Introduction
Many faculty were interested in teaching linear algebra with inquiry in Spring 2020 so we had a mixture of visits and collaborations happening:
Chrissi von Renesse (Westfield State, MA) and Rachel Schwell (CCSU, CT) are both members of the NE-IBLM leadership team, and co-creators (along with the other members of the team) of the Faculty Fellowship & Coaching Program. Erin Rizzie (UConn, CT) was an applicant to this program specifically for linear algebra for spring 2020, and as Chrissi and Rachel were both teaching linear algebra that semester, we created a team of three: Chrissi as lead mentor, Erin as faculty fellow, and Rachel as apprentice mentor. Megan Heenehan (ECSU, CT) had been informally working with Erin and Chrissi and so she became a fourth member of the team in an unofficial capacity. Debbie Borkovitz (Boston University, MA) was also teaching linear algebra using the same book as Chrissi, Erin, and Megan, and so Debbie and Chrissi exchanged visits during the online phase of the spring semester. Our linear algebra classes differed in sizes: Erin had the largest with two classes of about 35 students, Chrissi had 20, Rachel had 15, Megan had 30 and Debbie had two classes of about 30 students each. We reflected together on our experiences in a series of blogs...
Blog 4: Debbie's Experience
Last semester Chrissi and I visited each other's classes when I was about three weeks into remote teaching. I was starting to come out of the acute crisis phase and moving into more of a routine for all three of my classes, albeit one laced with anxiety. In addition to the stressors facing all students during the switch to remote, about two-thirds of my 90 students were international students, predominantly from China, and I had many students who were abroad when remote teaching was announced on our spring break, some who were trying to leave and having flights cancelled, some who were in quarantine with possibly bad Wifi, and some who needed to apply for permission to stay when the dorms officially closed. I was overwhelmed with trying to keep track of where everyone was today and whom I should prioritize reaching out to. As with everyone else teaching at the time, I was tired from all the thought and work involved in trying to learn to teach remotely and decide how to modify the course structures mid-semester. But three weeks in, I had a plan, I had some classroom routines, and I was ready to take advantage of how much easier it was to visit our classes than it would have been in person.
I am used to visiting classes and having visitors -- I was the department chair for many years in a collegial, teaching-focused department at Wheelock College, before Wheelock merged with Boston University two years ago. However, I was nervous about having Chrissi visit, much more so than I'd have been for an in-person visit. I had a bit of imposter syndrome around being a person who supposedly knows a lot about IBL/active learning, because I was doing many more whole class activities than I thought I should be. Students referred to what I thought of as interactive discussions as "lectures" and told me how much they liked them, how they thought I should do more of them, and how helpful the videos of them were. Attendance was way down in my afternoon linear algebra class, which met at 2 p.m. (that's 2 a.m. in China and 3 a.m. in Korea), so many students could only access the live class by watching videos later.
When I visited Chrissi's class, the first thing I noticed was the differences between the populations we were teaching. Her students were mostly white, mostly native English speakers, and mostly tuning in from their bedrooms in Massachusetts. Next I was relieved to see that she was also spending a lot of time in whole class discussions, but she was conducting them differently than I was. She worked through an activity in the book, asking questions and then calling on students to answer them. I was very impressed that students seemed fine with being called on and with saying they didn't know an answer or sharing their confusion; I know that a lot of work goes into creating a classroom culture that is both emotionally safe and intellectually challenging.
Chrissi came to my morning class the next day, and I had the best Zoom class I'd had up until that point. Partly class went well because I spent extra time planning it due to my nervousness, and partly it was luck (my afternoon class on the same topic didn't go quite as well). In reflecting now, I think visiting Chrissi's class also improved my own class, because seeing her call on students reminded me of how much my students -- including many English Language Learners -- used to talk in class before we went remote. Since I relied so much on non-verbal cues to decide who to gently encourage or who to call on, in moving to remote learning, I'd backed off some on encouraging students to talk, but I pushed more that day.
In remote learning I often used the "3-2-1 Go" Technique, which I learned from Maria Andersen. The day Chrissi visited, I gave students some time in breakout rooms to discuss some true/false questions; then when we came back together I asked students to type whether they thought a question was true or false, but not to hit return until I said, "3-2-1 Go," and then we discussed the question. A few of my questions that day ended up having much dissent about whether they were true or false; one such question was, "If u and v are both eigenvectors of matrix A, then u + v is also an eigenvector of A." About half the class said true and half false, and I excitedly said that such a distribution meant I'd written a good question. In our debrief the next day, Chrissi pointed out that my giving myself the responsibility to write a good question was a good frame for the students, since it relieved them of feeling the responsibility was on them to always get the right answer. I found Chrissi's way of articulating what I was doing very helpful, and hope to be able to use it more consciously in the future.
We had a lively discussion in the class that Chrissi visited, where many students showed their videos and I was able to circle back to incorrect answers and have students think about what in their thinking might have been true. In my second linear algebra class that day, only two students showed their videos and fewer students volunteered to talk. I did start calling on some people, perhaps emboldened by seeing Chrissi's class, to ask things like, "Can you tell me why you answered false?" Some of these prompts restarted the discussion, and some of them yielded silence.
To write this reflection, I went back and watched the videos of both my classes that day. Now it's clear to me that even if the students labelled the class “a lecture,” I was using active learning strategies, that students were thinking about interesting questions that expanded their conceptual understanding, and they were discussing these questions with each other and with me. I think some of my initial nervousness and fears that I wasn't really doing IBL right were because Chrissi had never visited my classes live, so a part of me wanted to fixate on "this isn't really how I teach!" and then think of some labels for how I teach that I might not be living up to. As Chrissi said in the debrief, it's vulnerable to say that we're new to this, not necessarily very good at it, but we're going to let someone else join us so we can both get better together. I'm pleased that we both took that risk, and that in doing so, we were able to do a little better by our students.
