"Using the Mathematica notebooks, we could design a course in which students make their own observations and learn in much the same way researchers do: through discovery, visualization, and experimentation."

--Jerry Uhl, Professor of Mathematics

Throughout the last decade, many math departments in U.S. colleges and universities have been quietly (and, in some cases, not so quietly) taking steps to improve introductory calculus courses. These courses have traditionally served students majoring in disciplines other than mathematics (e.g., engineering, biology, physics, chemistry, economics) who require competency in calculus for advanced study in their respective fields. The fact that students who are otherwise academically solid often struggle with learning calculus has fueled efforts to reform how calculus has been taught. To create a learning environment better suited to non-math majors, many reform courses have focused not only on teaching calculus but also on applying it effectively and meaningfully in other fields.

At the University of Illinois at Urbana-Champaign, Professor Jerry Uhl has been working to develop and implement reform calculus courses since the late 1980s. Well known for the Calculus&Mathematica, courseware that he and colleagues developed at UIUC, Uhl has used his expertise and experience to assist the UIUC School of Life Sciences (SOLS) in the creation of an introductory calculus course offered specifically to life science students. The course, called BioCalc, is just one example of the efforts taking place across campuses to improve introductory calculus education for non-math majors.

An example of a Mathematica notebook from the Mathematica web site.

What is BioCalc?
BioCalc is a special section of Math 120 (Calculus I), an introductory calculus course required of all life science majors at UIUC. Rather than lectures and textbooks, however, the instructional medium for this course is a sophisticated symbolic manipulation software program, Mathematica, that integrates text, lots of graphics, and commands into an electronic "notebook" format. The program is used to run the Calculus&Mathematica (C&M) courseware developed by Uhl, Horatio Porta and William Davis.

The idea for a BioCalc course was conceived when Uhl, already teaching a number of math courses with C&M courseware, was approached by a SOLS faculty member who was concerned because life science students were not performing as well as expected in traditional, lecture-based calculus courses. After pointing out that many of the examples and applications used in C&M courses were in fact drawn from the life sciences, Uhl suggested that a C&M calculus course could be designed specifically for life science students. Such a course would place a greater emphasis on the crucial connections between calculus and life sciences.

Jerry: Life science growth models reinforce the idea of the derivative [because] the derivative measures growth rates. [The C&M courseware lessons] include problems on modeling the growth of animals, predator-prey models, blood alcohol levels, cigarette smoking and lung cancer correlation, carbon dating, as well as data analysis of the U.S. population in historical context, including plots of yearly growth.

The new course would use the same format and instructional materials as the C&M Math 120 courses already being offered. The difference would be the greater emphasis on life science applications. BioCalc was soon being offered as the introductory calculus option for life science majors.

What happens in BioCalc on a typical day?
Students spend most of their class time working through C&M lessons on the computer. The basis of each lesson (roughly akin to a textbook chapter) is a section entitled "Basics," which introduces students to the key concepts and ideas of the lesson, and another section entitled "Tutorial," where students learn methods and applications through a series of interactive questions and answers. At the end of each lesson, students are asked to complete a section of questions called "Give It a Try," which they then submit electronically for grading and review. Also included with each lesson is a "Literacy Sheet," which students are required to complete by hand. There is an example C&M homework problem available to view.

Students are encouraged to work together. Thus, in a BioCalc classroom there tends to be a good deal of conversation. The instructor often wanders about the room, checking on students' progress and offering help in the problem-solving process. For the most part, however, students are engaged in learning from the interactive lessons and from one another.

"What's calculus good for, anyway?"
Students in calculus courses frequently lament, "What's this stuff good for, anyway?" It's a question that's being given serious consideration by biology departments, as well. Do students in the biological sciences really need calculus? If so, how can calculus education be improved to more adequately serve their academic needs? Is there room in the curriculum--and the budget--for such efforts?

There's little doubt that most life science students do need and will make use of calculus, especially as advances in fields such as genetics and bioengineering highlight the need for higher-level math skills. To keep pace with such advances, departments are beginning to require students to take more advanced math and computer courses. Additionally, the nature of undergraduate biology education is changing as departments attempt to keep pace with the demands of the workplace. Charles Miller, director of the School of Molecular and Cellular Biology, noted:

There are many employment opportunities now for students in the biological sciences at all levels, from bachelor's to master's. Undergraduate biology education is serious business now. Years ago, [the thing to do with a life science degree] was go to med school. But now there's a serious career path, and biology departments have to respond to that. At UIUC, we're trying to design a curriculum that allows students--those who aren't pre-med, for example--to take advantage of the opportunities that are waiting for them when they graduate.

To be adequately prepared, students need to have the appropriate quantitative skills. Courses like BioCalc are part of the effort to better prepare these students for the challenges they'll meet beyond the university.

Is it working?
An assessment conducted at UIUC on the BioCalc Math 120 course has concluded the followingi: following¹

• BioCalc students receive higher grades in Math 120 than non-BioCalc students.
• BioCalc students are as well-prepared for Math 130 [the second semester of introductory calculus] as non-BioCalc students.
• BioCalc students are significantly more likely to take an additional math course than non-BioCalc students.
• BioCalc students are slightly more likely to remain in a biological science major than non-BioCalc students.

The Bricoleurs
Throughout the LT² case studies, we refer to the creators of new learning environments as bricoleurs.^a It's a French term that roughly means "handyman." We use it to describe a person who is adept at finding (sometimes disparate) resources that can be used to achieve this person's goals, particularly as they pertain to creating learning environments that encourage student participation and interaction. In this case study, the bricoleurs are Jerry Uhl, Bruce Carpenter, and Brad Edge.

Uhl's success with and enthusiasm for C&M courses has drawn interest and support from international, national, and local colleagues. In particular, at UIUC both Bruce Carpenter, a teaching associate, and Brad Edge, a graduate teaching assistant, have been instrumental in promoting BioCalc as a resource for life science students at UIUC.

Jerry Uhl is a professor of mathematics at the University of Illinois, Urbana-Champaign. Since the late 1980s, he has devoted much of his time to Calculus&Mathematica and other computer based courses in differential equations, linear algebra and probability. Uhl is also involved with NetMath, a distance education program that utilizes C&M courseware. He has just completed a term on the Mathematical Sciences Education Board of the National Research Council (NRC), and in 1998 he received an award for distinguished teaching from the Mathematical Association of America (MAA). Uhl has lectured across the country, as well as in England, Ireland, Germany, Greece, Egypt, Switzerland, Puerto Rico, Japan, Singapore and South Africa.

Bruce Carpenter is a teaching associate in the Department of Mathematics. He frequently teaches BioCalc and other C&M courses. In addition, he is instrumental in coordinating and teaching in the Calc&ChemPrime Program, a summer math and chemistry program for life science students who do not score high enough on placement tests to directly enroll in Math 120. Bruce has also developed interactive learning tools to be used with Mathematica and is a consultant with Math Everywhere, Calculus&Mathematica's publisher.

Brad Edge is a graduate student in the Department of Mathematics and a frequent BioCalc instructor. Brad was thirteen years old when he had the sudden realization that he wanted to be a mathematician when he grew up and has spent much of his time since that moment working to become one. While teaching a Calculus&Mathematica BioCalc section, he realized (somewhat to his surprise) that he was enjoying the process and involved himself more in C&M and teaching in general. Eventually, part of his graduate assistantship was acting as assistant director of the C&M program, handling many of the administrative details. He has since given up the job to pursue work toward his degree but remains interested in education and convinced of the effectiveness of the Calculus&Mathematica program. He is married, and has two young daughters.