Modeling Transport in Streams

Abstract

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent variables (distance downstream and time) graphed the data and developed a first, partial differential equations model. We took the students through a second cycle of the modeling process to improve the model to account for leaves that got stuck to the bottom or sides of the stream. Given the appropriate, inquiry-based pedagogy, our lab maintains high levels of cognitive demand and introduces students to the modeling process.

KEYWORDS:

• Mathematical modeling
• pollution
• ecology
• data collection
• inquiry-based instruction
• problem-based learning
• transport
• lab
• stream

Acknowledgements

We thank Jim Powell for fruitful discussions, Brynja Kohler and Jill Ashby for testing the lab in their classes, and Matthew Lewis for adding the lab to the LEMB website.

FURTHER READING

1.	Bahls, P. 2012. Student Writing in the Quantitative Disciplines: A Guide for College Faculty. San Francisco, CA: Jossey-Bass.
2.	Board on Life Sciences, Division on Earth and Life Studies, National Research Council of the National Academies. 2003. BIO 2010: Transforming Undergraduate Education for Future Research Biologists. Washington, DC: National Academies Press.
3.	Committee on Developments in the Science of Learning. 2000. How People Learn: Brain, Mind, Experience and School. Washington, DC: The National Academies Press.
4.	Schoenfeld, A. H. 1992. Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In Grouws, D. (Ed), Handbook of Research on Mathematics Teaching and Learning, pp. 334–370. New York, NY: Macmillan.
5.	Snee, R. D. 1993. What’s missing in statistical education? The American Statistician. 47(2): 149–154.

Additional information

Funding

Our work was supported by the National Science Foundation through NSF TUES grants 1245421 and 1245407.

Notes on contributors

Andrea Bruder

Andrea Bruder is an associate professor in the Department of Mathematics and Computer Science at Colorado College. Her mathematical interests lie in the areas of differential equations and applied mathematics. Andrea received her Ph.D. from Baylor University. She was hired at Colorado College in 2009 and takes a project-based approach to teaching. When not teaching or writing she enjoys mountain biking and rock climbing.

Miro Kummel

Miro Kummel is an associate professor in the Environmental Program at Colorado College. He is a population ecologist whose research connects the boundaries of mathematics, biology, and climatology. Miro received his bachelors in ecology and evolutionary biology at Princeton University, and earned his Ph.D. in biology at the University of Michigan. Miro spends his free time organic gardening and riding horses.