By Sarah Adams, Rick Gillman,
Externally or internally funded Research Experience for Undergraduates (REU) programs offer students the opportunity to work with faculty on unsolved problems and can serve as a highlight of their undergraduate career. The overall goal of these formative programs is that students and faculty have an enjoyable experience as they investigate the horizon of knowledge. However, there is a question on how much a program should focus on research and how much emphasis should be placed on the experience. In the end, both aspects should be given considerable weight.
While research is clearly a fundamental part of an REU program, there is sometimes a question about the level of research that students should undertake. Some problems are genuinely difficult, while others are trivial or routine from the faculty perspective. In either case, students should also experience the highs and lows that occur in the step function of mathematical research. An essential part of the learning experience is for students to struggle and overcome obstacles. It might seem ideal if students have an incredible summer where they routinely solve the problems they are given. However, one cannot help but wonder what might happen to these students when they hit their first road-block while working on their dissertation or on the job. Learning to persevere in the face of steep challenges will engender success in graduate school and beyond.
It can be difficult and risky for REU directors to choose problems that will allow students to achieve new results while also allowing them to experience some challenging set-backs along the way. For example, last summer the graph theory group in the NSF-REU at Rochester Institute of Technology worked on a generalization of vertex coloring. Since the solution was straightforward for some families of graphs and NP-complete for all graphs, they had a wide range of problems to choose from. Instead of choosing a problem that they knew the students could solve, they chose a problem that they knew would be difficult. This group of three students and two faculty mentors struggled together for nearly six weeks before arriving at the solution. This approach carried some risk, since failing to solve the difficult problem would have meant sacrificing time that would have likely produced a stream of smaller results on easier problems. A set of small results can also lead to a publication, but it would not necessarily provide a challenge and an opportunity for the students to grow. Fortunately, in this case, the larger risk paid off with a larger reward – publishable results and a realistic, challenging experience.
There is no doubt that publications and conference presentations are valuable, concrete outcomes from REU programs. From a faculty standpoint, these items serve as benchmarks when one is applying for both external and internal funding. From a student standpoint, many enter REU programs hoping to walk away with a publication and with the opportunity to present their results on a national stage. Not only can these become capstones of a student’s experience, they can be substantial additions to their resumes as they continue to graduate school, industry, or government.
It is important to realize, however, that although a project can lead to research publication(s), the role of the student often becomes diminished after they leave the program. Although the research towards a publishable paper occurs during the REU, the final editing, communication with a journal editor, and revision process usually falls to the faculty mentor. Whenever possible, we recommend including students in these stages, however practicalities often hamper student involvement after the program officially ends.
Students do not necessarily have to publish their work to have a beneficial experience. However most REU sites require their students to write papers and to learn LaTeX with some level of proficiency. The rationale is that there is considerable value in the process of writing a paper, even if it does not result in a publication. As part of this practice, students learn how to organize their results and present them in a precise and coherent manner. Writing will not only allow students to appreciate their results, but also see the general context into which their contribution fits. With or without a publication, students are often empowered through this experience, and this stays with them well beyond the program.
Analogously, even if presenting their work on a national stage is not practical, most REUs require participants to do some public speaking, and we advocate that home institutions provide venues for returning REU students to speak about their work. Through this experience, students become adept at explaining what they have done and better prepared when a graduate program director or potential employer asks them about their research. Developing written and oral presentation skills have tangible benefits for students, particularly when the REU program attends to them carefully. Participants learn to communicate their ideas and results clearly and concisely – a skill that they will need whatever career path they choose.
While these experiences of conducting research and writing up and speaking publicly about results or knowledge gained are well-regarded cornerstones for a successful REU program, the less tangible benefits of REU programs are equally important. For example, the social benefits of REU programs can be significant. Many directors have noted (for example, see ) that social activities, such as weekly movie nights, group lunches, or rafting trips, are integral parts of a successful student experience. If one goal of an REU is to encourage students to pursue further mathematics, we need to ensure that students have fun during their summer experiences. For some students, their REU provides their first opportunity to be surrounded by like-minded students who also love and excel at mathematics. Students develop friendships and relationships with each other and with their mentors. These relationships serve as a valuable network as they progress through the remainder of the undergraduate career and beyond. Students in REU programs often keep in touch after the program to discuss graduate school programs and potential job possibilities. There are several cases where REU participants later become REU directors, as they strongly believe in the myriad benefits of these programs.
The format and goals of an REU program largely will depend on the students and faculty involved, and in the end, success of programs should be gauged on how well we meet our stated goals and our students’ expectations. We support the idea that the portfolio of REUs available nationally should reflect a broad range of goals, including some REUs focused more heavily on research and others focused more heavily on the experience. No matter where their REU falls on this spectrum, it might be the case that students remember the E even more than the actual R when reflecting on their REU experiences. Thus, while choosing appropriate research problems will remain an integral part of the REU director’s job, directors must also consider how they will help students navigate through the ups and downs of research, how they will coach their students in writing and presenting, and how they will facilitate the development of meaningful relationships with and among the students. Above all else, it is hoped that REU programs will continue to instill a love of mathematics and a thrill of discovery in the next generation of mathematicians.
 J. Gallian, The Duluth Undergraduate Research Program, Proceedings of the Conference on Summer Mathematics Research Programs, American Mathematical Society, J. Gallian Ed. (2000) 163-168.
Sarah Adams is an Associate Professor of Mathematics at the Franklin W. Olin College of Engineering.
Rick Gillman is the Department Chair and Professor of Mathematics and Computer Science at Valparaiso University.
Darren Narayan is a Professor and Director of Undergraduate Research in Mathematics at the Rochester Institute of Technology.