Problems		Goals
1. Students failing or performing poorly in required math courses for life science majors--can't continue in chosen field of study		1. Improve student learning by motivating students to learn and dispell the myth that some students "can't do math"
2. Faculty don't expect students to be able to connect what they learn in math with what they study in life sciences		2. Help students bridge the gap between what they do in a math class and what they study in life sciences by emphasizing relationships between ideas, concepts and processes

Formal Assessment of C&M Courses
Do C&M students learn as well as their cohorts in traditional courses? Can they perform on par, both conceptually and computationally (hand calculations)? Two independent studies have been done comparing students in traditional, lecture-based courses with their C&M counterparts, and in each study, the results were positive: C&M students have been shown to perform slightly better on conceptual problems and as well as their traditional counterparts on hand calculations.

At the U.S. Air Force Academy, for example, an anchored final exam was administered to students in a C&M course and a traditional, lecture-based course. The study found "that students in Calculus&Mathematica scored significantly higher on conceptual questions and slightly higher on computational questions" (Holdner, 1997).

Table 3. Results of an anchored final at the U.S. Air Force Academy, Fall 1995

Source: (Holdner, 1997)

Another study of C&M courses, conducted at UIUC by researchers in the College of Education, concluded that C&M students not only performed as well as or better than traditional calculus students, but also developed a more positive outlook on mathematics in general (Park & Travers, 1996):

Generally, the findings from an achievement test, attitude survey, concept maps, and interviews were all favorable to the C&M students. The C&M group obtained a higher level of conceptual understanding than did the standard group without loss of computational proficiency. Furthermore, the C&M group's disposition toward mathematics and computers was far more positive than that of the standard group.

Formal Assessment of BioCalc at UIUC
An assessment of BioCalc is being conducted as part of two on-going projects at UIUC. One project, funded through the Howard Hughes Medical Institute, will involve a direct assessment of BioCalc.¹⁰ As Susan Fahrbach, director of the Howard Hughes Program at UIUC, told us, the assessment is important because it will provide "hard data to share with the rest of the faculty."

SusanFahrbach: Under our current four-year award from the Howard Hughes Medical Institute, we're charged with assessing the success of the program in the hopes that we can recommend to those who make decisions about the curriculum, whether or not this should be a required or recommended course for our undergraduate life sciences majors.

For that reason, Susan explained, the assessment will focus primarily on getting that "hard data:"

Susan: Jerry and I and the people involved with BioCalc are very interested in mastery, concept development, intellectual growth. And actually the audience for our assessment is primarily interested in outcomes. So, we're probably going to use most of our resources on doing statistical comparisons of matched-pair students in BioCalc and non-BioCalc sections and looking at many aspects of their performance.

Tony (interviewer): I'm not an educational researcher, but it sounds like a tough task because the courses really have such different emphasis.

Susan Fahrbach: Right, but one can look at how BioCalc has impacted our students' subsequent careers in life sciences. We can look at course grades, courses taken, retention rates--did they actually graduate as a life sciences major? We've been told by the current directors of the School of Life Sciences and other colleagues who are on the curricula committee that that's the type of information that will sway their recommendation for inclusion of BioCalc in the curriculum....And we'll be looking not only at outcomes but also attitudes. For that, we are going to take data that is being collected by an NSF-funded Indicators project, which is looking at all the students in the Math 120 sections and doing pre-evaluation: what is your attitude, are you scared, are you happy, do you think this will be relevant to your life, to your course, to your major? Then doing a similar post-evaluation. We will have access to the data for both BioCalc and non-BioCalc sections.

At the time of our interviews, the Department of Mathematics was in the midst of this NSF-funded project, which will include an assessment of the first two years of the engineering calculus program at UIUC (all sections of Math 120, 130, 135, 242 and 245).¹¹ It was not known at that time when the project might be completed, because, due to the complexity of the department's instructional program,^a data were still being compiled and methodologies had yet to be established.

The BioCalc assessment for the Howard Hughes Program was completed in April, 2001. For a summary of the results, please see Discussion 2.

Measuring Success in Other Ways
When it comes to C&M courses, however, Jerry Uhl believes strongly that the Indicators project will show the same results as other formal studies: C&M students perform as well conceptually and no worse with hand calculations than their counterparts in typical lecture-based calculus courses. These studies focus, perhaps too narrowly, on the statistical outcomes. As the UIUC faculty and administrators pointed out to us, there are other ways to measure success.

An administrator in the School of Life Sciences, for example, remarked that BioCalc students' attitudes about math seemed to change as a result of the course:

Right from the start, it seemed that--for whatever reasons--BioCalc went better. The kids liked it. They didn't have so many negative attitudes. They stopped viewing [calculus] as a terrible hoop they had to jump through.

In fact, as Jerry, Bruce and Brad noted, many BioCalc students go on to take math classes beyond the prerequisites of their major. Some even take a minor in mathematics.

Jerry: A number of students have actually come out of BioCalc and become math minors.

Bruce: Students have taken BioCalc and then gone on to take, what is for them, unnecessary math courses.

Brad: In fact, one of theBioCalc students with whom you just spoke stopped me in the hall when he left and said, "I also want to talk to you about becoming a [C&M] class assistant because I think that would be a good thing to do." Students who have gone into the life sciences are finding that mathematics is something they enjoy well enough to come work in our math program [as classroom and lab assistants]. They don't give up their interest in life sciences--we don't convert them and we're not trying to by any stretch of the imagination--but they do find out that mathematics is not as separate from what they're doing as they thought it was.

Susan Fahrbach echoed their observations and added that students' growing interest in math was an indication of BioCalc's success, which she believes the assessments will show:

One interesting phenomenon has emerged which Jerry is quite convinced is true, and I think we'll have the data to support it: We now have life science majors who are going on and taking other math courses--for fun. That is really a new thing for us. It's really interesting. It's a small number, but it certainly suggests that BioCalc is preparing the students well for any math they want to do in the future.