Bruce: What happens when a new type of technology becomes available? Take, for example, the CD-ROM. When the CD-ROM first came out, the very first thing that happened was to take a book and just slap it on CD-ROM. Now that's just transplanting the old onto the new. The same thing happens with these computer labs: just slap on a computer, which means just duplicating the classroom in a computer lab. There's no new thinking. It's very natural, but it's very bad in the long term. For one thing, when you go to a new medium, you often leave behind lots of things that were easily done before and that requires more work. And sometimes you don't make full use of the new medium's full capabilities. So what you end up with is the worst of both possible worlds (more work and less efficiency), and that has a tendency to turn people off. They blame the medium and not the way it's being utilized.

In the following sections, we tell the story of how BioCalc got off the ground, presenting as we go the advice and suggestions that UIUC faculty and administrators had for others who are about to embark on the path of implementation. We begin with an examination or the necessary resources--personal as well as institutional--then follow with a discussion of potential problems and how to address them.

I. Necessary Resources

A. Personal Resources: "It takes commitment."

When we asked Jerry Uhl how it was possible to get a course like BioCalc going, his first comment was, "In the beginning of this, we had someone very committed from life sciences and someone very committed from math." And, without a doubt, most of the people with whom we spoke attributed BioCalc's development and implementation to the strong commitment made by Jerry Uhl (math) and Sondra Lazarowitz (life sciences). They were what we would call "champions"--people who embrace a cause and creatively and vigorously support it.

Jerry's and Sandy's championing of BioCalc got it off the ground, but as Susan Fahrbach pointed out, keeping the program going has meant tapping into and relying on the abilities of others. She particularly stressed the point that while BioCalc's initial success had a great deal to do with its champions, since that time BioCalc seems to work regardless of who is teaching it.

Susan Fahrbach: My initial impression was that Jerry Uhl and Sandy Lazarowitz were true believers and just through their energy alone they were able to carry the program. They also had help from incredibly able and committed people like Bruce Carpenter. That's how things got started. But since then, there have been lots of sections of BioCalc that have been taught by TAs who don't need to be such true believers.

The "true believers" were able to get the program up and running, but its success now lies with those who are teaching it and interacting with the students on a daily basis.

B. Institutional Resources

The UIUC faculty and administrators commented on a number of institutional resources that were necessary to secure in order to establish the BioCalc program.

1. Funding

   It's no secret that technology-based courses generally cost more, at least initially, than traditional lecture-based courses. Therefore, finding both initial and sustained funding is vitally important. In the case of BioCalc, the first four years of the program were funded primarily through a Howard Hughes Medical Institute (HHMI) grant. That money, Susan Fahrbach (faculty director of the Howard Hughes Program at UIUC) pointed out, "was then used to leverage funds from the math department."

   But, as Charles Miller noted, that was just the initial phase of funding.

   Originally the Hughes program put money into BioCalc. But, as is common, the outside funding organizations see such projects as seedlings which will eventually become "institutionalized" (the word we all know and love). The major support now is through the College of Liberal Arts and Sciences and the math department. Life Sciences also helps by providing space, computers and network support.

   Sustainable funding of BioCalc has been somewhat problematic in light of financial constraints facing the math department. But because the program has garnered strong support both within the department and in the College of Liberal Arts and Sciences, funding has continued.

   Jerry: Right now the College of Liberal Arts and Sciences is underwriting the extra expenses in BioCalc. The decision was made that we didn't want to stop [offering sections of BioCalc]. We wanted to make it available to the students who needed it, and everyone agreed--with a little teeth pulling.

2. Space

   With technology-based courses, finding the appropriate class space is as important as finding funding. BioCalc, for instance, meets four days a week in a computer lab. At UIUC, there are numerous computer labs on campus where students have access to Mathematica and the C&M courseware. In addition, C&M classes are taught in two dedicated labs, which are also open to students at most times during the day and evening.

   With BioCalc, however, it was decided early on that there should be a computer lab available in one of the life sciences buildings rather than the math building. The funding for the BioCalc lab was included in the original grant from the Howard Hughes Medical Institute.

   Susan Fahrbach: The funding for the first computers and the first computer lab came from the HHMI. It was in our proposal, the money to make a computer lab to be used specifically for BioCalc students.

   Jerry noted the value of providing a lab specifically for BioCalc students: "The kids in BioCalc feel more comfortable taking this course because it's in a life science building."

3. Technical Resources: Computers, Servers, and Software

   Unless you're a tekkie, the array of necessary technical resources for a course like BioCalc can be mind-boggling. We asked Tim Braun, a C&M lab technician, and Barbara Meyer, a computer-assisted instructional specialist in the School of Life Sciences, for specific advice on what's necessary to get a course of this technological caliber up and running smoothly.

   Computers:
   First things first. BioCalc (as well as the other C&M courses) require, as Tim put it, "reasonably fast computers with reasonable amounts of memory and hard drive space." This doesn't necessarily mean that the computers have be the newest on the market, but neither should you expect to get very far with, say, an IBM 286 or Apple IIe...

   Tim: The oldest computers in our lab right now are six years old, and they're scheduled to be replaced soon. These older computers will run the programs; they're just a little slow at it. Students know they're slower and generally avoid them.

   Keep in mind, too, that in technology-based courses like BioCalc, enrollment numbers are circumscribed in part by the number of available computers.

   Bruce: BioCalc is well-suited to 30 students, but that cap is driven primarily by the computing facilities available. There are roughly 15 computers in the lab, and therefore, having two students work at each computer, you get 30.

   Brad: That's a good point. The design of the course doesn't restrict the number of students; it's basically the physical facilities that dictate the enrollment caps.

   Networks:
   In order for a class like BioCalc to run smoothly, Tim told us, a good network is critical.

   Tim: [If you're going to implement a class like this], look at implementing a network solution like we've got. You can't run this class on individual computers. Without a network, it gets to be a monstrous stack of floppy disks; and the lessons are usually too big for floppy disks. They did try for a couple years doing it without the network and everyone I talked to said it got really bad--just disks everywhere.

   Software:
   BioCalc and other C&M courses use Mathematica software in conjunction with Calculus&Mathematica courseware. The University has a site license with Wolfram, the producer of Mathematica, so students do not need to purchase individual copies of the program if they are going to be using campus computers. If they want to use Mathematica on their home computer, however, they do need to purchase a copy. (Wolfram offers a relatively inexpensive student edition of the program.) All students are required to purchase the C&M courseware package (akin to a textbook in a traditional course), which includes a lesson CD.

   Tim: They have to buy the lesson CD whether they're going to use it in the lab or at home. If they want to use a public computer, that CD is all they have to buy. If they want to use their own computer, they also have to buy a copy of the Mathematica program. But there are plenty of students who have never owned a computer, who always use the public computers, and they get through the classes just fine. There are thousands of copies of Mathematica available on the campus computers. Some of these computers are available 24-7 and some are available during the day only.

4. What about support staff?

   Both Barbara and Tim agreed that technical support staff are vital to maintain the resources necessary for the BioCalc and C&M courses. "You have to have someone," Barbara told us, "who knows how to troubleshoot."

   Barbara: The network has to be good. The computers have to be up and running. The operating systems have to be perfect. The last thing you want is hardware problems. Students will get frustrated, for example, if they can't reach the server. You want to make the computer interface as transparent as possible. ...My feeling is that you have to have fast computers. You have to have memory. And you have to have someone who knows how to troubleshoot.

   Tim reiterated that point:

   Tim: You need someone to take care of the labs. Every academic computer lab has to have someone watching over it, taking care of it, some way to prevent the few students who decide they'd like to hack around with the system from causing any damage.

   By way of example, we asked Tim to explain just what his job as lab technician entailed.

   Tim: With the BioCalc course, I advise the instructors on their lab set-up. I take care of the servers that hold onto the lessons and the homework. I also take care of the main Calculus&Mathematica lab, from choosing which machines to buy to setting them up and maintaining them and deciding when to retire them.

   Support staff, the BioCalc folks agreed, are truly instrumental in keeping the labs and courses running smoothly.

II. Getting Started

Personal and institutional resources are an important part of the story, but it's also important to know what others in similar situations have done. We know that every faculty member develops his or her own style and will only rarely simply adopt a new approach without modifications of their own. (This characteristic of faculty is one of the greatest strengths of higher education.) At the same time, we suspect that, with respect to knowledge about how to create and implement new approaches to learning, the vast majority of faculty innovators and early adapters end up "reinventing the wheel," and that, quite frankly, is an inefficient use of faculty time and effort.

With this point in mind, we asked the people involved with BioCalc what they would tell those who are interested in implementing a similar type of reform on their own campuses. By far the most common answer was, "Seek out the folks who have or are doing it." Such people, the bricoleurs agreed, are a valuable resource in themselves.

Brad: My predecessor was a graduate student in the mathematics program doing the same sort of work I'm doing now. I would go to him and say, "Such-and-such seems to be going on. What would you do about it? What do other people do about it? Who's a good person to talk to about this?" And then I'd hang around a lab when Bruce or Jerry was teaching and see the way that they dealt with things. Ultimately, there are a lot of ways you can learn about what has succeeded for other people, but the best way is by being someplace where they're doing it. The modeling I saw was in the classrooms, and it was a result of my wanting to go find people who were doing things and doing things well. One of my jobs now is to advise instructors who come to me and say, "Hey, what can I do about this or where can I talk to someone about this?"

Tim told us that, in addition, it's important for someone interested in this type of course to get a first-hand feel for the program and courseware.

Tim: I think the very first thing someone should do is get one computer set up with Mathematica and the courseware that they're planning to use and just play with it and get a little bit of a feel for it. [It's important to know how it works] because there's a different teaching style involved, as well as a different learning style. Then after they do that, they can talk to people like me, who've taken the class, and other instructors who've taught the class to see what they think. It's especially useful to talk with other instructors and see what they thought, where they saw potential problems and where they thought it was stronger, etc.

III. Potential Problems and Ways to Address Them

In an effort to provide (as closely as possible) a conversation like the one recommended above, the BioCalc people with whom we spoke very generously shared with us the problems and issues that they had to address (and still do address, from time to time), as well as recommendations for improving the likelihood of successful implementation for others.

A. Individuals: Champions and Otherwise

One of the first things the BioCalc folks talked about was the role of individuals in the implementation process. Specifically, they mentioned the need for course "champions" like Jerry Uhl and Sondra Lazarowitz. Champions have the energy and commitment to get the ball rolling.

Ruth Wene: From life sciences, it was the passionate true believer, Sandy Lazarowitz, who [got things going]. She surveyed other faculty to find out what they thought students needed. She worked very hard, out of her passion to improve the lot of our students.

Champions are able to attract the attention needed to secure funding--from both internal and external sources--and garner high-level support in their own departments.

Susan Fahrbach: [In addition], Sandy had the support of the director of the School of Life Sciences (SOLS). She had the high level administrative support that was necessary. That was due in part to generally good feelings about the Howard Hughes Program [of which Lazarowitz was faculty director]: any program that attracts more than a million dollars in funding every time it gets a grant must be doing something right. She took the positive image of the Hughes program and her own intense commitment--which just goes above and beyond what most faculty would do--and leveraged that into good relationships with our School of Life Sciences director, who I must say happened to be from her home department. So she was in a very favorable situation.

Developing this kind of support and respect is crucial to reform efforts. As one person whom we interviewed noted, "Jerry Uhl was very savvy in securing top level support in the math department, which was crucial to getting BioCalc going because UIUC, like most universities, is a very hierarchical place." Having the support of the department head and others in the administration can get reform efforts on the path to implementation, whether or not others in the department are on board.

Taking on the role of champion, however, is not for everyone, the BioCalc bricoleurs warned. Only tenured faculty should take on the challenge of developing this type of program from the ground up (including development of the instructional materials). As Jerry noted, "Untenured assistant professors [need to be cautious] because showing too much interest in something like this can be taken negatively."

Which is not to say, Bruce was quick to add, that assistant professors can't teach reform courses.

Bruce: When I was referring to how it's not advisable for an untenured person to get involved in reform, I wasn't talking about teaching courses. I was talking about developing similar types of materials, or developing a similar type of program. Developing materials is extremely difficult and very labor intensive. It's very difficult to get non-tenured faculty interested in developing an entire program to improve the education of a group of students. But if the materials already exist and just need to be adapted to the course, then that's much easier.

B. Cultural and Historical Factors

It's also important to consider how cultural and historical factors will affect change--in some cases impeding it; in others, accelerating it. Being aware of these factors can help reformers anticipate difficulties and recognize and make use of opportunities that present themselves.

C. Consider your department culture

At UIUC, BioCalc's implementation was facilitated by the culture of the math department, which was generally supportive of experimental instruction and valued an array of instructional approaches. In fact, the department currently offers three different sections of Math 120 (Calculus I): traditional lecture/discussion using a standard text; computer-based instruction using Mathematica (C&M courses); and small group, collaborative learning sections that use graphing calculators (the Harvard section).^c

Jerry: One thing about the math department here: they didn't try to stop us, even if not everyone agreed with us. The result is that we have standard lecture calculus, we have calculator calculus, and we have computer-based calculus.

Paul Weichsel, associate chair of the Department of Mathematics, explained further, noting that even in the midst of financial crisis, the math department as whole maintains its commitment to diverse instructional approaches.

Paul: About three years ago, we ran into a very serious financial pinch. The math department was really constrained to make some rather draconian cuts, so people were looking at all kinds of ways to do this. The small group structure, for example, is obviously very labor intensive, and the cost per student is substantially above that of a traditional course. So the question was, do we need this type of course? It was under severe attack, and the people who came to its defense most vigorously were the graduate students who had been teaching it. Then the question of C&M courses came up. The [financial] support from the Hughes Institute and the NSF was long since gone, and the cost per student is relatively high. But a member of the department, who is very influential, got up and said, "Look, Mathematica is our reform project. One of our colleagues has put his professional life on the line and has devoted himself to this. That deserves our support."

Now [this kind of support for C&M in the face of financial constraints] was a kind of a cultural statement. It wasn't based on statistics and studies that said, "Hey, this stuff really works!" And that's generally the way we do things: try different approaches. Then we look back and ask, "Is there a principle that governed the way this operated?" And, in this case, the retrospective principle is simply this: One size does not fit all. The fact is, different students learn different ways. And offering people an array of possibilities in choosing their instructional style is a very sound thing to do, educationally.

D. Consider your timing (Ride the wave...)

BioCalc was initiated in 1994 at a time when calculus reform efforts were being mainstreamed into math curricula across the country. Five years earlier, when reform efforts were getting under way, Jerry Uhl and colleagues at UIUC and Ohio State University began developing the C&M courses (with funding from the National Science Foundation). By the time BioCalc came on line, several sections of C&M courses were up and running.

Susan Fahrbach: It really was a time when the math department was beginning to diversify. So this was sort of part of the zeitgeist of "Let's serve our undergraduates better."

Ruth Wene: They started teaching sections of Harvard calculus at about the same time. So calculus reform was in the air, and this was part of it.

Susan Fahrbach: The math department had started offering other courses with Mathematica, some special sections for engineering undergraduates. BioCalc was definitely separate and life science oriented, but we sort of caught that wave.

E. Use reform efforts to strengthen service to client departments

Faculty in departments that require mathematics courses for their majors ("client" departments) often are not satisfied with the way these courses are taught. They frequently view the mathematics faculty as concerned primarily with the mathematics majors and not with the needs of other majors. In these cases, they fault the courses with being too abstract and the mathematics too divorced from the subject matter and research themes of their own disciplines.

Reform efforts like BioCalc, however, can help bridge this gap in expectations and offer math departments the opportunity to position themselves as a resource, rather than hindrance, to client departments and students. At UIUC, for example, BioCalc has become a resource that life science faculty can draw on to help achieve their own goals for student learning, especially at a time when study in the life science fields is demanding higher-level quantitative skills.

As Jerry pointed out, the ability--and willingness--of math departments to respond and meet the needs of not only their own students but those of students from other disciplines, as well, is vital to insure their survival. Other departments can (and, in many cases, do) teach the math their students need, if math departments don't.

Jerry: One idea is for a life science department to try this out and teach it themselves.

Susan (interviewer): What about all those math TAs who would be out of business?

Jerry: If Ford Motor Company still marketed 1950 Fords, they would have been out of business a long time ago.

F. Be Aware of the Need to Convince Others

New courses like BioCalc have to be actively "sold"--first, to faculty and administrators; then to students and advisors.

G. Niche marketing is important

The BioCalc bricoleurs put it simply enough: students won't enroll in a course if they don't know about it. To ensure that students who can benefit (the "niche") will choose the course, they must effectively receive information about the course.

As one life science faculty member told us, an easy way to generate student interest in a class is through its name.

Susan Fahrbach: If a student has a strong identification with his or her major, having "bio" in the course name, for example, almost sells it for you. They don't even look and see what's different about it: "If that's the calculus for biologists, that must be the calculus for me."

But the BioCalc folks warn, targeting a course to particular students is not enough to ensure enrollment. Students have to be aware of not just the options available but which option might be best for them.

Brad: No one ought to feel like they're being forced to take this course. If they feel forced, it undercuts what we're trying to accomplish. We very much want to present the material so that the students take it, rather than having us feed it to them.

Bruce: Ideally, if they have sufficient instructional options, they can select for themselves the style of course that's for them.

Brad: Exactly. We've seen here that sufficient options aren't enough. We have to somehow reach the students so that they really understand what those options are.

At the time of our interviews (February, 2000), BioCalc did in fact have a rather low enrollment. Describing the situation, the associate chair of the math department implied that this was due to a "marketing" problem.

Paul Weichsel: BioCalc consists of one course, Math 120. It's generally the only calculus course that most of the life science students take [and it's usually offered in the fall]. Then someone suggested that we offer a section in the spring, as well. We went to the life science advisors and said, "Let's open this up. Let's spread the net a little wider." But that hasn't worked so far. Right now we have one section with eight students in it. That's absurd to run a class like that.

The bricoleurs explicitly attributed this to a lack of proper marketing; that is, the students were not enrolling because they weren't aware of their option to do so, either through direct advertising or through advisors.

Brad: My opinion--and I don't have anything solid to base it on-- is that students are faced with a very large number of choices when they hit college and one of those choices, which is relatively unimportant to them, is what kind of mathematics class to take. Unless they really understand that this course was designed to help people who don't do well in a traditional environment, then they don't have any particular reason to look our direction. We inform them about the different approaches to calculus that we offer, but they tell us in focus groups when they are about to graduate, "We had four thousand different pieces of information in two days during orientation." It just goes right out of their minds. My opinion is, we're losing enrollments because we are not successfully getting information to students either by advertising or by going through the advisors.

Advising, as one interviewee told us, is crucial; it can make or break a course: "I think it would be fair to say that advising in the School of Life Sciences had changed somewhat over the last several years, and as a result there is a smaller fraction of students enrolling in BioCalc."

H. Don't expect to convince all your colleagues

Another point that the BioCalc folks stressed is that some faculty will not support reform efforts, despite evidence of success.

Paul Weichsel: Now, Jerry will say that advisors are telling the students that Mathematica is worthless, et cetera. [But we've talked with some of the faculty], and the thing that I have found very interesting was not that these people were saying, "Our students need to know W, X, Y, Z, and they are not getting X, Y, Z." What they really were telling us was, "I learned calculus in this way, and my students now are not being taught calculus in that way. They are not going through the ordeal of fire that I did. This is new, this is different. There are certain specific topics that they don't seem to be very conversant with." Now, they never make the argument that those topics are very central to the lives of their students; rather, it's this terrible discomfort with the fact that they are not cloning.

We've had cases, actually, where a professor will give an exam and a bunch of kids in the class will display a clear lack of understanding of a some mathematical technique, and the professor with say, "Aha! It's the Mathematica!" So in one of these cases, we looked into it. We looked at all the grades, and it was simply not true. The kids who had not performed well were not the kids who had taken Mathematica. But those impressions die hard. You know, otherwise intelligent people are saying, "Don't bother me with the facts, I've already made up my mind." You see that all the time.

Such resistance is common because, as Jerry put it, "math faculties have very mixed opinions about computer-based teaching"--for many of the reasons mentioned above: it's not the way they learned calculus; it's new and different and hasn't been "proven." And as Susan Fahrbach noted, reform can have a polarizing effect.

Susan Fahrbach: A small number [of the life sciences faculty] are enthusiastic about BioCalc, but the vast majority [don't know much about it]. Then, there's a small number who seem to feel that if this course is different from the traditional calculus, it must be worthless. So we have three groups: a small group with a positive view, a small group with a negative view, and a large group with no view. But it's the small groups that are often more vocal when course requirements are set.

I. Respect the skeptics' need for evidence

While it's not likely that those with negative views of reform efforts will change their minds, it is important to provide evidence of reform successes for those who have a healthy skepticism. These are the folks who are concerned that efforts to help students could in fact end up hurting them and believe that unless there is evidence that a new approach is better, caution is called for. Charles Miller, for example, was initially concerned about the quality of math education the School's major were receiving.

Biochemistry has [been added to our school], so we now have a segment of students who are more quantitatively inclined. We also have programs in bio-physics and computational biology, which will be in our school. Some of these students probably ought to take a math course every semester. So I was concerned that we not give students a second rate, watered down experience that wouldn't provide them with the skills and knowledge they needed to go ahead, because if we're giving a kind of elementary math appreciation kind of thing, we're really not doing right by them. Jerry Uhl feels very strongly that this is not the case and claims that they have data to show that some of the BioCalc students have gone on to further study in math, sometimes extensive study, and do just as well or better than those who have take the standard sequence. I haven't really seen that, but if that's the case, I think that's another endorsement of BioCalc.

This need for evidence is one reason why assessment is critical to reform efforts. (See the Outcomes and Assessment section as well as Discussion 2 for information on BioCalc assessment at UIUC.)

J. Expect Student Resistance to the C&M Approach

Students, like faculty, have expectations of what a course should entail. When they find that a course differs from what they expected, they may begin to question what they are learning.

Susan Fahrbach: We have a high percentage of students who know somebody who went here, and from that they get their own idea about what their courses are going to be like. If a course is very different from the picture they have in their head, they require some reassurance that they are still going to learn as much as every body else.

For instance, a common expectation among calculus students it that, unless you suffer, you haven't learned "real"calculus.

Brad: One of the problems we face in our courses is that people come out of them thinking they didn't have the character-building experience that a calculus class is supposed to be. All through high school, calculus is spoken of as if it is the ultimate mathematics class on steroids and, boy, you better be brilliant to get through that. In my experience, calculus is easy to teach: there are four or five main ideas and if you can get those through, people will follow what's going on. But because students have been given to believe that it's not calculus unless they've hurt themselves over it, they conclude that they must not have done it right.

Jerry: As one C&M student put it, "If you take the standard calculus, you're regular army, and if you take C&M, you're National Guard."

Moreover, some students view the computer as a crutch: "The computer is doing the work and therefore I'm not learning what I should."

Bruce: The BioCalc students typically are not as comfortable with the computer technology as engineering students. They're very interested in what you do with computers, but they're not focused on the computers themselves, and so they frequently have a concern that because they're doing the mathematics on computer, that somehow they're not going to be able to carry that into other courses; they're not going to be able to do the kinds of calculations that the engineering students do. The BioCalc students are concerned about using the computer as a crutch.

Jerry: Now, what they don't know is that the people coming out of the standard calculus courses also can't do those calculations very well, either.

For some students, just the fact that they're not doing paper and pencil calculations is cause for alarm.

Ruth Wene: There is resistance in the incoming students to using the computer. Some students start BioCalc, and they're in my office two weeks later saying, "I want to get into the regular sections because I'm not learning anything." They really don't know what they're learning, but what they do know is that they're not doing paper and pencil problems, which is the only method that they have ever used to learn math. They're very anxious that they are somehow being denied access to mathematical information because they're not using paper and pencil.

In a course like BioCalc, faculty need to be prepared to address students' concerns about learning.

K. Expect a Learning Curve for Instructors and Students

BioCalc is a learning environment that requires both students and instructors to adjust to new approaches to learning and teaching. Most faculty and students--including those featured in this case study--bring to their courses complex assumptions about teacher and student roles that can present formidable barriers to implementing such approaches. We examine some of these barriers below.

1. For Instructors

   Need to orient instructors and CAs. Each BioCalc class has an instructor as well as a class assistant (CA). The CA is an undergraduate student who has taken C&M courses. Because of their prior experience, CAs are often the ones who have the best advice for how to run the class.

   Jerry: We depend on the class assistant to break in the new instructor because the class assistant has been through this. The instructor is the lieutenant and the class assistant is the sergeant.

   As Brad noted, this situation is a bit of a turn-around for instructors--it is not often that they find themselves receiving instruction from and relying upon their undergraduates. Instructors, who find it difficult to make this adjustment, often end up doing more work in the course than they otherwise need to.

   Brad: We make a very big deal during the [instructor] orientation of pointing out to the instructors, especially the new ones, that the class assistants have experience with the program, they have experience with the lessons, and they know a lot about what might or might not work in a C&M class--principally because they've taken it as a student themselves. We make a big point of the fact that we don't utilize our CAs as well as we could. We tell them, "Ask your class assistant what they can do for you, because they know better than we do." I've never worked as a class assistant; the class assistants themselves know better than I do what they can offer. But we still have trouble with underutilization, partly because of what people think of working with an undergraduate and partly because Calculus&Mathematica is a very different teaching model. A teaching assistant or faculty member going into that environment, I think, tries to maintain more control until they become comfortable with the situation, and as a result they don't have someone else doing as much as they could.

   Need to adopt "guide-on-the-side" role and come to terms with the "Atlas complex." As Brad noted above, new instructors often find it difficult to relinquish control, even to a class assistant. But the philosophy upon which BioCalc is based--actively engaging students in their own learning--requires just that: instructors must adopt a "guide-on-the-side" role, rather than the traditional "sage-on-the-stage" role, in order to help students self-discover concepts and connections.

   Finkel and Monk use the term "Atlas complex" to refer to the very common difficulty faculty experience in relinquishing this kind of control. As they put it, instructors need to abandon the notion that they, like Atlas, must bear the weight of the entire classroom world on their shoulders.

   Jerry: Some people who have taught in our program say, "I want to contribute more to my students than your program allows." What they're really saying is, "I want to think for my students."

   Breaking out of the Atlas complex involves a willingness to step aside from the authority and power of center-stage and a desire to empower students. It requires asking questions instead of providing answers, listening instead of talking, and feeling comfortable with student confusion instead of rushing to fix things. This is an on-going process, Bruce pointed out, of which faculty must be aware and actively pursue.

   Bruce: You could say I'm in touch with my Atlas complex: I still have it, but I actively push it to the side. I actually like giving lectures, and I still occasionally teach a lecture course. But the reasons I enjoy it are not the reasons why the students learn. It's just nice, as a mathematician, to have a captive audience. And I like organizing the ideas. So, yes, there are a lot of things about the lecture system that I really enjoy, but almost none of them contribute effectively to teaching. Or learning. When I'm lecturing, the focus of the class is upon me. But that's not where the focus should be, because I'm the one who already knows the material. In BioCalc, we place the focus on the student.

   Need to expect students will be very "answer-oriented." When instructors do assume more of a guide-on-the-side approach, they should expect that students will need time to adjust. Students are used to the idea that the instructor has all the answers and that proper teaching involves giving them those answers.

   Bruce: There's also a tendency with a lot of students to be very answer oriented. They ask a question, and they want an instant answer. Typically what that means is that they don't want to think about the problem--they don't really want to flesh out their conceptual understanding of how things fit together. They just want to get the answer to this one problem and move on.

   We really try to resist that. We don't refuse to answer a question, but we do resist just giving answers straight out. Instead, I start asking them questions in return, find out places where they really need to go back and review the material or they need to go back and think about a point that's covered in a prior homework problem. The students really need to flesh out that understanding on their own. Once they've done that, then they can see for themselves how to proceed in solving the problem. By answering someone's question right away, you prevent them from knowing the material, and you strip of them of the joy of discovery.

   
   

2. For Students

   Students, like instructors, have their own set of unique issues in a course like BioCalc. Aside from adjusting to the different roles of instructors and learners (the Atlas complex), students also often experience start-up difficulties in learning to use--and learn from--a computer.

   In particular, the first two to four weeks of the course are generally the most difficult for students, the BioCalc folks told us, because it can take some time to learn the Mathematica code.

   Tim: Sometimes the students will get bogged down with the Mathematica code. They don't realize that it's a basic programming language and once you understand a few commands, you can pretty much understand what it's doing. Generally, most of them get over the frustration. A few drop the class and go for a tradition calculus course, but most stick with it. They realize it's just a new method of learning, like the first time they picked up a scientific calculator: "Hey, what are all these buttons? How does this work?"

   One student with whom we spoke confirmed Tim's point.

   Mark: At first, I thought the class was going to be hard because of the computer. But the program is actually pretty easy to use, once you figure out how to cut and paste commands and stuff. You definitely don't have to be a genius at computer script in order to get it.

   Ruth Wene, an advisor in life sciences, told us that when students express concern over learning the code, it's important to remind them of the greater payoff down the road.

   Ruth: I think the first couple weeks are rough because the [Mathematica] program is complicated. It takes a fair amount of input at the beginning to get comfortable with the program, and then you begin to see the payoff. If they stick it out for a month, they're usually fine. I just report to them what other students tell me, which is that you're not going to have to solve calculus problems per se in your biology classes. But, it's going to be enormously helpful for you to be able to look at graphs and charts and be able to use the calculus you know to understand the meaning of these depictions. That's mostly what calculus is going to be used for. This method of presentation in math is going to be much more helpful to you than paper and pencil problems will be.

   The BioCalc folks noted that this start-up period can be more difficult for students who are computer illiterate or computer phobic, but the payoff is relatively greater.

   Ruth: I see many students for whom computers have been part of their high school education, or they have them at home; they're not nervous about using them. I still see some who are kind of computer phobic and don't see them as learning instruments. For these students, a course like BioCalc is wonderful because they begin to see that the computer can do some of the work and allows you to learn in a different way. Do you really want to get a problem wrong because you added or multiplied wrong? Or would you like the computer to do all of that correctly for you and you work on the concepts?