From biology to mathematical models and back: teaching modeling to biology students, and biology to math and engineering students

Abstract

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a "live" textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology.

Figure 1.

Classroom design to enhance teamwork and a continuous progress method of instruction. (A) Layout of the classroom. Each hexagonal table can be separated into two independent tables if necessary. Six Ethernet connections to the CWRU fiber optic network are shown. A power strip runs along the front side of each half table. (B) Students working in the classroom.

Figure 2.

Total enrollment in the course from 2001 to 2010 by gender.

Figure 3.

Distribution of students enrolled by year (freshman, sophomore, junior, senior, or graduate student) over all years that the course has been offered.

Figure 4.

Distribution of majors among students enrolled in the course from 2001 to 2010.

Figure 5.

Grade distribution for all students that have taken the course from 2001 to 2010.

Figure 6.

Student evaluations of the course. The fractions at the top of each bar indicate the number of students who provided evaluations over the total number of students in the course that semester. For example, in spring 2008, only 17 of the 35 students in the course provided evaluations (interestingly, this corresponded to the year in which CWRU switched from paper forms that were filled out in class to online evaluations that students could fill out at any time). Compliance was higher in 2010 (34/37) when the instructors repeatedly requested that students fill out the evaluations before the deadline.

Figure 7.

Student attitudes toward and sense of competence in biology, math, and computer programming. The figure shows the average and s.e.m. for answers to six questions (e.g., How much do you like biology? How competent are you in biology?) that were rated on a scale from 0 to 10 at the beginning and at the end of the semester. The bar charts show all biology majors (N = 17) separately from all engineering majors (N = 14), i.e., students majoring in either biomedical engineering (N = 8) or chemical engineering (N = 6). It is clear that the initial attitudes and sense of competence of biology students significantly differs from that of engineering students. It is also clear that all students show a significant change in their responses after taking the course (for details, see Results, Assessment of Student Attitudes and Competence).