Draft of an Undergraduate Research Philosophy

I am working on establishing a sustainable undergraduate research program. I want to record some ideas that I have here.

First, I think that this might mean a shift toward searching for problems that undergraduates can understand the research question. This is actually pretty close to what I have been doing anyway, although I hope to more consciously seek out easily-understood problems. I had lunch last weekend with Andy Rundquist (#brag), and he told me that he changed his research focus so that it would be easier for undergraduates to work with him. Fortunately for me, he did this in part because of non-academic considerations (lasers are expensive), but I understand that his main focus was to allow students to work with him immediately after their freshman year. I still will study group theory, although I will see if there are questions that students could quickly understand after just having had one or two semesters of calculus. In particular, I might start learning something about finite fields, which I think could be accessible (it is just like the real numbers, only there are only a finite number of points!).

If I can find good questions (that is part of my goal for my sabbatical next spring), then I would like to form a research group. I hope to work with several students at once. The model I have in mind is that each student will work on solve the research question for a specific case—likely a specific family of groups. The students will be able to talk to each other, since each knows the question being asked, although not every student will know the structure of each, say, particular group.

Essentially, these students would be working on the examples that I would do myself if I were trying to solve the problem on my own. After the students complete their work, they perhaps write a thesis on the problem and I see if I can use their work to solve the entire problem.

This gives students a chance to do undergraduate research, gives them a chance to do it in a more collaborative manner (they get to work with a research team), and it gives me a chance to kill two birds with one stone—the undergraduate research is actually supporting my own research, so time spent with undergraduates is really time spent on my own research.

Do you have anything thoughts on this model? Do you have any alternative models for undergraduate research that work?

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11 Responses to “Draft of an Undergraduate Research Philosophy”

  1. suevanhattum Says:

    It sounds fun.

  2. TJ Says:

    This is a reasonable way to handle this. You want things to mesh together nicely. Give students something they can do, _and_ make sure that it is useful in some way that they can understand. Computing explicit examples and handling special cases is a good way to start.

  3. Dana Ernst Says:

    This sounds great! I love working with a small research group. Most of my experience mentoring undergraduate research has been with groups of 2-3. Most of the time the group works on the same problem, but I’ve also carved up the problem I had in mind into separate chunks for individuals to work on. I recommend being flexible with regards to this. You might think it’s a good idea to split the problem up, but after you get the students working, it may be more natural not to. The reverse is also true.

    My impression is that most undergraduate research experts suggest not having students work on your pet research project. However, so far this has worked great for me. As I’ve gained more experience, it’s been easier to branch out and try new things.

    Nearly all of my undergraduate research projects have involved the combinatorics of Coxeter groups. To date, roughly half of my students hadn’t had a class in abstract algebra prior to beginning research. I just teach them a good chunk of what they need to know and then we get to work. In order for this to go well, I want to work with students for two semesters. I can’t get a student up to speed, have them discover something cool, and get them to write stuff up in one semester.

    • bretbenesh Says:

      Thanks, Dana. I hadn’t really considered not splitting up the research problems for each student, so I thank you for (once again) giving me alternatives to consider.

      I am also not yet certain that I can support both an undergraduate research program and my own research at the same time (at least, not if I am also teaching and doing service). So I think that students will have to work on my pet research project by necessity (either that, or my undergraduate research projects will become my pet research project). I hope I am wrong about this, but I don’t think I can become efficient-er (it’s a word!) enough to carve out enough time for both; it makes me happy that you have had success with this.

      For your students who have not had abstract algebra: how much abstract algebra/combinatorics do you need to teach your students to get them to a place where they can work? I guess I am asking for what specific topics they need to know before they can do individual research.

  4. Undergraduate Reseach: Jump Before Looking | Solvable by Radicals Says:

    […] « Draft of an Undergraduate Research Philosophy […]

  5. Joss Ives Says:

    I think a really important point here is that you will be building off of their research, meaning that the work they do has an authentic audience (as opposed to being something that they could perceive as busy-work)

    • bretbenesh Says:

      I agree. Fortunately for me, this research team is completely voluntary, so I hope that they threaten to quit if I do not do a good job of this.

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