Math teachers around the United States are finding that geography and maps in the form of Geographic Information Systems (GIS) are an excellent way to engage students at all levels. They have found that interactive digital maps are an excellent way to make classes more engaging while helping students relate studies to their lives.
Maps, cartography, and geographic information systems can all be viewed as ways of visualizing numbers and geometry. By focusing on specific aspects of these, teachers can use them to illustrate mathematical and geometric concepts at a range of levels appropriate to their students. While desktop GIS can be arcane and complicated for beginners, pre-packaged interactive maps can be made easily available, and can cover virtually any topic with a geographic element.
Kindergarteners can be taught orientation, shapes, and spatial relations, while senior students can be taught statistics, modelling, density per area and other advanced concepts. By exploring these concepts graphically and spatially, students are better able to relate them to the world at large. This linkage addresses the common issue of students feeling that what they are learning does not relate to the wider world or their lives after school. Students are able to learn about diverse topics such as biodiversity, natural hazards, climate, energy, water, and other relevant issues of the day in a self-directed interactive manner.
Interactive digital maps can be used to address a wide range of critical concepts as defined by the National Council of Teachers of Mathematics (NCTM), including representing numbers, understanding patterns, relationships, 2D and 3D geometric and spatial relationships, probability, statistics, change, models, measurements, problem solving, reasoning, connections, and communications. Educational digital maps also connect well with NCTM’s curricular “focal points”. These focal points must pass three rigorous tests; Is it mathematically important, in and outside the classroom?; Does it fit with what is known about learning mathematics?; Does it connect logically with the mathematics in earlier and later grade levels? Concepts that can be taught with GIS fit in with these criteria, as a wide range of mathematical concepts can be both visualized and applied using these systems.
There are a wide range of ready made projects and tools available online for educators, with specific grade appropriate projects available. These cover a vast range of techniques and topics, and are mostly made for freely available platforms such as Google Earth and ArcGIS online.
Real world math features over 30 exercises based on Google Earth and Sketchup that cover a wide variety of topics. The ‘Concepts’ collection uses Google Earth to demonstrate mathematical topics in unique ways, including rates of change and scientific notation. The ‘Measurement’ lessons make extensive use of the ruler function in Google Earth to solve a variety of problems. The ‘Exploratory’ section investigates mathematical topics that are not often taught in schools such as fractals, topology, and modern geometry. There is a collection of ‘project-based learning’ exercises that simulate real world problem solving in teams, including search and rescue, remote race mapping, and typhoon mapping. Finally, they have a ‘Space’ section dedicated to mathematical lessons using Google Moon, Mars, and Sky.
Nasa’s Jet Propulsion Laboratory (JPL) features a geospatial problem set based on teaching students how scientists assess wildfires using remote sensing. The problem set includes grade appropriate problems and use of true and false color satellite imagery. This set will teach students skills including co-ordinate location, ground truthing, fire speed calculations, and length and area measurement. The JPL also features a number of other educational problem sets featuring various intriguing topics from space exploration to earth observation.
BarbareeDuke.com also features a comprehensive set of common core mathematics educational resources for students from K – 12. They have a simple system of ArcGIS online maps that link to downloadable zip files of activities. They cover a range of topics from basic spatial orientation and awareness through to measurement, fractions, geometry, and volume calculation. At senior levels they have topics on geographical modelling, statistics, and density.
The open educational resources commons project has a ready made geographical project available that will teach students about length, perimeter and area, distance and time calculations, unit conversion and percentages, as well as the basics of online interactive maps like navigating the interface and changing basemaps. This project also utilizes ArcGIS online paired with a problem sheet for ease of access.
GIS software company Esri has an excellent page on using GIS for math education, including a spatial educational rationale as well as links to a large and diverse range of resources. They publish a series of textbooks for educators to use for GIS-based education, ‘Thinking Spatially’, ‘Mapping Our World’, ‘Analyzing our world’, and ‘Making Spatial Decisions’. These all link back to project modules that can be used with ArcGIS online or ArcGIS for desktop.
Additionally, they host a series of educational tools called ‘ArcLessons’ that are pre-packaged modules with data sets and problems to solve. These address problems from measuring the circumference of the Earth to analyzing water use, investigating extreme temperatures, and examining the spatial patterns of crops.
The book ‘GIS Tutorial’ is an excellent offline resource for introducing classes to geographic information systems. It uses an easy-to-follow format to combine ArcGIS tutorials with self-directed study in order to gradually build upon basic skills. It is adaptable to many different levels of learner, and features two additional chapters on ArcGIS spatial analysis and 3-D analysis.
‘Spatial Mathematics’ is a title that combines spatial mathematics and analysis to look at real world issues that have mathematics as a critical, yet often overlooked, component. It presents mathematical concepts as ways to approach specific problems, rather than in the abstract. It covers basic principles and theories as well as practical applications like GIS tools, web mapping, and GPS data collection, and would be an excellent resource for senior and more advanced students.
The use of GIS in education presents myriad possibilities, from the pre-packaged lessons showcased here to the potential of GIS literate educators designing problem sets relevant to their local area. One thing is for certain, these skillsets are becoming ever more relevant in todays world, and the opportunities will only continue to grow.
Teaching Math with GIS Resources:
- Real World Math: http://www.realworldmath.org/lesson-downloads.html
- Esri Math Lessons: http://edcommunity.esri.com/educational-roles/Instructors/Math
- Jet Propulsion Laboratory: https://www.jpl.nasa.gov/edu/teach/activity/fired-up-over-math-studying-wildfires-from-space/
- Open Educational Resources Commons: https://www.oercommons.org/authoring/19783-using-gis-and-maps-to-teach-mathematics-measuremen/view
- Barbareduke GIS for Common Core Math: http://www.barbareeduke.com/ccmath/