The Wall

Big week for me—I took down a bunch of sticky notes. This made me really happy, though it doesn’t sound so hot. You see, one of my office walls looks like this:

The view from my desk.

The view from my desk.

My students probably think this is weird, especially since the words on the notes likely mean different things (or nothing) to them: “What makes maximal curves, besides natural embedding theorem?” or “graph zeta for student?” or “Julia Robinson Math Festival.” These are things I’d like to figure out in my research, work on in my teaching, or just generally do in my career. I have them arranged in a sort of tree (nobody else can tell it’s a tree, because I don’t think the department would love me writing on my wall), with doable tasks branching off from some big general research hopes, and other stuff arranged vaguely by relationship and difficulty.

I put these on my wall in February, when I got back from re:boot 2016, a grant writing workshop organized by Alina Bucur, Heekyoung Hahn, Pirita Paajanen, Lillian Pierce, and Caroline Turnage-Butterbaugh.* As part of the workshop, we were given a poster board and told to make a big map of our research plans. Many people made beautiful, artistic posters with color and good graphic design. I covered mine in sticky notes, maybe because I have some kind of fear of commitment and I couldn’t bear to put the marker directly to the poster board. Also, I had no idea what to do when I began, so I just started writing all the things I could think of on sticky notes and spreading them out on the table. Apparently sticky notes are a pretty common way to organize stuff—see 3M’s amazing array of uses for Post-Its, and this excellent event facilitation wiki (thanks Ben Smith). But I’d never really appreciated sticky notes until this.

When I was done (or stopped to take a breath), I had a sea of ideas—way more than I realized that I had. Then it was organization time, and I found the whole process of physically moving the notes around really fun. It helped me take a research agenda that could have looked really scattered and organize it into one overarching theme, with a few different directions, with some auxiliary projects that I put on their own branches and didn’t include in the grant proposal.

This helped me write my CAREER proposal, and I liked the way it gave me a big picture look at where I could go, and also the flexibility to add and remove parts if my interests change. So when I got home I transferred the whole mess to my wall. Now, every time I look up from my desk I see this web of ideas. I might have thought that would stress me out, like a giant to-do list, but for some reason this is inspiring instead of daunting. Maybe because it is only the stuff I really want to do, none of the tasks, like grading, that get to be a grind. This is at least partially a picture of my daydreams and ideas—not a list of things that must happen so I can keep my job.

Victory looks like this.

Victory looks like this.

I made a few changes these last few months, mostly thinking of new ideas and sticking them on the wall. This was a big week because, for the first time, I took some notes down because I had done the things on them, or because I don’t want to do them anymore.  Major fun, by my standards.

As I wrote this blog, I suddenly freaked out: “Oh my god, is this a vision board?” Over the years, some great friends have tried to get me to make a “vision board” and I have respectfully refused. It’s just not for me. I have always cringed at the question “where do you want to be in 10 years?” and all its relatives. I value the idea of being open to the unexpected awesomeness of life and haven’t wanted to even try to visualize my one ideal life path. I don’t believe in the “law of attraction” and I’m not reading The Secret. However, applying for a grant is kind of like answering the question “where do you want to be in 3-5 years?” so this is a place where visualizing a narrative is important. Still, I’m not calling my wall a vision board. I guess there are a bunch of math things I think it would be cool to do. I refuse to even call these goals, exactly. My memory isn’t great, so stuff disappears if I don’t write it down, and my desk is a mess, so ideas that land in a pile of other stuff on my desk will probably stay buried. So, I’m okay with writing down a bunch of my math-related ideas and thinking about how they fit together, using one of the great inventions of modern office technology. That I can handle.

How do you organize all the stuff you want to do? Do you think I’m giving vision boards a bad rap? Let me know in the comments.

* I have mentioned this before, and I really can’t say enough good things about the workshop. Good news—I just heard that re:boot 2017 is being funded, so for any women in number theory, watch out for details here!

 

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Anamorphic Art for High School Students

I’ve written here before about our annual Sonia Kovalevsky Day at Hood, where we invite local high school girls to campus to learn more about math and careers in STEM in honor of Sonia herself, the first woman to earn a Ph.D. in mathematics. This year I was co-organizing the event and also running one of the workshops. I dithered for way too long about what I wanted to do with the students, but I finally settled on a topic I’ve liked since I was a kid: anamorphic art. We’re often called on to show off our discipline to kids, and I think this is a neat topic that’s cheap to implement and easy to adapt to most grade levels.

By Hans Holbein the Younger (1497/1498–1543) - bQEWbLB26MG1LA at Google Cultural Institute, zoom level maximum, Public Domain, https://commons.wikimedia.org/w/index.php?curid=22354806

The Ambassadors, By Hans Holbein the Younger (1497/1498–1543) – bQEWbLB26MG1LA at Google Cultural Institute, Public Domain,

Anamorphic art refers to art that needs to be viewed from a specific angle or using a specific device like a mirror in order to be seen properly. The classic example is in a painting called The Ambassadors by Holbein, which holds a Halloween-appropriate secret message when seen at the right angle. I put it on the screen and had the students wander around the room until they found the sweet spot.

I showed a few more examples of these types of paintings, both old and new, and talked a little bit about how images can be transformed via different types of grids. Most of them knew about one- and two-point perspective, so they seemed to get how that type of transformation would work.

Then we got to the fun stuff: circular mirror anamorphosis. I passed out a bunch of examples without really explaining anything, and asked them to figure out what was going on. Most of them started bending the pages into a cylinder right away. I gave them small sheets of mylar I’d cut to roll into a cylinder to see the images properly. Mylar comes in a big roll for about $20, and you can find it online or in hydroponic gardening stores. Then they spent awhile looking at a bunch of examples. Some came from an old book of examples from a Victorian toy, now out of print but still widely available. Most I found online in various places, and the most notable examples came from an artist named Istvan Orosz, who makes incredible prints where the mirror reveals a hidden portrait. img_1494

Last I had them make their own examples, using pre-made grids I found online. These grids aren’t completely accurate, and someday I’ll probably make my own, but I just didn’t have the time. The students drew their own pictures and transcribed them onto the circular grid, and admired their handiwork in the mirror. Biggest advice for doing these: keep your drawing simple. Pixel art is highly recommended if you’re not artistically inclined.

I finished by talking very briefly about the mathematics behind img_8493-1all this, and gave some applications: painting road signs or logos on sports arenas, snapchat filters, and projection mapping. I showed a couple cool videos of those at the end, while they finished their drawings.

I was worried about hitting the right level with my audience: didn’t want to be too technical, but also didn’t want to dumb it down too much. Also, we only had 45 minutes together, so I couldn’t include everything I wanted. These students aren’t necessarily already math-inclined; in fact we encourage teachers to bring students who don’t think they’re strong mathematically. This was my shot to talk to a bunch of young women about why I love math, and I didn’t want to blow it by either confusing or boring them. Their evaluations of the day aren’t quite processed yet, but I think I hit the sweet spot.

 

 

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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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