The Psychological Validity of Qualitative Spatial Reasoning in One Dimension

One of the central questions of spatial reasoning research is whether the underlying processes are inherently visual, spatial, or logical. We applied the dual task interference paradigm to spatial reasoning problems in one dimension, using Allen's interval calculus, in order to make progress towards resolving this argument. Our results indicate that spatial reasoning with interval relations is largely based on the construction and inspection of qualitative spatial representations, or mental models, while no evidence for logical proofs of derivations or the involvement of visual representations and processes was found.     

Learning to Reach to Locations Encoded from Imaging Displays

We examined the use of hand gestures while people solved spatial reasoning problem in which they had to infer motion from static diagrams (mental animation problems). In Experiment 1, participants were asked to think aloud while solving mental animation problems. They gestured on more than 90% of problems, and most gestures expressed information about the component motions that was not stated in words. Two further experiments examined whether the gestures functioned in the mechanical inference process, or whether they merely served functions of expressing or communicating the results of this process. In these experiments, we examined the effects of instructions to think aloud, restricting participants' hand motions, and secondary tasks on mental animation performance. Although participants who were instructed to think aloud gestured more than control groups, some gestures occurred even in control conditions. A concurrent spatial tapping task impaired performance on mechanical reasoning, whereas a simple tapping task and restricting hand motions did not. These results indicate that gestures are a natural way of expressing the results of mental animation processes and suggest that spatial working memory and premotor representations are involved in mental animation. They provide no direct evidence that gestures are functional in the thought process itself, but do not rule out a role for overt gestures in this type of spatial thinking.     

Expert Algorithmic and Imagistic Problem Solving Strategies in Advanced Chemistry

Abstract

Visualization and imagistic reasoning appear central to expert practice in science; however, expert use of these strategies on authentic tasks has not been examined in detail. This study documents how science experts use both algorithms and imagistic reasoning to solve problems. Using protocol analysis, we report expert chemists' preferential use of algorithms for solving spatial problems and imagistic reasoning for deducing spatial transformations. We observed experts employ algorithms to solve the majority of spatial tasks while reserving imagistic strategies to solve a class of tasks that required translating between representations. Strategy used varied widely among experts and tasks.     

Gesture in Spatial Cognition: Expressing,Communicating, and Thinking About Spatial Information

Do hand gestures play a role in spatial cognition? This paper reviews literature addressing the roles of gestures in (1) expressing spatial information, (2) communicating about spatial information, and (3) thinking about spatial information. Speakers tend to produce gestures when they produce linguistic units that contain spatial information, and they gesture more when talking about spatial topics than when talking about abstract or verbal ones. Thus, gestures are commonly used to express spatial information. Speakers use gestures more in situations when those gestures could contribute to communication, suggesting that they intend those gestures to communicate. Further, gestures influence addressees' comprehension of the speech they accompany, and addressees also detect information that is conveyed uniquely in gestures. Thus, gestures contribute to effective communication of spatial information. Gestures also play multiple roles in thinking about spatial information. There is evidence that gestures activate lexical and spatial representations, promote a focus on spatial information, and facilitate the packaging of spatial information in speech. Finally, some of the observed variation across tasks in gesture production is associated with task differences in demands on spatial cognitive processes, and individual differences in gesture production are associated with individual differences in spatial and verbal abilities. In sum, gestures appear to play multiple roles in spatial cognition. Central challenges for future research include: (1) better specification of the mental representations that give rise to gestures, (2) deeper understanding of the mechanisms by which gestures play a role in spatial thinking, and (3) greater knowledge of the sources of task and individual differences in gesture production.     

Effects of Communication Methods on Communication Patterns and Performance in a Remote Spatial Orientation Task

Abstract

An experiment was conducted to examine the impact of communication methods (text-only, audio-only, and audio-plus-video) on communication patterns and effectiveness in a 2-person remote spatial orientation task. The task required a pair of participants to figure out the cardinal direction of a target object by communicating spatial information and perspectives. Results showed that overall effectiveness in the audio-only condition was better than the text-only and audio-plus-video conditions, and communication patterns were more predictive of errors than individual differences in spatial abilities. Discourse analysis showed that participants in the audio-plus-video condition performed less mental transformation of spatial information when communicating, which led to more interpretation errors by the listener. Participants in the text-only conditions performed less confirmation and made more errors by misreading their own display. Results suggested that speakers in the audio-plus-video condition minimized effort by communicating spatial information based on their own perspective but speakers in the audio-only and text-only conditions would more likely communicate transformed spatial information. Analysis of gestures in the audio-plus-video condition confirmed that iconic gestures tended to co-occur with spatial transformation. Iconic gesture rates were negatively correlated with transformation errors, indicating that iconic gestures more likely co-occurred with successful communication of spatial transformation. Results show that when visual interactive feedback is available, speakers tend to adopt egocentric spatial perspectives to minimize effort in mental transformation and rely on the feedback to ensure that the hearer correctly interprets the information. When visual interactive feedback is not available, speakers will put more effort in transforming spatial information to help the hearer to understand the information. The current result demonstrated that allowing two persons to see and communicate with each other during a remote spatial reasoning task can lead to more errors because of the use of a suboptimal communication strategy.     

Qualitative Spatial Reasoning in Interpreting Text and Narrative

Abstract

Simple natural language texts and narratives often raise problems in commonsense spatial knowledge and reasoning of surprising logical complexity and geometric richness. In this article, I consider a dozen short texts—five taken from literature, the remainder contrived as illustrations—and discuss the spatial reasoning involved in understanding them. I conclude by summarizing their common features, and by tentatively drawing some morals for research in this area.     

Preferred and Alternative Mental Models in Spatial Reasoning

The mental model theory postulates that spatial reasoning relies on the construction, inspection, and the variation of mental models. Experiment 1 shows that in reasoning problems with multiple solutions, reasoners construct only a single model that is preferred over others. Experiment 2 shows that inferences conforming to these preferred mental models (PMM) are easier than inferences that are valid for alternatives. Experiments 3 and 4 support the idea that model variation consists of a model revision process. The process usually starts with the PMM and then constructs alternative models by local transformations. Models which are difficult to reach are more likely to be neglected than models which are only minor revisions of the PMM.     

Path visualization: a method for objective measurement of spatial visualization

ABSTRACT

The ability to mentally represent spatial information is a fundamental cognitive process. To many people, this process feels a bit like visual perception, hence the term ‘spatial visualization’. In this paper, we describe a method for measuring the accuracy of spatial visualization, specifically visualization of a complex path in imaginary space. A critical feature of this method (called Path Visualization) is that it relies on the detection of intersections in a visualized path. Intersection detection is an inherently spatial task that requires a spatial representation. In this paper, we show how the Path Visualization method works, and how it can be customized to address several key research issues in human spatial cognition.     

Qualitative Spatial Reasoning for Topological Map Learning

Abstract

In this paper we investigate the application of qualitative spatial reasoning methods for learning the topological map of an unknown environment. We develop a topological mapping framework that achieves robustness against ambiguity in the available information by tracking all possible graph hypotheses simultaneously. We then exploit spatial reasoning to reduce the space of possible hypotheses. The considered constraints are qualitative direction information and the assumption that the map is planar. We investigate the effects of absolute and relative direction information using two different spatial calculi and combine the approach with a real mapping system based on Voronoi graphs.     

Spatial Thinking in Undergraduate Science Education

Spatial thinking is central to many scientific domains and professions spatial ability predicts success and participation in science. However spatial thinking is not is not emphasized in our educational system. This paper presents a selective review of four types of studies regarding spatial thinking in undergraduate science curricula; (1) correlational studies examining the relations between measures of spatial ability and performance in science disciplines, (2) studies that attempt to train aspects of spatial thinking, (3) studies of how students understand specific spatial representations in sciences (4) studies that use dynamic spatial representations to promote scientific understanding. For each type of study, the evidence is critically evaluated and conclusions are drawn about how to nurture spatial thinking in science.     

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.     

Virtual to Real Transfer of Spatial Learning in a Complex Environment: The Role of Path Network and Additional Features

The effects of the amount and type of spatial information on the orientation accuracy and metric properties of mental representations of a large-scale built environment were evaluated in a virtual-real transfer study. Four groups of participants explored different virtual versions of a campus before being tested in the real environment. Learning with or without additional features and with or without a network of pathways led to different patterns of data. Although direction measures and straight-line and route distance estimates were least accurate in the absence of either type of information, the combination of both types of information did not produce more accurate knowledge than either did alone. In particular, the presence of additional features had a facilitating effect only on the direction estimates. The results highlight the respective importance of amount and type of spatial information in the acquisition and use of mental spatial representations.     

Analyzing Qualitative Spatio-Temporal Calculi using Algebraic Geometry

Abstract

Qualitative spatial reasoning is based on calculi which comprise relations and operation tables that encode operations like relation composition. Designing a calculus involves determining these tables and analyzing reasoning properties—a demanding task that is susceptible to errors if performed manually. This paper is concerned with automating computation of operation tables and analysis of qualitative calculi over real-valued domains like the plane ². We present an approach to specify qualitative relations using polynomial equations that allows methods from algebraic geometry to be applied. This paper shows how reasoning with qualitative relations can be posed algebraically and demonstrates algebraic reasoning using Gröbner base analysis. We evaluate this approach and describe our implementation, which is freely available as part of the spatial reasoning toolbox SparQ.     

Revisiting Perspective-Taking: Can People Maintain Imagined Perspectives?

Abstract

Three experiments were conducted to examine whether people can adopt and maintain imagined perspectives in the absence of target information. The task used entailed providing information about an imagined perspective in advance of target information to examine whether this would facilitate perspective-taking performance and reduce or eliminate alignment effects that are commonly reported in the literature. The three experiments employed different types of spatial environments: an environment learned from navigating a computer screen (Experiment 1), and an immersive environment that was either remote (Experiment 2) or immediate (Experiment 3) at the time of retrieval. Across the three experiments, results showed that information about an imagined perspective can be utilized ahead of target information. Furthermore, they suggested that alignment effects can be reduced as a result of processing information about perspective ahead of target information, but only when reasoning about specific nonimmediate spatial relations (Experiments 1 and 2). Results are discussed in connection with previous findings on spatial updating and the organizational structure of spatial memory.     

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.     

Heading south with a north-up map: A choice processing analysis of map alignment effects

This study employed an information accumulation model of choice reaction times to investigate alignment effects in mental representations of maps. University students studied a map from a single orientation (with north at the top). In a subsequent two-choice reaction time task, the students’ spatial knowledge of the map was assessed employing spatial left/right judgments, which were made from imagined perspectives that were either north-aligned or south-aligned. Data showed a standard alignment effect, favoring north- over south-aligned trials. To examine the locus of this effect, data were fit using the Linear Ballistic Accumulator (LBA) model of speeded decisions (Brown & Heathcote, 2008). Of interest were three model parameters: drift rate, the speed at which evidence accumulates toward a response; response threshold, the amount of evidence demanded from the decision maker before selecting a response; and non-decision time, the time consumed by pre- and postdecisional processes. The best-fitting model suggested that non-decision time accounted for the alignment effect. The difference in non-decision time between north and south-aligned judgments suggests a mental alignment stage on south-aligned trials, accounting for the longer reaction times for judgements misaligned with the presented north orientation of the map.