Spatial Thinking Across the College Curriculum: A Report on a Specialist Meeting

This report presents findings from a specialist meeting of spatially-minded researchers and administrators from education and industry to consider prospects for introducing courses and curricula on spatial thinking in higher education. More than 40 participants explored the rationale for expanding student exposure to concepts, tools, and applications of spatial reasoning across a range of science, engineering, and humanities disciplines. The focus was on what we know and what we need to know to make the case for space, underscoring basic research on what is meant by spatial thinking and on variations in the spatial reasoning skills required in different domains of knowledge. The need for rigorous assessments of learning outcomes associated with different approaches to teaching spatial thinking was emphasized.     

Route generation and description using the notions of object's influence area and spatial conceptual map

In the GRAAD Project we aimed at creatinga system which could generate route directions thatare comparable to route directions created by humanparticipants. With this goal in mind, we started froma linguistic and cognitive study of route directionsproduced by people and the study of cognitive modelsof mental maps. We proposed a new qualitative spatialmodel that can support the spatial properties of humanroute directions. This model is based on the notion ofobject's influence area which is used to modelneighborhood, orientation and distance. The proposedapproach relies on the manipulation of spatialentities in a spatial conceptual map (SCM) which isthe computarized analog of a mental map used bypeople. We developped the GRAAD System, software thatgenerates routes in a SCM and describes them innatural language. Finally, we conducted an experimentin order to compare GRAAD's route directions androutes described by human participants in similarexperimental conditions. GRAAD's output was notdistinguishable from route directions created by humanparticipants. In this paper we present the mainresults obtained during all phases of the GRAADProject.     

An Investigation into Vertical Bias Effects

ABSTRACT

In three experiments, after exploring a virtual environment (VE), adult participants made spatial judgments about the location of target objects that were higher and lower than their perceived test location within the VE. In Experiment 1, the locations of the target objects were inferred from verbal instructions. The main results were a tendency to judge objects as closer to the horizontal plane than their true locations, and more efficient downward than upward judgments. Both effects generally accord with findings reported by Wilson et al. (2004a Wilson, P. N., Foreman, N., Stanton, D. and Duffy, H. 2004a. Memory for targets in a multilevel simulated environment: Evidence for vertical asymmetry in spatial memory. Memory & Cognition, 32: 283–297. [Crossref] , [Google Scholar], 2004b Wilson, P. N., Foreman, N., Stanton, D. and Duffy, H. 2004b. Memory for targets in a multi-level simulated-environment: A comparison between able-bodied and physically disabled children. British Journal of Psychology, 95: 325–338.  [Google Scholar]). In Experiments 2 and 3, which were closely modeled on the design of the Wilson et al. studies, regression to the horizontal plane was noted but no downward bias was observed. A misperception in the viewing height between the floors and ceilings of the virtual rooms was apparent in both experiments. The results from the present study together with earlier investigations suggest different hierarchical encoding of between-axis and within-axis information.     

Categorical Bias in Line Angle Judgments: Sex Differences and the Use of Multiple Categories

According to the Category Adjustment (CA) model, spatial estimates (e.g., of location) involve Bayesian combination across multiple, hierarchical pieces information, each weighted by its relative certainty. Recent work, though, has shown that men and women differ in terms of their certainty regarding fine-grained and categorical information in location memory. Here we demonstrate that this reflects a more general sex difference in visuospatial processing by examining bias patterns in a line angle judgment task (JLAP-15). In addition, the data suggest that multiple, hierarchical levels of categorical information influenced spatial judgments. These results imply that the hierarchical combination outlined by the CA model extends beyond two levels, and that men and women apply differential weighting to these representations.     

Environmental reference systems for large-scale spaces

Human navigation in well-known environments is guided by stored memory representations of spatial information. In three experiments (N = 43) we investigated the role of different spatial reference systems when accessing information about familiar objects at different locations in the city in which the participants lived. Our results indicate that two independent reference systems underly the retrieval of spatial knowledge. Environmental characteristics, e.g., the streets at an intersection, determine which headings are easier to imagine at a given location and lead to differences in accessibility of spatial information (orientation-specific behavior). In addition, access to spatial information depends on the relative direction of a location with respect to the imagined heading, such that information about locations imagined in front of oneself is easier to access than about locations towards the back. This influence of an egocentric reference system was found for environmental knowledge as well as map-based knowledge. In light of these reference system effects, position-dependent models of spatial memory for large-scale environments are discussed. To account for the simultaneous effect of an environmental and an egocentric reference system, we present a 2-level model of spatial memory access.     

Human Four-Dimensional Spatial Judgments of Hyper-Volume

The dimensionality limitation of human spatial representations has been a long-lasting, unsolved issue in psychology, mathematics, and philosophy. The present study examined the possibility of human four-dimensional spatial representations using a spatial judgment task on hyper-volume, a novel property unique to higher dimensional space. Observers studied visual simulations of random wireframe hyper-tetrahedrons (4-simplexes) rotating around the y-z plane and judged their hyper-volume by adjusting the size of a 4-D block. Multiple regression analyses showed a significant correlation between the responses and the actual hyper-volume but not the definition-based, lower-dimensional cues such as the mean 3-D volume, providing empirical evidence of human 4-D spatial representations that can support judgments of certain novel, high-dimensional properties.     

A systematic spatial bias in remembering eye positions

Categorical bias in location memory in geometric spaces is well established. The present study assessed the presence of the bias in locating eyes in images of human faces. Participants were presented with digital faces and indicated the position of one of the eyes in both upright and inverted orientations. Biases resulted from participants using multiple sources of accessible information. No differences were found for upright vs. inverted face images. Overall, the data were consistent with the retrieval category adjustment model. These distortions may be considered within the forensic context, when eyewitnesses work with a sketch artist or use a computer program to generate an image of the culprit.     

Assessment of between-floor structural and topological properties on cognitive map development in multilevel built environments

The present study investigated cognitive map development in multilevel built environments. Three experiments were conducted in complex virtual buildings to examine the effects of five between-floor structural factors that may impede the accuracy of humans’ ability to build multilevel cognitive maps. Results from Experiments 1 and 2 (of three experiments) revealed that difficulties in developing multilevel cognitive maps are not solely caused by the z-axis offset, as is suggested in the literature, but are due to the factorial combination of a between-floor overlap and a z-axis offset. Results from Experiment 2 showed that this process becomes substantially more difficult when the reference directions between different floors have an angular offset from each other. Finally, results from Experiment 3 demonstrated that confusing between-floor heading shifts in aligned buildings did not make it reliably harder to build multilevel cognitive maps. The implications of these findings are discussed in terms of theories of mental representations in multilayered three-dimensional spaces, as well as for architectural design.     

Coordinating signs and eye gaze in the depiction of directions and spatial scenes by fluent and L2 signers of Norwegian Sign Language

The current study investigates the coordination of signs and eye gaze during depictions of directions and spatial scenes by fluent and second language (L2) signers of Norwegian Sign Language. First, findings show that fluent and L2 signers make different choices regarding the perspective they use to depict spatial scenes. Second, there is variation within and across groups in relation to how eye gaze is directed during these depictions. Findings suggest that eye gaze is used to establish a vantage point upon a depicted scene, but L2 learners may not always engage in this type of coordination. This study contributes to our understanding of how visual perspective is depicted in signed languages and has implications for signed language pedagogy.     

实数域中的投影法及其在单次快摄阵处理中的应用

阵列处理中计算简单的投影法避免了矩阵特征分解(ＥＶＤ)的庞大计算量,然而仍需进行复数计算。为了进一步减小计算量,提出一种实数域中的投影法,它将投影矩阵及空间谱的计算均简化为实数的计算,从而。使阵处理的计算量大大减少,而且使估计性能保持不变。计算机模拟与实际外场实验数据的计算结果表明了算法的有效性。