The Problem Many modern characterizations of biological systems have reached an unparalleled level of detail. Mathematics is playing an important role by allowing scientists to organize this information and arrive at a better fundamental understanding of life processes. In fact, mathematical modeling of biological systems is evolving into a partner of experimental work. Not only for the statistical analysis of experimental data but also in deterministic models predicting future outcomes. Introducing biology students to mathematics early provides the biology department with the ability to expand the level of quantitative emphasis in their courses and their research labs. As a result, students will be better prepared for the growing job market in the biological sciences.

Fulfilling a need Biology major is the largest major on campus. A large number of undergraduates participate in research projects in the biological and chemical sciences. In the past three years, there have been at least 36 freshman declaring a biology major with AP Calculus or Statistics credit. However, only one math course is required for most biology concentrations. Most biology majors take elementary statistics.

Methodologies & Types of Evidence of Student Learning Gathered I administered two surveys to the class at the beginning of the semester. The first survey solicits student’s opinions about math and its relevance to their future careers. The second survey measures student’s connection of biological scenarios with the mathematical graphs modeling those scenarios. I distributed the second survey again during week 7 and week 14 of the semester. Math Opinions and Demographic Survey BioMath Connections Survey

Sample Survey Question When a disease spreads through a small population, the number of new infections in a week is directly proportional to the product of the number of infected people with the rest of the population. Which of the following graphs would describe the number of infected people (horiz. axis) vs. new infections in a week (vertical axis)

Project Summary The University of Wisconsin - La Crosse is currently developing a biomathematics course, BioMath, introducing biology majors (with no calculus pre-requisite) to calculus and statistics-based mathematical modeling in biology. Unlike a traditional calculus course for the life sciences, BioMath takes the perspective of a biologist trying to set up a mathematical model based upon experimental observations. Students are asked analyze data, provided in part by the biology faculty, drawing sound conclusions about the underlying processes using their developing knowledge of calculus and statistics. My project measures the students' connections of biological scenarios and mathematical models during the course of the semester.

Learning Outcomes Students will have an enhanced knowledge and understanding of mathematical modeling and statistical methods in the study of biological systems; be better able to assess biological inferences that rest on mathematical and statistical arguments; be able to analyze data from experiments and draw sound conclusions about the underlying processes using their understanding of mathematics and statistics.

BioMath I Outline 1. Functions and mathematical models 2. Discrete-time dynamical systems 3. Limits and the derivative 4. Differential equations 5. Integration 6. Probability

Example Application: Spread of a disease *Students are first introduced to the model for the spread of an infectious disease when learning about functions and variable relationships. 1. Quadratic Model The number of new infections N in a week is proportional to the product of the size of the infected population I with the size of the healthy population, N = r I (Total - I), r = parameter *We revisit the model three more times; each time using our previous work to increase the complexity. 2. Discrete-time Dynamical System The future size of the infected population is equal to the current size plus the number of new infections in a week. 3. Differential Equations We use the graph of the equation from the quadratic model to sketch the solutions to the differential equation. 4. Two Compartment Models(infectious and recovered populations) We increased the complexity of the model by studying the effects of transmission and recovery rates on equilibrium solutions.

* Question 5 was designed as a control. Preliminary Findings, Results, Conclusions, & Implications Fall Semester 2007. Each of the question topics except Respiration was discussed in class within the first seven weeks. The number of correct answers increased (up 20.6%) or remained the same on all questions from week 1 to week 7. However, at the end of the semester the number of correct answers decreased (down 16.8%) suggesting that the students did not retain the connection throughout the semester. Spring Semester 2008. I will introduce simple versions of the model early in the semester and increase the complexity and realism as the course progresses. By building upon the foundations established in the first half of the semester, students will use their new mathematical tools to revisit and modify the simple models. Since each topic will be covered in more depth (see Example Application), I think they are more likely to retain the material. I will use homework and exam problems to assess their ability to apply the same modeling skills to biological processes not discussed in class.

Career Relevance & Impact I would like to acknowledge and thank my fellow Wisconsin Teaching Fellows and Scholars for their assistance in focusing my SoTL question. You can view their KEEP Gallery. I acknowledge the support and encouragement from the UW-L mathematics and biology department. I presented the results of this work at the national Mathematical Association of America-American Mathematical Society Joint Mathematics Meetings in San Diego, CA on January 8th, 2008.

Annotated List of Helpful Resources & References Steen, L. (Editor) Math & Bio 2010 Linking Undergraduate Disciplines, Mathematical Association of America, 2005