Math research is cool.

August 1, 2008 at 1:45 pm | Posted in conference, life, math | 7 Comments

This summer of 2008, I took part in an REU, Research Experience for Undergraduates.  It’s the acronym that has stuck for a summer program where talented undergraduates work with a Mathematics professor on a research problem.  The Potsdam/Clarkson REU has been running for about 11 years now. This is my first time doing it. The professors here who are involved with it find it a good way to stay active in research in a school with such a high teaching load. (The current 24 credit per year teaching load is being reduced to 21 credits per year, with plans to further reduce it to 18. But recent changes in the state government make me wary of being too optimistic.)

I was very apprehensive going into this. Actually, I was downright nervous. Finding a tractable research problem for myself is enough of a challenge, but finding one appropriate for someone with an undergraduate background, where they could learn enough of the area to understand and make progress on the problem, seemed an incredibly daunting task. Nevertheless, people do it. There are REU programs all over the country, so surely it can be done.

I prepared for this in a few different ways. I talked with professors in the department who have done it in the past. We talked about selecting a problem, getting the students up to speed, managing the group dynamics, etc. Also, I attended an excellent workshop at the spring 2008 meeting of the MAA Seaway Section by Francis Su of Harvey Mudd college. He has been doing research with undergrads for years, and he really broke it down and made seem manageable.

My biggest obstacle seemed to be how to get the students up to speed and actually working on the problem quickly. Do it too quickly and they won’t have a good sense of the context or a deep enough understanding of the problem. This could lead to initial attempts that are overly naive, or a lack of motivation. Do it too gradually, and too much of the eight weeks is taken up by learning background before they even start the problem. This could lead to a drain on the initial excitement and enthusiasm of starting the REU, enthusiasm that should be harnessed, not squandered. After all, research is hard. There will be frustration enough.

I decided on the essentials they needed to have, and to avoid too much of me lecturing, I assigned them mini-presentations in the first week. We met for the first time on Monday, and at the end of the afternoon session, I gave each student (there were 3) the equivalent of a short chapter to read, learn, and present a 10 minute talk to the other 2 students and me. It was not a formal presentation, they would not be judged on their speaking style or anything, and if they got stuck we would help them through it. It was understood that this was new material to them and they weren’t yet expected to speak as an expert, but they should attempt to do as thorough a job as they could in the time given. This was assigned at the end of our first day, Monday, and they were to present on Wednesday morning. I would be available for questions before the presentations if they wanted or needed it.

I thought the talks went very well. No one ran screaming, and they all took their assignment seriously. So I followed it up with a more in-depth talk, about 30 minutes long, to be delivered on Friday morning. They were doing pretty well by this time, so I assigned topics that, if they understood them, would enable them to understand the main question our research was to be centered on. It worked! The talks went well; they knew from the friendly atmosphere I took the effort to create for the first talk that this wasn’t something they would be judged harshly on, and they seemed much less stressed. They did a nice job, and in the afternoon session of the first Friday, we were able to state the problem in an appropriate amount of detail. I was so happy to be able to get to that point before the first week ended.

A large part of this was due to my having high expectations of them, and communicating those expectations. Also, the talks early on got them involved in learning the background more than if they were just listening to me and reading books and papers. (All these happened too, and were essential.) I think those early talks gave them a sense of teaching each other, collaborating with each other. Whatever it was, I rested much easier after that first week was over.

The rest of it was very good. They made good progress, they got stuck, they got unstuck, they went down dead ends, … in short, they got a good idea of what math research is like. They were also successful in making conjectures, proving some of them, giving a great presentation to the other groups in the REU, and writing a nice paper about it. At this point I suspect the paper is at least worthy of being published in an undergraduate journal, perhaps more. I’ll be reading it next week with fresh eyes after having put it down for a week. One of the students is giving a talk about our results at a national conference in a session on student research this week.

I am incredibly proud of and impressed by these guys. They did a fantastic job, they worked hard and long, they were tenacious and creative, and they produced a nice paper at the end. I’m also very happy with myself that I was able to provide an environment that let them achieve what they did. What a great feeling! This is one of my most fulfilling professional moments ever. I hear that not every experience doing research with undergrads is this fulfilling, but I’m so looking forward to doing it again!



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  1. Wow. What a neat way to teach. After all, teaching is the best way to learn things, so by giving them material to present you gave them an oportunity to really learn it. I wonder if maybe hearing material from a fellow student they learned/listened more too. Plus, no one likes to be unprepared for a presentation, so it gave them motivation to really spend time on it.

    And finally, I find that a lot of people are really uncomfortable giving presentations, so practice is a great remedie for that. It’s like back in undergrad when we were all given free computers as freshman and the profs were told to make sure we used them, so we programed in every class, and most of us became programmers. Imagine a school where everyone had to give presentations in every class, and they all go on to be leaders.

    I like this “mini-presentations” idea so much for training, I’m going to think about where I can apply it in my own “teaching” opportunities.

    I’m telling you, the speed at which ideas are exchanged and take root have gone way up in the age of the Internet. Isolating? I don’t think so.

    P.S. I knew you’d make a great prof. Looks like I underestimated you.

  2. Aw, shucks. (*blush*)

    It is true that you REALLY learn something when you have to explain it to someone else. I certainly learned stuff these past 8 weeks that I didn’t fully understand before. Though that’s not only from me presenting it to them, they taught me stuff, too. If they continue in this area in grad school, I’ll have collaborators! How cool is that!

    Now you know why I haven’t been blogging very much recently. 🙂

  3. See, I want to send a comment to the previous person’s comment, but I don’t think he’ll see it because they don’t get emailed. Pooh, sometimes LJ is better.

    Anyway, if he does ever read it (scd), I’d have to say that I’ve been watching him in “teacher” mode lately as he’s been an integral part of helping me learn some new skills. I’m really impressed at his ability to both sit back and let the student make errors and his ability to jump in with suggestions. His knowledge of when to sit back and let a frustrated student kick something and when to come over and hold the frustrated, upset student’s hand was what impressed me the most, though. There’s a very, very fine line there, and he knows it with me. I wonder if he’s as able to read it with his non-partner students. Anyway, it’s a non-math situation but still very interesting and unusual.

    Other side note – making regular presentations very much helps those who are upset and uncomfortable at making presentations 🙂

  4. I thought there was a way to subscribe to all subsequent comments to an entry you commented on. Anyway, I think scd has me on bloglines or somesuch. Maybe if/when he comments again, he’ll tell us.

  5. I see followup comments via your blog’s comment-RSS feed: feed://

    It contains all the comments, not just those for a single article, but that’s not a problem here, unlike much bigger blogs where it would be drinking from the fire hose.

    WRT learning by teaching, that’s definitely true. When I was in grad school, Dr. Geller (my advisor) had weekly all-hands meetings, for all his students. Every week, someone had to give a half-hour presentation on the status of his work – the rotation generally meant 2 presentations per semester. We would get commentary on our speaking/presentation abilities, not just the content.

    This left me extremely well prepared for the real world. I quickly learned that knowledge is useless if you can’t explain it to somebody else. And I had absolutely no problem when, as an employee of Visix, I was occasionally tapped to conduct training seminars for customers, or to man the company booth at software development expos. (Sadly, I don’t get these jobs at Ericsson. When the company has tens of thousands of employees, it isn’t possible for one person to do a little bit of everything the way he can in a company with less than 50 employees.)

  6. I’m back! And I am seeing your comment Jenny! Thanks for thinking of me. I wonder where he learned THAT skill (the fine line of when to jump in)? I’ll bet he learned it by teaching!

    As for learning by teaching, I’ve done a lot of tutoring (formal and informal) and I can say with certainty that nothing cements your own knowledge, finds gaps where you thought there wasn’t any, and clarifies your grasp of a subject like teaching it does. Plus, as I touched on before, not wanting to look like an idiot can be a powerful motivator. If you just say to a person, “go learn this,” they may or may not do it, but if you say that they have to teach it to others, by golly they’ll learn it, to avoid said idiot likening.

    When I was in graduate school, we had to learn new skills a lot, so we had a mantra, “See one, do one, teach one.” To me, that is leaning in a nutshell.

    As for the mystery of how I get all of the wonderful comments on this site, I do it the old fashioned way. With interest. I just like the conversation, so I come back every few days (usually not on weekends) and check the recent comments and posts. I’ve never gotten into RSS feeds and such. (what is bloglines?) Don’t know how they work and I’m not sure I want to. I’m sure once I get into them, I’ll love them and won’t want to be without them, which in my twisted logic, is another good reason to wait.

    P.S. Thanks for referring to me by my chosen moniker, SCD. Not sure I want to be totally “out there” and my given name is fairly distinctive. Parinoid, probably, but my own parinoia.

  7. Rats. A little birdy implied there might be a new post or comment here. Oh well.

    Hey, I guess there is something new here.


    I will now diliver a monologue…

    WRRRRRRRRRRRRRP. We interupt this monologue, banned by all standards of decency and taste.

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