Constructive Summer

The first week after finishing a class I am usually kind of a wreck. I stress through the end, turn in the grades, and collapse into a heap. Then there’s this weird time when I want to relax and recreate, but I don’t quite know what to do without all the responsibilities of teaching. I dream all semester about having nothing that needs to be done for tomorrow, but when it happens, I feel vaguely anxious and at loose ends. So it was a surprise this summer when that didn’t happen at all (not yet, anyway). I feel great! What was different? I think it was that, instead of determining to do absolutely nothing for a while like I usually do, I scheduled a bunch of research related meetings as soon as teaching ended. This turned out to be a great choice.

Often, serious research just sounds too daunting as I finish teaching. Probably because so much of my math research life involves being stuck. Things are going along okay, until I hit a snag. I think I can fix it one way, it doesn’t work, I try something else, it doesn’t work, and at some point I feel truly stuck. Then there is nothing to do but put it aside for a while. Maybe when I pick it back up I get a new idea, but it’s a little scary to pick it up again because I’m so stuck on it.

I was willing to jump right in this summer because I actually had a few projects on which I wasn’t totally stuck (yet). The first is a collaborative project in coding theory with Katie Haymaker and Gretchen Matthews, which we’d talked about briefly in person but hadn’t had time to flesh out. Gretchen came to visit for few days right after finals week, and starting with this meeting set a great tone for me. All that energy I had been using to grade papers could suddenly go in to math. This was a brand new project, but we were starting with an existing construction and could get going right away by computing some examples. We all brought different backgrounds to the project, so what was basic for someone would be really interesting and new to someone else. By the time we’d done a bunch of examples, we had some ideas of how a paper could work and realized the kinds of things we still needed to work out. Spending several days together got us through the confusing, unsure parts. We got to ask each other questions that would have been hard to figure out alone but were often very easy for the others to answer. We got to a place where we could really start writing up our work and each add some new ideas. Score one for collaboration with great people who know very different things.

Another project I’ve worked on this summer is an expository paper, arising from an email I got a few years ago from a friend’s mom. She was asking a question about passing quilts in her quilting group. This simple question led me to learn a lot about a certain kinds of Latin squares. I’d been thinking about this for a few years and finally had started a paper in the fall (again, with my colleague Katie Haymaker), but we just hadn’t had time to do anything with it for months. By the time teaching ended I was just really looking forward to it. This is my first expository paper, and it is fun to work on because I have found that I can’t really get stuck! There is investigation, organization, and writing, but there is no way to go into a mathematical black hole. Unsolved problems are just another section of the paper. Score one for expository papers.

Finally, I spent several days working on a long-term project with friends in Colorado. I had been pursuing a particular line of thinking for the last year or so, proving small lemmas and inching closer to proving a conjecture that we had made. One of my collaborators did yet another literature search, and we started reading some new papers. We made some great strides in understanding! We also discovered that our conjecture had already been proven by others. This could have been discouraging, but it fact it was great that we found this out. First of all, our conjecture was totally true! Score one for us! Also, I would have spent many more hours following my same line of inquiry, never realizing that we could just move on to the next stage of the project. Of course, that stage is hard, but hey, at least we still have all summer.

Here’s what I’m taking away from all this:

  • Again, I am reminded that collaborations really work for me. They are the most fun way for me to do math.
  • I should always have at least one project that I can actively work on. By “actively work” I mean compute examples, write background, something concrete that doesn’t require me to have some enormous idea to make any progress at all. That way I can always pick up this project when everything else sounds too hard.
  • Expository papers can be a good way for me to organize learning new math. Nobody has agreed to publish our expository paper yet, so it may have no real payoff-towards-tenure, but it was still really fun to write and gave me a great sense of accomplishment.
  • If I can’t figure out what to actually do on a problem, it can pay off to keep searching the literature relentlessly. Maybe somebody has already solved this awful part of the problem.

This has been an excellent math summer so far. However, just so I don’t give the wrong impression that I gave up on my dream of doing nothing productive: I have also binge-read five wonderful novels, watched two full seasons of 30 Rock, and gotten some massive bruises roller skating with my sister. I have still been collapsing into a non-mathematical heap; just for smaller periods. Hooray for summer!

Any thoughts on the best parts of an academic summer, or the best ways to use it?

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Graduation (1 of n)

Many of the Hood College new faculty cohort.

Many of the Hood College new faculty cohort.

The year flew by, and my first commencement as a faculty member is over. We sat in the hot sun in our hotter robes as the Hood College Class of 2016 paraded across the stage. I hadn’t taught many Seniors this year, so most of the faces were unfamiliar, but it was fun watching the students beaming as they shook the college president’s hand. What I didn’t expect was all the students wanting photos with the department after the ceremony. It was really touching to see how much they valued my colleagues time and patience. And luckily the clouds had moved in a bit by then so nobody passed out from the heat.

When our students complete a math course at the 200 level or higher, they receive a button that represents the class. They’re simple and a little corny, but the students love them. A lot of these buttons live on student backpacks for years, and then get worn on their robes or mortarboards at graduation. It’s a nice symbol of the progress they made during their time here, and it really livens up their regalia.

One of our students with her impressive collection.

One of our students with her impressive button collection.

This wasn’t the most productive semester of my career, but I hit a good number of my targets. I applied for and received an internal grant to do summer research with two undergraduates – ambitious freshman I had all year for their calculus sequence. We’ll begin working in June, and I’m sure I’ll be posting about that later. I’ve never guided any undergraduate research projects before, so it will be a learning experience for all of us. I got accepted to some other summer programs that I’m really excited about – one for inquiry-oriented curriculum, and one for developing online interactive resources. I chugged away at a couple of papers and one’s starting to get close to the finish line. I implemented standards-based grading in my graduate class, which was wildly successful with some students and much less so with others. I dipped my toes into helping at my MAA section meetings, and got nominated to a few committees, both on campus and in the wider mathematical world. And I was on a couple of masters student committees. Pretty much checked all the expected boxes for my first year.

I’m thinking about all this not because I’m independently reflecting on my year like everybody says you’re supposed to. We have a short annual report due soon, in which we all have to express our accomplishments as eloquently as possible and explain our goals for the future. It’s not nearly as big an undertaking as a mid-tenure review, and these reports should help me organize myself once that time comes, so I definitely see the value. It’s also nice to see how much I really got done all in one place, especially after what felt like a somewhat lackluster semester. I think a lot of us focus so hard on the goals we didn’t meet that it’s easy to ignore the ones we did. I can’t say I’m thrilled about the paperwork, but I am glad my institution requires us to brag as hard as possible about ourselves at the end of every year.


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Lecture-less Modern Algebra and Foundations, Part II

This semester I decided to move away from the lecture format in my Foundations and Modern Algebra courses. I wrote about this back in March so I will refer readers to my earlier blog post for the reasons and outline of the course. That entry was Part I—the idea and how it looked at mid-semester. It seems like it’s now time for Part II—what it looks like a few days after grades have been submitted, and what I would change and keep on second pass.

THE GOOD. I would keep (with slight modification):

Required before-class reading, reading assignments, and notes. The students were truly prepared for class and ready to engage with material when they walked in the door. I sensed some irritation with the amount of work, but students more often seemed actually happy to be ready for class. It was important that I collected the assignments and checked notes. This got to be difficult as the semester went on, but I would actually be more diligent in checking notes if I did this again.

Blogs. I really worked to sell the blogs to my students by talking about the importance of being able to communicate mathematics, both to their peers and to non-mathematical audiences. Not every blog post was interesting, or even wholly mathematically accurate, but some students really hit it out of the park, and just the effort of considering how to communicate seemed to have an effect on everyone. Many students didn’t know that math blogs existed, and hadn’t thought much about how to communicate about math outside of the classroom, so when I assigned them to read and respond to some pieces by Steven Strogatz, it felt like some students saw math and its possible place in the world differently. I think I would make the posts due every two weeks, instead of every week as I first planned, and I would more reliably set aside a short time for discussing their work. I did this several times but not often enough.

LaTeX and Proof Portfolios. The students did not love learning LaTeX. Some students never became wholly proficient with it, and saw it as a burden to have to write up their work this way. However, most students came to appreciate its capabilities and enjoyed creating really professional looking work. The vast majority of the students made substantial revisions to their old work and submitted very strong portfolios. I was so proud of what they had done! Several students told me that they were also impressed with their own work and seemed surprised by what they were capable of. All I would change is actually putting a little more time into teaching/demonstrating LaTeX in class at the beginning. I gave a brief demo and gave the students a template, but some people did not get the idea on the first pass. I should have made a short assignment due by the end of class one day, just to get everyone working in one place. Also, I used Share LaTeX for the course and it worked pretty well, but I might use the LaTeX sharing capabilities of Sage Math Cloud in the future.

Tests. I decided to keep traditional exams as a component of the course and I am glad that I did. I felt that the tests that were a good combination of definitions, computation, and proof, were not too difficult to grade, and gave students some solid feedback on what they should revisit. The final was cumulative and many students had mastered the material they had missed on the first round. They also were a traditional aspect in a generally non-traditional course, so gave students something familiar to work on.

THE BAD. I would drastically modify:

The homework structure. In both classes, I collected and graded weekly homework. This was reasonable for Foundations, which had 13 students. Grading the homework for my 31-person Algebra class was a Sisyphean task. I could not keep up, no matter how many hours I graded. I returned one enormous stack of assignments only to pick up another. I felt a responsibility to give a lot of feedback, perhaps because I really wanted to help people learn to write proofs, and I was nervous about the new structure of the class. But grading became a black hole that sucked in all my time and energy. It kept me from spending time outside of class doing other preparation that might have been more rewarding for the students. I could have spent more time preparing for discussion about the blogs, or devising mini-lessons on important topics, or meeting one-on-one with students. Or, dare I say, doing research or playing the accordion or just not grading? In the next iteration I will absolutely get away from this homework structure. I think that giving a list of suggested problems with posted solutions is probably the key. I will only collect one or two problems a week from the students, and I will focus on the proofs.

The daily in-class routine. The plan was that the students would spend the class-time everyday working on problems with their classmates. I thought there would be a daily reading assignment, and I would check their notes at the beginning of class. I would then answer any questions that they had about the reading assignment and let them loose on problems. The reading would have prepared them to get started, and I would be there to guide and help them as they worked. This sort of happened, but it sure wasn’t what I imagined. Checking notes every day took forever, so I switched to doing it during group work. However, this interrupted their group work and also kept me busy checking notes when I could have been answering questions and really getting to know my students.

Also, students often needed to just sit and read the problems for a while. It wasn’t really that useful to put them immediately into groups. I also found that the students craved more lecture, more examples, than I had planned to share. Responding to this, I would often end up talking for a long time (I am not always great at shutting up), then breaking them into groups, only to find that the end of class was near. So they didn’t always get to the place where I have found collaboration is most useful—when I have understood the problem, tried it on my own, and found a way to get stuck.

I wish that I had somehow gotten the students to engage with the actual problems before they broke into groups. Next time, instead of having a daily reading assignment, I would maybe try  longer, weekly assignments that the students would work on over the weekend. Imagining a 3-day class week, we would then have different structures on each day of the week. Monday would be a discussion of the reading assignment, questions, perhaps examples. At the end of the first day I would give the homework questions and some kind of assignment that they needed to start on by themselves before the next class. Wednesday the students would work in groups most or all of the time. On Friday, I would really like to have more group work, presentations, and a group discussion to sort of tie things together. I think a weekly routine would have given the class some rhythm.

The way I calculated grades. My syllabus included

  • 30% exams
  • 30% homework
  • 10% blogs
  • 10% notes/reading assignments
  • 10% proof portfolio
  • 10% presentations

There were just too many things to grade! I didn’t have time to be critical on the blogs, so these all got an A for effort. Same with the notes/reading assignments. The proof portfolio was easy to grade and most students did very well, but it seemed to be worth too much in comparison to the homework they had stressed over. The presentations didn’t even happen—there was no time for real in-class presentations, so I changed tactics and had the students create chapter review materials for the final. I would make the exams worth more and merge the blogs and proof portfolio into the homework portion. This would give me more flexibility on how to weigh these. I would keep the notes and reading, and the presentations, but only if I managed to incorporate… real presentations.


Overall, I have mixed feelings about the semester. I liked my students a lot. I believe they learned an enormous amount, more than they would have learned in a lecture class with me. Most of them are now impressively competent at writing proofs. However, I worked an unsustainable amount every week and still didn’t feel that I was doing enough to do justice to the teaching ideas. Some of the students didn’t like the course, and probably didn’t agree with the choices I made. I worry that my evaluations will be lower than I would like.

I will definitely revisit this style of somewhat-flipped classroom in future courses, because it worked. And all of the things I included in the course were worthwhile activities/good ideas. However, I think it was too much for one course. Whatever I do in future semesters, I will certainly do less of it, and make sure there is enough time for everything. I now pledge to carefully consider that every good idea that I include in the syllabus is something I have to design, help with, and grade. I will remember that I can do everything, but that means I will do nothing really well. Why is that so hard to remember? Maybe this time I will learn. Putting it on my calendar now, for future, full-of-good-ideas-and-energy me: reread this in August.



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