Teaching during a pandemic I.

Author’s note: This blog post is an effort to record, perhaps just for myself, some of my experiences teaching during the spring of 2020, as higher education rapidly transitioned to remote learning in the face of the coronavirus pandemic. I have numbered this "I." as I may write more of my thoughts about approaches to teaching for the fall in the coming months. The opinions expressed herein are entirely my own, and do not represent the views or policies of Rutgers University or its Department of Mathematics.

 

The spring semester of 2020 was always going to be a bit rough for me, though nothing could have prepared me for the difficulty the semester would actually present. It would begin with a difficult job search, probably include some stressful travel, and somewhere in there I would have to find time to restart to my research program. It would also be the last semester of my three-year postdoctoral position at Rutgers University, a place that I have come to deeply value and whose students I have loved teaching. It is cliché to say that I was able to see myself in them, but there, I said it, and it has meant a great to deal to me.

 

I was given a prime teaching assignment consisting of two upper-division undergraduate math courses; an honors section of undergraduate real analysis, my favorite subject to teach, and mathematical logic, my area of specialization. Both had the usual complement of 20-25 students, a mix of sophomore, junior, and senior math majors. The logic class would be a fairly traditional lecture-based course, using notes I’ve been compiling since the last time I taught it. There would be weekly homework, plenty of in-class back-and-forth participation, two midterms, and a final. The analysis course would be more intense and bespoke, being both a core course for the math major and an honors section. It would include assigned readings that we would discuss in lecture (a “semi-flipped" class, if you like), online quizzes to keep students on top of the readings, weekly homework, two midterms, a final, and crucially, weekly workshop sections where students would work together in groups (assigned randomly and fixed at the start of the semester) on difficult problem sets, led by a graduate student (the wonderful Yonah Biers-Ariel, now Dr. Biers-Ariel).

Things were proceeding well, with few bumps along the way, through early March. The students were, as they always do, impressing me with the quality of their thinking, their questions, and their work. On one impromptu visit to my analysis workshop, I saw students in their groups, standing up at the boards or sitting at desks, drawing figures, arguing (in the best sense) about the details, and doing mathematics.

 

Concern about the coronavirus rumbled in the background throughout this time. In late January, the first cases in the US were identified, with cases in New York and New Jersey identified by March 1^st and 4^th, respectively (though we now know there were likely cases much earlier). A few students began to wear masks. From here, things changed rapidly.

 

On Friday, March 6^th, the same day the University of Washington cancelled in-person classes (the first major school in the US to do so), the Rutgers - New Brunswick provost asked “all instructors to immediately begin thinking through how to continue course instruction, and other teaching-related activities, in the event we need to suspend in-person instruction”. By Tuesday, March 10^th, the President of Rutgers suspended in-person instruction, effective two days later. Higher education everywhere was upended; classrooms went dark, libraries closed, conferences were cancelled, offices and labs emptied. The last time I saw my students in person was in my logic class and the office hours for my analysis class, both on Wednesday, March 11^th. There were probably 10 of my analysis students crammed in my office that day, some sitting on the floor, an unimaginable scene and a heartbreaking memory today.

 

There was a small silver lining, at least for Rutgers, in this timing; Spring Break was scheduled for the following week, so in addition to the cancelled class days on the 12^th and 13^th, we had a week to prepare for teaching online. The math department quickly organized emergency training sessions for its well over 100 instructors. The leadership shown by the chair of the department, Prof. Michael Saks, as well as the expertise and patience of the crew assembled to facilitate the transition (especially Prof. Joseph Guadagni and Chloe Urbanski Wawrznyiak, now Dr. Urbanski Wawrzniak) was remarkable and they are owed a great deal of credit for all the labor they put in, both during and after the transition. Chalkboard-loving math faculty, myself included, are not exactly known for their tech-savvy, or, frankly, their willingness to change, but in these circumstances, we all had to learn and adapt quickly.

The “standard model” recommended for most instructors in our department was to set up a course Canvas page, if you hadn’t already done so, and use the integrated web conferencing software (BigBlueButton) to stream a live lecture during regularly scheduled class times. The lectures would automatically be recorded and uploaded for later viewing. Office hours, workshops, recitations, etc, would be handled similarly. This was quick, sensible, relatively easy, and fit within Rutgers requirements for continuing synchronous teaching and student contact.

There was some flexibility, which I took advantage of due to my own concerns about synchronous instruction. Student’s lives, as well as that of their families, were being disrupted, many forced out of on-campus housing and back to hectic, sometimes unwelcoming, homes. I believed then, and still do, that flexibility is paramount in these extreme circumstances, and that I couldn’t expect my students to always carve out specific, scheduled, time slots for remote learning. I chose to use a mixed model, using pre-recorded lectures, posted (ideally, though I often missed the mark) a few days in advance of the usual class time which the students could watch on their own schedule, and then to use scheduled class time for live questions and discussion, akin to recitation or office hours (in effect, a “flipped" class).

 

It should be said that this is not how to teach a “fully online" or "flipped" class; teaching online requires a tremendous amount of preparation, far more than for a traditional class, in carefully scheduling material, meting out doses compatible with vanishingly small attention spans, and developing new modes of evaluation to go with it. Instead, we were transitioning traditional, in-person classes online in emergency circumstances, with barely a week’s notice. (There was an excellent post somewhere, perhaps the Chronicle of Higher Education, a few months ago on exactly this topic, but I haven't been able to find it. A link would be much appreciated!)

 

Evaluation had to change accordingly. While I kept weekly homework assignment in both classes, now submitted online, any quizzes and presentations were scrapped, and I increased the number of automatically “dropped” homework and workshop assignments from 1 to 2. Everyone got 100% for their participation scores for the last half of each course. This was the least I could do. Rutgers adopted an opt-in pass/no credit system: after final grades were posted in May, students could opt-in on an individual class basis to change grades C and above to “pass”, and below to “no credit”, requiring no input from instructors, having no effect on GPAs, and meeting all graduation requirements. I believe this was a reasonable middle-ground between leaving grades as-is and the universal pass/no credit approaches employed elsewhere.

 

I had planned to head into my office and record lectures in front of my chalkboard. I managed to do this exactly once for each class before it became clear that returning to my office regularly was an unnecessary risk for both myself and those, such as the cleaning and IT staff, still required to be in the building.

Me explaining the difference between free and bound variables in my mathematical logic class, in one of the few lectures I recorded at my chalkboard.

I had to get creative. An iPad, using screen sharing, is probably the ideal tool to deliver a handwritten lecture remotely, but I didn’t have one. I had bought an inexpensive drawing tablet, which I thought I might use in connection with a note taking program (like Microsoft OneNote) to give a lecture, but it reduced my writing speed and legibility to that of an adept 3 year old. I had also bought an external web cam, originally to record lectures at my blackboard. I ended up tacking that webcam onto a desk lamp and using it to record myself (or at least, my hands, increasingly raw from CDC-approved hand washing), writing with a Sharpie on a legal pad, and using an external microphone to help with audio. This was the method of delivery I ended up sticking with for the rest of the semester. Necessity, the mother of invention.

The rig I used to record lectures at home in my kitchen; a webcam strapped to a desk lamp (covered with a towel for "soft lighting"), a legal pad, and a Sharpie.

 

A pre-recorded lecture, without all of the (pedagogically useful) interruptions, questions, and discussion from and amongst students, goes by much faster than you think. My 80 minute in-person lectures became 30-60 minute video lectures, split into 10-20 minute segments (even this is verging on far too long for most attention spans, but again, not ideal circumstances). The length of the lectures was guided by the material I would have covered in a normal class and I never felt the need to fill the “extra” time. The last thing our students needed was in increase in workload under these circumstances. I managed to cover all of the course material I had originally intended, though without some optional topics, in both classes.

My cat Ellie (left) would sometimes join me in introducing a lecture. I think the students appreciated her.

Me explaining the epsilon-delta definition of continuity in a pre-recorded lecture on a legal pad.

An added difficulty was the need for captions; we were told that Rutgers requires captions on any video content which students are required to view. This is a sensible policy, given the need for accessibility in education. However, given the hours of material I was now uploading every week, and the mixed results of the automated captions (which were extremely sensitive to audio quality, to say nothing of how they handled symbolic expressions and jargon), correcting captions became a major burden. Preparing notes, recording videos, and editing captions would frequently take me 4+ hours for a single hour-long video lecture, leaving me tired and horse.

 

The live online class meetings were a mixed bag. While I viewed the live meetings as help sessions, and therefore more “optional” than the pre-recorded lectures, it is very difficult, for both instructor and student, to make this change suddenly, mid-semester. At least one student, on an anonymous evaluation at the end of the semester, expressed concern about doubling their time commitment for the course, and I agree with that sentiment now. I think these live meetings are what I am least satisfied with from the whole online teaching experience. A few vocal students were able to get a lot out of them by asking a lot of questions, but I think these sessions failed to serve the classes as a whole, and I struggled to get broader participation in this new medium.

 

For the analysis workshops, we kept the same schedule  (a somewhat painful 8:40am on Wednesdays), as required, but now virtually, and had students use the “breakout rooms” functionality in BigBlueButton (other platforms, including Zoom, have something similar) to continue to work in their groups. The community developed in the first half of the semester during workshops made this much easier, as students were already used to working together in their groups, including via online communication over the weekend to complete their assignments. Yonah did a miraculous job making all of this work and keeping a sense of community going with the switch to online workshops; he, together with the students, deserve the credit for the continued success of this crucial part of the course. I gave the same challenging workshop problem sets I would have given had we been in-person, posted online the night prior, and saw work of the same, or higher, quality as I had seen before the transition.

 

As the second round of midterms, and later finals, approached, there was a lot of concern amongst faculty everywhere about cheating and academic integrity. Some of this concern was fully justified; reports of violations, particularly using online “homework help” services like Chegg, skyrocketed. Teaching upper-division, proof-intensive courses meant that my concerns about cheating were substantially less than they would have been in a more computational or introductory class like calculus. I have always allowed students to work together on homework assignments and consult other resources (within reason, I specifically prohibit Chegg, and more relevant for upper-division math majors, Stack Exchange, on my syllabus), provided they give credit and cite their sources. I don’t close my web browser or shut my books when I’m doing research mathematics, and I don’t think my students should either. Exams, however, are a different matter. I trusted my students to work on their own on midterms and finals, submitted online, and I gave them ample time (a week in both cases); I stand by these decisions. While violations have to be addressed in the interest of fairness to all students, I don’t think the emergency situation caused by a global pandemic, which in April and May was ravaging New Jersey and the New York metropolitan area where most of Rutgers' students live, was the right time to excessively police for cheating. If we are still teaching online in the fall, as I suspect many of us will be, we will have had time to better consider ways to address these problems.

 

The crisis exacerbated the gaps and inequities that already existed amongst students. Those who excelled before the closures continued to do well afterwards. Students who struggled or where on the edge before, risked getting tipped over. I hope that I did my best to catch them before they fell too far behind, but it was a struggle for all of us, and I wish I could have done better.

 

At the end of the semester, after grading 40+ exams on Canvas, and spending a lot of time starring at my grading spreadsheets, I did my best to be fair and human(e) in assigning final letter grades. Given the extraordinary circumstances, I was truly humbled by what my students had accomplished; they learned, absorbed, and demonstrated understanding of advanced mathematics in a situation that I couldn’t have imagined going through when I was their age, a decade ago.

 

What higher education will look like come the fall of 2020 is being anxiously debated right now, both internally among faculty and administrators, and externally on op-ed pages and petitions. I will be teaching at a different university, in a different state, and don’t know (as of this writing) whether I’ll be in a classroom again any time soon. I know that the lessons and experiences of the emergency situation we faced in the spring will help all of us to teach as well, and as safely, as we can in this new reality.