A System Approach in Teaching With Data in Hydrology
Hari Kandel, School of Natural Resources and the Environment, Lake Superior State UniversityOne of the capabilities of a quantitatively literate college graduate as listed in 1989's definition of Quantitative Literacy (QL) requirement committee of National Council of Teachers of Mathematics, Committee on the Undergraduate Program in Mathematics (NCTM, CUPM) is that such graduate should be able to "interpret mathematical models and draw inferences from them" (Gillman, 2006). My approach of using quantitative reasoning in college teaching echoes this particular capability and involves students in understanding and applying models (formulas, graphs, and concept maps etc.) in order to have them a deeper grasp of the content. For example, I use thermodynamic models to explain stability of minerals in geochemistry, and continuity equations to explain water budgets in hydrology. While quantitative reasoning extends the concept of mathematical power to the real-world context of a discipline or interdisciplinary world, activities that invite learners for critical thinking are crucial for the successful achievement of this learning outcome by students.
Using real-world data in any model requires either an easy access of the archived data or data collected primarily for the class or research purpose. Teaching effect of urbanization on stormwater runoff, for example, could be carried out using long-term data from a typical urban stream where there is discharge data available for pre- and post-urbanized period. Creating hydrographs for pre-and post-urbanized periods works perfectly for the classroom demonstration purpose where a simple objective of differentiating time-to-peak and total discharge can be achieved. To go beyond that and to develop quantitative reasoning skill in students, a group-project works better. In a group project, each member in a group can be assigned with tasks, such as differentiating stormwater related variables: peak-flow, total discharge, lag-time, probability of flooding, water quality indices, and health of aquatic habitat with respect to watershed characteristics (intensity of urbanization, topography, land use, soil type, and precipitation pattern). After all the groups compile their final report on stream response on various watershed characters, the whole class will be informed on how a system study with data helps analyze the problem better. I have started using stormwater runoff models in my upper-level hydrology class, and I plan to use this holistic approach of study in my next term.
The foremost challenge in using the exemplified data-driven inquiry is to get long-term data with consistent temporal scale representing individual characteristics of watershed. To work around with this particular approach, we can choose a well-examined river from its headwaters to mouth and use different sections of it to characterize natural vs altered areas. Also, groups need to be formed with due consideration of students' individual skills, i.e. data retrieving, graphing, interpreting.
Reference:
Sons, L. (2006 ) Some Historical Notes in Current Practices in Quantitative Literacy, Notes – 70, Edited by Gillman, R., Mathematical Association of America.