undergraduate seminar in mathematics--opportunity and challenge, The

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Sep 2001 by Arnow, Barry J

ADDRESS: Department of Mathematics, Kean University of New Jersey, Union NJ 07083 USA.

INTRODUCTION TO SPECIAL ISSUE

This issue of PRIMUS is focused on the undergraduate seminar in mathematics and many of the surrounding educational issues. The impetus for this endeavor grew out of the Contributed Paper Session on The Undergraduate Seminar in Mathematics organized by Professors Barry J. Arnow and George A. Averappattu at the New Orleans Joint AMS/AMA Mathematics Meetings, 10-13 January 2001. Presenters were invited to submit papers and we are grateful to those that have accepted our invitation and whose papers have been included.

We have divided the papers into two parts. Part I and II. Part I papers appear in this issue and Part II papers will appear in the December 2001, Volume XI, Number 4 issue. In the description below papers that appear in Part I are denoted with (I) while those to appear in Part II are denoted with (II).

Why the undergraduate seminar? Well, consider the following brief list of educational buzzwords and ask yourself how often you've heard them discussed at department or committee meetings at your institution.

"Capstone Course"

"Program Review and Assessment"

"Cultural Diversity"

"Writing Intensive"

"Presentation Skills"

"Group Dynamics"

"Team Teaching"

"Cooperative Learning"

"Education Across the Curriculum"

"Integration of Mathematical Ideas"

"Written and Oral Communication of Mathematical ideas"

The list of course goes on but what is very apparent is that the standard mathematics curriculum comprised of a dozen or so courses beyond the calculus sequence does not even begin to deal with these issues in a serious way. That is, unless the curriculum happens to include an undergraduate seminar. This is not to say that the undergraduate seminar is the "end all" and "cure all" or that any one seminar can incorporate all of these items or address all of the associated issues adequately. But the undergraduate seminar does provide an opportunity to address many of the issues and provides a great platform for educational dynamism and creativity.

Implementing the items listed above is no small matter. Each one is important and complex enough to be the focus of a massive amount of educational material and each presents a unique set of challenges and opportunities. Exactly how some of these issues have been addressed in undergraduate seminars is spelled out in detail in the articles that follow.

In the announcement of the contributed paper session on the undergraduate seminar, we asked authors to consider:

appropriate topics and focus for such seminars

seminar objectives and how they are achieved and measured

requirements from student participants

equitable student participation

developing and measuring student presentation skills

the role of the faculty leader(s)

relationship and interplay with other mathematics courses

appropriate place within the undergraduate curriculum

prerequisites and credits for enrollment

equitable grading

The papers that follow have for the most part addressed these issues. Some describe seminars that focus on a single theme - like W. Abrams' (I) description of the seminar at Longwood College based on the BanachTarski paradox or J. Lorch's (II) description of the student/faculty seminar at Ball State University in which a faculty coordinator selects a central mathematical theme each year. The seminar described by B. Mayfield (I) at Hood College is based on the history of mathematics. Other authors describe seminars in which a different topic is presented each week. Another interesting variation is the extent to which the seminars include program review or assessment tools. This plays a significant role in the seminar at Union University described by C. Dawson (I). Students are required to review the material covered in the required courses of their program in preparation for a "Major Field Achievement Test". The senior seminar at Olivet Nazarene University described by D. Hathway and D. Atkinson (II) includes among its requirements a career resume prepared by each student. Students in that seminar are required to learn about the job market in their field of interest or different graduate schools depending upon their plans after graduation.

This special issue of PRIMUS includes articles about seminars that are designed for students at each level of their undergraduate education ranging from first to senior year. In fact, at Westfield College, a seminar is held at both freshman and senior levels. These two seminars and the appropriate problems and expectations for each are contrasted very nicely in the paper by J. Fleron and P. Hotchkiss (II). The article by D. King (I) offers an excellent description of a "lecture-free" seminar approach that can be taken in virtually every undergraduate mathematics course.

There is also a great deal of variation in the extent of faculty involvement in the seminars described in this issue. At Ball State, for example, each meeting of the seminar is run by a faculty/student team. At Hood College, a different student team is given complete responsibility for each class meeting.