GIS provides an excellent way to teach mathematical concepts and skills. The value of visualizing numbers is affirmed throughout the US Principles and Standards for School Mathematics, designed by the National Council of Teachers of Mathematics (NCTM). Representing numbers, understanding patterns, relationships, and function, 2-D and 3-D geometric and spatial relationships, probability, statistics, change, models, measurements, problem solving, reasoning, connections, and communications are critical concepts. Every one of these can be explored using GIS tools and methods. Comparing graphs and maps of birth and death rates over time and region, analyzing the response of a stream to a recent storm through a real-time hydrograph, and creating cross-sections of terrain are three common activities in geography instruction, easily done in a GIS environment. All of them—and thousands more geographic activities—involve analyzing numbers. One might say that GIS is visualizing numbers, since its basis is representing numbers as cells, points, lines, or polygons on a map.
NCTM’s curricular “focal points” also connect well with GIS. A focal point must pass three rigorous tests: Is it mathematically important, both in mathematics and for use in applications in and outside of school? Does it “fit” with what is known about learning mathematics? Does it connect logically with the mathematics in earlier and later grade levels? When we connect latitude and longitude to the Cartesian coordinate system, when we measure area, shape, size, and distance in different map projections, when we compare geometric to exponential growth rates of agricultural output, even when we explain the Earth’s shape, rotation, and revolution, we are applying geographic and mathematical concepts and can use GIS to teach it.
Why should we build bridges with mathematics educators? Mathematics is funded, assessed, and is strong in all levels of primary, secondary, and university education. The more that GIS is seen as indispensable to the teaching of mathematics, the more likely it will be that spatial analysis will be taught in schools and universities. In addition, our own curriculum and professional development will be enriched by what we learn from our colleagues in mathematics.
–Joseph Kerski, ESRI Education Manager
