By Sarah Spence Adams
A summary of the discussion by panelists Sarah Spence Adams, Rebecca Garcia, Rick Gillman, Darren Narayan, and Daniel Schaal at the January 2009 Joint Mathematics Meetings panel organized by MAA CUPM Subcommittee on Research by Undergraduates members Michael Dorff and Zsuzsanna Szaniszlo.
Undergraduate research experiences often take place in the summer when students and their mentors can focus intensely on the research experience, for example in programs such as NSF-sponsored REUs (Research Experience for Undergraduates). As undergraduate research becomes an increasingly important part of the undergraduate experience, many departments or individual faculty members have started to implement academic year research programs as well. Mentoring research projects during the academic year brings unique rewards as well as certain challenges. In assembling the panel on “Starting and Maintaining an Academic Year Undergraduate Research Program,” Michael Dorff and Zsuzsanna Szaniszlo asked the panelists to focus on the following topics: (1) Purposes for doing undergraduate research; (2) Finding students to do undergraduate research; (3) Characteristics of good undergraduate research problems and how to find them; (4) Logistics of an academic year undergraduate research program; and (5) Student presentations and written reports/papers.
The panelists represented a diverse set of experiences and institutions: Rebecca Garcia of Sam Houston State University, Rick Gillman of Valparaiso University, Darren Narayan of the Rochester Institute of Technology, Daniel Schaal of South Dakota State University, and this author Sarah Spence Adams of Franklin W. Olin College of Engineering. A theme throughout the discussion was that the goals of a research experience can vary widely, and these varied experiences are all valid and important. Recruiting students, choosing problems, and deciding on presentation/publication venues will vary widely from institution to institution, from mentor to mentor, and from student to student. This article is based on the comments of the panelists; their full presentations or presentation notes are included at the end of this article. It is not necessarily the case that all panelists agree with all statements in this article.
(2) Finding students to do undergraduate research
An obvious way to find research students is in upper-level electives, but excellent research students can also be found in introductory courses. Sometimes a student with no experience in a given area can still become a valuable member of a research team. To help convert your classroom students into your research students, mention research at any given opportunity – every class if possible! Devote a special day to deliver an appropriate-level talk on your research, or better yet, bring in a collaborator to do the same. (Sometimes the students will listen more intently if there is a new body at the front of the classroom.) Adding a project-based component to your classes can help you determine who might succeed in the open-ended research environment. Outside the classroom, it can be helpful to find (or create) a venue to give a talk to undergraduates about your research. A math club or a Pi Mu Epsilon chapter meeting are ideal venues. Posting flyers about your research around campus is another means for attracting student researchers. Finally, in addition to these efforts, it is very effective to personally approach students. Do not overlook the enthusiastic but “not great” students – sometimes these students need the excitement of original research to really shine. Once you get one or two students, formalize your group by coming up with a name for your group. Ask the students to design a sign for your research group that you can hang on your door. Make them feel like they are part of something important (they are!), and soon more students will be knocking on your door.
A more formal and very effective way to recruit students is by offering a seminar course with the goal of preparing students for research. By offering the course “by invitation or permission,” students already feel that they are part of something special. Proof techniques should be an important part of the course, especially techniques that will likely be useful in the research you have planned for a future semester. The topical coverage of the seminar, as well as the topic of the future research, should not require much background.
(3) Characteristics of good undergraduate research problems and how to find them
A crucial component to any successful undergraduate research program is having good problems for the students to attack! Finding such problems takes some practice, and the panelists weighed in on the characteristics of good undergraduate research problems and then how to find them.
Research problems should be engaging. They should be easy to state and relevant to the students. Ideally, the problem should not require too much background. If a student can repeat the problem to friends and relatives, then you are on your way. The problem should also be such that students can easily generate data to build conjectures. The ideal problem can also be broken into smaller parts so that you can stage a sequence of work for the students as the semester progresses. A computing component can be a beneficial feature for many students who may have more programming than advanced mathematics training. Students can derive a great sense of accomplishment by writing a program to generate data or otherwise advance the research program. A problem should be chosen that lends itself to partial results, preferably with several potential levels of partial results. Accessible literature is another factor to consider. Students can benefit greatly from reading primary sources, and their first introduction to the research literature should be as gentle as possible. It is also preferable for the chosen problem to be on a topic that is potentially worthy of publication in the literature. Finally, it is important to set up your students for success as much as possible: Choose a problem that is likely to be solved using techniques that they have seen before, perhaps in a previous course or in a special research-preparation seminar.
It is often advantageous to find subproblems or special cases within your own research program. Some ideas are to look at initial cases, special examples, counter-examples, or what happens when relaxing certain conditions. Networking can also be an important way to find problems: Attending specialized conferences in your research area and talking with current graduate students can lead to new problems. Mining recent doctoral dissertations is also a great way to find appropriate-level problems in your general research area.
When looking beyond your research area, consider other areas of interest that are easily accessible to undergraduates: recreational mathematics, combinatorics, graph theory, and experimental/computational mathematics. You may find good problems in these areas by exploring some recently published advanced undergraduate textbooks or articles in undergraduate journals. Also, you can consider contacting research advisors for current undergraduate research programs, e.g. NSF REUs, MSRI-UP. For example, they might be happy to have your students extend the work of their recent students.
(5) Student presentations and written reports/papers.
Note: Issue 2 of this column included ideas for venues for undergraduate presentations and papers, so the comments below do not duplicate this information.
Having students work towards an oral/poster presentation or a report/publication can be highly motivating. If funding is available, you can consider regional/national professional meetings and undergraduate research conferences. Closer to home and not requiring a budget, a departmental colloquium series is an ideal place for a student’s first professional talk. The experience of planning a talk and standing in front of an audience is more important than the actual venue of choice. If your institution does not have a colloquium series, start one!
There is no doubt that publishing a paper is a tremendous thrill for an undergraduate student. However the process of writing a paper is also of significant value, whether or not it leads to a publication. It is beneficial and important to include students in all stages of the process from the first draft of the paper to the final version that appears in print. Students should be asked to contribute to all aspects of the paper, from the abstract to the conclusions. This will require careful mentoring and many drafts. If the paper is not suitable for publication in a regular journal or undergraduate journal, consider formalizing the paper as a technical report with your university. If the paper is suitable for publication, explain the choices, risks, and rewards when considering where to submit the paper, and have students help make the final decision. Share the referee reports and include students in the revision process, the resubmission process, and ultimately in the final approval of galley proofs. Students will derive a great sense of accomplishment through this experience, and they will gain skills that will be important in most any future career.
The panelists’ original presentations or presentation notes are linked below.Sarah Spence Adams: (1) Purposes for doing undergraduate research, and (2) Finding students to do undergraduate research.
Rebecca Garcia: (3) Good research problems for undergraduates, and (4) Logistics of an academic year undergraduate research program.
Rick Gillman: (3) Good research problems for undergraduates, and (4) Logistics of an academic year undergraduate research program.
Darren Narayan: (3) Good research problems for undergraduates, and (5) Student presentations and written report/paper.
Daniel Schaal: (2) Finding students to do undergraduate research, and (3) Good research problems for undergraduates.