BioMathLab: Laboratory Experiences in Biomathematics

Provided by Dr. James Haefner, Department of Biology, Utah State University

Colleagues in the Departments of Biology and Mathematics and Statistics at Utah State University were frustrated by the lack of retention of mathematics by biology undergraduates.  We perceived two main causes of this: (1) mathematics is not taught in the context of biological systems, and (2) math classes are either postponed until the end of the undergraduate career or they are taken early but never used again in the biology curriculum.  To address these problems we obtained funding from the U.S. Department of Education FIPSE (Fund to Improve Post-Secondary Education) program to develop biomathematics laboratory exercises at all levels of the biology curriculum (freshman to senior level courses).

The participants were from Biology:  Jim Haefner, Alice Lindahl, and Dick Mueller; and from Math/Stat:
Jim Cangelosi, Joe Koebbe, and Jim Powell .  Other participating Biology faculty (course instructors) were: Kim Sullivan, Ted  Evans, Jon Takemoto, Keith Mott, Paul Wolf, Dana Vaughn. and Bill Brindley.

The modules were intended to be "discovery-based" in the sense that students were presented with a system or problem and led through a series of directed discussions from (primarily) graduate student teaching assistants to formulate mathematical models of the system.  Students then performed experiments that allowed them to estimate the necessary parameters of the models permitting a test of their model.  

Implementing the discovery process in a biology laboratory classroom is challenging for many reasons.  We experimented with interactive computers for each student group, but hardware and software limitations
(in 1998-2001) proved this approach to be ineffective.  We then converted the web-based content to hardcopy with empty boxes to be completed by student groups during the laboratory period followed by whole-class group discussions. The following attachments (all pdf files) are the student versions (empty boxes) and instructor versions (boxes with answers) for many of the biomath lab exercises we developed.  Not all the modules have these handouts, but used a more traditional approach.
(Freshman level) Students answer the question:  Was the cougar killed legally?
Cougar Cooling (Student Version) 
Cougar Cooling (Instructor Version) 
(Freshman level) Students answer the question: Why don't cells in water explode?
Osmosis (Student Version)
Osmosis (Instructor Version)
(Freshman level) Students answer the question: How does light control photosynthesis in a lake?

To set the stage, we introduced the problem and had a large lecture hall of students simulate light decreasing with depth using strips of paper for light levels and lecture rows (back-to-front) as lake depth:
Lecture that sets the stage (with in-class game)
This module spanned two weeks of labs.  The first week the students developed a model for light extinction with depth (Beer's Law) and tested it with light shining horizontally through multiple aquaria.
Beer's Law (Student Version)
Beer's Law (Instructor Version)
In the second week, students developed a model for the effects of light on photosynthesis and tested the models with oxygen evolution from Elodea:
Photosynthesis (Student Version)
Photosynthesis (Instructor Version)

The base of natural logarithms  (e) arises in Beer's law, and here's why:
Why e?
(Freshman) Students answer the question:  How many M&Ms can a blind-folded student eat?
(Actually, we use little discs of sandpaper with thumbtacks, and to date, no student has tried to eat them.)
Holling Disc (Student Version)
Holling Disc (Instructor Version) (Lots of hints on how to teach math to students)
Holling Disc ZIP file   (All the pdf files with homework.)
(Freshman and Senior/Grad) Students answer the question: Are Guppies picky eaters?
Following on the Holling Disc exercise, students test the hypothesis that fish (Guppies) forage optimally by choosing the most  profitable prey (Artemia/Daphnia).
First, the students generate an expectation using sandpaper discs and they measure fish behavior:
Human Foraging Decisions
Then they test the predictions:
Fish Foraging (Student Version)
Fish Foraging (Instructor Version)
(Senior Level) Students answer the question:  Why are some leaves hairy?
This exercise uses a Windows based program to calculate a leaf's heat balance.  The approach is quantitative, but not discovery-based:  the model and equations are given to the students.  
Heat Balance (zip file with MS Word and exe files).
(Junior/Senior level) Students answer the question:  Why do large islands have so many species?
This exercise is preceded by a directed discussion of recursion equations, but most of this is not included in the following reprint of:  
Haefner, J. W., D. E. Rowan, E. W. Evans, and A. M. Lindahl. 2002. Island biogeography: students colonize islands to test hypotheses.  Pages 191-218 in Tested Studies for Laboratory Teaching. Volume 23.  (M. A. O'Donnell, editor). Proceedings of the 23rd Workshop/Conference of the Association for Biology
Laboratory Education (ABLE). University of Chicago, Chicago, IL.
Island Biogeography Paper

(Senior level) Students answer the question: What is the best way to estimate the Michaelis-Menten constants?
Basics of Michaelis-Menten (derivation)
Basics of Non-linear Regression
Michaelis-Menten (zip file with all lecture pdf files of:  (1) pre- and post test; (2) derivation of M-M; (3) non-linear regression; (4) homework.
SAS Code and Data Sets    SAS code to do linear regression on transformed data and non-linear regression
(Junior/Senior level) Students answer the question:  How can a bird fly across the ocean without eating?
No pdf files for this Ornithology module, but here is a link to the module webpage.

Jim Haefner's homepage  at Utah State University

Last Updated: 2 Oct 2008