In his introduction to this volume, Bernie Madison has described the process by which the MAA in the early 1990s became involved in the issue of assessing the mathematics major. Out of that effort came the document "Assessment of Student Learning for Improving the Undergraduate Major in Mathematics."  (You will find it reprinted on pages 279-284.) At about the time this document was published by the MAA (1995), a relatively small number of undergraduate mathematics programs across the country were faced with developing an "assessment plan" and the hope was that some of them would find the MAA's work helpful as a map to guide them in these uncharted waters. By this time (1999), the reality is that almost all undergraduate programs will have to have some type of assessment plan in place within the next couple of years. The hope is that what you will read in the next few pages will be helpful to you as you face this brave new world.
We, the editors, have chosen a representative sample of assessment programs from among those college and university mathematical sciences departments which have gotten into the game early. The sample contains articles from mathematics faculty at small schools, medium-size schools and large schools; at liberal arts colleges, regional comprehensive universities and major research institutions.
These departments are using a variety of methods to assess their programs, e.g., capstone courses, comprehensive exams, diagnostic projects, focus groups, student portfolios and surveys of various types. However, these techniques are not described in isolation; they are to be understood within the context of the assessment cycle. As you read these articles, you will see that each of the authors has provided that context. What follows is a brief description of each author's paper.
In the first two articles student portfolios are the principal assessment methods. Laurie Hopkins describes the assessment process at Columbia College in South Carolina. In this program certain courses are designated as portfolio development courses, and in these courses the student is asked to reflect in writing on the connection between the material included in the portfolio and the departmental goals. Linda Sons describes assessment portfolios at Northern Illinois University, which contain students' work from various points in their mathematics program and are examined by a department committee after the students have graduated.
Capstone courses as assessment techniques are discussed in two articles, one by Charles Peltier at St. Mary's College in Indiana and the other by Deborah Frantz of Kutztown University in Pennsylvania. Peltier describes a full-year senior seminar in which independent study projects (written and oral presentations) are developed as part of the seminar. Frantz provides us with the details of a one-semester Senior Seminar in Mathematics in which oral and written presentations are just two among a number of assessment techniques used.
Bonnie Gold and Dan Callon present us with different models for using comprehensive exams as assessment instruments. Gold describes a two-part exam consisting of a written component in the mathematics major and an oral component over the liberal arts. Callon discusses a rather unique approach to giving a comprehensive: a one-week, joint, written exam given to seniors during their fall semester. John Emert and Charles Parish discuss a "less" comprehensive exam developed to assess the core courses taken by all undergraduate mathematics majors.
Next we are introduced to an entirely different approach to assessing the mathematics major: the use of focus groups. Marie Sheckels gives us some insight as to how focus groups with graduating seniors can be incorporated into an assessment process.
The next two articles describe overall departmental assessment plans involving a variety of techniques to assess the major. Dick Groeneveld and Robert Stephenson describe the assessment measures used in their statistics program, particularly the use of grades of graduates, surveys of graduates and surveys of employers of graduates. Janice Walker also discusses all of her mathematics department's assessment techniques including the use of exit interviews and the Educational Testing Service's Major Field Test in Mathematics.
Three of the articles deal with assessing the mathematics program either at the midway point of a student's four-year career or at the freshmen level. Mark Michael discusses a semester-long Diagnostic Project which is part of a required Discrete Mathematics course, usually taken by mathematics majors in their sophomore or junior year. Judith Palagallo and William Blue of Akron University in Ohio describe a sophomore-level Fundamentals of Advanced Mathematics course and what information it reveals about the major early on. Elias Toubassi introduces us to a major effort at a large university to reform the entry-level mathematics courses through assessment and its subsequent effect on the mathematics major.
Finally, Deborah Bergstrand discusses assessing the major from the point of view of students who are potential graduate students in mathematics. Three measures an Honors Project, a Senior Colloquium and Summer Undergraduate Research project are used.
This section has been organized so that you can look at every article or pick and choose those which are of most interest to you. In some sense each of our undergraduate mathematics programs is unique and yet there is enough commonality so that you might be able to adapt at least one of the assessment processes described here to fit your own situation.
 Committee on the Undergraduate Program
in Mathematics (CUPM). "Assessment of Student Learning for Improving the Undergraduate Major
in Mathematics," Focus: The Newsletter of
the Mathematical Association of America, 15 (3),
June 1995, pp. 24-28. Reprinted on pp. 279-284 of