Case Study: Geographic Information Systems

A working draft of resources and reports from an NSF-sponsored project intended to strengthen the role of mathematics in Advanced Technological Education (ATE) programs. Intended as a resource for ATE faculty and members of the mathematical community. Comments are welcome by e-mail to the project directors: Susan L. Forman or Lynn A. Steen.

Geographic Information Systems (GIS) integrate maps, charts, tables, and data into a coherent system that is related logically, quantitatively, and spatially. Typically, such systems are employed to organize and present information that has both geometric structure (e.g., maps, blueprints, photographs) as well as quantitative structure (e.g., population, area, density). GIS is widely used as a means of displaying quantitative information for purposes of scientific research, public policy, and media presentations. It is an important contemporary tool of quantitative communication.

Examples of Use

Examples of GIS implementations include:

Maps that show the location of street lights in Los Angeles together with data concerning electrical circuits, operating costs, repair histories, and maintenance schedules.
Three-dimensional orthophotographic views of lower Manhattan created for the New York Department of Environmental Protection in order to accurately represent potential building sites.
A study of urbanization patterns on the abundance of breeding birds in the Santa Monica mountains, based on a linkage of GIS data with statistical packages such as S-Plus.
Reduction of response times for 911 emergency service in Beaufort County, South Carolina, a rural region of islands linked by bridges and ferries with a large transient population.
By linking postal codes with customers' shopping patterns at its different stores, chains such as Best Buy or Target can ensure inventory that matches customers' demand.
Census data linked with urban, state, and national maps provide numerous and varied visual representations of the characteristics the U. S. population.
Analyses of satellite images of the same county over a twenty-year period are used to determine changes in vegetation, urbanization, surface water, and other features important for regional planning.

One of the applications of GIS with the largest potential benefit is its linkage with Global Postitioning Systems (GPS) in what is now called Precision Agriculture--the integration of data on geographic position, soil conditions, crop yield, market prices, productivity, and other information to optimize profit or yield from farms.

Underlying Mathematics

Although mathematics underlies every aspect of GIS, most software implementations are designed to be used by people who know relatively little mathematics. Indeed, virtually the entire content of school mathematics can be found (or easily embedded) in activities based on GIS software:

In scaling figures and maps, students use ratio, proportion, similarity, perspective, and projection.
In dealing with associated data, students use percentages, algebra, and elementary statistics.
In relating data to spatial images, student use coordinate geometry both in two and three dimensions.
In dealing with distances and areas, students convert between different coordinate systems and different units of measurement.
In analyzing data from, for example, population samples or satellite photographs, students use elementary functions to identify patterns embedded in the data.
In making maps, students use both raster (matrix) and vector (polygon) methods and convert from one to the other in the underlying database.

However, sophisticated GIS software hides much of this good mathematics behind a facade of fascinating pictures. GIS provides an ideal tool to illustrate and apply an enormous variety of fundamental mathematical concepts and tools. With GIS, as with many computer-based implementations of mathematics, users who understand the underlying mathematics are able to imagine and execute more powerful ways to use these systems.

Geography majors need a lot of mathematics, but of a type suitable to their work. Most important is a good undertanding of coordinate systems and the relations among such systems. Students need to know how to correct satellite images by accounting for the spherical shape of the earth and the angle of the satellite. They also need to be able to use the "state plane" system to relate satellite data to local coordinate systems.

Projects and People:

GIS: Geographic Information Systems for 21st Century (Indiana). Indiana State University, Terre Haute IN 47809. E-mail: geogis@scifac.indstate.edu. Project Directors: William A. Dando, Paul M. Mausel, Denis E. Mudderman, Department of Geography and Geology.

BASIS: Spatial Information Systems. Berry & Associates.

Community-Based GIS Education. Henry Ford Community College, 5101 Evergreen Road Dearborn, MI 48128-2407. Project Director: Stuart Waddell.

GIS/GPS Laboratory based on Workplace Scenarios. Houston Community College System, Southwest College, 9910 Cash Road, Stafford, TX 77477. Project Director: Dean Ayres.

CCITT: Community College for Innovative Technology Transfer (CCITT). Science & Technology Resource Center, Prince George's Community College, 301 Largo Road, Largo, MD 20772-2199. Project Director: Patricia A.Cunniff. Remote sensing, imaging processing, and GIS.

Remote Sensing ATE Project. Brevard Community College, 250 Community College Parkway, Palm Bay, FL 32909. Project Director: Goodchild, Michael F.

Geographic Information System Project, Pasedena City College, Pasedena, CA. Director: Douglass, David.

National Center for Geographic Information and Analysis, University of California, Santa Barbara, CA 93106. Director: Paladino, Steve.

Iowa GIS Council. Iowa Lakes Community College, 300 S. 18th Street, Estherville, IA 51334. Coordinator: Roger R.Patocka.

Terrain Analysis, Hunter College. Director: Clarke, Keith C.

GIS in Forestry. National Center for Sustainable Resources (NCSR) Central Oregon Community College. Contact: John Schaeffer.

Resources:

Software that implements GIS is available on all major computer platforms. The most common is ArcView GIS, distributed by Environmental Systems Research Institute (ESRI), 380 New York Street, Redlands, CA 92373-8100. The software includes tools for importing tabular and spatial data (including both feature and image sources); for displaying, measuring, manipulating, and joining tables and images; for creating shapes, highlights, and address coding; and presenting maps and tables in visually attractive forms.

Image Handler. Avaiable for free from PCI Geomatics.

NASA Education Tools.. Source for satellite images.

Satellite Imagery. Information on remote sensing.

Spatial Insights. A Geographic information services company offering software, services, as well as geographic and demographic data.

ESRI: Environmental Systems Research Institute, 380 New York Street, Redlands, CA 92373-8100. E-mail: info@esri.com. President: Jack Dangermond.

References

"Teachers Find Plenty of Uses for Software that Covers the Map." Education Week, (April 15, 1998) 16.

Monmonier, Mark and De Blij, H.J. How to Lie With Maps. Chicago, IL: University of Chicago Press, 1996.

Supported by the Advanced Technological Educaiton (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation.