechanisms, perhaps related to different evolutionary selective pressures, for the representation of environmental geometry used for navigation.

The Neurocognitive Basis of Spatial Reorientation

The ability to recover one's bearings when lost is a skill that is fundamental for spatial navigation. We review the cognitive and neural mechanisms that underlie this ability, with the aim of linking together previously disparate findings from animal behavior, human psychology, electrophysiology, and cognitive neuroscience. Behavioral work suggests that reorientation involves two key abilities: first, the recovery of a spatial reference frame (a cognitive map) that is appropriate to the current environment; and second, the determination of one's heading and location relative to that reference frame. Electrophysiological recording studies, primarily in rodents, have revealed potential correlates of these operations in place, grid, border/boundary, and head-direction cells in the hippocampal formation. Cognitive neuroscience studies, primarily in humans, suggest that the perceptual inputs necessary for these operations are processed by neocortical regions such as the retrosplenial complex, occipital place area and parahippocampal place area, with the retrosplenial complex mediating spatial transformations between the local environment and the recovered spatial reference frame, the occipital place area supporting perception of local boundaries, and the parahippocampal place area processing visual information that is essential for identification of the local spatial context. By combining results across these various literatures, we converge on a unified account of reorientation that bridges the cognitive and neural domains.

Spatial orientation assessment in preschool children: Egocentric and allocentric frameworks

Spatial orientation is an important function in daily life because it allows us to reach a target place when moving through our environment, using self-centered (egocentric) or environmental information (allocentric). Compared to other cognitive functions, spatial orientation has been studied less in preschool ages. Some brain areas, such as the hippocampus and the temporal as well as the parietal and frontal cortices, are involved in spatial orientation. Therefore, when these brain regions are altered in neurological conditions or in atypical development in children, we would expect impairment of spatial abilities. The aim of this study is to review studies, published in recent years, that use egocentric and allocentric spatial orientation tasks for assessing spatial memory in preschool children, with the final goal of finding out which tests could be included in a clinical neuropsychological evaluation. We observed that although egocentric spatial orientation emerges first during development, allocentric spatial orientation tasks are employed at very early ages. Most of these tasks are performed in real environments, allowing children's self-movements and using environmental modifications, but technologies such as virtual or augmented reality are increasingly used. Other aspects are discussed, such as the lack of consensus in the nomenclature, the difficulty of tracing the course of development of spatial orientation, or the ecological validity of the tests used. We finally observed that there is greater interest in studying the allocentric framework than the egocentric one, which makes it difficult to compare the use of the two frames of reference during a neuropsychological evaluation in preschool-aged children.

Boundary shapes guide selection of reference points in goal localization

In this study, we contrasted two hypotheses theorizing the role of the global shape of a boundary in object location memory: People might differentiate reference points based on the global shape extracted from the environment configuration and choose appropriate parts for encoding a specific location, or, alternatively, only the number of reference points provided by a shape might be important for accurate encoding. We designed a location memory task in an immersive virtual environment in order to examine these two hypotheses. Participants first learned four target locations with a circular wall and a landmark array. During testing, participants recalled the locations with either one entire cue or part of one cue removed. Location memory was impaired when the testing cues did not form a circle, but it was not impaired when the testing configuration retained the circular shape. In Experiment 2, the circle formed by a landmark array and the circular wall did not share the same center during learning. Memory performance decreased when either the wall or the landmark array was removed during testing. These results indicated that participants might segment the shape of the circular wall into parts (similar to segmenting a clock face into 12 hours) and encode target locations relative to the differentiated parts. When such segmentation could be recovered from the testing configuration, object location memory was retained. Otherwise, impairment occurred during testing. These findings suggest that although the individual reference points on a boundary are important for encoding specific target locations, the global shape of the boundary nonetheless affects segmentation and the selection of individual reference points.

Características de los Sistemas Centrales de Conocimiento en niños de 3 a 6 años de edad

Los Sistemas Centrales de Conocimiento son la base de las habilidades cognitivas de la especie humana. Teniendo en cuenta el valor evolutivo de los mismos, se buscó reconocer las relaciones o diferencias entre estos y otras variables de crecimiento (sexo y edad) y variables ambientales (nivel socioeconómico). Para ello, se evaluó cada sistema central de conocimiento y el desarrollo sociocognitivo de 164 niños y 164 niñas, entre los 37 y 71 meses de edad (M  = 54 meses; DE = 0.55). Al aplicar una prueba Kruskal-Wallis se encontró que la edad tuvo un efecto significativo sobre el índice general de desarrollo sociocognitivo (p < 0.001) y sobre el reconocimiento funcional del objeto (χ2 = 54.221, p < 0.001), del número (χ2 = 85.735, p < 0.001) y la ubicación espacial (χ2 = 8.258, p < 0.016). En contraste, no se hallaron efectos del sexo ni del nivel socioeconómico para las diferencias en los sistemas centrales de conocimiento ni en el índice de desarrollo sociocognitivo.

Language, gesture, and judgment: Children's paths to abstract geometry

As infants, children are sensitive to geometry when recognizing objects or navigating through rooms; however, explicit knowledge of geometry develops slowly and may be unstable even in adults. How can geometric concepts be both so accessible and so elusive? To examine how implicit and explicit geometric concepts develop, the current study assessed, in 132 children (3-8 years old) while they played a simple geometric judgment task, three distinctive channels: children's choices during the game as well as the language and gestures they used to justify and accompany their choices. Results showed that, for certain geometric properties, children chose the correct card even if they could not express with words (or gestures) why they had made this choice. Furthermore, other geometric concepts were expressed and supported by gestures prior to their articulation in either choices or speech. These findings reveal that gestures and behavioral choices may reflect implicit knowledge and serve as a foundation for the development of geometric reasoning. Altogether, our results suggest that language alone might not be enough for expressing and organizing geometric concepts and that children pursue multiple paths to overcome its limitations, a finding with potential implications for primary education in mathematics.

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.

The developing role of transparent surfaces in children's spatial representation

Children adeptly use environmental boundaries to navigate. But how do they represent surfaces as boundaries, and how does this change over development? To investigate the effects of boundaries as visual and physical barriers, we tested spatial reorientation in 160 children (2-7 year-olds) in a transparent rectangular arena (Condition 1). In contrast with their consistent success using opaque surfaces (Condition 2), children only succeeded at using transparent surfaces at 5-7 years of age. These results suggest a critical role of visually opaque surfaces in early spatial coding and a developmental change around the age of five in representing locations with respect to transparent surfaces. In application, these findings may inform our usage of windows and glass surfaces in designing and building environments occupied by young children.

Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter

The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.

Young Children's Use of Surface and Object Information in Drawings of Everyday Scenes

Pictorial symbols such as photographs, drawings, and maps are ubiquitous in modern cultures. Nevertheless, it remains unclear how children relate these symbols to the scenes that they represent. The present work investigates 4-year-old children's (N = 144) sensitivity to extended surface layouts and objects when using drawings of a room to find locations in that room. Children used either extended surfaces or objects when interpreting drawings, but they did not combine these two types of information to disambiguate target locations. Moreover, children's evaluations of drawings depicting surfaces or objects did not align with their use of such information in those drawings. These findings suggest that pictures of all kinds serve as media in which children deploy symbolic spatial skills flexibly and automatically.

The use of front-back arrays by young children to code locations

Research suggests that during the first 2years of life, children use an egocentric reference system and an extrinsic reference frame, the latter being one allocentric reference system, to encode locations. However, little is known about children's use of an object's intrinsic structure, another allocentric reference system. The current study focused on the role of the front-back relationship, one of the simplest intrinsic reference frames, in children's location encoding. Children (3- to 5-year-olds) participated in a hide-and-find game with one of three different intrinsic front-back array conditions: a facet-induced front-back array, a motion-induced front-back array, or no array. The results showed that whereas the ability to use a facet-induced front-back array began by 3years of age, children used a motion-induced front-back array to encode locations at 4years of age. These results provide evidence that the developmental trajectories of using an intrinsic reference frame to encode locations vary and depend on the specific spatial array involved.

Navegación Espacial en Niños de 3 y 6 Años en un Laberinto Circular: La interacción entre diferentes marcos geométricos de referencia

Introducción: Diversas teorías intentan explicar las estrategias de navegación que utilizan los niños menores de 6 años, siendo el uso de la geometría el principal tema de debate. Objetivo: Estudiar los sistemas de navegación espacial en niños de 3 y 6 años y su utilización de diversos marcos de referencia geométricos y de la guía proximal. Hipótesis: Los niños emplearán la geometría como predice la teoría de los módulos geométricos. Participantes: 20 niños de 6 años y 20 de 3. Métodos: Se utilizó un laberinto circular donde los niños tenían que buscar un objeto escondido. Se formaron dos grupos: desorientados respecto a la habitación exterior y no desorientados. Resultados: Los niños de 3 años necesitaron la información geométrica de la habitación exterior, los de 6 años también son capaces de emplear la guía proximal y pueden usar la geometría del recinto experimental si su aprendizaje se ha realizado en presencia de la geometría de la habitación. Conclusiones: Los resultados apoyan la teoría de la combinación adaptativa, en lugar de la de módulos geométricos. Por otro lado, la presencia de marcos de referencia geométricos fiables facilita la utilización de otros tipos de claves que en su ausencia no son empleadas.

Individual differences in the learning potential of human beings

To the best of our knowledge, the genetic foundations that guide human brain development have not changed fundamentally during the past 50,000 years. However, because of their cognitive potential, humans have changed the world tremendously in the past centuries. They have invented technical devices, institutions that regulate cooperation and competition, and symbol systems, such as script and mathematics, that serve as reasoning tools. The exceptional learning ability of humans allows newborns to adapt to the world they are born into; however, there are tremendous individual differences in learning ability among humans that become obvious in school at the latest. Cognitive psychology has developed models of memory and information processing that attempt to explain how humans learn (general perspective), while the variation among individuals (differential perspective) has been the focus of psychometric intelligence research. Although both lines of research have been proceeding independently, they increasingly converge, as both investigate the concepts of working memory and knowledge construction. This review begins with presenting state-of-the-art research on human information processing and its potential in academic learning. Then, a brief overview of the history of psychometric intelligence research is combined with presenting recent work on the role of intelligence in modern societies and on the nature-nurture debate. Finally, promising approaches to integrating the general and differential perspective will be discussed in the conclusion of this review.

The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers

During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a "geometrical language" with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them.

Spatial Processing in Infancy Predicts Both Spatial and Mathematical Aptitude in Childhood

Despite considerable interest in the role of spatial intelligence in science, technology, engineering, and mathematics (STEM) achievement, little is known about the ontogenetic origins of individual differences in spatial aptitude or their relation to later accomplishments in STEM disciplines. The current study provides evidence that spatial processes present in infancy predict interindividual variation in both spatial and mathematical competence later in development. Using a longitudinal design, we found that children’s performance on a brief visuospatial change-detection task administered between 6 and 13 months of age was related to their spatial aptitude (i.e., mental-transformation skill) and mastery of symbolic-math concepts at 4 years of age, even when we controlled for general cognitive abilities and spatial memory. These results suggest that nascent spatial processes present in the first year of life not only act as precursors to later spatial intelligence but also predict math achievement during childhood.

Neural representation of scene boundaries

Three-dimensional environmental boundaries fundamentally define the limits of a given space. A body of research employing a variety of methods points to their importance as cues in navigation. However, little is known about the nature of the representation of scene boundaries by high-level scene cortices in the human brain (namely, the parahippocampal place area (PPA) and retrosplenial complex (RSC)). Here we use univariate and multivoxel pattern analysis to study classification performance for artificial scene images that vary in degree of vertical boundary structure (a flat 2D boundary, a very slight addition of 3D boundary, or full walls). Our findings present evidence that there are distinct neural components for representing two different aspects of boundaries: 1) acute sensitivity to the presence of grounded 3D vertical structure, represented by the PPA, and 2) whether a boundary introduces a significant impediment to the viewer's potential navigation within a space, represented by RSC.

Core geometry in perspective

Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world.

Geometric and featural systems, separable and combined: Evidence from reorientation in people with Williams syndrome

Spatial reorientation by humans and other animals engages geometric representations of surface layouts as well as featural landmarks; however, the two types of information are thought to be behaviorally and neurally separable. In this paper, we examine the use of these two types of information during reorientation among children and adults with Williams syndrome (WS), a genetic disorder accompanied by abnormalities in brain regions that support use of both geometry and landmarks. Previous studies of reorientation in adolescents and adults with WS have shown deficits in the ability to use geometry for reorientation, but intact ability to use features, suggesting that the two systems can be differentially impaired by genetic disorder. Using a slightly modified layout, we found that many WS participants could use geometry, and most could use features along with geometry. However, the developmental trajectories for the two systems were quite different from one other, and different from those found in typical development. Purely geometric responding was not correlated with age in WS, and search processes appeared similar to those in typically developing (TD) children. In contrast, use of features in combination with geometry was correlated with age in WS, and search processes were distinctly different from TD children. The results support the view that use of geometry and features stem from different underlying mechanisms, that the developmental trajectories and operation of each are altered in WS, and that combination of information from the two systems is atypical. Given brain abnormalities in regions supporting the two kinds of information, our findings suggest that the co-operation of the two systems is functionally altered in this genetic syndrome.

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.

Is height a core geometric cue for navigation? Young children's use of height in reorientation

With respect to reorientation, children older than 1.5 to 2 years can use geometric cues (distance and left/right sense). However, because previous studies have focused mainly on the plane geometric properties, little is known about the role of information with respect to vertical dimension in children's reorientation. The current study aimed to examine whether and how 3- and 4-year-old children use height information to search for a hidden toy when disoriented in a small enclosure. In a slant-ceiling rectangular room and a slant-ceiling square room, 4-year-olds were able to use height information to reorient and search for the toy in the correct corner, whereas 3-year-olds were not able to do so. Our results suggest that children can, at least by the age of 4 years, use height information and that height is not used as early as other geometric properties that are in the core geometry system for navigation.