Earlier this week I posted some initial reflections on how it's been going this fall in the form of student responses to the Five Question Summary. Here's a little more on that front, not from any survey instruments but from my own observations.

First of all, to repeat something from earlier, it seems unreal that it's already the halfway point in the semester. People connected to higher ed theorized, speculated, and at times fretted about Fall 2020 for what seemed like ages during the summer. But now it's halfway over, and I suspect the remaining seven weeks of the semester will go by fast as well.

## What's been working

The first two weeks of the semester were rough going, but once I made a few false starts and figured things out, my students and I started to find our rhythm. Our class meetings, whether online or face-to-face, tend to go like this:

• Before class: Students do Daily Preparation assignments and turn those in.
• First 10-15 minutes of class: Quick announcements and then polling activities to activate the main ideas of the Daily Prep and field questions.
• 5-15 minutes after that: Some minilecturing to demonstrate a harder example or two.
• 10-15 minutes after that: Working in groups/breakout rooms on the Jamboard while I look in and leave notes and questions on people's work
• Then a few minutes to debrief, field major questions, and wrap up.

So you could say that regular routines have worked for us. This setup is very similar to the workflow of a regular F2F class, at least the way I do it. So there's a familiarity with this routine that (I think) lessens the cognitive load on students and feels like the way they've done things in the past. It's not something radically different at its core from a F2F class; the only thing really difference is the level of technology used and of course the fact that only a portion of students are physically present.

So that's another thing that's worked well for us, and that's the tech tools we use. That's Poll Everywhere, Desmos, Jamboard and Classkick for the most part (as well as the usual suspects such as Zoom, email, Blackboard, etc.). I somehow resisted the temptation to use every tool I found that I liked (including Flipgrid, Google Meet, Miro, Padlet, and others) — which is a major change in my behavior! The Calculus students particularly have enjoyed using Desmos, especially Desmos student activities which I had not used until this semester, and which are awesome for all kinds of tasks.

But by far, what's been the most important factor not only in helping my students not only hold it together under incredible pressure but to thrive in this online environment are some of the design principles that I committed to early on, namely:

1. Keep everything as simple and minimal as possible. I mentioned before that in Calculus, I eliminated more than a few topics from the syllabus that would raise eyebrows if my higher-ups found out. But I don't miss them, nobody really cares that they're not in the course, and I seriously doubt anybody will notice a year or five years from now – and it's given me time and space to spend lots of time helping students really master some of the actually essential topics in the course rather than give away attention to something else that I really don't think matters.
2. Maintain a culture of open, honest communication. My students are under standing orders to let me know what you need, the moment you need it and I think that's helped them feel comfortable telling me when something's not working.
3. Have clear, measurable learning objectives and align everything with them. I've lost track of the number of times I've found myself in a complex situation in my classes that I've resolved by asking What's the learning objective here? That question has cut through tricky situations in course planning, grading, communicating with students, you name it. It's the "What's the next action?" for educators. In particular the focus on aligning class activities and assessments with learning objectives has greatly simplified my course prep and grading activities — which constitute about 90% of my work these days – and allowed me to find a repeatable, almost automated workflow for doing these things that has saved me immense amounts of time.

I saw this article on Facebook recently and what struck me about the truly sad student experiences in it, is that most of them revolve around professors giving too much work and not having adequate lines of communication. It seems like the worst of the bad student experiences could be avoided just by doing these three things for every class — minimize and simplify, communicate, and organize. But I also realize all too well that many profs have never had to prioritize around these ideas. I think moving forward — since I think it's pretty clear the Big Pivot will be with us for a while longer — higher education people are going to have to start taking things like GTD, time boxing, and essentialism a lot more seriously if they want to survive.

Finally, something that surprised me about how well it worked was giving students a detailed breakdown of how to spend their time on the class each day. Each week I've posted a "guide" for the week, with all the major announcements, due dates, topic schedules, and so on for the week. At the end I have a "suggested schedule". Here's this week's for Calculus:

I tend to do my own work in terms of pomodoros — a 25 minute sprint on one task, followed by a 5 minute break, repeated throughout the day. I thought that might be helpful for students to try as well, and a few of them have commented that this has really helped them focus and get things done. I also think it's important to explicitly tell students to take substantial breaks during their work time, and put the work away.

## What needs work

I'm still lecturing way too much and I don't think this is helping students. We end up short for time on active work, which is the whole point of having the F2F meetings, because my lecturing goes on too long – and this also defeats the purpose of having a flipped learning structure. I told myself that early on in the semester, I was going to lecture more than I usually do to give a gradual release of responsibility to the students. But I haven't released much. I need to work on that.

At the same time, I need to improve the quality of the examples that I do present through minilecturing and don't just leave students to fend for themselves. Example: I picked $y = \frac{\sin(x)}{x \cos(x)}$ as a more complex example of the Quotient Rule in Calculus – not a bad function but the simplification went way into the weeds with trigonometric substitution and students were confused about whether they were expected to both with it at all, or if so, whether they were expected to know all the trig needed to completely simplify the result. I ended up just waving my hands at it and saying that students should work on the simplification in their practice time, which is a dumb thing for a professor to do and students let me know about it.

Some of the technology we use has been problematic and it's possible we're using too much. For instance, we've used Blackboard for files, grades, assignments, and announcements and Campuswire for all other forms of communication. This feels like one tool too many. I'm not sure which one of these two is superfluous. Regardless, Campuswire hasn't been the active space for student discussions that I'd hoped it would be and Blackboard is just awful in general, so maybe the answer is to replace both with a single tool that works better on both fronts.

And Classkick — it's a tool with incredible potential, but it suffers from very slow load times during peak usage hours (during the middle of the day in the US) and a strangely complicated login process that is not explained well anywhere and which has made it hard to know whether students have submitted work or not. It's also missing some features that to me seem like no-brainers. I've stopped using it in my Discrete Structures course because of these issues, and I'm cutting way back on its use in Calculus.

## Questions I am asking at this point

• So, to be real here: My students are extremely quiet. They keep to themselves before class; don't really interact during class, even when explicitly prompted; leave as soon as class is over; and I rarely hear from them or see them in drop-in hours in between classes. Those who attend online, leave themselves muted and their video off 99% of the time. I don't think you have to be an extrovert to be a successful math student, but the lack of interaction is hurting them, and I am wondering a lot about this. Is it me? Is it what I have them doing in class? Is it just that they're stressed and tired? Or what? And, how can I change the learning environment to jumpstart student interaction?
• I'm starting to wonder whether my implementation of polling tools and activities might inadvertently be shutting down student interaction. Polling activities have students focusing on their individual internal thoughts, done in silence, focused on a phone or other device. Real peer instruction would balance that out with a lot of student-to-student interaction, but very often I just run the polling questions and debrief the results, and skip the turn-to-your-neighbor part of peer instruction because of time and logistical issues. I think this might be a big mistake.
• How do I improve my messaging about the mastery grading setup in the course? I am still getting students who ask for "partial credit" or "extra credit", or students who don't realize they can retake Learning Target assessments, and so on. These are critical misunderstandings that will hurt students in the end. How do I surface those misunderstandings and head them off before it gets too late?
• The eternal question of Calculus instruction: How do I best help students who struggle with pre-calculus mathematics? This came up big this week after a unit on derivatives of logarithmic and inverse trig functions, in which most students struggled with both of those fundamental concepts. I responded by putting together a 40-minute refresher tutorial on that material and replaced the in-class activities for the day with it — and that was a mistake, since a 40-minute lecture on the natural logarithm and arctangent helps absolutely nobody. And yet, we have to move forward. In past years I would just say "You need to review this material too" but in the pandemic environment, where students are quite clearly overloaded with school and work and life, how does that work?

## And a verdict on the staggered hybrid modality

I like teaching online. In fact I think I like it better in a lot of ways than teaching F2F, and I intend to keep teaching online even once Covid is over and F2F instruction becomes the norm again. But, I don't think I will do the asynchronous staggered hybrid thing again. This is the format I use for Calculus. Each Calculus section is split into two groups, one meeting Monday/Wednesday and the other Tuesday/Thursday, and when they are not F2F they are doing asynchronous class work. And each student can opt out of their F2F meetings and attend online.

While this was a good idea on paper, in practice it's meant that there are four subgroups within each section: the students in the Monday/Wednesday group who choose to come F2F, the students in the MW group who choose to be online, and two more such groups for  Tuesday/Thursday. Times two sections of the course. So instead of teaching two 24-person sections it feels like teaching eight 6-person sections.

Although the amount of grading is basically the same as pre-Covid, and the course prep work is only marginally greater, somehow this setup is just terribly exhausting and hard to manage. "Being put on a hamster wheel attached to an outboard motor" is the metaphor I've used. Even if I were teaching my courses with the hyflex model, I don't think it would be so tiring; I think it comes down to my students being split up into so many subdivided groups attending on different days, and having them attend class in different modalities simultaneously and not knowing who will be doing which until class starts — rather than having them all attending class at the same time in one modality or another.

My other class (Discrete Structures) is more like the hyflex model — students are split into groups, but instead of spreading the groups over different days of the week, these groups just determine whether you attend F2F or online on a given day. So all 24 students are present each day either F2F or remotely. (Students can choose to opt out of their F2F meetings and join online if they want, and most do; F2F attendance is usually just 2-4 people.) It feels much more like a coherent community; the prep work is not much worse than pre-Covid and the interactivity between students is much better.

While the time's gone by fast this semester, it's easy to forget that we're only eight months into the Big Pivot. Not even a full year! So I think it's important to remember that we're still learning, still figuring this whole thing out, and still not fully optimized for what we are being asked to do. In other words, we haven't got this figured out yet and shouldn't be expected to, so let's give ourselves and our students a break. But also, let's continue to learn and adapt, because as any sports fan knows, halftime adjustments are everything.