Mentoring Undergraduate Research

I wrote a short piece for the Early Career section of the Notices of the American Mathematical Society, and you can read it online:  https://www.ams.org/journals/notices/202005/rnoti-p663.pdf

Working at odd hours

Due to a combination of too much screen-time and an out-of-date glasses prescription, I get really bad headaches if I work for too long in front of the computer. (I know, right?) 

To compensate for the breaks I take during the day, I've been finding myself up at 1 or 2 am trying to catch up. I used to do this before This Happened, but not as often: I intentionally left work physically at work so I would break the habit.

Anyway, a few weeks into this habit confirms for me that it's not actually worth the tiredness the next day even if I do get caught up. But I can't seem to shake the feeling that I am falling behind. Maybe a better way to say it is that I can't seem to make peace with falling behind.

Hamilton's Spring 2020 Grading Policies

Last night, faculty voted to make Hamilton's Spring 2020 grade policy universal Credit/No Credit/Incomplete (Cr/NC).

The faculty's formal process for making decisions is (surprise!) complicated, so the purpose of this blog post is to give a little more information: how it worked and some things I considered while voting on policies.

Process

The process began with a proposed policy that a committee created based on faculty and student input. The committee's proposal was opt-in Cr/NC, and grades earned would be included on the transcript but no semester GPA would be calculated.

The process for moving from this policy to others we considered required proposing changes to the policy, voting on those changes, or substituting in a new policy and voting on which one we wanted to move forward. There were several rounds, and it took an extra long time because we were also adapting to the technical challenges of conducting what is supposed to be an in-person meeting online.

My Thoughts

For students trying to understand some of the things faculty were weighing, here are some of the elements of my own decision-making. It's not exhaustive; I'm listing only those things that I think might not already be evident to students.

• What happens to students if their professor(s) get sick?
  The numbers and projections for Oneida County scare me.
  Writing with my own grade book in mind, if I were incapacitated by COVID19, my students would probably be forced to take their courses Cr/NC. Because I teach one section of a multi section class, it seems extra unfair that the other section might be able to elect grades because of something that happened to me. My own back-of-the-envelope estimate for faculty with elevated risk factors and comorbidities reinforced this point.

• Hamilton's faculty had only 2 weeks to figure out how to adapt courses to remote instruction.
  I had to revise how I'm going to assess my students' progress using new types of assignments (including plenty of Professor-introduced-error!), and each of the policies we considered have consequences not just at Hamilton, but for employment and post-bac degree programs.

• Many schools have already elected Cr/NC.
  Employers, graduate programs, and med schools are already figuring out how to make that Cr/NC work. Some graduate and medical schools will accept Cr/NC grades only if it is a universal policy, which means that any policy intended to provide students with flexibility ironically left many students without choice.
  There were nuanced and unique proposals that came up during the meeting that weren't as simple as "grades with optional Cr/NC" or "universal Cr/NC." By last night, I thought that if we enacted something unique among colleges, it would come back to bite us. The work that grad schools and employers are doing to adapt to college grading policies is based on what the most prevalent policies are. This is one time we don't want to stand out from the pack.
  Here's an incomplete list of colleges with universal Cr/NC policies:

  • Harvard
  • Yale
  • Columbia
  • Dartmouth
  • Stanford
  • Johns Hopkins
  • Duke
  • MIT
  • Williams
  • Smith
  • Wellesley

• Hamilton needs a policy now that's still a good policy at the end of the semester when the true toll of COVID19 on our community is more evident. That's not an unambiguous point in favor of Cr/NC, but it was compelling to me combined with the points above and with the perspectives of students who were initially in favor of opt-in policies and changed their minds as they faced unexpected challenges.

Workflows: "live" Office Hours

As I’m figuring this out, here’s what works for me.

1. Have course materials (weekly assignments, textbook with bookmarked pages, a blank Overleaf document) to hand.
   I have the luxury of a second monitor at home, so I pull up the assignments, etc. and tile that monitor with them so I can more easily share them on Zoom.
2. Have a way of sharing a view of what I’m writing with students.
   I have the luxury of an iPad that I can use with a stylus to create a digital document while sharing its screen on Zoom.
3. Post a summary of questions and answers to our online course space.
   Piazza is what I’m using – I was already using it before the online adventure to allow for asynchronous office hours, which I really like. Definitely going to use the iPad in regular office hours and keep this part of the workflow going.
4. Record and (selectively) share the recordings with students.
   I feel weird about this part, so I have been editing the recordings down to just me to share with them. I need to get better at rephrasing their questions if I I plan to continue doing this.
   At times, I stop the recording to do a more personal check-in with students if there are only a few of us there. And then I forget to record again. A nice hack: put a post-it on your computer screen/keyboard/mouse to remind you to start recording again when it’s business time.

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Adaptations

So far, the technologies I’m using for the remote semester are working pretty well (relative to expectations). Now I’m looking at pedagogy and (a) trying to abandon principles that are noble but irrelevant in the face of a global pandemic while (b) trying to maximize the joyful opportunities to engage with mathematics.

A few ideas so far at various stages of implementation:

• Mathematics for Human Flourishing: an invitation to read, reflect, and write about the value of mathematics independent of its applications. This seems to be a particularly timely opportunity for students, especially math majors, to reconnect with the joy of mathematics. The only hurdle right now is finding a way for students to access Francis Su’s book remotely. I’m honestly tempted to just buy and ship this book to students interested in this option.
• Student designed exam (thanks to @katemath on Twitter!):
  • Choose/create 4 problems whose complete and correct solutions show mastery of the big ideas in the course
  • Justify your choices
  • Submit complete and correct solutions
• Choose Your Own Adventure:
  • Select from a series of predefined Adventures
  • Adventure materials include YouTube playlists, books that can be accessed online through Hamilton’s library, and additional content created or curated by me for the students
  • For the interested: topics include…
    • Applied Cryptography. Extra stuff comes from a very nice Udacity course, https://www.udacity.com/course/applied-cryptography--cs387.
    • Elliptic Curves and Lenstra’s Algorithm. Additional content created by me that gives a very, very brief introduction to elliptic curves over finite fields and projective space.
    • Continued Fractions and Convergence. Additional content from a fair-use selection from one of my favorite texts, Hardy and Wright’s Introduction to Number Theory. I’ve also selected a portion of an MIT open courseware Number Theory course for undergraduates.
    • Quadratic Reciprocity and Polynomial Congruences. Content follows Number Theory through Inquiry. Still curating fun resources on the internet – send me your suggestions?
    • Pythagorean Triples to Pell Equations. Ditto the previous.
  • Students are also free to pitch me their own adventure and I will help as much as possible.

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