Summer Research with Undergraduates Plus Fun

Sam Kottler, Garrett Figueroa, Jerrell Cockerham, Hanqui Li, and Zhaopeng Li, standing on the shoulders of giants at Colorado State University.

I had my first-ever summer research students this year: sophomore Jerrell Cockerham and senior Zhaopeng Li worked together on a problem about row complete Latin squares, and senior Sam Kottler is working on a cool project in locally recoverable codes. They have all done very good work, and it has been fun for me, too.  I met with the students most days for five weeks, and they’ve written up their results, which I hope will find their way into published papers sooner than later.  I like my students and it was really worth it. It was also a lot more work than I had anticipated.  “What a deal! They’ll work on my research problems and learn a lot, and I’ll get the answers I want,” I thought. “I’ll meet with them each a couple times a week for an hour and I’ll get so much of my own research done in the rest of the time.” Indeed, they did work on my research problems, I think they learned a lot, and they did figure out some very nice things.  Sam is still working I have a good feeling that he will prove even more.  But the fact is that I worked really hard, didn’t get anything of my own done during those weeks, and I still felt like I wasn’t entirely keeping up as a research mentor.  Where did all that time go? I still don’t know.  I do know now that a couple times a week is probably not going to work when undergraduates are learning a whole new area and learning how to do research for the first time.  I also learned that it’s really hard to motivate myself to read drafts and make good comments when I just finished an intense bout of teaching. Next time I’m going in with my eyes open, and I’m taking a few weeks off between classes and student research responsibilities.  That said, I think it was a success, and I thought I’d share a couple of non-research activities that we did together that were really fun.

One of the best things I did with this group was to organize a lunch for all the research students in the department and their mentors, so everyone could talk about their progress and just hang out for a while. This was pretty fun. It was the first time that many of the students had tried to describe what they were working on to anyone else. As we all know, this can be really challenging, and it was cool to see them struggle with it and figure out how to tell the story. One of the mentors practiced a conference presentation on us, based on work that had been done with a student, and the students seemed to engage and be able to see themselves talking about their own work in the future.

Another fun activity: with some of the other research students from Colorado College, we took a field trip up to Fort Collins and met with undergraduate research groups at Colorado State University led by Rachel Pries and Patrick Shipman.  The students got to meet each other and again share what they were working on and hear about what it was like to study at a totally different kind of school.  Both CSU groups were doing really interesting things—studying curves related to coding theory for one group, and modeling a chemical/physical process using differential equations for another.  We had a lunch with everyone together, visited the dynamical systems group’s lab, and then met with the staff member who runs parts of the graduate program. The students had plenty of questions about the graduate school admissions process and some were interested to hear that yes, a teaching or research assistantship usually covers your tuition and a living stipend.  We met with the wonderful Research Scientist Elly Farnell, who told us about her work in the Pattern Analysis Lab and gave the students another chance to talk about their own research projects. Not only is her work fascinating, but somehow talking to Elly the students really hit their stride in their own exposition.  Having heard them talk about their work many times, I was silently cheering as they gave their best explanations yet.  Made me hope that my talks just get better and better as I give them, too.  Our final stop was visiting with my old friend, CSU Statistician Ben Prytherch (sharing his music page because why not), whose enthusiasm for his subject is infectious.  He asked the students what they were working on and explained a few of his favorite statistical ideas/techniques. At one point he said, “Oh, let me just make a quick applet for this,” and he whipped up some visualization with a sliding bar. Again, the students had lots of questions, and Ben was an amazing stats ambassador. Overall, it was a great experience and the students came out a little more connected to students and faculty at another regional school, and enthusiastic about research and maybe about graduate school. I am really grateful to everyone who took the time to hang out with us at Colorado State.

Back to work for me!  Let me know if you are doing any fun summer research activities in the comments.

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How I’m Spending My Summer Vacation

I’m editing. It’s hell. I haven’t looked at these papers in…awhile, and they’re hot messes that I can’t even believe I’ve showed to other human beings. But they’re getting better. Slowly. They can’t get published sitting on my desk.

I’ve got a new class starting Tuesday, one I’ve never taught before. It’s one of our Masters-level electives for inservice teachers: Calculus for Middle School Teachers. I have no idea how this one’s gonna go, but I’m excited, except for the part where it starts at 8am and lasts until lunchtime.  I’m sure you’ll hear more about it next month.

I’m also ripping apart my digital piano again. Just needs a little more sanding on one of the pins. This time I really think I’ve got it.

But I’d rather talk about something more recreational. I’m sure somebody must have taught me compass and straightedge constructions at some point in my life, but I don’t really remember it. As a young person I didn’t have this awe of the beauty of Euclidean constructions that mathematicians are supposed to have, and mostly was just annoyed with two column proofs like most other 15 year olds. I might’ve encountered them later on when I took a geometry class, but that was just to pad out my credits and I’m embarrassed to say I never devoted much energy to it.

At some point I ran across Euclid the Game, developed by Kasper Peulen, and completely fell for it. It uses a web-based Geogebra interface to guide you through a number of Euclidean constructions, more or less in the order they occur in Elements. Once you develop a construction, like an angle bisector, it adds it to your toolbar for future use, just like Euclid intended.

I know I’m a total sucker for gamification, but I think this goes beyond that: just laying out these constructions in an easy-to-follow, step by step, mistake-friendly way helped me to unlock the beauty and fun that others had found more obvious. If you find yourself teaching a geometry class, I can’t recommend this highly enough.

This is going somewhere, I promise. I visited my mom a couple weeks back. Her wife is a talented folk artist and quilter, and every once in awhile I get called in as a mathematical “consultant” for one of their projects. Lately she’s been making barn quilts and had an idea for a new one on an old salvaged sawmill blade. Could I figure out a way to reproduce this eight-pointed star design on the blade? They had a compass, but apologized for not having a protractor.

I almost felt like I was being set up. This was too perfect.

8 pointed star laid out on a sawblade, with compass and straight edge

Nailed it.

So there you go kids: when are you gonna use compass and straightedge constructions in real life? I used ’em on vacation in my mom’s garage. Get on my level.

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One thing I learned from Calculus, this time around

Turns out that this story actually doesn’t have anything to do with anything Erdos or Darwin said.
Erdos Photo by Topsy Kretts – Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=2874719.

Darwin photo from Public Domain, https://commons.wikimedia.org/w/index.php?curid=3560761

 

 

 

 

 

 

 

 

 

 

This blog post is about how I gave an assignment that I regret and am embarrassed about. It all starts four years ago, when I gave my Calculus II students a review assignment in which they were supposed to solve calculus problems to earn letters for a key to decipher some quotes, which had been encrypted using a simple substitution. I looked for math-relevant quotes on the internet and had found the following:

“A mathematician is a device for turning coffee into theorems.”

“A mathematician is a blind man in a dark room looking for a black cat that isn’t there.”

The first was credited to Paul Erdös, the second to Charles Darwin.

This spring, I dusted off my old assignment.  At first I couldn’t find my original key, so I had to solve the cryptoquips myself.  I recognized the first quote as soon as I got the word ‘mathematician’.  The second I didn’t remember at all, and had to work out again.  As I remembered the second quote, I felt uncomfortable.  I realized that since the first time I gave this assignment, I had read a lot more about the idea of ableism—bias against people with disabilities.  I was not sure that it was okay with me (or with others) to use the word ‘blind’ in this way.  I have read that the term blind is correct and not offensive in referring to the condition of not possessing vision.  It is potentially offensive to use the term to indicate a condition of ignorance. Some people point out that the word blind has many meanings, only one of which is sightlessness; I can see what they’re saying, but my rule is to try to avoid any words in my own speech and writing in a way that I know could hurt someone, even if other people think the words should be okay.  In my interpretation of the quote, the man is supposed to be blind, as in physically not able to see.  However, the man does not actually exist; the quote in its larger structure is a metaphor, which uses blindness to describe something else entirely.

As I said, I felt slightly uneasy when I read the quote again, but at the time I didn’t fully work this reasoning through. I was in a hurry, and I trusted my past self, so I decided that this use was okay. I wanted to make sure that the quotes were actually correctly phrased, though, so I did a (very) little Googling. I learned that the coffee quote probably wasn’t from Erdös at all, but his fellow Hungarian mathematician Alfréd Rényi.  Ha, I thought, I will make that part of the assignment!  I will ask the students to do some research and figure out if these are real quotes and are correctly attributed!  This will be good practice in always carefully sourcing any quote you use. (I cringe now reading this thought.)

After I passed out the assignment, I started thinking even more about the second quote. I did my own assignment and started investigating more.  It turns out, the second quote was also misattributed. On Quote Investigator, I learned that the second quote has a long history, and is descended from one that involves racist language/images. The Quote Investigator entry has a trigger warning at the beginning. I thought, wow, this quote was a terrible mistake.  I didn’t make this assignment so that the class could discuss the power of language for good and ill, racism, ableism, or the problematic history and culture of mathematics. My Calculus II students are not likely to have been at all interested in ‘mathematician’ as an identity, and there was no reason at all to use either of these quotes to begin with.  What was I doing, sending my students into this complex terrain, when all I wanted them to do was practice their anti-derivatives? Especially when I had no idea how to unpack the whole thing? I now really regret using the second quote in class, this time and four years ago.

In some ways, this was a “teachable moment”—a real-life example of how mathematical culture is (obviously) every bit as problematic as culture at large, how innocuous-seeming assignments and utterances can carry enormous baggage, and how well-meaning people can make potentially hurtful mistakes, especially if they try to hurry through and never question their past judgments. As I mentioned, I don’t feel that I have the tools and background knowledge to lead the best discussion on all of this.  But I felt that, tools or not, I needed to say something about the assignment in class. I messed up, and I needed to acknowledge that.

I gave this assignment out on Monday.  On Wednesday, the last day of class, I told my students that I was sorry and why.  They didn’t have anything to say about it. Except one student who asked, “Are we still going to get credit for doing the assignment?”  I said yes, and after waiting a while to see if anyone wanted to talk more, we moved on to Lagrange Multipliers.  From the response, it seems possible that none of the students found the assignment offensive or distracting, and probably nobody would have brought it up with me if I had just kept quiet. However, I don’t think that would have been the right thing to do. In my classroom, I have power. I am the expert, I give the grades, I get to decide what is okay, and I choose what I/we talk about.  I could tell myself, “If nobody brings it up with me, nobody was hurt, no harm done.” But that ignores the real power imbalance in the classroom. Since I am in the professor, students would likely not feel comfortable telling me that something I said hurt them. It is hard to speak up. If I can’t bring myself to admit mistakes and speak frankly about difficult things, how can I hope that my students will find the courage to do this, or to tell me when I am wrong?

I feel that it is my job to manage the classroom climate and call out disrespect. If a student said something I viewed as potentially hurtful in my classroom, even/especially to another student, it would be my job to identify that as unacceptable, whether the other student spoke up or not.  This is actually my number one job, as a person, much more important to me than teaching mathematics: in any situation where I have power, I must use that power responsibly.  Whether or not any student in this particular classroom was bothered by the assignment, I was bothered by the assignment, which is proof that it had the power to hurt. Therefore it was my job to speak up.

I have told a couple people about this experience since it happened.  Honestly, nobody really seems to know how to respond to me. I can’t tell if people are appalled that I ever thought that quote was okay, or if they think I’m being ridiculously politically correct, or if they think I am moralizing about what they should do in their classroom. I guess the fact that the same thing could provoke any of these reactions shows how complicated this terrain is. After thinking about it for a long time, I came to the conclusion that using the quote was not right. Now that I see it that way, I can only respond from that place. I am not saying that everybody has to see it that way or else be a bad person.  I am just doing my best to do what I think is right.

That assignment wasn’t what I wanted my students to remember about Calculus II.  But it is one thing that I will not forget about this class. The math classroom does not exist in a vacuum, and of course we need to reckon with the same issues as the larger culture.  For me, right now, that means re-examining everything—including old calculus assignments.

Thoughts? Ideas? Please share in the comments.

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