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External representations powerfully support and augment complex human behavior. When navigating, people often consult external representations to help them find the way to go, but do maps or verbal instructions improve spatial knowledge or support effective wayfinding? Here, we examine spatial knowledge with and without external representations in two studies where participants learn a complex virtual environment. In the first study, we asked participants to generate their own maps or verbal instructions, partway through learning. We found no evidence of improved spatial knowledge in a pointing task requiring participants to infer the direction between two targets, either on the same route or on different routes, and no differences between groups in accurately recreating a map of the target landmarks. However, as a methodological note, pointing was correlated with the accuracy of the maps that participants drew. In the second study, participants had access to an accurate map or set of verbal instructions that they could study while learning the layout of target landmarks. Again, we found no evidence of differentially improved spatial knowledge in the pointing task, although we did find that the map group could recreate a map of the target landmarks more accurately. However, overall improvement was high. There was evidence that the nature of improvement across all conditions was specific to initial navigation ability levels. Our findings add to a mixed literature on the role of external representations for navigation and suggest that more substantial intervention--more scaffolding, explicit training, enhanced visualization, perhaps with personalized sequencing--may be necessary to improve navigation ability.

Understanding and reasoning about phenomena at scales outside human perception (for example, geologic time) is critical across science, technology, engineering, and mathematics. Thus, devising strong methods to support acquisition of reasoning at such scales is an important goal in science, technology, engineering, and mathematics education. In two experiments, we examine the use of analogical principles in learning about geologic time. Across both experiments we find that using a spatial analogy (for example, a time line) to make multiple alignments, and keeping all unrelated components of the analogy held constant (for example, keep the time line the same length), leads to better understanding of the magnitude of geologic time. Effective approaches also include hierarchically and progressively aligning scale information (Experiment 1) and active prediction in making alignments paired with immediate feedback (Experiments 1 and 2).

Popular sources often assume the existence of a male advantage in navigation, but the scientificdata are inconsistent. This meta-analysis evaluates the literature on behavioral sex differences inhuman navigation. We quantify the overall magnitude of sex differences in a variety ofparadigms and populations and examine potential moderators in large-scale navigation skills,using 694 effect sizes from 266 studies and a multilevel linear modeling approach. Overall, wefound that male participants outperform female participants, with a small to medium effect size(d= 0.34 to 0.38). The type of task, the type of dependent variable and the testing environmentsignificantly contribute to variability in effect sizes. Pointing and recall tasks show larger sexdifferences than distance estimation tasks or learning to criterion; among the dependent variables, the deviation scores associated with pointing tasks show larger effect sizes. The largestestimate was d = .55 for tasks than required coordinating indoor and outdoor views.Interestingly, studies with children younger than 13 years showed very small effect sizes (d= .15) as compared to older age groups. We discuss the implications of these findings for thestudy of sex differences and identify avenues for future navigation research.

Research on spatial thinking needs reliable and valid measures of individual differences in skills.Visuospatial Perspective Taking (PT)—the ability to mentally maintain and transform spatialrelationships between objects within an environment—is one kind of spatial skill that isespecially relevant to navigation and building cognitive maps. However, the psychometricproperties of various PT tasks have yet to be examined. The present study examines three mainpsychometric properties of PT tasks: 1) the reliability of two tasks developed for children butadapted in difficulty level for use in adult populations, 2) item difficulty and discriminabilitywithin and between four tasks using item response theory, and 3) relation of scores with generalintelligence, working memory, and mental rotation. Results showed that two of the four PT taskshave promising psychometric properties for measuring a wide range of PT ability based on itemdifficulty, discriminability, and efficiency of a test information function.

Background: One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In a series of three experiments, we investigate whether searching for an algebraic formalism before receiving direct instruction facilitates appropriate generalization. Results: (1) Searching buffers against negative transfer: participants who first searched for an equation were less likely to overgeneralize compared to participants who completed a tell-and-practice activity. (2) Likelihood of creating a correct new adaptation varied by performance on the searching task. (3) Asking people to sketch alleviated some of the negative effects of tell-and-practice, but sketching did not augment the effect of searching. (4) When participants received more elaborate tell-and-practice instruction, the advantages of searching were less notable. Conclusions: Searching for an algebraic formula prior to direct instruction may be a productive way to help learners connect a formula to its referent and avoid overgeneralization. Tell-and-practice instruction that only described the mathematical procedures led to the greatest levels of overgeneralization errors and worst performance. Tell-and-practice instruction that highlighted connections between the mathematical structure of the formula and the visual referent performed at similar or marginally worse levels than the search-first conditions.

Many scientific theories and discoveries involve reasoning about extreme scales, removed from human experience, such as time in geology, size in nanoscience. Thus, understanding scale is central to science, technology, engineering, and mathematics. Unfortunately, novices have trouble understanding and comparing sizes of unfamiliar large and small magnitudes. Relational reasoning is a promising tool to bridge the gap between direct experience and phenomena at extreme scales. However, instruction does not always improve understanding, and analogies can fail to bring about conceptual change, and even mislead students. Here we review how people reason about phenomena across scales, in three sections: (a) we develop a framework for how relational reasoning supports understanding extreme scales; (b) we identify cognitive barriers to aligning human and extreme scales; (c) we outline a theory-based approach to teaching scale information using relational reasoning, present two successful learning activities, and consider the role of a unified scale instruction across STEM education. [At the time of submission to ERIC this article was in press with "Educational Psychology Review."]

How do toddlers learn the names of geometric forms? Previous work suggests that preschoolers have fragmentary knowledge and that defining properties are not understood until well into elementary school. The current study investigated when children first begin to understand shape names and how they apply those labels to unusual instances. We tested 25- and 30-month-old children's (N = 30 each) understanding of names for canonical shapes (commonly encountered instances, e.g., equilateral triangles), noncanonical shapes (more irregular instances, e.g., scalene triangles), and embedded shapes (shapes within a larger picture, e.g., triangular slices of pizza). At 25 months, children knew very few names, including those for canonical shapes. By 30 months, however, children had acquired more shape names and were beginning to apply them to some of the less typical instances of the shapes. Possible mechanisms driving this initial development of shape knowledge and implications of that development for school readiness are explored. [This article was published in the "Journal of Cognition and Development" (EJ1090613).]

The author discusses four specific strategies for enhancing and supporting the spatial aspects of the science, mathematics, and social studies curricula. However, these four strategies are examples of what can be done, not an exhaustive list. The overarching concept is to embrace the spatial visualizations used for discovery and communication in these subject areas, helping students learn to read, discuss, and even create these visualizations. Doing so will aid the transmission of content and the future learning of new content, and the meta-analysis indicates it will probably act as a spatial skills training of its own. Spatial ability can be improved both inside and outside the classroom, as well as by instruction in other subject areas, notably the visual arts. Spatializing the curriculum by including and explicitly teaching the spatial symbol systems that lie at the heart of science, mathematics, and social studies is an achievable and worthwhile goal. (Contains 4 figures and 32 endnotes.)

Spatial thinking--such as visualizing the earth rotating--is crucial to student success in science, technology, engineering, and mathematics (STEM). Since spatial thinking is associated with skill and interest in STEM fields (as well as in other areas, such as art, graphic design, and architecture), the immediate question is whether it can be improved. While some students are better at spatial thinking than others, everyone can improve. The need to develop students' spatial thinking is currently not widely understood. The author stresses that educators already have some excellent techniques for developing it, through practice, language, gesture, maps, diagrams, sketching, and analogy. Systematically building these techniques into the curriculum could yield important dividends for American education. In this article, the author offers some suggestions on how to foster spatial thinking. (Contains 57 endnotes.)

Previous research has shown sketching to be useful tostudents solving math problems. The present studyexamines which aspects of middle school students’sketching are related to, or predict, successfullyanswering math problems. The effects of individualdifferences in cognitive factors – working memory,spatial ability, and prior math knowledge – on answeraccuracy are also analyzed. Stepwise regressionanalysis indicates that prior math knowledge and theinclusion of numerical representations of key problemrelationships in sketches positively predict answeraccuracy, whereas including irrelevant relationships ina sketch is associated with lower answer accuracy.Methodological implications for future research arediscussed.

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.

This report summarizes the major conclusions from a 2-day meeting of educators and researchers from more than a dozen disciplines that regard spatial thinking as a core activity that warrants consideration for a more prominent role in the education of undergraduate students.To make the case for space in the curriculum, the meeting concluded that basic research must come to a more fundamental understanding of what is meant by spatial thinking, including different varieties of spatial thinking across the college curriculum, and identifying what is common to spatial thinking across disciplines. At the same time there is a need to continue to develop methods of teaching spatial thinking. Additionally, there is a need for research on teaching spatial thinking, including assessments of what is learned from programs that aim to teach spatial thinking. Finally, there is a need to document and demonstrate where and how spatial thinking prepares students for academic success and allows them to better compete in the job market and global economy.

Memory for spatial location is typically biased, with errors trending toward the center of a surrounding region. According to the category adjustment model (CAM), this bias reflects the optimal, Bayesian combination of fine-grained and categorical representations of a location. However, there is disagreement about whether categories are malleable. For instance, can categories be redefined based on expert-level conceptual knowledge? Furthermore, if expert knowledge is used, does it dominate other information sources, or is it used adaptively so as to minimize overall error, as predicted by a Bayesian framework? We address these questions using images of geological interest. The participants were experts in structural geology, organic chemistry, or English literature. Our data indicate that expertise-based categories influence estimates of location memory--particularly when these categories better constrain errors than alternative ("novice") categories. Results are discussed with respect to the CAM.

Previous research has suggested that performance for items requiring memory-binding processes improves between ages 4 and 6 (J. Sluzenski, N. Newcombe, & S. L. Kovacs, 2006). The present study suggests that much of this improvement is due to retrieval, as opposed to encoding, deficits for 4-year-olds. Four- and 6-year-old children (N = 48 per age) were given objects, backgrounds, and object + background combinations to remember. Younger children performed equivalently to 6-year-olds during a working memory task for all types of memory questions but were impaired during a long-term memory task for the object + background combinations. Furthermore, this deficit was completely due to differences in false alarm rates, suggesting that separate analyses of hits and false alarms may be preferable to corrected recognition scores when studying memory development.

It is frequently claimed that the human mind is organized in a modular fashion, a hypothesis linked historically, though not inevitably, to the claim that many aspects of the human mind are innately specified. A specific instance of this line of thought is the proposal of an innately specified geometric module for human reorientation. From a massive modularity position, the reorientation module would be one of a large number that organized the mind. From the core knowledge position, the reorientation module is one of five innate and encapsulated modules that can later be supplemented by use of human language. In this paper, we marshall five lines of evidence that cast doubt on the geometric module hypothesis, unfolded in a series of reasons: (1) Language does not play a necessary role in the integration of feature and geometric cues, although it can be helpful. (2) A model of reorientation requires flexibility to explain variable phenomena. (3) Experience matters over short and long periods. (4) Features are used for true reorientation. (5) The nature of geometric information is not as yet clearly specified. In the final section, we review recent theoretical approaches to the known reorientation phenomena. Keywords: Modularity; Adaptive combination; Spatial reorientation; Development; Geometric module DOI: 10.1111/j.1551-6709.2009.01081.x