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Understanding measurement units is critical to mathematics and science learning, but it is a topic that American students find difficult. In 3 studies, we investigated the challenges underlying this difficulty in kindergarten and second grade by comparing performance on different versions of a linear measurement task. Children measured crayons that were either aligned or shifted relative to the left edge of either a continuous ruler or a row of discrete units. The alignment (aligned, shifted) and the measuring tool (ruler, discrete units) were crossed to form 4 types of problems. Study 1 showed good performance in both grades on both types of aligned problems as well as on the shifted problems with discrete units. In contrast, performance was at chance on the shifted ruler problems. Study 2 showed that performance on shifted discrete unit problems declined when numbers were placed on the units, particularly for kindergarteners, suggesting that on the shifted ruler problems, the presence of numbers may have contributed to children's difficulty. However, Study 3 showed that the difficulty on the shifted ruler problems persisted even when the numbers were removed from the ruler. Taken together, these findings suggest that there are multiple challenges to understanding measurement, but that a key challenge is conceptualizing the ruler as a set of countable spatial interval units., ((c) 2015 APA, all rights reserved).)

The purpose of this article is to review and evaluate the range of theories proposed to explain findings on the use of geometry in reorientation. We consider five key approaches and models associated with them and, in the course of reviewing each approach, five key issues. First, we take up modularity theory itself, as recently revised by Lee and Spelke (Cognitive Psychology, 61, 152-176, 2010a; Experimental Brain Research, 206, 179-188, 2010b). In this context, we discuss issues concerning the basic distinction between geometry and features. Second, we review the view-matching approach (Stürzl, Cheung, Cheng, & Zeil, Journal of Experimental Psychology: Animal Behavior Processes, 34, 1-14, 2008). In this context, we highlight the possibility of cross-species differences, as well as commonalities. Third, we review an associative theory (Miller & Shettleworth, Journal of Experimental Psychology: Animal Behavior Processes, 33, 191-212, 2007; Journal of Experimental Psychology: Animal Behavior Processes, 34, 419-422, 2008). In this context, we focus on phenomena of cue competition. Fourth, we take up adaptive combination theory (Newcombe & Huttenlocher, 2006). In this context, we focus on discussing development and the effects of experience. Fifth, we examine various neurally based approaches, including frameworks proposed by Doeller and Burgess (Proceedings of the National Academy of Sciences of the United States of America, 105, 5909-5914, 2008; Doeller, King, & Burgess, Proceedings of the National Academy of Sciences of the United States of America, 105, 5915-5920, 2008) and by Sheynikhovich, Chavarriaga, Strösslin, Arleo, and Gerstner (Psychological Review, 116, 540-566, 2009). In this context, we examine the issue of the neural substrates of spatial navigation. We conclude that none of these approaches can account for all of the known phenomena concerning the use of geometry in reorientation and clarify what the challenges are for each approach.

Individual differences in spatial skill emerge prior to kindergarten entry. However, little is known about the early experiences that may contribute to these differences. The current study examined the relation between children's early puzzle play and their spatial skill. Children and parents (n = 53) were observed at home for 90 min every 4 months (6 times) between 2 and 4 years of age (26 to 46 months). When children were 4 years 6 months old, they completed a spatial task involving mental transformations of 2-dimensional shapes. Children who were observed playing with puzzles performed better on this task than those who did not, controlling for parent education, income, and overall parent word types. Moreover, among those children who played with puzzles, frequency of puzzle play predicted performance on the spatial transformation task. Although the frequency of puzzle play did not differ for boys and girls, the quality of puzzle play (a composite of puzzle difficulty, parent engagement, and parent spatial language) was higher for boys than for girls. In addition, variation in puzzle play quality predicted performance on the spatial transformation task for girls but not for boys. Implications of these findings as well as future directions for research on the role of puzzle play in the development of spatial skill are discussed., (PsycINFO Database Record (c) 2012 APA, all rights reserved.)

In this paper we examine the relations between parent spatial language input, children's own production of spatial language, and children's later spatial abilities. Using a longitudinal study design, we coded the use of spatial language (i.e. words describing the spatial features and properties of objects; e.g. big, tall, circle, curvy, edge) from child age 14 to 46 months in a diverse sample of 52 parent-child dyads interacting in their home settings. These same children were given three non-verbal spatial tasks, items from a Spatial Transformation task (Levine et al., 1999), the Block Design subtest from the WPPSI-III (Wechsler, 2002), and items on the Spatial Analogies subtest from Primary Test of Cognitive Skills (Huttenlocher & Levine, 1990) at 54 months of age. We find that parents vary widely in the amount of spatial language they use with their children during everyday interactions. This variability in spatial language input, in turn, predicts the amount of spatial language children produce, controlling for overall parent language input. Furthermore, children who produce more spatial language are more likely to perform better on spatial problem solving tasks at a later age., (2011 Blackwell Publishing Ltd.)

When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when direct non-geometric information (i.e. a beacon) was also available for localizing a hidden object. Children were tested on a disorientation task with multiple phases. Across experiments, boys relied more heavily than girls on geometry to guide localization, as indicated by their errors during the initial phase of the task, and by their search choices following transformations that left only geometry available, or that, under limited conditions, created a conflict between beacon and geometry. Analyses of search times suggested that girls, like boys, had encoded geometry, and testing in a square space ruled out explanations concerned with motivational and methodological variables. Taken together, the findings provide evidence for an early sex difference in the weighting of geometry. This sex difference, we suggest, reflects subtle variation in how boys and girls approach the problem of combining multiple sources of location information., (2011 Blackwell Publishing Ltd.)

The ability to locate objects in the environment is adaptively important for mobile organisms. Research on location coding reveals that even toddlers have considerable spatial skill. Important information has been obtained using a disorientation task in which children watch a target object being hidden and are then blindfolded and rotated so they cannot track their changing relation to the target. Even toddlers under two years of age search successfully for the hidden object, which shows that they can use geometric features of the spatial environment to determine object location. It has been claimed that these results show innate geometric abilities, but there is evidence that these early spatial skills are not simply geometric. The article presents an overview of experimental findings that provide the basis for a different interpretation of spatial development.

Both animals and human toddlers can find an object in a rectangular enclosure after they have been disoriented. They use geometric cues (relative lengths of walls) to discriminate among different corners (e.g. long wall to the left, short to the right). It has been claimed that this ability is 'modular', i.e. exclusively geometric. The present study demonstrates that the ability toddlers exhibit is a more general one, namely, an ability to discriminate relative quantity. Using a square enclosure, we show that toddlers use the relative sizes of the figures on different walls to characterize different corners. We also show that they do not use simple non-relative features to distinguish different corners. Possible reasons for differences in the ability to use relative versus non-relative cues are discussed.

Spatial judgments and actions are often based on multiple cues. The authors review a multitude of phenomena on the integration of spatial cues in diverse species to consider how nearly optimally animals combine the cues. Under the banner of Bayesian perception, cues are sometimes combined and weighted in a near optimal fashion. In other instances when cues are combined, how optimal the integration is might be unclear. Only 1 cue may be relied on, or cues may seem to compete with one another. The authors attempt to bring some order to the diversity by taking into account the subjective discrepancy in the dictates of multiple cues. When cues are too discrepant, it may be best to rely on 1 cue source. When cues are not too discrepant, it may be advantageous to combine cues. Such a dual principle provides an extended Bayesian framework for understanding the functional reasons for the integration of spatial cues., (Copyright 2007 APA)

The study of spatial cognition has benefited greatly from a technique known as the disorientation procedure. This procedure was originally used with rats to show that they relied on the geometry of an enclosed space to locate a target hidden in that space. Disorientation has since been used with a variety of mobile animals, including human children, to examine the coding of geometric information. Here, we focus mostly on our recent work with young children. We examine a set of issues concerning reorientation--namely, the nature of geometric coding, the processes invoked by disorientation, and the developmental origins of using geometric information to determine location. We have employed a variety of methods to examine these issues; the methods include analyzing search behaviors, using spaces of different shapes, varying viewing position, and comparing different disorientation procedures. The implications for how children and nonhuman animals code geometric information are discussed.

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.

We examined whether the male spatial advantage varies across children from different socioeconomic (SES) groups. In a longitudinal study, children were administered two spatial tasks requiring mental transformations and a syntax comprehension task in the fall and spring of second and third grades. Boys from middle- and high-SES backgrounds outperformed their female counterparts on both spatial tasks, whereas boys and girls from a low-SES group did not differ in their performance level on these tasks. As expected, no sex differences were found on the verbal comprehension task. Prior studies have generally been based on the assumption that the male spatial advantage reflects ability differences in the population as a whole. Our finding that the advantage is sensitive to variations in SES provides a challenge to this assumption, and has implications for a successful explanation of the sex-related difference in spatial skill.

In the present study, we examined how people code object location when an object is hidden in an enclosed space. On object location tasks involving disorientation, viewers must code the location of an object in relation to the spatial environment because they cannot directly track their changing relation to the object. Recently, we showed that viewers also code their perspective relative to the entire space (inside vs. outside) in such tasks. To determine whether viewers code perspective whenever they must locate an object, we examined young children's performance on a task in which coding perspective would be difficult. Our task involved both disorientation and translation (i.e., movement from inside to outside the space or vice versa). When translation preceded disorientation, performance was comparable to performance on tasks with no translation. However, when disorientation preceded translation, performance was at chance. The implications of these findings for location coding are discussed.

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., (Copyright 2004 American Psychological Association)

Four experiments are reported in which people organize a space hierarchically when they estimate particular locations in that space. Earlier work showed that people subdivide circles into quadrants bounded at the vertical and horizontal axes, biasing their estimates towards prototypical diagonal locations within those spatial categories (Psychological Review 98 (1991) 352). In this work Huttenlocher, Hedges, and Duncan showed that the use of such spatial categories can increase the accuracy of estimation of inexactly represented locations. The stimulus locations we examined were uniformly distributed across the circle. In the present study we explore whether variation in the distribution of locations affects how the circle is categorized. Other things being equal, categories that capture high density regions in a stimulus space should contribute most to accuracy of estimation. However, precision of boundaries is also important to accuracy; with imprecise boundaries stimuli may be misclassified, leading to large errors in estimation. We found that people use the same spatial categories regardless of the distribution of the locations. We argue that this spatial organization nevertheless can maximize the accuracy of estimates because vertical and horizontal category boundaries are the most exact, minimizing misclassification of stimuli.

Spatial judgments and actions are often based on multiple cues. The authors review a multitude of phenomena on the integration of spatial cues in diverse species to consider how nearly optimally animals combine the cues. Under the banner of Bayesian perception, cues are sometimes combined and weighted in a near optimal fashion. In other instances when cues are combined, how optimal the integration is might be unclear. Only 1 cue may be relied on, or cues may seem to compete with one another. The authors attempt to bring some order to the diversity by taking into account the subjective discrepancy in the dictates of multiple cues. When cues are too discrepant, it may be best to rely on 1 cue source. When cues are not too discrepant, it may be advantageous to combine cues. Such a dual principle provides an extended Bayesian framework for understanding the functional reasons for the integration of spatial cues. [ABSTRACT FROM AUTHOR]