by that time, a vast array of techniques had been implemented, either as part of the basic GIS products offered by vendors or as extensions developed by users. Several texts describe the advanced analytic capabilities of GIS (Burrough and MacDonnell, 1998; Fotheringham and Rogerson, 1994; Lee and Wong, 2001). In principle, there is no limit to the range of functions that can be implemented in a GIS, but in practice, priorities are established by the demands of different user communities.

There have been several efforts to systematize the often overwhelming range of functions and to make it easier for users to navigate through them. These efforts range from simplifying schema to interface formats. Tomlin (1990) devised a schema termed cartographic modeling that has been widely adopted as the basis for spatial querying and analysis, despite the fact that it is limited in scope to operations on raster data. The schema classifies GIS transformations into four classes and is used in several raster GIS as the basis for their analysis languages: (1) local operations, which examine rasters cell by cell; (2) focal operations, which compare the value in each cell with the values in its proximate cells; (3) global operations, which produce results that are true of the entire layer, such as its mean value; and (4) zonal operations, which compute results for blocks of contiguous cells that share the same value. The development of so-called WIMP interfaces—based on windows, icons, menus, and pointers—has also helped user interaction, allowing spatial querying and analysis through pointing, clicking, and dragging windows and icons (Egenhofer and Kuhn 1999; Figure 8.3). Nonetheless, navigating through the multitude of capabilities of a modern GIS remains challenging, especially given the lack of a standard nomenclature for operations. Much work remains to be done to simplify user interfaces, standardize terminology, and hide irrelevant detail if GIS is to be adopted widely for use in K–12 education.

A typical GIS can be expected to perform a wide range of transformations, operations, and analyses. Transformations include changes in the map projection or coordinate system. For example, one can change the familiar Mercator projection to one more suitable for areal comparisons, such as the Albers Equal Area, which unlike the Mercator does not distort areas. Transformations might also include conversion from a raster to vector data model, or the reverse. An example of an operation is the point-in-polygon operation, which identifies whether a given area contains a given point. Operations in a GIS may be performed on points, lines, or areas and may involve considerations of spatial proximity or of changes over time. These operations, often highly complex, enable the analysis of spatial data. They can be used to detect whether clustering exists in patterns of points, to select optimal locations for new roads or businesses, and a host of other tasks. More specifically, the major operational functions of a GIS include (1) query, (2) buffer, (3) overlay, (4) proximity, (5) connectivity, and (6) modeling (Box 8.1). Various combinations of these functions are commonly used during the data analysis process.

By and large, the analysis capabilities of a GIS are more advanced than those that will probably be needed in most K–12 education applications. For students, the software’s functionality is generally more complex than is necessary. However, system designers could help students perform analyses with the provision of age- and task-appropriate assistance in the form of wizards, which would guide students through the morass of functionality and options exposed on standard user interfaces.

There is one potential exception to the statement that GIS has more analytical capabilities than most students will ever need. In some desktop GIS, such as ArcView and MapInfo, there is a lack of support for topology, which is the science and mathematics of relationships and is one of the most important parts of geometry. Although topology is a difficult subject, it does present an excellent opportunity to explore and motivate logic-mathematical skills (such as reflexive, transitive, and symmetric relationships).

Where special-purpose analysis capability is missing in GIS, it can usually be added via the API that exposes some of the basic product functionality to a conventional programming language

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