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Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum http://www.nap.edu/catalog/11019.html SPATIAL THINKING IN EVERYDAY LIFE, AT WORK, AND IN SCIENCE 53 normal, everyday cognitive processing; the novice-expert difference is a consequence of the degree and type of practice and experience in a domain. Getting to work is not the only spatial task shared by different occupations. In order to operate, workers need a mental model of the structure and functioning of the institution: they need to know who to turn to for help on what task. Sometimes information is mentally represented as a spatial network, much like a rudimentary mental map of an environment. In this institutional mental space, links are tasks and nodes are people who perform tasks. Often information is explicitly represented in an organizational chart and depicted as a spatial network that must be “navigated.” Managers must decide how to allocate resources or what new projects to undertake. To do so, they consult charts and graphs of performance. Charts and graphs provide spatial representations of data, but do not in themselves provide solutions to problems. Solutions depend on making inferences from charts and graphs, projections of future sales, changes in personnel and equipment, and more. Beyond generic problem-solving similarities, many jobs require the use of specific spatial skills. Recognition of complex patterns is required in many professions. Think of the time you saw an X-ray image in a doctor’s office. You could probably pick out bones but little else. In the clouds that X-rays resemble, highly trained radiologists can discern tumors, blood clots, and faulty valves. Recognizing these patterns takes years of training and is by no means perfect (see Ericsson, 1996, for an overview of the literature on expertise; see the November 2003 issue of the Educational Researcher on expertise in the context of education). Recognition skill does not transfer to other domains. Skilled radiologists are no better than novices at recognizing skin diseases that dermatologists are expert in diagnosing or plant diseases that botanists excel at discerning. Expertise in pattern recognition is domain specific. It requires discerning features characteristic of specific sensory categories. Typically, domain expertise in pattern recognition also requires learning the proper configurations of distinctive features. The practice that polishes this skill requires categorizing many examples of related and different phenomena and getting feedback on the categorization process. Simply seeing examples is not sufficient; to become expert, people must learn to differentiate and discriminate one category from another (Nickerson and Adams, 1979). A classroom demonstration illustrates that seeing, however frequent, is insufficient to ensure learning critical features. Students are asked to name what is shown on both sides of a penny or whether their (analog) watch dial has lines or numbers to mark minutes. Few succeed at the penny task, and many are surprisingly poor at the watch task. Although we “look” at pennies and watches frequently, often many times a day, we do not have to distinguish one penny or watch face from another (Nickerson and Adams, 1979). We do, however, need to distinguish a penny from a nickel or dime, and we do so based on color or shape or size without paying attention to the face of the coin. In watches, we only consult the lengths of hands and their angles. When we need to make fine distinctions, such as those required to differentiating types of tumors or diagnosing skin diseases, we must learn the fine details distinguishing among tumors or skin diseases. Pattern recognition, then, is a spatial skill demanded by many disciplines. People learn to distinguish critical features in their proper, two-dimensional spatial configurations. Other professions, however, require skill in thinking about three-dimensional configurations, a process especially difficult for the human mind. Although the physical world is (at least) three dimensional, the image captured on the retina and represented topographically in visual areas of the cortex is two dimensional. Thus, the three-dimensional world is a mental construct built from numerous cues to depth as well as experience navigating the world. Experience teaches us how to integrate twodimensional views into three-dimensional representations. Integration of two-dimensional views can be accomplished by means of features, objects, and landmarks common to different views. Integration of two-dimensional views is also accomplished by means of a frame of reference that is Copyright © National Academy of Sciences. All rights reserved.
Learning to Think Spatially: GIS as a Support System in the K-12 Curriculum http://www.nap.edu/catalog/11019.html 54 LEARNING TO THINK SPATIALLY shared by the views (Tversky, 2003). Expertise in dealing with three-dimensional representations is, like pattern recognition, also domain specific. Buildings and devices are three-dimensional structures; so architects and product designers face the challenge of three-dimensional thinking. They cope with the challenge by externalizing thought to the sketch-pad or computer screen, working with a series of two-dimensional slices. This is, of course, what radiologists do; they examine two-dimensional images of the human body. For architecture, there is a canonical set of two-dimensional slices: plan, elevation, and cross section. The slices facilitate design by simplifying a three-dimensional problem to a standard set of twodimensional ones. Each slice serves different functions in the design process (Arnheim, 1977; O’Gorman, 1998). Plans or overviews capture spatial relations among the rooms of a building or among the buildings, open spaces, and paths of a complex. They are important for understanding the functions of the structure because they show the proximity of rooms or buildings to each other and ways to navigate among them. Elevations show how a building or complex will appear; the outside skin establishes the aesthetic value of the building. Finally, cross sections show how the infrastructure—for example, plumbing, heating and air-conditioning systems—interconnects parts of the structure. Design in architecture is facilitated by partitioning three-dimensional space into two-dimensional representations. Architects typically begin with sketches of plans or overviews of the site. Early in the process, architects like to keep designs sketchy, literally and figuratively. They do not want to commit too soon to specific shapes or exact spatial relations. Sketches are a test bed for architects (Goldschmidt, 1994; Schon, 1983). Architects begin with an idea and turn it into a sketch. When they inspect the sketch, they often see spatial features and relations that they did not explicitly design, but that were a consequence of other design decisions (Suwa et al., 2001). Unintended spatial features and relations have implications that may or may not be desirable. As a consequence of such discoveries, architects revise ideas. They re-sketch the building and critically reexamine the new sketches. Architects interact with the sketches in a kind of conversation that refines their ideas (Goldschmidt, 1994; Schon, 1983). Experienced architects are more expert at this conversation. They get more new ideas from examining sketches than do novice architects. They see more functional implications than do novices (Suwa and Tversky, 1997). For example, experts see functional information such as changes in traffic flow and lighting throughout the day and year. Novice architects are less likely to make functional inferences from sketches. As is true for pattern recognition, considerable experience is needed to “see” behavior or function in sketches. For pattern recognition, the necessary information is in the depiction; experts learn to pay attention to the right features in the right organization. In the case of architecture, information about traffic flow or lighting is not in the depiction; it must be inferred from the depiction. The inference process is analogous to the expertise required to read written text or music. The sounds and meanings of words and notes must be derived from the depictions, and this process requires training and practice. As architects’ ideas become more refined, sketches become more specific. The three-dimensional task of the architect is, therefore, simplified by the set of two-dimensional layers. It turns out, however, that simplification—division into planes—serves design in another important way because the different planes also correspond to differing sets of design considerations. Plans determine how people will navigate a building; elevations determine how a building will look; cross sections determine how the infrastructure is organized. Air traffic control is another profession that requires spatial thinking in three dimensions. The process is even more difficult because of the added dimension of time; controllers must operate in three-dimensional space-time. Aircraft are in motion, so controllers must keep track of the changing positions of numerous aircraft at different and changing altitudes, speeds, and directions. As in the case of commuting routes on the ground, the key to success in the air is simplifying the Copyright © National Academy of Sciences. All rights reserved.
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