concepts of one discipline might inform or interfere with learning about concepts in another discipline. For example, in algebra, geometry, and science, the concept of function has different meanings. Similarly, in geometry, a point is a dimensionless location, whereas in geography, a point in space is a specific place with a small but definite area.

Spatial Ways of Thinking and Acting

People draw upon strategies that emphasize the use of spatial thinking to carry out projects. They set ideas into spatial contexts, seeing similar things as being close together and dissimilar things as far apart. They draw diagrams and graphs. They look for patterns and note outliers (anomalies) from the patterns. They look for clusters. They use statistical analyses to test for spatial relationships. They look for relationships among different spatial patterns. They disentangle change over space from change over time. Some representations are sketches used only during the thinking process, whereas others are created for an audience. In each case, there is an interplay between thinking and acting, between ideas and their representation, between expression for one’s self and communication and dissemination to others.

The educational challenge is to teach students strategies for spatial thinking; to teach how, where, and when to use them; and to convey a critical awareness of the strengths and limitations of each strategy.

Spatial Capabilities

Skills in spatial thinking are learned within a specific context. Skills can be supported by tools and technologies (see Chapter 6 for the concept of support systems and Chapter 7 for a range of high-tech spatial support systems). Disciplines adapt particular supporting tools and technologies: in mathematics, students learn to use graphing calculators; in design, students learn to use CAD programs; and in geography, students learn to use GIS. As a result of the human genome project, students must learn new representational schemes and develop sophistication in spatial thinking.

Tools and technologies support different tasks: concept maps are used for structuring ideas, CAD for design, GIS for geospatial data analysis, and so forth. For each task category, there are often competing versions of tools: for GIS, there are low-tech approaches, such as traditional techniques for overlaying paper or mylar maps at the same scale on a light table; for high-tech approaches, there are software programs by Environmental Systems Research Institute (ESRI), Intergraph, Idrisi, etc. (see Chapters 7 and 8). Moreover, new categories of tools and technologies emerge as fields advance. For example, developing a robust spatial representation of the brain has become feasible as magnetic resonance imaging (MRI), functional magnetic resonance imaging (fMRI), and other techniques become available.

The educational challenge is threefold: (1) to provide students with experience using low-tech tools (paper, pencils, protractors, compasses, etc.); (2) to provide students with opportunities to learn several, general-purpose, high-tech applications that support spatial thinking (e.g., Excel, Powerpoint, Photoshop); and (3) to develop the skills that will allow them to learn new low- but especially new high-tech applications. When students specialize in a discipline, they often need to learn a complex application relatively quickly. However, expert use of many high-tech support systems requires a lengthy investment of time. Often students have difficulty determining how support systems work. Moreover, teachers question the value of investing in the instruction time necessary for students to attain a level of proficiency that allows them to solve interesting problems with the tools.

Taken together, the educational challenges for teachers and students are complex. On the one hand, students need to learn how to use a relatively small number of discipline-specific tools as



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