Young children's spontaneous use of geometry in maps

Two experiments tested whether 4-year-old children extract and use geometric information in simple maps without task instruction or feedback. Children saw maps depicting an arrangement of three containers and were asked to place an object into a container designated on the map. In Experiment 1, one of the three locations on the map and the array was distinct and therefore served as a landmark; in Experiment 2, only angle, distance and sense information specified the target container. Children in both experiments used information for distance and angle, but not sense, showing signature error patterns found in adults. Children thus show early, spontaneously developing abilities to detect geometric correspondences between three-dimensional layouts and two-dimensional maps, and they use these correspondences to guide navigation. These findings begin to chart the nature and limits of the use of core geometry in a uniquely human, symbolic task.     

Kindergarten children's sensitivity to geometry in maps

Geometrical concepts are critical to a host of human cognitive achievements, from maps to measurement to mathematics, and both the development of these concepts, and their variation by gender, have long been studied. Most studies of geometrical reasoning, however, present children with materials containing both geometric and non-geometric information, and with tasks that are open to multiple solution strategies. Here we present kindergarten children with a task requiring a focus on geometry: navigation in a small-scale space by a purely geometric map. Children spontaneously extracted and used relationships of both distance and angle in the maps, without prior demonstration, instruction, or feedback, but they failed to use the sense information that distinguishes an array from its mirror image. Children of both genders showed a common profile of performance, with boys showing no advantage on this task. These findings provide evidence that some map-reading abilities arise prior to formal instruction, are common to both genders, and are used spontaneously to guide children's spatial behavior.     

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

Geometry is one of the highest achievements of our species, but its foundations are obscure. Consistent with longstanding suggestions that geometrical knowledge is rooted in processes guiding navigation, the present study examines potential sources of geometrical knowledge in the navigation processes by which young children establish their sense of orientation. Past research reveals that children reorient both by the shape of the surface layout and the shapes of distinctive landmarks, but it fails to clarify what shape properties children use. The present study explores 2-year-old children's sensitivity to angle, length, distance and direction by testing disoriented children's search in a variety of fragmented rhombic and rectangular environments. Children reoriented themselves in accord with surface distances and directions, but they failed to use surface lengths or corner angles either for directional reorientation or as local landmarks. Thus, navigating children navigate by some but not all of the abstract properties captured by formal Euclidean geometry. While navigation systems may contribute to children's developing geometric understanding, they likely are not the sole source of abstract geometric intuitions.     

Children’s mapping between symbolic and nonsymbolic representations of number

When children learn to count and acquire a symbolic system for representing numbers, they map these symbols onto a preexisting system involving approximate nonsymbolic representations of quantity. Little is known about this mapping process, how it develops, and its role in the performance of formal mathematics. Using a novel task to assess children’s mapping ability, we show that children can map in both directions between symbolic and nonsymbolic numerical representations and that this ability develops between 6 and 8 years of age. Moreover, we reveal that children’s mapping ability is related to their achievement on tests of school mathematics over and above the variance accounted for by standard symbolic and nonsymbolic numerical tasks. These findings support the proposal that underlying nonsymbolic representations play a role in children’s mathematical development.     

Using hippocampal‐dependent eyeblink conditioning to predict individual differences in spatial reorientation strategies in 3‐ to 6‐year‐olds

The hippocampus is a subcortical structure in the medial temporal lobe involved in cognitive functions such as spatial navigation and reorientation, episodic memory, and associative learning. While much is understood about the role of hippocampal function in learning and memory in adults, less is known about the relations between the hippocampus and the development of these cognitive skills in young children due to the limitations of using standard methods (e.g., MRI) to examine brain structure and function in developing populations. This study used hippocampal‐dependent trace eyeblink conditioning (EBC) as a feasible approach to examine individual differences in hippocampal functioning as they relate to spatial reorientation and episodic memory performance in young children. Three‐ to six‐year‐old children (N = 50) completed tasks that measured EBC, spatial reorientation, and episodic memory, as well as non‐hippocampal‐dependent processing speed abilities. Results revealed that when age was held constant, individual differences in EBC performance were significantly related to individual differences in performance on the spatial reorientation test, but not on the episodic memory or processing speed tests. When the relations between hippocampal‐dependent EBC and different reorientation strategies were explored, it was found that individual differences in hippocampal function predicted the use of geometric information for reorienting in space as opposed to a combined strategy that uses both geometric information and salient visual cues. The utilization of eyeblink conditioning to examine hippocampal function in young populations and its implications for understanding the dissociation between spatial reorientation and episodic memory development are discussed.     

The ontogeny of relational memory and pattern separation

Episodic memory relies on memory for the relations among multiple elements of an event and the ability to discriminate among similar elements of episodes. The latter phenomenon, termed pattern separation, has been studied mainly in young and older adults with relatively little research on children. Building on prior work with young children, we created an engaging computer‐administered relational memory task assessing what‐where relations. We also modified the Mnemonic Similarity Task used to assess pattern discrimination in young and older adults for use with preschool children. Results showed that 4‐year‐olds performed significantly worse than 6‐year‐olds and adults on both tasks, whereas 6‐year‐olds and adults performed comparably, even though there were no ceiling effects. However, performance on the two tasks did not correlate, suggesting that two distinct mnemonic processes with different developmental trajectories may contribute to age‐related changes in episodic memory.     

Route learning in Korsakoff's syndrome: Residual acquisition of spatial memory despite profound amnesia

Korsakoff's syndrome (KS) is characterized by explicit amnesia, but relatively spared implicit memory. The aim of this study was to assess to what extent KS patients can acquire spatial information while performing a spatial navigation task. Furthermore, we examined whether residual spatial acquisition in KS was based on automatic or effortful coding processes. Therefore, 20 KS patients and 20 matched healthy controls performed six tasks on spatial navigation after they navigated through a residential area. Ten participants per group were instructed to pay close attention (intentional condition), while 10 received mock instructions (incidental condition). KS patients showed hampered performance on a majority of tasks, yet their performance was superior to chance level on a route time and distance estimation tasks, a map drawing task and a route walking task. Performance was relatively spared on the route distance estimation task, but there were large variations between participants. Acquisition in KS was automatic rather than effortful, since no significant differences were obtained between the intentional and incidental condition on any task, whereas for the healthy controls, the intention to learn was beneficial for the map drawing task and the route walking task. The results of this study suggest that KS patients are still able to acquire spatial information during navigation on multiple domains despite the presence of the explicit amnesia. Residual acquisition is most likely based on automatic coding processes.     

Reorientation in a rhombic environment: No evidence for an encapsulated geometric module

Reorientation behavior of young children has been described as dependent upon a geometric module that is incapable of interacting with landmark information. Whereas previous studies typically used rectangular spaces that provided geometric information about distance, we used a rhombic space that allowed us to explore the way children use geometric information about angles. Reorientation was studied in manipulatory space (Experiment 1) and locomotor space (Experiment 2) in the presence and absence of a salient landmark. In the absence of salient landmarks, 4- to 6-year-olds used geometric features to reorient in both spaces. When a salient landmark was available in manipulatory space, 4-year-olds used the landmark and ignored the geometry. Five- and 6-year-olds used the geometry, but in combination with the landmark. In locomotor space, this combined use was already seen at age 4, and increased with age. Taken together, these results offer no support for the notion that reorientation behavior in young children depends on an informationally encapsulated geometric module.     

THE CREDIBLE SHRINKING ROOM:

Abstract— Becoming a proficient symbol user is a universal developmental last in the first years of life, but delecting and mentally representing symbolic relations can be quite challenging for young children To test the extent to which symbolic reasoning per se is problematic, we compared the performance of 2-year-olds in symbolic and nonsymbolic versions of a search task. The children had to use their knowledge of the location of a toy hidden in a room to draw an inference about where to find a miniature toy in a scale model of the room (and vice versa) Children in the nonsymbolic condition believed a shrinking machine had caused the room to become the model They were much more successful than children in the symbolic condition, for whom the model served as a symbol of the room The symbol understanding and use.     

幼儿地图定向任务中几何线索的运用及发展

几何线索对儿童理解地图与现实空间之间的对应关系具重要意义。目前研究以几何地图为材料,通过定向任务,考察儿童对不同几何线索(拓扑关系、欧式几何特征、度量结构)的利用与发展,揭示了儿童对地图与现实空间之间对应关系的认知过程。研究发现,3岁儿童已初步发展出使用欧氏几何特征和度量结构表征空间位置的能力;但不同欧式几何特征(相对距离、角度、方向)被儿童掌握的时间存在明显差别;关于拓扑关系的研究较少,尚未掌握儿童利用该线索的发展规律。提高生态效度是未来研究需解决的主要问题。     

Early development of scaling ability

The map is a small-scaled version of the space it represents. It has been argued that children have difficulty interpreting maps because they do not understand scale relations. Recent research has shown that even preschoolers can solve problems that involve scaling in one dimension. This study examined whether early scaling ability extends to tasks involving two-dimensional maps and referent spaces of different sizes. Results showed that about 60% of the 4-year-olds and 90% of the 5-year-olds tested used distance information presented on a map to locate an object in a two-dimensional spatial layout. Children had more difficulties in solving mapping tasks with a larger referent space. This decrease in accuracy as a function of space size on the mapping task was greater than would have been expected on the basis of performance on a parallel nonmapping task. The results are discussed in terms of their implications for the mechanisms underlying early scaling ability.     

Young children reorient by computing layout geometry, not by matching images of the environment

Disoriented animals from ants to humans reorient in accord with the shape of the surrounding surface layout: a behavioral pattern long taken as evidence for sensitivity to layout geometry. Recent computational models suggest, however, that the reorientation process may not depend on geometrical analyses but instead on the matching of brightness contours in 2D images of the environment. Here we test this suggestion by investigating young children's reorientation in enclosed environments. Children reoriented by extremely subtle geometric properties of the 3D layout: bumps and ridges that protruded only slightly off the floor, producing edges with low contrast. Moreover, children failed to reorient by prominent brightness contours in continuous layouts with no distinctive 3D structure. The findings provide evidence that geometric layout representations support children's reorientation.     

Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.     

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.     

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics.     

Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude ( Butterworth, 1999 , 2005 ; A. J. Wilson & Dehaene, 2007 ) and/or to access that number magnitude representation from numerical symbols ( Rousselle & No?l, 2007 ). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.     

幼儿在地图任务中自我位置与自我朝向表征能力的发展

使用地图定向任务, 探讨了不同任务模式下, 4~6岁幼儿自我位置与自我朝向表征能力的发展特点。结果发现, 位置表征能力的获得先于朝向表征能力, 幼儿从4岁起即开始使用地图表征自我位置, 但到5岁才表现出对自我朝向的表征能力。此外, 对于年龄较小的儿童, 相比于空间–地图的任务模式, 地图–空间的任务模式更有利于完成任务。上述结果第一次从个体发展层面证明了位置与朝向表征的分离现象, 说明位置与朝向的表征能力在发展过程中具有一定的顺序性。     

How do young children determine location? Evidence from disorientation tasks

Previous studies show that following disorientation children use the geometry of an enclosed space to locate an object hidden in one of the corners [e.g. (Hermer, L., & Spelke, E. (1996). Modularity and development: A case of spatial reorientation. Cognition, 61, 195-232)]. These studies have used a disorientation procedure that involves rotating the viewer (with eyes closed). Here, we examine 18- to 25-month-olds' spatial coding in two disorientation tasks--involving either viewer or space rotation. Importantly, the rotational movements in both tasks could not be visually tracked. Children were tested in either task (viewer- or space-movement) from either inside or outside a triangular (isosceles) space (with one unique and two equivalent corners). In the viewer-movement task, performance was above chance, regardless of which corner contained the object. In the space-movement task, performance was above chance at only the unique corner. On both tasks, performance was better from inside the space than from outside. The implications for how children determine location are discussed.     

Advanced Spatial Skills and Advance Planning: Components of 6-Year-Olds' Navigational Map Use

Two domains of cognitive development that have captured significant research attention are children's spatial cognition and children's planning skills. Children's ability to use maps for navigational purposes is a task in which these domains necessarily intersect. This study was designed to examine 6-year-olds' complex route formation and reorientation skills. Thirty-six kindergartners navigated through a large-scale environment using a map. Participants were required to plan their own routes to end-points designated only on the maps. Success at navigation, as well as route length and types of error, were assessed. The results indicate that kindergartners are able to use maps to plan and execute routes, and that they demonstrate advance planning skills by reliably selecting optimally efficient routes.     

Young children's use of features to reorient is more than just associative: further evidence against a modular view of spatial processing

Proponents of a geometric module have argued that instances of young children's use of features as well as geometry to reorient can be explained by a two-stage process. In this model, only the first stage is a true reorientation, accomplished by using geometric information alone; features are considered in a second stage using association ( Lee, Shusterman & Spelke, 2006 ). This account is contradicted by the data from two experiments. Experiment 1a sets the stage for Experiment 1b by showing that young children use geometric information to reorient in a complex geometric figure without a single principal axis of symmetry (an octagon). In such a figure, there are two sets of geometrically congruent corners, with four corners in each set. The addition of a colored wall leads to the existence of three geometrically congruent but, crucially, all unmarked corners; using the colored wall to distinguish among them could not be done associatively. In Experiment 1b, both 3- and 5-year-old children showed true non-associative reorientation using features by performing at above-chance levels on all-white trials. Experiment 2 used a paradigm without distinctive geometry, modeled on Lee et al. (2006) , involving an equilateral triangle of hiding places located within a circular enclosure, but with a large stable feature rather than a small moveable one. Four-year-olds (the age group studied by Lee et al.) used features at above-chance levels. Thus, features can be used to reorient, in a way not dependent on association, in contradiction to the two-stage version of the modular view.