Beyond core knowledge: Natural geometry

Going Round in Circles: A Cognitive Bias in Geometric Reasoning

Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got "locked" on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations into the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.

On finding one's way: a comment on Bock et al. (2024)

In a recent issue of Psychological Research, Bock, O., Huang, J-Y., Onur, O. A., & Memmert, D. (2024). The structure of cognitive strategies for wayfinding decisions. Psychological Research Psychologische Forschung, 88, 476-486. https://doi.org/10.1007/s00426-023-01863-3 .) investigated cognitive strategies purported to guide wayfinding decisions at intersections. Following experimentation in a virtualised maze, it was concluded that intersectional wayfinding decisions were based on a 'generalized cognitive process', in addition to 'strategy-specific' processes. The aim of our comment is not to challenge these findings or their methodological rigour. Rather, we note how the study of human wayfinding has been undertaken from entirely different metatheoretical perspectives in psychological science. Leaning on the seminal work of James Gibson and Harry Heft, we consider wayfinding as a continuous, integrated perception-action process, distributed across the entire organism-environment system. Such a systems-oriented, ecological approach to wayfinding remediates the organismic asymmetry pervasive to extant theories of human behaviours, foregrounding the possibility for empirical investigation that takes seriously the socio-cultural contexts in which inhabitants dwell.

Tactile cues compensate for unbalanced vestibular cues during progression on inclined surfaces

A previous study demonstrated that rodents on an inclined square platform traveled straight vertically or horizontally and avoided diagonal travel. Through behavior they aligned their head with the horizontal plane, acquiring similar bilateral vestibular cues - a basic requirement for spatial orientation and a salient feature of animals in motion. This behavior had previously been shown to be conspicuous in Tristram's jirds. Here, therefore jirds were challenged by testing their travel behavior on a circular arena inclined at 0°-75°. Our hypothesis was that if, as typical to rodents, the jirds would follow the curved arena wall, they would need to display a compensating mechanism to enable traveling in such a path shape, which involves a tilted frontal head axis and unbalanced bilateral vestibular cues. We found that with the increase in inclination, the jirds remained more in the lower section of the arena (geotaxis). When tested on the steep inclinations, however, their travel away from the arena wall was strictly straight up or down, in contrast to the curved paths that followed the circular arena wall. We suggest that traveling along a circular path while maintaining contact with the wall (thigmotaxis), provided tactile information that compensated for the unbalanced bilateral vestibular cues present when traveling along such curved inclined paths. In the latter case, the frontal plane of the head was in a diagonal posture in relation to gravity, a posture that was avoided when traveling away from the wall.

Effects of a 3-factor field intervention on numerical and geometric knowledge in preschool children

The main aim of this study was to develop and test the effects of a field math intervention program on both number and geometry knowledge. The intervention was developed based on three basic skills previously associated with mathematical performance: symbolic number knowledge, mapping processes and spatial reasoning. The participants were 117 preschoolers from six schools in Cali and Bogotá. The children were assigned to an intervention group (N = 55) or a control group (N = 62). The intervention lasted 11 weeks with 3 sessions per week where the children participated in different game-based activities. Tests of numerical and geometric knowledge were administered before and after the intervention. The effects of the intervention were tested twice, immediately after the program ended and six months later. The results show that the children in the intervention group improved more than the control group in both number and geometry. The second posttest revealed a significant intervention effect for geometry, but not for numerical knowledge. The implications of these mixed patterns of results are discussed in the paper.

Visual perception and linguistic abilities, not quantitative knowledge, count in geometric knowledge of kindergarten children

Geometric knowledge is one of the important mathematical skills acquired by children at a young age and is a major area of future mathematical learning; however, there is no direct research on the factors influencing kindergarteners' early geometric knowledge. The pathways model to mathematics was modified to examine the cognitive mechanisms underlying geometric knowledge in Chinese kindergarten children aged 5-7 (n = 99). Quantitative knowledge, visual-spatial processing, and linguistic abilities were stepped into hierarchical multiple regression models. The results revealed that after age, sex, and nonverbal intelligence were statistically controlled, visual perception, phonological awareness, and rapid automatized naming in linguistic abilities significantly predicted the variation in geometric knowledge. For quantitative knowledge, neither dot comparison nor number comparison test could be a significant precursor of geometry skills. The findings indicate that visual perception and linguistic abilities, not quantitative knowledge, account for the geometric knowledge of kindergarten children.

Understanding the complexities of mathematical cognition: A multi-level framework

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

A cross-cultural study of language and cognition: Numeral classifiers and solid object categorization

One of the central issues in cognition is identifying universal and culturally specific patterns of thought. In this study, we examined how one aspect of culture, a linguistic part of speech known asclassifiers, are related to categorization of solid objects. In Experiment 1, we used a numeral classifier elicitation task to examine the classifiers used by speakers of Hmong, Japanese, and Mandarin Chinese (N = 34) with 135 nouns that referred to solid objects. In Experiment 2, adult speakers of English, Japanese, Mandarin Chinese, and Hmong (N = 64) rated the similarity of 39 pictured objects that depicted a subset of the nouns. All groups classified the objects into natural kinds and artifacts, with the category of humans anchoring both divisions. The main difference that emerged from the study was that speakers of Japanese and English rated humans and animals as more similar to each other than Hmong speakers; Mandarin speakers' ratings of the similarity between humans and animals fell in between those of Hmong and English speakers. However, the pattern of categorization of humans and animals found among speakers of the classifier languages contradicted their patterns of classifier use. The findings help to tease apart the effects of language from other cultural factors that impact cognition.

Graded human sensitivity to geometric and topological concepts

In a seminal study, Dehaene et al. (2006) found evidence that adults and children are sensitive to geometric and topological (GT) concepts using a novel odd-one-out task. However, performance on this task could reflect more general cognitive abilities than intuitive knowledge of GT concepts. Here, we developed a new 2-alternative forced choice (2-AFC) version of the original task where chance represents a higher bar to clear (50% vs. 16.67%) and where the role of general cognitive abilities is minimized. Replicating the original finding, American adult participants showed above-chance sensitivity to 41 of the 43 GT concepts tested. Moreover, their performance was not strongly driven by two general cognitive abilities, fluid intelligence and mental rotation, nor was it strongly associated with mathematical achievement as measured by ACT/SAT scores. The performance profile across the 43 concepts as measured by the new 2-AFC task was found to be highly correlated with the profiles as measured using the original odd-one-out task, as an analysis of data sets spanning populations and ages revealed. Most significantly, an aggregation of the 43 concepts into seven classes of GT concepts found evidence for graded sensitivity. Some classes, such as Euclidean geometry and Topology, were found to be more domain-specific: they "popped out" for participants and were judged very quickly and highly accurately. Others, notably Symmetry and Geometric transformations, were found to be more domain-general: better predicted by participants' general cognitive abilities and mathematical achievement. These results shed light on the graded nature of GT concepts in humans and challenge computational models that emphasize the role of induction.

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.

Geometry-based navigation in the dark: layout symmetry facilitates spatial learning in the house cricket, Acheta domesticus, in the absence of visual cues

The capacity to navigate by layout geometry has been widely recognized as a robust strategy of place-finding. It has been reported in various species, although most studies were performed with vision-based paradigms. In the presented study, we aimed to investigate layout symmetry-based navigation in the house cricket, Acheta domesticus, in the absence of visual cues. For this purpose, we used a non-visual paradigm modeled on the Tennessee Williams setup. We ensured that the visual cues were indeed inaccessible to insects. In the main experiment, we tested whether crickets are capable of learning to localize the centrally positioned, inconspicuous cool spot in heated arenas of various shapes (i.e., circular, square, triangular, and asymmetric quadrilateral). We found that the symmetry of the arena significantly facilitates crickets’ learning to find the cool spot, indicated by the increased time spent on the cool spot and the decreased latency in locating it in subsequent trials. To investigate mechanisms utilized by crickets, we analyzed their approach paths to the spot. We found that crickets used both heuristic and directed strategies of approaching the target, with the dominance of a semi-directed strategy (i.e., a thigmotactic phase preceding direct navigation to the target). We propose that the poor performance of crickets in the asymmetrical quadrilateral arena may be explained by the difficulty of encoding its layout with cues from a single modality.

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.

Three cortical scene systems and their development

Since the discovery of three scene-selective regions in the human brain, a central assumption has been that all three regions directly support navigation. We propose instead that cortical scene processing regions support three distinct computational goals (and one not for navigation at all): (i) The parahippocampal place area supports scene categorization, which involves recognizing the kind of place we are in; (ii) the occipital place area supports visually guided navigation, which involves finding our way through the immediately visible environment, avoiding boundaries and obstacles; and (iii) the retrosplenial complex supports map-based navigation, which involves finding our way from a specific place to some distant, out-of-sight place. We further hypothesize that these systems develop along different timelines, with both navigation systems developing slower than the scene categorization system.

Knowledge, belief, and moral psychology

Phillips et al. make a strong case that knowledge representations should play a larger role in cognitive science. Their arguments are reinforced by comparable efforts to place moral knowledge, rather than moral beliefs, at the heart of a naturalistic moral psychology. Conscience, Kant's synthetic a priori, and knowledge attributions in the law all point in a similar direction.

Searching high and low: domestic dogs' understanding of solidity

Physical reasoning appears central to understanding how the world works, suggesting adaptive function across the animal kingdom. However, conclusive evidence for inferential reasoning about physical objects is limited to primates. We systematically tested a central feature-understanding of solidity-in domestic dogs, by adapting a validated procedure (the shelf task) previously used to test children and non-human primates. Dogs watched a treat dropped into an apparatus with a shelf either present (treat landing on the shelf) or absent (treat landing on the bottom surface) and chose where to search for it (above or below the shelf). Across four studies (n = 64), we manipulated visual access to the treat trajectory and apparatus interior. Dogs correctly inferred the location of treats using physical cues when the shelf was present (Study 1), and learned rapidly when visual cues of continuity were limited (Study 2), and when the shelf was absent (Study 3). Dogs were at chance when the apparatus was fully occluded, and the presence and absence of the shelf varied across trials within subjects, and showed no evidence of learning (Study 4). The findings of these four studies suggest that dogs may be able to make some inferences using solidity and continuity and do not exhibit proximity or gravity biases. However, dogs did not always search correctly from Trial 1, and failed to search correctly when the rewarded location varied within-subjects, suggesting a role for learning, and possible limits to their ability to make inferences about physical objects.

The cognitive profiles for different samples of mathematical learning difficulties and their similarity to typical development: Evidence from a longitudinal study

Several cognitive deficits have been suggested to induce mathematical learning difficulties (MLD), but it is unclear whether the cognitive profile for all children with MLD is the same and to what extent it differs from typically developing (TD) children. This study investigated whether such a profile could be distinguished when cognitive skills and math performance are compared between TD children and children with MLD. This was accomplished by employing two-way repeated-measures analyses of covariance in 276 10-year-old participants (60 with MLD) from fourth and fifth grades. In addition, we investigated whether more restrictive selection criteria for MLD result in different mathematical and cognitive profiles by means of independent-samples t tests. Results revealed that cognitive mechanisms for math development are mostly similar for children with MLD and TD children and that variability in sample selection criteria did not produce different mathematical or cognitive profiles. To conclude, the cognitive mechanisms for math development are broadly similar for children with MLD and their TD counterparts even when different MLD samples were selected. This strengthens our idea that MLD can be defined as the worst performance on a continuous scale rather than as a discrete disorder.

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.

Geometry intuitions without vision? A study in blind children and adults

Geometry intuitions seem to be rooted in a non-verbal system that humans possess since early age. However, the mechanisms underlying the comprehension of basic geometric concepts remain elusive. Some authors have suggested that the starting point of geometry development could be found in the visual perception of specific features in our environment, thus conferring to vision a foundational role in the acquisition of geometric skills. To examine this assumption, a test probing intuitive understanding of basic geometric concepts was presented to congenitally blind children and adults. Participants had to detect the intruder among four different shapes, from which three instantiated a specific geometrical concept and one (the intruder) violated it. Although they performed above the chance level, the blind presented poorer performance than the sighted participants who did the task in the visual modality (i.e., with the eyes open), but performed equally well than the sighted who did the task in the tactile modality (i.e., with a blindfold). We therefore provide evidence that geometric abilities are impacted by the lack of vision.

Mental compression of spatial sequences in human working memory using numerical and geometrical primitives

How does the human brain store sequences of spatial locations? We propose that each sequence is internally compressed using an abstract, language-like code that captures its numerical and geometrical regularities. We exposed participants to spatial sequences of fixed length but variable regularity while their brain activity was recorded using magneto-encephalography. Using multivariate decoders, each successive location could be decoded from brain signals, and upcoming locations were anticipated prior to their actual onset. Crucially, sequences with lower complexity, defined as the minimal description length provided by the formal language, led to lower error rates and to increased anticipations. Furthermore, neural codes specific to the numerical and geometrical primitives of the postulated language could be detected, both in isolation and within the sequences. These results suggest that the human brain detects sequence regularities at multiple nested levels and uses them to compress long sequences in working memory.

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.

Core knowledge of geometry can develop independently of visual experience

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.

Visuo-spatial mental imagery and geometry skills in school-aged children

The relationships between visuo-spatial abilities and geometry performances in school-aged children were examined. A battery of tests assessing non-verbal reasoning, visuo-spatial mental imagery, and academic achievement in geometry (i.e., geometric knowledge and geometric problem-solving competencies) was presented to 162 8-9.5-year-old pupils attending primary school. After controlling for age, significant associations were found between non-verbal reasoning abilities and knowledge in geometry (r = .31, p = .013) and geometric problem-solving skills (r = .35, p = .005), respectively. Similarly, using age as covariate, mental imagery abilities were significantly related to geometric knowledge (r = -.28, p < .001) and geometric problem-solving skills (r = -.24, p = .002), respectively. Furthermore, pupils with high visuo-spatial mental imagery abilities outperformed their peers with low visuo-spatial competences in the geometry tasks and further visuo-spatial abilities measure computed by their teachers. Finally, male participants showed better geometry skills than females.

Measurement of Cognition for the National Children's Study

The National Children's Study Cognitive Health Domain Team developed detailed plans for assessing cognition longitudinally from infancy to early adulthood. These plans identify high-priority aspects of cognition that can be measured efficiently and effectively, and we believe they can serve as a model for future large-scale longitudinal research. For infancy and toddlerhood, we proposed several paradigms that collectively allowed us to assess six broad cognitive constructs: (1) executive function skills, (2) episodic memory, (3) language, (4) processing speed, (5) spatial and numerical processing, and (6) social cognition. In some cases, different trial sequences within a paradigm allow for the simultaneous assessment of multiple cognitive skills (e.g., executive function skills and processing speed). We define each construct, summarize its significance for understanding developmental outcomes, discuss the feasibility of its assessment throughout development, and present our plan for measuring specific skills at different ages. Given the need for well-validated, direct behavioral measures of cognition that can be used in large-scale longitudinal studies, especially from birth to age 3 years, we also initiated three projects focused on the development of new measures.

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.

Play enhances visual form perception in infancy-an active training study

Motor experiences and active exploration during early childhood may affect individual differences in a wide range of perceptual and cognitive abilities. In the current study, we suggest that active exploration of objects facilitates the ability to process object forms and magnitudes, which in turn impacts the development of numerosity perception. We tested our hypothesis by conducting a preregistered active exploration intervention with 59 8-month-old infants. The minimal intervention consisted of actively playing with and exploring blocks once a day for 8 weeks. In order to control for possible training effects on attention, we used book reading as a control condition. Pre- and post-test assessments using eye-tracking showed that block play improved visual form perception, where infants became better at detecting a deviant shape. Furthermore, using three control tasks, we showed that the intervention specifically improved infants' ability to process visual forms and the effect could not be explained by a domain general improvement in attention or visual perception. We found that the intervention did not improve numerosity perception and suggest that because of the sequential nature of our hypothesis, a longer time frame might be needed to see improvements in this ability. Our findings indicate that if infants are given more opportunities for play and exploration, it will have positive effects on their visual form perception, which in turn could help their understanding of geometrical concepts.

The role of learning and environmental geometry in landmark-based spatial reorientation of fish (Xenotoca eiseni)

Disoriented animals and humans use both the environmental geometry and visual landmarks to guide their spatial behavior. Although there is a broad consensus on the use of environmental geometry across various species of vertebrates, the nature of disoriented landmark-use has been greatly debated in the field. In particular, the discrepancy in performance under spontaneous choice conditions (sometimes called “working memory” task) and training over time (“reference memory” task) has raised questions about the task-dependent dissociability of mechanisms underlying the use of landmarks. Until now, this issue has not been directly addressed, due to the inclusion of environmental geometry in most disoriented navigation paradigms. In the present study, therefore, we placed our focus on landmark-based navigation in fish (Xenotoca eiseni), an animal model that has provided fruitful research in spatial reorientation. We began with a test of spontaneous navigation by geometry and landmarks (Experiment 1), showing a preference for the correct corner, even in the absence of reinforced training. We then proceeded to test landmarks without the influence of informative geometry through the use of square environments (Experiment 2–4), varying the numerosity of present landmarks, the distance of landmarks from the target corner, and the type of task (i.e., spontaneous cued memory or reference memory). We found marked differences in landmark-use in the absence of environmental geometry. In the spontaneous memory task, visual landmarks acquired perceptive salience (and attracted the fish) but without serving as a spatial cue to location when they were distal from the target. Across learning in the reference memory task, the fish overcame these effects and gradually improved in their performance, although they were still biased to learn visual landmarks near the target (i.e., as beacons). We discuss these results in relation to the existing literature on dissociable mechanisms of spatial learning.

Interference in geometry among people who are blind

BACKGROUND

Geometry, a central branch of mathematics, is challenging for schoolchildren. Studies have shown that, when comparing perimeters of geometrical shapes, many sighted participants experience interference from the area variable, possibly stemming from the visual differences between the geometrical shapes. Accordingly, we hypothesized that such interference would not be observed in participants who are blind, who use the tactile modality to detect the properties of shapes.

METHODS

Thirty participants, 15 who are blind and 15 with sight, explored pairs of geometrical shapes tactilely or visually, respectively, and compared areas and perimeters.

RESULTS AND CONCLUSIONS

Surprisingly, accuracy and response time findings suggested that the two groups had a similar pattern of performance, and hence that area also interferes in comparison of perimeters among people who are blind.

Young children's representation of geometric relationships between locations in location coding

From an early age, children are able to use surface layout geometry and landmarks to search for a hidden toy when disoriented. Theoretical debate remains regarding whether children represent locations based on the global environment or on local cues. Exploring whether children construct and use the relationships between discrete locations of the global environment can provide direct evidence regarding this issue. We investigated young children's representation of two geometric relationships: diagonal relationships (Experiment 1) and same-side relationships (Experiment 2). Children (4- and 5-year-olds) were tested in a square room with a distinctively colored wall. Children completed two tasks. In a two-location task, children watched two toys hidden in two corners that formed one of the two relationships. After disorientating children, the experimenter uncovered one toy and children searched for the other one (target). In a one-location task, only one toy was hidden. In both experiments, children's performance was better in the two-location task than in the one-location task. Furthermore, accuracy in the two-location task of Experiment 1, in which the two corners formed a diagonal relationship, was higher than that of Experiment 2, in which the two corners formed a same-side relationship and a correct location required the combination of this relationship and landmark. These findings suggest that at least by 4 years of age, children can construct geometric relationships between individual corners in their spatial representation and support the global accounts of young children's location coding.

Places in the Brain: Bridging Layout and Object Geometry in Scene-Selective Cortex

Diverse animal species primarily rely on sense (left-right) and egocentric distance (proximal-distal) when navigating the environment. Recent neuroimaging studies with human adults show that this information is represented in 2 scene-selective cortical regions-the occipital place area (OPA) and retrosplenial complex (RSC)-but not in a third scene-selective region-the parahippocampal place area (PPA). What geometric properties, then, does the PPA represent, and what is its role in scene processing? Here we hypothesize that the PPA represents relative length and angle, the geometric properties classically associated with object recognition, but only in the context of large extended surfaces that compose the layout of a scene. Using functional magnetic resonance imaging adaptation, we found that the PPA is indeed sensitive to relative length and angle changes in pictures of scenes, but not pictures of objects that reliably elicited responses to the same geometric changes in object-selective cortical regions. Moreover, we found that the OPA is also sensitive to such changes, while the RSC is tolerant to such changes. Thus, the geometric information typically associated with object recognition is also used during some aspects of scene processing. These findings provide evidence that scene-selective cortex differentially represents the geometric properties guiding navigation versus scene categorization.

Discrimination of Small Forms in a Deviant-Detection Paradigm by 10-month-old Infants

Using eye tracking, we investigated if 10-month-old infants could discriminate between members of a set of small forms based on geometric properties in a deviant-detection paradigm, as suggested by the idea of a core cognitive system for Euclidian geometry. We also investigated the precision of infants' ability to discriminate as well as how the discrimination process unfolds over time. Our results show that infants can discriminate between small forms based on geometrical properties, but only when the difference is sufficiently large. Furthermore, our results also show that it takes infants, on average, <3.5 s to detect a deviant form. Our findings extend previous research in three ways: by showing that infants can make similar discriminative judgments as children and adults with respect to geometric properties; by providing a first crude estimate on the limit of the discriminative abilities in infants, and finally; by providing a first demonstration of how the discrimination process unfolds over time.

Rapid Invariant Encoding of Scene Layout in Human OPA

Successful visual navigation requires a sense of the geometry of the local environment. How do our brains extract this information from retinal images? Here we visually presented scenes with all possible combinations of five scene-bounding elements (left, right, and back walls; ceiling; floor) to human subjects during functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG). The fMRI response patterns in the scene-responsive occipital place area (OPA) reflected scene layout with invariance to changes in surface texture. This result contrasted sharply with the primary visual cortex (V1), which reflected low-level image features of the stimuli, and the parahippocampal place area (PPA), which showed better texture than layout decoding. MEG indicated that the texture-invariant scene layout representation is computed from visual input within ∼100 ms, suggesting a rapid computational mechanism. Taken together, these results suggest that the cortical representation underlying our instant sense of the environmental geometry is located in the OPA.

The development of symmetry concept in preschool children

Young children are exposed to symmetrical figures frequently before they are taught the concept of symmetry, which is a valuable experience for the development of geometry; however, limited research has explored how this concept develops. This study investigated the developmental sequence of "general symmetry" concept and "specific symmetry" concepts (i.e., bilateral, rotational, and translational symmetry) with 106 4-6-year-old children using a symmetry deviant detection task. The test examined children's conception of general symmetry against asymmetry, specific symmetry against asymmetry, and discrimination of specific symmetries. The results suggested that the concept of symmetry develops as a differentiation process. The concept of general symmetry was acquired first, followed by specific symmetries which were acquired in sequential order.

A novel virtual plus-maze for studying electrophysiological correlates of spatial reorientation

Quick reorientation is an essential part of successful navigation. Despite growing attention to this ability, little is known about how reorientation happens in humans. To this aim, we recorded EEG from 34 participants. Participants were navigating a simple virtual reality plus-maze where at the beginning of each trial they were randomly teleported to either the North or the South alley. Results show that the teleportation event caused a quick reorientation effect over occipito-parietal areas as early as 100 ms; meaning that despite the known stochastic nature of the teleportation, participants built up expectations for their place of arrival. This result has important consequences for the optimal design of virtual reality locomotion.

Navigation and the developing brain

As babies rapidly acquire motor skills that give them increasingly independent and wide-ranging access to the environment over the first two years of human life, they decrease their reliance on habit systems for spatial localization, switching to their emerging inertial navigation system and to allocentric frameworks. Initial place learning is evident towards the end of the period. From 3 to 10 years, children calibrate their ability to encode various sources of spatial information (inertial information, geometric cues, beacons, proximal landmarks and distal landmarks) and begin to combine cues, both within and across systems. Geometric cues are important, but do not constitute an innate and encapsulated module. In addition, from 3 to 10 years, children build the capacity to think about frames of reference different from their current one (i.e. to perform perspective taking). By around 12 years, we see adult-level performance and adult patterns of individual differences on cognitive mapping tasks requiring the integration of vista views of space into environmental space. These lines of development are continuous rather than stage-like. Spatial development builds on important beginnings in the neural systems of newborns, but changes in experience-expectant ways with motor development, action in the world and success–failure feedback. Human systems for integrating and manipulating spatial information also benefit from symbolic capacities and technological inventions.

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.

Dissociable Neural Systems for Recognizing Places and Navigating through Them

When entering an environment, we can use the present visual information from the scene to either recognize the kind of place it is (e.g., a kitchen or a bedroom) or navigate through it. Here we directly test the hypothesis that these two processes, what we call "scene categorization" and "visually-guided navigation", are supported by dissociable neural systems. Specifically, we manipulated task demands by asking human participants (male and female) to perform a scene categorization, visually-guided navigation, and baseline task on images of scenes, and measured both the average univariate responses and multivariate spatial pattern of responses within two scene-selective cortical regions, the parahippocampal place area (PPA) and occipital place area (OPA), hypothesized to be separably involved in scene categorization and visually-guided navigation, respectively. As predicted, in the univariate analysis, PPA responded significantly more during the categorization task than during both the navigation and baseline tasks, whereas OPA showed the complete opposite pattern. Similarly, in the multivariate analysis, a linear support vector machine achieved above-chance classification for the categorization task, but not the navigation task in PPA. By contrast, above-chance classification was achieved for both the navigation and categorization tasks in OPA. However, above-chance classification for both tasks was also found in early visual cortex and hence not specific to OPA, suggesting that the spatial patterns of responses in OPA are merely inherited from early vision, and thus may be epiphenomenal to behavior. Together, these results are evidence for dissociable neural systems involved in recognizing places and navigating through them.SIGNIFICANCE STATEMENT It has been nearly three decades since Goodale and Milner demonstrated that recognizing objects and manipulating them involve distinct neural processes. Today we show the same is true of our interactions with our environment: recognizing places and navigating through them are neurally dissociable. More specifically, we found that a scene-selective region, the parahippocampal place area, is active when participants are asked to categorize a scene, but not when asked to imagine navigating through it, whereas another scene-selective region, the occipital place area, shows the exact opposite pattern. This double dissociation is evidence for dissociable neural systems within scene processing, similar to the bifurcation of object processing described by Goodale and Milner (1992).

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.

Motor and Perceptual Recovery in Adult Patients with Mild Intellectual Disability

Introduction

The relationship between intellectual disability (ID) and hand motor coordination and speed-accuracy, as well as the effect of aging on fine motor performance in patients with ID, has been previously investigated. However, only a few data are available on the impact of the nonpharmacological interventions in adult patients with long-term hand motor deficit.

Methods

Fifty adults with mild ID were enrolled. A group of thirty patients underwent a two-month intensive ergotherapic treatment that included hand motor rehabilitation and visual-perceptual treatment (group A); twenty patients performing conventional motor rehabilitation alone (group B) served as a control group. Data on attention, perceptual abilities, hand dexterity, and functional independence were collected by a blind operator, both at entry and at the end of the study.

Results

After the interventions, group A showed significantly better performance than group B in all measures related to hand movement from both sides and to independence in activities of daily living.

Discussion

Multimodal integrated interventions targeting visual-perceptual abilities and motor skills are an effective neurorehabilitative approach in adult patients with mild ID. Motor learning and memory-mediated mechanisms of neural plasticity might underlie the observed recovery, suggesting the presence of plastic adaptive changes even in the adult brain with ID.

Motor and Perceptual Recovery in Adult Patients with Mild Intellectual Disability

INTRODUCTION

The relationship between intellectual disability (ID) and hand motor coordination and speed-accuracy, as well as the effect of aging on fine motor performance in patients with ID, has been previously investigated. However, only a few data are available on the impact of the nonpharmacological interventions in adult patients with long-term hand motor deficit.

METHODS

Fifty adults with mild ID were enrolled. A group of thirty patients underwent a two-month intensive ergotherapic treatment that included hand motor rehabilitation and visual-perceptual treatment (group A); twenty patients performing conventional motor rehabilitation alone (group B) served as a control group. Data on attention, perceptual abilities, hand dexterity, and functional independence were collected by a blind operator, both at entry and at the end of the study.

RESULTS

After the interventions, group A showed significantly better performance than group B in all measures related to hand movement from both sides and to independence in activities of daily living.

DISCUSSION

Multimodal integrated interventions targeting visual-perceptual abilities and motor skills are an effective neurorehabilitative approach in adult patients with mild ID. Motor learning and memory-mediated mechanisms of neural plasticity might underlie the observed recovery, suggesting the presence of plastic adaptive changes even in the adult brain with ID.

Electrophysiological Signatures of Spatial Boundaries in the Human Subiculum

Environmental boundaries play a crucial role in spatial navigation and memory across a wide range of distantly related species. In rodents, boundary representations have been identified at the single-cell level in the subiculum and entorhinal cortex of the hippocampal formation. Although studies of hippocampal function and spatial behavior suggest that similar representations might exist in humans, boundary-related neural activity has not been identified electrophysiologically in humans until now. To address this gap in the literature, we analyzed intracranial recordings from the hippocampal formation of surgical epilepsy patients (of both sexes) while they performed a virtual spatial navigation task and compared the power in three frequency bands (1-4, 4-10, and 30-90 Hz) for target locations near and far from the environmental boundaries. Our results suggest that encoding locations near boundaries elicited stronger theta oscillations than for target locations near the center of the environment and that this difference cannot be explained by variables such as trial length, speed, movement, or performance. These findings provide direct evidence of boundary-dependent neural activity localized in humans to the subiculum, the homolog of the hippocampal subregion in which most boundary cells are found in rodents, and indicate that this system can represent attended locations that rather than the position of one's own body.SIGNIFICANCE STATEMENT Spatial computations using environmental boundaries are an integral part of the brain's spatial mapping system. In rodents, border/boundary cells in the subiculum and entorhinal cortex reveal boundary coding at the single-neuron level. Although there is good reason to believe that such representations also exist in humans, the evidence has thus far been limited to functional neuroimaging studies that broadly implicate the hippocampus in boundary-based navigation. By combining intracranial recordings with high-resolution imaging of hippocampal subregions, we identified a neural marker of boundary representation in the human subiculum.

Effects of two-dimensional versus three-dimensional landmark geometry and layout on young children's recall of locations from new viewpoints

Spatial memory is an important aspect of adaptive behavior and experience, providing both content and context to the perceptions and memories that we form in everyday life. Young children's abilities in this realm shift from mainly egocentric (self-based) to include allocentric (world-based) codings at around 4 years of age. However, information about the cognitive mechanisms underlying acquisition of these new abilities is still lacking. We examined allocentric spatial recall in 4.5- to 8.5-year-olds, looking for continuity with navigation as previously studied in 2- to 4-year-olds and other species. We specifically predicted an advantage for three-dimensional landmarks over two-dimensional ones and for recalling targets "in the middle" versus elsewhere. However, we did not find compelling evidence for either of these effects, and indeed some analyses even support the opposite of each of these conclusions. There were also no significant interactions with age. These findings highlight the incompleteness of our overall theories of the development of spatial cognition in general and allocentric spatial recall in particular. They also suggest that allocentric spatial recall involves processes that have separate behavioral characteristics from other cognitive systems involved in navigation earlier in life and in other species.