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- W2395701935 abstract "Modeling Spatial Abstraction during Mental Rotation Andrew Lovett (andrew@cs.northwestern.edu) Holger Schultheis (schulth@sfbtr8.uni-bremen.de ) Cognitive Systems Group, Universitat Bremen top of each other, or one might even group the squares together to form one large approximate triangle. Spatial abstraction is critical in mental rotation tasks (Figure 1A), where participants are asked whether one shape could be rotated in space to produce the other. Researchers believe individuals do this by incrementally transforming their mental representation of one shape to line it up with the other (Shepard & Metzler, 1971; Shepard & Cooper, 1982). Furthermore, there is evidence that representations are transformed in a piecemeal manner, rotating one part at a time (Yuille & Steiger, 1982; Just & Carpenter, 1976). If this is true, then the speed and ease of mental rotation will depend on the complexity of the representations. If one abstracts out details to produce a simpler representation, one can mentally rotate more effectively. Of course, it is important to only remove the spatial detail that is unnecessary for performing a task. In mental rotation, one must keep the details that distinguish a base shape from its distractors, those items that are not valid rotations of it. Thus spatial abstraction must be sensitive to the nature of the task and the specific stimuli being processed. Computational models can play a key role in testing abstraction strategies, concretely evaluating which details can be removed for a given task. Our previous model represented the edges going along a shape’s contour, such as the 12 edges in the Figure 1A shape (Lovett & Forbus, 2013). The model encoded features for each edge and relations between edges. It performed abstraction by either a) removing the shorter edges from its representation, or b) removing all features of a particular type, e.g., ignoring the orientations of the edges. Edge-based representation and abstraction proved effective in an initial simulation. However, this approach requires considering a great many details, such as the 12 sides in Figure 1A or the 24 sides in Figure 1B (lower row). Here we present a new model that represents the parts of Abstract We present a computational model of mental rotation and shape comparison. The model posits that spatial abstraction, in which spatial details are removed to simplify a representation, is a key skill underlying spatial ability. Shapes are represented as collections of two-dimensional parts, and abstraction is applied by merging parts or ignoring certain part features. Using the model, we simulate a classic mental rotation experiment, demonstrating how abstraction explains the study’s key finding. Finally, we compare the part-based approach to a previous edge-based approach, demonstrating that the current approach better explains human shape comparisons. Keywords: Spatial Cognition, Cognitive Modeling, Mental Rotation. Introduction Spatial ability is a critical component of cognition. Children who exhibit higher spatial ability, independent of math or verbal ability, are more likely to engage in the STEM disciplines (Science, Technology, Engineering, and Mathematics) as students and later as professionals (Shea, Lubinski, & Benbow, 2001; Wai, Lubinski, & Benbow, 2009). Spatial ability is evaluated using tasks like paper- folding and mental rotation, where children must imagine a shape being transformed through space. If we can better understand the skills used on these tasks, it may be possible to teach these skills, improving students’ spatial abilities and preparing them to become scientists and engineers. We believe spatial abstraction is an important underlying spatial skill. Spatial abstraction is the ability to remove unnecessary detail from a mental representation, producing a simpler representation that supports faster and more effective spatial reasoning. For example, consider the leftmost shape in Figure 1A. This shape contains 12 sides. However, one might represent it as three squares stacked on Base Shape A Mirror- Reflection Base Shape 6-Sided Simple 24-Sided Complex B High-Sim Distractor Low-Sim Distractor C Figure 1: A: Mental rotation task. B: Stimuli from (Cooper & Podgorny, 1976). C: Stimuli from (Folk & Luce, 1987)." @default.
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- W2395701935 date "2014-01-01" @default.
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- W2395701935 title "Modeling Spatial Abstraction during Mental Rotation" @default.
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