1988); and meteorologists learning to see patterns on satellite images (Lowe, 2001). Just as Chase and Simon indicated that chess masters rapidly distinguished meaningful chess configurations from random patterns, work on perceptual learning shows analogous results for a wide variety of materials. These range from increasing sensitivity to smaller and smaller gaps between simple lines with practice (Fahle et al., 1995), to comprehending variations in elevation when reading topographic maps (Pick et al., 1995), to discriminating relevant from irrelevant information in mathematics problems (Littlefield and Rieser, 1993; Schwartz and Bransford, 1998). These findings apply directly to the tools (e.g., models, graphics, maps) for learning about spatial patterns that are used in schools (Rieser, 2002).
The third feature of working memory is its structural differentiation. Working memory consists of multiple subsystems, some of which operate in parallel and do not interfere with others. So, for example, Brooks (1968) showed that effectiveness at solving a spatial problem is reduced more by a simultaneous spatial task than by a verbal task. Baddeley (1986) argued that there are three storage systems in working memory. One serves central executive functions such as reasoning and decision making. The other two store different types of information—the articulatory loop for verbal information and the visuospatial sketch-pad for spatial information. A broad range of research has built on these observations. Thus, for example, in the case of readers elaborating on their understanding of verbal information, spatial representations can be more helpful than additional verbal information because they result in less mutual interference.
Kosslyn (1978) distinguished four stages in the cognitive processing of spatial information:
generating a representation, either by recalling an object or event from long-term memory or by creating an image from words or ideas;
maintaining a representation in working memory in order to use it for reasoning or problem solving;
scanning a representation that is maintained in working memory, in order to focus attention on some of its parts; and
transforming a representation, for example, by rotating it to a new viewing perspective, shrinking it, or imagining its shape if it were transformed by being folded or compressed.
Each of these stages requires cognitive effort and uses some of the resources and capacity of working memory (Kosslyn et al., 1990). Shepard and his colleagues (Shepard and Metzler, 1971; Shepard and Cooper, 1986) pioneered studies of the relationship between spatial imagery and the cognitive effort involved in mental rotation. Shepard and Metzler (1971) showed adults representations of pairs of novel three-dimensional objects in various orientations (Figure 4.1). On a given trial, the two objects were either the same (sometimes they were oriented in the same direction and sometimes their orientations differed relative to each other) or they were different, representing mirror images of each other. Subjects were asked to say whether the two were the same or different and decision times were recorded. The results showed consistent patterns—response times for correctly judging two shapes as the same increased linearly with increasing angular differences in orientation. The response time increase applied to stimuli differing in orientation in the two-dimensional picture plane and stimuli differing in orientation in three-dimensional depth (that is, rotated through the picture plane).
Practice does make it easier to create and to transform spatial representations. Familiarity and practice imagining specific types of objects and events sharply improves the ease of cognitive processing of spatial representations. For example, Lohman and Nichols (1990) asked adults to