Rereading Noah’s graduate school advice post, I realized I’d forgotten to stir up trouble at the time about his comments on REUs. In part, one should understand this post as an attempt to goad him into explaining.

First, a little personal history. I’m basically the poster-child for REUs; doing an REU in the year between my junior and senior years was the only organized math outside of school I participated in before grad school, and was the only experience with research I had before grad school, essentially. I had an excellent relationship with my advisor from the REU, met several people I liked a lot, did good enough research to turn it into a solo paper (admittedly, several years later), and generally had a really excellent experience. I’ve always recommended REUs to students, especially if they were considering grad school.

This has always seemed like a no brainer to me. If nothing else, since an REU is essentially the only real chance that an undergrad has to test drive grad school before committing years of their life to it. So, I’ll admit, I was a little surprised to find out that “REU-hater” is a category of person that exists. And now I’m curious; are there any more of you out there?

15 thoughts on “REUs

  1. A large part of it is just a cultural thing. Arnold Ross was strongly opposed to REUs. Counselors at the Ross program are necessarily people who are doing something other than an REU with their summer, so it’s not surprising that they’re less inclined than a random person to like REUs. Furthermore, the culture of Ross while I was there valued the inherent quality of math over original research or problem solving. Basically all this is to say that my opinions of REUs should be taken with a grain of salt as it’s more something that’s part of my identity than something I’ve thought through deeply.

    That said my opposition to REUs is less that I think they’re bad as that I disagree with the NSF’s pushing of research for undergraduates to the exclusion of other opportunities that would also get people interested in math and that I think graduate admissions committees emphasis (perceived or real) on REUs is misguided. I would prefer that original research was only one model competing with similarly well-funded opportunities for exploring top quality (but not original) mathematics and with better funded opportunities for teaching highschool students. I would strongly prefer that students not feel like they have to do an REU in order to get into graduate school.

    I’ll also say that my impression has been that an REU is not an accurate model of grad school and hence isn’t useful as a test-drive. But since I’ve never actually been to one I can’t really disagree too strongly with your experience on this point. We’d need more anecdata.

  2. I’ll also say that my impression has been that an REU is not an accurate model of grad school and hence isn’t useful as a test-drive.

    Obviously, it’s not exactly the same as grad school, since it’s so much shorter, but it certainly has much more the same flavor than being a counselor at a math camp. One is fundamentally a research experience, the other I think of as more a teaching experience.

    Now both of those are important components of being a mathematician, but I think research experience is much harder for students to get through other channels than teaching experience, which I think is a real and serious argument for doing an REU.

    On the other hand, there is a certain bizarre aspect to such a program. Someone at the NSF at some point decided REUs were a good idea, and somehow their existence was decreed. One could certainly imagine some completely different model for how undergraduates should spend their summers coming to the fore, and taking over rather suddenly if it had the imprimatur of the NSF.

    Of course, if you have ideas, I’m sure the NSF would love to hear them. You’ll have to finish your NSF postdoc first, but after that, you can apply for a CAREER grant and get gobs of money to do your own thing.

  3. One of my issues with REUs is that in general they tend to focus on the advisor’s, rather than the advisee’s, interests. While this makes some sense—after all, what does an undergraduate really know?—it is in conflict with my philosophy of working on things you find interesting.

    In one of my own REUs I was practically handed a problem and expected to work on it, even though I did not have an understanding or an appreciation of the context from which this problem had emerged. Needless to say I made pretty much no progress on the problem; I think part of the reason for this was that I did not grow to care about the problem (still don’t care about it, in fact).

    That said, not all REUs are bad. I have had a very enjoyable, although perhaps nonstandard, REU where I was part of a group and our duties consisted of independently working through a couple of textbooks and then taking turns giving seminar-style lectures on what we had learned. These seminars would be attended by our advisors and some of their graduate students, who would interrupt us with questions, ranging in difficulty from trivial to unsettled. The questions we could not answer during the seminar were compiled and we were encouraged to think about them later. The nice thing here is that you choose which question(s) you want to think about, if any. This, in my opinion, is much better than being handed a problem and forced to look at it.

    For me this REU was a very productive use of my time. Even if you don’t get to solve an open problem, you at least learn how to give better talks, think on your feet and communicate mathematics more clearly.

  4. I have the same sort of background and biases as Noah on this issue.

    Obviously, it’s not exactly the same as grad school, since it’s so much shorter, but it certainly has much more the same flavor than being a counselor at a math camp.

    My counselor experience actually felt very much like graduate school. We spent a lot of time thinking about math, exploring questions that seemed interesting to us, organizing our own seminars about advanced topics, etc. I’ve never been to an REU, so I can’t compare them, but when I ended up in grad school it felt like a natural continuation of my summer experiences (as opposed to my undergraduate experiences).

    One thing that bothers me about REUs is that they often end up imitating what I’d consider a problematic model for research: someone much more knowledgeable than you gives you a specialized research problem they feel should be tractable, and then they guide and encourage you as you work on it. I know some REUs do a much better job than others at coming up with good problems and motivating them for the students, and it’s hard to make any other approach fit in a single summer, but I just don’t really like this way. It doesn’t sound like much fun to me, I doubt it gives a good picture of what life is like as a mathematician, and I don’t even think grad school should work this way (although it often does).

  5. I suppose someone should say it:

    In one of my own REUs I was practically handed a problem and expected to work on it, even though I did not have an understanding or an appreciation of the context from which this problem had emerged.

    This actually sounds like a pretty accurate model of the way some people describe their grad school experience.

    More seriously, I have no experience with REUs from either side, but I always thought they sounded good in principle, mostly as a tool to help students decide whether grad school might be a good option for them. (And I know some people who did REUs and felt they were good in that way.) I’m not sure I believe an REU needs to be an accurate model of grad school to do that,
    and I don’t think most people running REUs think of them as a test-drive. Rather, they give students some experiences that are complementary to a lecture-course-oriented undergraduate program.

    The actual format and the emphasis on serious original research (as opposed to seminar-style lectures, problem solving, and exploration) seem to vary quite widely between different REU programs. Probably they also vary from year to year at individual institutions, depending on the advisors.

    Finally, I take issue with Noah’s implication that REUs are meant to “get people interested in math”, since the people running them assume the students in math REUs are already interested in math. I strongly agree with him, though, that there should be more support for other alternatives.

    As I said, I have no direct experience with REUs myself, so everything I said that sounds like hearsay or speculation is exactly that and should be salted accordingly.

  6. I don’t even think grad school should work this way

    To the contrary. Graduate school should work something closer to that model, albeit with a little more flexibility.

    A student masters the foundational material and learns about some areas of personal interest. An advisor within that area suggests an array of problems known to be interesting, and the student picks one to work on. The alternative, where the student is self-motivated from the beginning, has a significant risk of ending with the student specializing in problems that the community as a whole isn’t interested in, which works strongly against his future career as a mathematician.

  7. I’ve heard the argument both ways. Here’s my best attempt at accounting for the anti-REU position (which I find credible, but not my own final position).

    An REU, by design, sets students to work on a problem which is specially designed to be solvable in a few months with relatively little background. A non-careful student (and here’s where my faith in the argument breaks down: the proportion of non-careful students in these programs) might reach the following conclusions from the experience:

    a) I don’t really need much background to do mathematical research,

    b) Solving a research problem takes longer than solving a homework problem — perhaps even two or three months, but not more, and

    c) I am already an expert in the field of my REU research, and so would do better to concentrate my graduate studies there.

    Conclusion a could theoretically be a severe drain on student morale (already at a low) during the first year or two of graduate school, when most students will spend most of their time building necessary background. Conclusion b could theoretically be devastating on student persistence to degree in graduate school, when it takes more than six months to solve a problem. Conclusion c could simply be an annoyance by steering students into a weird collection of specialties.

    I know people who say they have seen the problematic effects of a and b among their graduate students. They tend to be the most heavily opposed to REU’s, and with pressure on many programs to control their attrition, I can’t say I blame them.

  8. When I was an undergraduate, I spent the summers after freshman and sophomore year teaching bright high school kids, and the summer after junior year at an REU. The teaching was fun and a good experience, but the REU played a critical role in my mathematical development.

    In the REU I was assigned to two research groups. The first was lame and I spent as little time on it as possible. The second was great. In fact it was years before I had another research experience that was as succeesful as what I did at the REU and in its aftermath. Indeed most research requires more background, but I didn’t have any illusions about this.

    I was doubtless kind of lucky in finding an REU that worked well for me. Still, I find it unfathomable that some people try to write a PhD thesis without any prior research experience. Doesn’t it seem like a good idea to have some easier research experience first, even if it is not with the most interesting problems?

  9. I had a rather successful summer research experience early in my undergrad career, and I think this altered my expectations so that I fell into Wesley Calvert’s group b for a while. I did some research projects with nominal faculty guidance for the following two summers, and was rather disappointed with how little I had managed to accomplish. Of course, it didn’t help that I had chosen the latter two projects by looking at web pages with lists of open problems.

    During the last summer, my mentor didn’t really like the project I had chosen, and suggested an alternative project that wasn’t original research. Somehow, I had gotten it into my head that moving away from open problems would be a waste of time, even though (with several years’ hindsight) the reading project he had proposed was really great.

    I might as well share a sketch of it for others who are looking for reading problems. It was basically a program to learn some tools necessary to understand the homotopy type of Diff(S^3), i.e., learning to read some of Hatcher’s proof of the Smale conjecture. It was pretty rich in topologically useful topics, like the long exact sequence of homotopy groups for a Serre fibration, Cerf’s birth-death theory, etc.

  10. Don’t lots of students entertain a) and b) anyways? I see the logic in your argument, but at its root it seems like a pretty strange notion that we should worry about students at REUs being too successful, and thus becoming overconfident. First of all, does this really happen? I mean, I don’t think I really took a rosy picture of what research is like away from my REU experience, and I was pretty successful.

    Also, I feel like the same could be said of almost any intervention to help students learn:

    “If you teach them graduate clases, they won’t learn how to get information from the original literature, and will just get frustrated when that’s their only option.”

    “If suggest problems for them, they’ll never learn that coming up with problems is hard.”

    “If you tell them which papers to read, they’ll think that there aren’t any other sources they should read.”

    It’s true that one has to strike a balance between helping students, and letting them do things on their own, but I’m not sure I believe REUs as an institution are way over the line.

  11. In Canada, there is a bit of a different model for undergraduate student research (and a different name – USRA). It tends to be more one on one with a professor, whereas in the US, my impression is that REUs are more team based.

    I did a couple of these Canadian USRAs and while they were fine, my guess is that a team-based approach might have been better. In a group, it seems like there would be more opportunity for exploration, rather than just being handed a problem from up high (namely the professor).

    Is it true that many of the successful REUs are team-based?

  12. Off topic: Do any of you know of REU’s that accept non-Americans? I wanted to recommend to some of the brighter undergrads that they apply, and then found to my surprise that the children of people with H1-B visas aren’t elligible (NSF restrictions). But I suppose that a few undergraduate summer programs may have some non-NSF funding too, though I didn’t find any.

  13. continuing the off topic thread — (the on-topic conversation is also very interesting, and I may contribute at some point, although I’m not far along in enough in grad school to say how well my REU experiences prepared me for it)

    Clifton — I know that the Duluth and UW Madison REUs (the two REUs I have personal experience with) have each taken international students at least once or twice in their history. Duluth’s official policy as I understand it is that it will accept international students but can’t offer them a stipend. Some colleges have programs to fund their students to do summer research elsewhere, and I know of one non-American Duluth student who was supported by such a program. I imagine that most REUs would be willing to accept an international student with such a source of funding. Madison officially doesn’t take non-American students but did manage to scrape up funding for one the year I was there (I think Jordan Ellenberg had some extra grant money that year). And apparently the Williams REU advertises on its website that it has some funding available for international students.

    The take-home message here is not to suggest those REUs specifically (although I did have good experiences at both the ones I attended — on the other hand, they are some of the more competitive REUs to get into) but just to say that even REUs that officially don’t take non-American applicants may occasionally have funds available to take one and may be open to taking students with their own source of funding. So it may be worth it for talented international students to contact the REUs they are interested in anyway.

  14. I have nothing against REUs, and do recommend them to people, but I don’t see them as a “test drive” for grad school.

    My main concern is not that people will love an REU and be led to grad school for the wrong reasons, but that people will hate an REU and be turned off from math research because of one experience. Any number of things can go wrong: the problem being worked on can be a poor match for the student’s developing tastes or interests; the student social environment can be wrong, or the faculty running the REU can be disengaged or apathetic.

    About this last point. There is a make-work aspect to some REUs. I don’t mean that the research is low impact (it’s undergrad research, it’s not going to shake the world). What I mean is that sometimes it is clear that the faculty involved did not make the REU a priority and threw something together at the last minute. (This would happen in any organized “research experience” program; I’m not knocking REUs specifically here.) Now in grad school, no matter where you go, you connect with people who are not phoning it in, and people who are not haphazardly improvising their contacts with you just to get a line on their CV. The same cannot be said of REUs. Students should be told this.

    Any recommendation of REUs should emphasize that there are many faces of research, and an REU is only one of them— and that there are many faces of grad school, and research is only one of them. In my experience, people do pretty well at marketing REUs honestly, but if there is any tendency away from this happy medium, it is toward presenting REUs as “the” way to math research as undergraduate. I wish this weren’t the case.

    As long as I’m wishing, I wish that people weren’t as single-minded about viewing REUs as a bridge between undergrad and math grad school. This is probably a specific part of the NSF’s mission for the program, so I’m in fantasyland here, but bear with me. In my ideal world, something like REUs exist to give motivated students with strong backgrounds who are interested in math research a taste of what it’s all about, whether they intend to go to grad school in math, or in something else, or not at all. The REU-like program would be not a training camp for academics-to-be, but a sort of evangelist for math research in the larger community. By the same token, this program would not be a default recommendation for students who are considering math grad school, because many just aren’t ready to get anything out of a research experience. (My opinion, based on a very small number of data points, is that students who are weaker on the fundamentals, e.g. because their school’s offerings aren’t up to a grad-school-prep standard, do not benefit as much from an REU as they do from reading courses with faculty on known material that goes beyond the course catalog.)

  15. “In science, I gather, a young student fresh from his First in the Tripos can really share in the work of one of his seniors in a way that is useful to himself and even to the subject. But this is not true of the man who has just got his First in English or Modern Languages. Such a man, far from being able or anxious (he is by definition no fool) to add to the sum of human knowledge, wants to acquire a good deal more of the knowledge we already have. He has lately begun to discover how many more things he needs to know in order to follow up his budding interests; that he needs economics, or theology, or philosophy, or archaeology (and always a few more languages). To head him off from these studies, to pinfold him in some small inquiry whose chief claim often is that no one has ever made it before, is cruel and frustrating. It wastes such years as he will never have again. . . “

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