Modeling Spatial Ability in Mental Rotation and Paper-Folding

Modeling Spatial Ability in Mental Rotation and Paper-Folding Andrew Lovett (Andrew@cs.northwestern.edu) Kenneth Forbus (Forbus@northwestern.edu) Qualitative Reasoning Group, Northwestern University, 2133 Sheridan Road Evanston, IL 60208 USA perform each task consistently. This analysis allows us to address a longstanding debate about the effects of shape complexity on mental rotation. It also provides hypotheses about the skills supporting fast, efficient mental rotation, and thus the skills underlying spatial ability. We begin with background on mental rotation and the question of shape complexity. We show how paper-folding appears to violate many researchers’ conclusions, as it involves simple shapes but requires great deliberation and effort. We next present our computational model, which builds on previous cognitive models of perception, comparison, and visual problem-solving (Falkenhainer, Forbus, & Gentner, 1989; Lovett & Forbus, 2011). We apply the model to the two tasks, determining the amount of information that must be carried through the transformations, and showing why paper-folding is a more difficult task. Finally, we discuss the results and consider the ramifications for spatial ability in general. Abstract Spatial ability tests like mental rotation and paper-folding provide strong predictions of an individual’s achievement in science and engineering. What cognitive skills are involved in them? We use a computational model to analyze these tasks, asking how much information must be processed to perform them. The models demonstrate that in some cases stimuli can be vastly simplified, resulting in consistent performance regardless of stimulus complexity. The ability to produce a scaled-down representation of a complex stimulus may be a key skill underlying high spatial ability. Keywords: spatial ability; mental rotation; paper-folding; cognitive modeling. Introduction There is strong evidence linking spatial ability to academic achievement. Children who perform well on spatial ability tests are more likely to study STEM disciplines (Science, Technology, Engineering, and Mathematics) and to go into a STEM profession (Shea, Lubinski, & Benbow, 2001; Wai, Lubinski, & Benbow, 2009). This effect holds even when controlling for verbal and mathematical ability, suggesting that spatial ability is an independent component of intelligence. If we are to improve STEM achievement, it is critical that we better understand the skills that compose spatial ability and how they can be taught. Traditionally, spatial ability has been evaluated using tasks such as mental rotation and paper-folding. In mental rotation (Figure 1A, 1B), individuals are shown two shapes and asked whether a rotation of one shape could produce the other. In paper-folding, they are shown a line-drawing of paper and asked to imagine the results of unfolding (Figure 1C) or folding up (Figure 1D) the paper. Both tasks appear to measure spatial visualization, the ability to manipulate mental representations of images (McGee, 1979). There is evidence that the tasks are linked, with training on one improving performance on the other (Wright et al., 2008). However, many questions remain about what skills enable people to perform them quickly and accurately. Here, we study the mental rotation and paper-folding tasks using a computational model. The model operates directly on 2D line drawings (sketches), automatically generating representations, transforming them, and evaluating the results of the transformation. We use the model to analyze the tasks, asking how much information must be encoded and carried through the transformations to Background Mental Rotation Mental rotation is frequently used to evaluate spatial ability (Vandenberg & Kuse, 1978). Typically the distractors—the shapes that aren’t a valid rotation—are mirror reflections. When they are presented sequentially, there is often a cue indicating what the orientation of the second shape will be (e.g., Cooper & Podogny, 1976; Figure 1B). A common finding across task variations is that the response time is proportional to the angle of rotation between the shapes. That is, response times increase linearly with angular distance. This finding has led to the claim that people use a mental space, analogous to the physical space, and that they rotate their representation through this space just as an object might rotate physically (Shepard & Cooper, 1982). One common question concerns how shapes are rotated through mental space. Are they rotated piecemeal, with one part rotated at a time, or are they rotated holistically, with every part rotated together (Bethell-Fox & Shepard, 1988)? These two possibilities produce different predictions about how shape complexity interacts with rotation speed. If shapes are rotated piecemeal, then people should rotate complex shapes more slowly, because there are more parts to rotate. If shapes are rotated holistically, then shape complexity may not affect rotation speed.