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ABSTRACT
Inspired by the approach first employed by C.S. Holling in his classic “disc experiment,” this article provides a sequence of learning activities that increase students' understanding of the mechanisms behind saturating effects in predator-prey scenarios. The proposed lesson is recommended for inclusion in courses that address mathematical biology or modeling from introductory to advanced levels. The featured activities include a theoretical derivation of Holling's type II functional response model, a hands-on experiment for data gathering, and tools for further exploration through individual-based computer simulations. This multi-faceted approach gives students the opportunity to gather different sets of data in order to meet multiple learning objectives. Classroom trials conducted in Spring 2019 indicate that the proposed instructional resources and activities are effective for improving students' understanding of the mechanisms in Holling's type II functional response equation, and deepen students' appreciation of authentic data-driven mathematical modeling in ecology.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge Jim Powell (Interim Head, Department of Mathematics and Statistics, USU) and Jim Haefner (Emeritus Professor, Department of Biology, USU) for introducing the authors to the experimental approach of this activity in their co-taught project-based Applied Math in Biology course, and the helpful comments from our reviewers.
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Notes on contributors
Melissa Pulley
Melissa Pulley is a master's student in mathematics at Utah State University. She obtained her bachelor's of science in mathematics from Campbell University. Her interests include differential equation models, agent-based modeling, climate science, bumble bees, and undergraduate mathematics education.
Leoncio Rodriguez
Leoncio Rodriguez is a post-doctoral fellow at Utah State University. He obtained a Ph.D. from Iowa State University. Along with prior experience in data analysis, and computer science, Leo's research interests lie in Geometrical Analysis and its applications to Shape Optimization problems arising from Physics, Engineering and Biology.
Matthew Lewis
Matthew Lewis is an assistant professor in the Department of Mathematics at Brigham Young University-Idaho. His research interests are centered on mathematical biology and mathematics education. Matthew received his B.S. from Westminster College and his M.S., M.Ed. and Ph.D. from Utah State University. When not teaching, Matthew enjoys hunting for tacos and watching whatever performance or sporting event his children are participating in.
Brynja Kohler
Brynja Kohler is an associate professor of mathematics at Utah State University. She graduated from the University of Chicago (B.S.), the Courant Institute of New York University (MS) and the University of Utah (Ph.D.). She has also taught high school mathematics in Los Angeles and New York City. Her research includes developing mathematical models of biological systems and conducting field-based courses for preservice teachers.
Luis Gordillo
Luis Gordillo is an associate professor of mathematics at Utah State University. He joined Utah State University in 2012 after obtaining a Ph.D. from Arizona State University. He has also done research and taught in the Caribbean and South America. His interests lie at the interface between natural sciences and mathematical modeling, including the impact that control measures have on the dispersal of pests, and the role of stochasticity and spatial/environmental structures in the spread of diseases.