Well, the whole history of this started when I got a call from Sandra Lazarowitz [in the Department of Microbiology at the time], and she said that she and other life science faculty were very upset with the standard calculus course. She said she had talked with someone in the math department and had told him that biology students just weren't tuning into this course--over sixty percent were getting Cs, Ds or Fs. The math professor said, "Well, we can't help it if you have stupid students.

--Jerry Uhl, Professor of Mathematics

We have high admission standards to the program. If you write 'biology' or 'life sciences' on your application, you will be subjected to greater scrutiny than in any other program in this University, with the possible exception of engineering.

--Charles Miller, director of the School of Molecular and Cellular Biology

In this section of our case study, we present the problems that provided the impetus to create this new learning environment, as well as the goals that our bricoleurs^a and others sought to achieve through its implementation.

Learning Problems
To learn about the problems that BioCalc was implemented to address, we talked with faculty and administrators in both the Department of Mathematics and the School of Life Sciences. In these discussions, two key problems were reiterated:

• First, what we call the "weed out" problem: students were unable to fulfill the math requirements of their intended life science major and, as a result, were leaving life sciences altogether.

• Second (to borrow a phrase from Jerry Uhl), the "preach and pray" problem^b faculty in the life sciences assumed that even those students who had successfully completed the required math course(s) were unable to connect what they had learned in math to what they were studying in life sciences.

The Weed Out Problem
Many students--not just at UIUC, but across the country--identify introductory SMET courses as major barriers to fulfilling the requirements of their chosen majors (Seymour & Hewitt, 1997). These "weed out" courses typically serve the dual purposes of curtailing enrollment while enabling certain types of students to proceed to advanced study in these fields.No one with whom we spoke at UIUC specifically labeled Math 120 (Calculus and Analytical Geometry I) as a weed out course. Yet, the students we interviewed described their experiences in traditionally-taught introductory calculus courses as confusing, frustrating and overwhelming--experiences that Seymour and Hewitt note are common in "weed out" courses. As a student hoping to major in biochemistry told us,

[My traditional calculus class] was so confusing and frustrating. I'd do homework for, like, 30 hours every night, and I'd still sit there and stare at the problems and not get it. And I really need this class. I can't declare my major until this class is out of the way. So I was trying, but I was getting a D. I went to [the instructor] and asked for help and she said, "Well, if you don't understand it, maybe you should be in another section or a different math course." So I dropped it.

Elizabeth, another life sciences student who had previously enrolled in a traditional calculus course, related her frustration with the fast pace of the course. She commented that it seemed to her that most of the other students in the course had taken calculus in high school and that the professor had adjusted the pace to suit those who were already familiar with the material.

He went through things really fast and assumed we all knew it, when we didn't. So it was really hard to follow. He would just write things across the board--derivatives of this-and-that--and I would copy it down, but I'd be so busy writing that I wouldn't have time to understand it. Then he would do the same thing in the discussion section, just write a bunch of problems. He wouldn't really take the time to explain each step, just "It goes from here to here to here, and that's that." ...After a while I just stopped going. I didn't understand it, so I didn't want to do it.

Another student commented that the language used in his calculus course was off-putting and hard to understand.

Mark: I don't remember anything from that class. The teacher explained it in a way that was--well, I guess the other students had had a lot of math, because they talked in, like, math talk. And I did not understand the teacher at all.

Other students related that they were intimidated by the math, even before actually enrolling in the course.

Steve: I'd say my biggest fear coming into the class was that, well, basically, it's calculus and in high school I took honors trig precalc, but not calculus. So, you know, words like "derivative" and "integral" scared me.

Paul Weichsel, associate chair of the Department of Mathematics, told us that students from other disciplines often balked at having to take math courses, especially when their scores on the University's math placement exam required that they enroll in pre-calculus courses.

These students were told they'd have to [first] take algebra, and they were saying to their advisors, "I don't want this. I want to study life sciences. Why do I need to take algebra?" And then they would say, "If you're telling me that the only way I can study life sciences on this campus is to take those courses, I'm not going to do it. I'm either going to leave or go to another program."

In short, some students, for the reasons cited above, were either leaving or not enrolling in life science programs because of one course: introductory calculus.

The "Preach and Pray" Syndrome
While the life science students we interviewed described, in effect, being "weeded out" of traditional calculus courses, BioCalc advocates identified another key problem: Neither faculty nor students in the life sciences viewed calculus--as it traditionally taught--as relevant or applicable to the study of life sciences.⁹ To Jerry Uhl, this traditional, lecture-based approach to teaching calculus boils down to a "preach and pray" approach--"Preach in your math class and pray [the students] make the connection." At UIUC, students often did not see the connection between math and their own course of study. Ruth Wene, an advisor in the School of Life Sciences, told us that to many life science students, calculus "seemed entirely irrelevant to anything that they thought they were going to be doing in the future."

As the students experienced it, required courses that seemed to them irrelevant were all the more uninteresting and difficult. One student with whom we spoke described the equations drawn on the board in his traditional calculus course as little more than scribbles: "I would sit in lecture, and the professor would just scribble on the board with chalk, just big scribbles everywhere. She would talk and talk and talk and scribble away on the board."

Such attitudes may be reinforced by the fact that, as often happens, instructors in non-math disciplines do not depend on their students being able to transfer math skills to a non-math context. This, as Jerry put it, is a catch-22: "The instructors don't expect their kids to know any calculus, even though the students have had calculus. So the instructors don't use it."

Faculty weren't using calculus in their courses because they perceived that students were not learning skills that they could transfer to their life science classes. Because of this, Ruth noted that some life science students weren't even taking the required introductory calculus courses until their senior year. And a student with whom we spoke told us he'd taken BioCalc two and a half years earlier and hadn't "had to use much calculus since, in any classes. I was taking science classes, but really there's no incorporation of math." It's important to point out, of course, that the disconnect between math and other disciplines is not limited to life science students, nor is it merely a problem at UIUC. Rather, as Bruce explained, the problem stems from the fact that most math courses provide little or no connections to other disciplines.

One of classic things that happens--and not just at this university (because this happened when I was an undergraduate in engineering)--is that [instructors in other disciplines] basically teach their students the math they'll need to know in order to take their course. Even though they have math courses as a prerequisite, instructors don't depend upon the students actually being able to use the mathematics as a tool to do, say, engineering.

This stems from the fact that "there's no real interdisciplinary approach to math courses," Bruce told us. Brad Edge, a BioCalc instructor and graduate student in the Department of Mathematics, pointed out that this problem is prevalent in math education and is related to the way in which mathematicians experience their discipline--that is, as purely abstract. Consequently, mathematicians often teach it that way, as well.

Brad: It's taught very abstractly. We're getting now to problems that are endemic to the entire mathematics education system. Students are used to the idea that mathematics is symbols; it's an abstract pursuit. ...Because we [mathematicians] don't teach it well. We don't successfully teach students mathematical concepts as tools that they can use in their future pursuits.

An abstract approach to teaching mathematics, while useful for students studying to be mathematicians, is problematic for those who need disciplinary application experiences.

Goals for Improving Student Learning
The UIUC bricoleurs expressed a variety of goals for student learning, all centering on remedying the deleterious effects of "weed out" courses and instilling in students not only a solid understanding of mathematical concepts, but also how those concepts apply outside the math classroom.When asked about his goals for student learning, Jerry commented that his first goal "was for students to come out of our course not thinking it was a waste of time." BioCalc, for example, uses real world problems and examples to emphasize the relationship between calculus and the study of life sciences. Students are more motivated to learn when they can see and understand this important connection.

Brad told us he wanted students to find the course useful, but also wanted them to enjoy it--to discover "the joy of mathematics itself." Perhaps more importantly, though, he wanted students to discover that they can indeed "do math:"

I want my students to come out of my classroom with some feeling that not only wasn't it a waste of their time, but that there's room to think of mathematics as if it could be fun. And I also want my students to believe that it's something they can do. Because one of the things that we really impose on people in mathematics education in this society is the impression that they can't do it. Now, I've taught a number of different classes. I've taught a number of different types of students. And I've not found anyone that just can't do math, despite their own belief that that's the case.