From problem sets and data to basic numeracy
Glenn Kroeger, Geosciences, Trinity UniversityAll of my courses require students to work with data in order to understand fundamental geoscientific processes. My courses include an introductory Oceanography course, and upper-division courses in GIS and Remote Sensing, Geophysics, and Tectonics. In each course, students also acquire some of the data they work with in order to gain an appreciation of the potential errors inherent in any data. This often involves simple observations. For example, in order to estimate the repeatability of measurements with a gravity meter, reading the manual is less useful than making a measurement, packing up the meter, walking a short circle, and then repeating the measurement at the original position.
All of my courses include problem sets. My upper-division courses ladder of shorter exercises with longer data-intensive projects. The exercises include detailed instructions (cookbook-style) while the projects require students to build on the skills introduced in the exercises and "find their own way" to analyze the data and draw conclusions. For example, in the GIS and Remote Sensing course, after working exercises involving both object and raster data sets, students tackle a project in which they use a mixture of data sets to identify watersheds feeding beaver habitats in Yellowstone National Park. To understand of the effects of the massive fires of 1988 on nutrient distributions, they find a control watershed outside of fire areas and a study watershed within the fire zone and find optimal access paths to both watersheds. Solving this problem involves the use remote sensing imagery of fire zones, digital elevation models and National Landcover data from the USGS National Map, extensive use of map algebra and surficial hydrology GIS tools. A major project in Geophysics includes the acquisition of gravity data along a 50 mile transect southeast of San Antonio, carrying out differential GPS measurements of the location and elevations of the measurements, processing the raw gravity data, and modeling the results with predicted gravity anomalies of geometric bodies that students have derived from basic principles of potential field theory.
Beyond the use of problem sets and exercises in all of my courses, I have recently started to focus more assignments, class discussion time and examination questions on basic numeracy. In a world with nearly instant access to online information, students find it difficult to decide what quantitative information is worth knowing and how to use that information to think about the world around them. The first question I pose in Oceanography is: "how deep is the ocean." Students research this question and come to the next class ready to discuss the issue. Virtually all of them come with the average depth. In the ensuing discussion, we explore more statistics describing bathymetry and the fact that statistics is about describing a large collection of numbers with a much smaller group of numbers. This comes as a revelation to many students who have taken a statistics class but never really thought about what statistics is really about. This exercise becomes the foundation for weekly discussions of numeracy in oceanography from temperature and salinity to wave dynamics to climate change. What's the coldest water, in degrees C, that you will swim in? Numeracy discussions in GIS and Remote Sensing involve fundamental dimensions of the Earth and data sets. How big is an arc second? How wide is a UTM zone? How large is a Landsat TM scene? In Geophysics, basic numeracy includes seismic wave velocities; wavelengths and Fresnel zones, estimates of gravity variability with elevation and more. My goal in all of these numeracy discussions is to encourage students to include quantitative measures in all of their scientific thought processes, not just assigned problem sets.