Melissa Pulley, Leoncio Rodriguez Quinones, Brynja Kohler, and Luis F. Gordillo
This lab contains a short sequence of lessons aiming to improve students’ understanding of Holling’s type II functional response equation. The lessons incorporate experience with an artificial predator-prey system, first employed by C.S. Holling in his classic “disc experiment”, which is also reproduced via individual-based computer simulations, giving students the opportunity to gather different sets of data to model and interpret. The independent components in the lesson plan (mathematical, experimental, and computational) engage students in various modeling activities to meet multiple learning objectives.
Andrea Bruder and Brynja Kohler
A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data.
Brynja Kohler, Rebecca Swank, Jim Haefner, and Jim Powell
Young brine shrimp movements within a petri dish are tracked by students. Students are challenged to determine and verify whether the brine shrimp move in a random walk. From this exercise students gain greater understanding of PDE models, diffusion and parameter estimation.
Miro Kummel, Andrea Bruder, Jim Powell, Brynja Kohler, and Matt Lewis
Dead leaves, ping-pong balls or plastic golf balls are floated down a small stream. The number of leaves/balls passing recording stations along the stream are tallied. Students are then challenged to develop a transport model for the resulting data. From this exercise students gain greater understanding of PDE modeling, conservation laws, parameter estimation as well as mass and momentum transport processes.
Matt Lewis and Jim Powell
Yeast are grown in a small, capped ask, generating carbon dioxide which is trapped in an inverted jar full of colored water. The volume of carbon dioxide produced can either be measured directly or using time-lapse imagery on an iPad or similar. Students are then challenged to model the resulting data. From this exercise students gain greater understand- ing of ODE compartment models, parameter estimation, population dynamics and limiting factors.
Jim Powell, Jim Haefner, and Brynja Kohler
Students test Torrecelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. From this exercise students gain experience and perspective using a classic model as well as greater understanding of ODE compartment models, parameter estimation and fluid flows.
Jim Powell and Matt Lewis
Students use transparencies and dry erase markers to simulate the spread of a zombie virus among a fixed population. Students are then challenged to create their own "disease" and develop an ODE model for the resulting data. From this exercise students gain greater understanding of population and SIR models, disease dynamics, parameter estimation and compartment modeling.