Launchings from the CUPM Curriculum Guide: Who are we teaching?

David M. Bressoud March, 2005

Recommendation 1. Understand the student population and evaluate courses and programs.

Mathematical sciences departments should

Who are those students in our classes? What preparation and expectations do they bring? What do they need from us? How well are we helping them to learn what they will need? How can we improve what we do? These are the questions that all departments should be asking. The answers can be unsettling, but they are also the starting point for meaningful and effective change.

Our student population has changed and is changing. More students making up a larger percentage of our high school graduates are continuing into 2- and 4-year colleges. The disparities in preparation are broadening. Over 10,000 students per year now take and pass Advanced Placement BC Calculus (equivalent to a full year of college calculus) before their senior year of high school [2]. At the same time, the number of students arriving with deficiencies in their mathematical preparation is exploding, threatening to overwhelm the mathematics departments of many colleges. Curricula, syllabi, pedagogical techniques that were adequate a generation ago may no longer meet the needs of the students we encounter today.

While we need to know where our students start, we also need to measure how well we succeed in moving them toward the goals we have set. The word is “assessment.” It is a term that is not always viewed kindly. To many, it connotes time-consuming studies that ultimately say what everyone already knew. The report of a recent departmental self-study at American University contains a frank description of opposition to formal assessment. The department was trying to specify learning objectives based on goals derived from the department’s mission statement:

“The discussion was spirited and sometimes negative. Faculty were not convinced that this process was useful and they were skeptical that there would be meaningful results. Several faculty opined that information for improving the programs could be obtained more simply by reflecting on their students’ performance and discussing their observations about students among one another. One faculty member was insistent that since our program was so small, we knew our students in terms of what their strengths and weaknesses were.” [1]

The response was that while such informal impressions can be helpful, they may not alert the department to those aspects of the program that really need attention. This faculty discussion began to make progress when it began to focus on goals in terms of observable activities their students should be able to do after graduation. One faculty member suggested that students should “be able to pick up a mathematics book and teach themselves some new mathematics using the skills they have gained in the program.” To general consent that this is a worthy goal, the department explored how to observe it. The result is that seniors are now required to give an oral/chalkboard presentation to three faculty members, explaining a concept in mathematics that immediately or closely follows the last concept discussed in one of the last courses in their program.

The Department of Mathematics and Statistics at American University received help and guidance in its self-study through the MAA’s project Supporting Assessment in Undergraduate Mathematics (SAUM). Their case study is one of many that are available on the SAUM website. The assessment might be an entire departmental self-study, but it could also be more restricted. Examples include the study at Monmouth University that focused on the Middle-school Mathematics Teacher Preparation Program and the study of Pre-Calculus undertaken at San Jose State University. SAUM sponsors workshops, sends consultants, runs sessions at national and regional meetings, and offers many other resources and forms of support for those departments that want to understand where they are so that they might move forward.

The CUPM Illustrative Resources contains additional information on placement exams, how to improve advising, how to help meet the needs of disadvantaged students, how to collect information through surveys, and how to find the money to fund this work.

No one claims that this is easy work, but accountability is important throughout higher education. The department that convinces its dean and upper administration that it is actively engaged in identifying weaknesses and validating successes will find support for its efforts.

[1] American University, Undergraduate Mathematics Program Assessment—A Case Study,

[2] APCentral, AP Research and Data,

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at