Lectureless Modern Algebra and Foundations, Part III: Through the Evaluations and What I Found There

No better way to move past last semester's evaluations than get a chance to teach the class again. I restructured and created some new activities for Algebra this time around. For example, this semester's Algebra class made this awesome color-coded group table for D_4.

No better way to move past last semester’s evaluations than get a chance to teach the class again. I restructured and created some new activities for Algebra this time around. For example, this semester’s Algebra class made this awesome color-coded group table for D_4.

The 10 minutes of the semester when we give student teaching evaluations have repercussions that can last for an entire career. The numbers that these students choose to rate us can become the major or sole metric of our quality as teachers, and can be central to tenure, promotion, and performance-based raises. Many people (including me) have been hesitant to incorporate non-lecture strategies in the classroom because they are afraid of the effects on their teaching evaluations.* Last semester I tried many non-standard and active learning strategies in my Modern Algebra and Foundations classes. My students and I did so many things—including pre-reading, structured group work in class, blogs, and proof portfolios—and I found some struggles and some great successes in the classes (see my previous two posts here: description of the class, and my spring retrospective on how it went). But, the story isn’t complete until I address the thing that people are most nervous about: what happened with my evaluations.

No lying: the numbers were not great. Some of them were not great, anyway. The students rated me highly in many categories, but in at least one course, they rated me medium to low in some of the big ones: uses class time effectively, organizes course effectively, explains class material clearly, and overall quality of instruction. The scores weren’t horrible, but they were well below average, and low enough to make me feel pretty bad. After I suffered for a while, I looked back at the numbers in those categories and, well, they were still not good. But in most categories I was at least average, and I noticed several other categories that made me think more about my success. For example, (in some cases way) above average numbers of students said that they learned a great deal in the course, that hard work was required to get a good grade, they spent a lot of hours each week working on the course, that I encouraged student participation in the course, was available for help outside of class, and treated students respectfully. And every student gave me the highest score for enthusiasm, always a great category for me. I was happy that my intentions had come through so clearly in these areas.

It was hard to take that the students didn’t think my instruction was high quality, but then again, how did I expect that category to turn out?** A central goal had been to avoid what most students think of as instruction. Same with explaining course material—I answered questions, but turned the responsibility for a lot of the explaining onto the students themselves. Why be surprised when the evaluations reflect that? And the class time and organization of course material—I used class time the opposite way that almost all of their classes had, and organized the course material from behind the scenes. Of course that did not appear effective to everyone. Unfortunately, those particular categories just seem like a judgment of me personally in ways that some categories don’t. I understand why the students would make those ratings, but I think that they really don’t reflect the quality of my teaching. The surveys are just not designed to evaluate the kind of course I taught.

I didn’t get to read the students’ comments on the courses until late in the summer, and the sting was mostly gone from the numbers. I was prepared for some harshness. In fact, the comments were surprisingly good. A couple students complained as I expected that I “didn’t really teach” and they had to “learn everything on their own,” but many others were positive about the experience and they could tell I really cared about their learning. They said that the class was hard, which I was fine with. They made many of the same useful critiques that I myself had made looking back: too many assignments, hard to keep up with the cascading deadlines, not quite enough structure in the group work. Overall, the students were really respectful and said a lot of positive things about how much they learned in the course. I think that the quality of their comments indicates that I earned their respect and that they responded to and appreciated my high expectations. Overall, even with the low numbers in the categories I mentioned, I am proud of the classes.

After reading the evaluations, my thoughts turned to my upcoming third year review. At Villanova, this is the sort of “halfway to tenure” evaluation. As part of this process, I need to discuss my teaching methods and respond to student evaluations. Even with the processing I discussed above, I was still not feeling great about discussing the numbers in my response. I realized that while my reasoning about the evaluations was, well, reasonable, it would be wonderful if there was some way that I could really show that the course had been effective. Luckily, my Algebra course had coincided with the department’s internal assessment of one of our curriculum goals, essentially that students should be familiar with the roles of definitions and theorems in mathematics. I had volunteered to share my students’ anonymized proof portfolios for use in this. The proof portfolios consisted of 10 proofs from the course, typeset in LaTeX, revised versions of homework or test responses. I chose 12 portfolios from math majors in my Algebra course, 4 portfolios each from the top, middle, and bottom thirds of the course (ranked by overall course grade). I shared them with the assessment committee at the beginning of the summer and then mostly forgot about them.

When I read my evaluations, I decided to go ask the committee if they had found the students’ work to be proficient, so I could cite their opinion in my response. This is where my colleagues proved themselves, yet again, to be wonderfully, incredibly supportive. They not only encouraged me in person by saying they were very impressed with the portfolios, but they wrote a letter to my department chair for my file, describing their assessment and their opinion that the portfolios reflected my effectiveness as a teacher (as well as the students tremendous efforts). I can hardly describe how much this effort from my colleagues means to me. It makes me feel like part of a really healthy, supportive community.

Also, it tempers the anxiety that comes from the central role of student teaching evaluations in professor assessment. Too often, it seems that these numbers are all that matter in assessing our teaching. The fact that my colleagues were willing to document other evidence of my teaching effectiveness gave me a spark of excitement: maybe it is possible to undermine the hegemony of student evaluation numbers. Supported by our colleagues, we can create our own multi-faceted portfolios of teaching effectiveness, and just maybe they will mean something to our departments, colleges, and tenure committees. I don’t know yet that it will work, but it is something to try and a way to channel my frustration with the shortcomings of using student evaluations as the main metric for teaching quality.

What do you think? Let me know in the comments.

* For many reasons, as outlined in these articles from Inside Higher Ed, The Chronicle of Higher Education, and Slate, I do not think that student teaching evaluations are a good way to assess teaching in general, but that’s another blog post. I will just focus on the practical issue of how I responded to the evaluations that I got.

** As a quick aside, I have heard from seasoned active-learning practitioners that you can improve student evaluations in these categories by carefully and consistently explaining the reasons behind your methods. I did strive to do this, but I could probably have done more. Next time I will share more science before I start, and check in more through the semester.


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Academic Writing Support

My second year is well underway, and it’s turning out to be a little more intense than last year. I have more classes, more students, more committees, and less time until my mid-tenure review. So I’ve been thinking a lot about how to ramp up my research productivity without burning myself out. I’ve got some new projects underway that are still in the early stages, but I also have some old ones that I really need to just finish already. Which means writing. And editing.

I wrote last year about the writing group for new faculty I started. We have some new blood this year with the new faculty, but interest from my colleagues has definitely waned as the grading and the meetings piled up. I still go, because I find that block of time out of my office really valuable, but it’s a little less fun without a larger group. So I’ve been trying to replicate a little bit of that experience online with Shut Up and Write Tuesdays, a group that “meets” via Twitter on the first and third Tuesdays of the month, with different time slots appropriate for different time zones (or circadian rhythms). It’s not quite the same, but I find even a slight amount of accountability better than none.

I’m also signed up for the National Center for Faculty Development and Diversity’s 14-Day Writing Challenge, from November 7th through the 20th. You commit to writing thirty minutes each weekday, and participate briefly in some online discussions with other academics in the challenge. I did this two years ago and loved it, and was shocked at how easy it was to meet these daily writing goals. But I could use a refresher, and you don’t need to be an NCFDD member to join the challenge for free.

So I am writing, at least. But I’m feeling stuck: I have this manuscript I started forever ago that’s been “finished” for probably six months. But it’s from a particularly notationally dense part of my thesis, and after staring it for such a long time I have no sense of if it’s even readable anymore, much less publishable. And I certainly don’t have a good idea of where to send it. So this paper is just sitting with me, trapped in between inexperience and imposter syndrome, when it should be working its way through the pipeline and into my tenure dossier.

This is where I’d like to have a couple paragraphs about how I solved this problem. But I don’t have the solution, at least not yet. I’ve been reading some posts from the AMS’s own E-Mentoring blog, like this great one from Mohamed Omar. And there was this article today on #GetYourManuscriptOut that I found inspiring. But at some point I’ll just have to pull the trigger and see what happens. I’ll let you know.


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A New Kind of Circle: Math Circle at Graterford Prison

This painting was done by a Graterford Math Circle participant, inspired by the question of how to test someone's claim that they could tell the difference between Pepsi and Coke by smell.

This painting was done by a Graterford Math Circle participant, inspired by the question of how to test someone’s claim that they could tell the difference between Pepsi and Coke by smell.

Like many other Math Circles, the Graterford Math Circle just had its first meeting of the fall. The leaders, Katie Haymaker and I, brought a question to the group: How can we understand the lottery, and when can you play to win? Following a plan from Michelle Manes (in turn inspired by Jordan Ellenberg’s book), we ran a mock lottery to illustrate how buying a certain slate of tickets can reduce risk and make the lottery a good investment (under very rare circumstances), but found that the lottery in general is a very bad investment. We talked about the MIT group that made at least $8 million in the Massachussetts lottery. We had several good laughs, students anticipated every “mathematical point” that we’d hoped to make, and I left feeling totally proud of the students, and jazzed about math and math circles. This was all very normal and fun and cool! There were two unusual things about our circle. First, the students are adults, though not teachers or necessarily parents. Second, the circle takes place in the education wing of Graterford Prison, a maximum-security men’s prison about 45 minutes from Philadelphia, where the students are incarcerated.

Katie and I started the Graterford Math Circle in January of this year. We both were interested in starting a new Circle of some kind, and in working with adults, but there is already a wonderful Math Teachers Circle in Philadelphia (also, see my earlier blog post). We were both interested in teaching at Graterford through Villanova’s degree program, but hadn’t had the opportunity yet. So we hit upon the idea of a Math Circle at Graterford. We hoped the Math Circle could teach problem solving techniques, help Graterford students to see mathematics in a new way, and hopefully make students more comfortable in future mathematics classrooms. Since many of the students also have children, I hoped that positive experiences with Math Circle would also influence how the students talk to their families about math, and at least slightly reduce the chance that their children would be anxious about math.

Of course, Math Circles are generally for K-12 students, teachers of K-12 students, or occasionally parents of K-12 students, so our Circle for adult students was really a new model. We were not sure if it would work, honestly. What if the questions were not interesting to these students? What if there were major institutional rules that kept us from being able to create a fun atmosphere? We envisioned armed guards watching sternly and students forced to remain in their seats at all times.

We did a trial run, giving a talk at Graterford to share some puzzles and see if there was enough interest to have a monthly meeting. As I described in my blog post, it was really fun, and convinced us that the Math Circle could work. Our first meeting was in January—we did the Pancake Problem that I described in another blog post. It went over really well! There was a guard in the hallway, but the classroom atmosphere was relaxed and fun. We moved desks, worked in groups, and interacted just like people in any other math circle. We met once a month for the rest of the spring, with groups varying from 4-15 students. These guys are really enthusiastic. Getting them interested in the problems has not been at all difficult—the only difficult parts have been getting into the institution, not being able to use any technology, and getting some of the more outspoken people to delay shouting out answers.

In May, Katie and I went to Graterford’s graduation ceremony. Seven students were graduating from the Villanova program, and many more were receiving GEDs or certificates for vocational training programs. One of our most consistent Math Circle participants was graduating, and was very happy to see us at the event. He sent us (and our department chair) the most beautifully typed (yes, on a typewriter) thank-you letters over the summer. At the latest Math Circle, he brought us three of his summer projects: careful solutions to some of the problems posed in the handouts for three of the spring’s Math Circle topics. For the pancake problem, he had written computer programs to sort stacks of pancakes and to produce disordered stacks. For the puzzles we had brought in our initial talk, he had typed up full solutions to each. His reasoning was very clear and the explanations were excellent. Reading these solutions, I was so impressed with his work, and I felt incredibly happy that we had taken the opportunity to share some of our favorite parts of math with these guys. It feels like recommending your favorite book to someone who really puts in the time and thinks about it, and then tells you that the book now means something to them, too.

This is a flowchart created by a Math Circle member to describe an algorithm to sort a stack of pancakes.

This is a flowchart created by a Math Circle member to describe an algorithm to sort a stack of pancakes.

Other members of the circle have also brought extensive and creative work on past problems to later math circles, and they have naturally come upon some really interesting ideas in mathematics. There was sort of an organically developed generating function approach to one problem, and steps towards abstract algebra in another. We also received letters from some of the other guys, including the drawing I included above, inspired by a math circle question on how you could test whether a person could tell the difference between Coke and Pepsi by smell. (adapted from a Math Teachers Circle problem by Amy N. Myers of Bryn Mawr College).

Katie and I are planning (if our Dean approves) to co-teach a math class at Graterford this spring. We were originally planning to suspend the Math Circle for the spring, since we would be busy with teaching, but after last week, I’m not sure I can give it up. This Math Circle only happens once a month, but it really reminds me why I wanted to be a math professor in the first place.

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