As I mentioned in my last post, I'll be devoting a lot of space on this website over the next several weeks and beyond to provide specific concrete examples of what I'm planning and doing for Fall 2020. The purpose here is partly selfish; I want free advice on these plans, to find blind spots and flaws that I have a hard time seeing myself. But also I think it's helpful for everyone to have something concrete to think about regarding Fall 2020 – something to get us moving forward. So, let's begin.

Calculus, Fall 2020

I have two preps in the Fall – Calculus, and Discrete Structrures 1. For the time being I'm just focusing on Calculus. This course is your basic Calc 1 class: 4 credits; populated mostly by students on the STEM track (at least half the students enrolled so far are engineers); covering limits through derivatives and up to and including the Fundamental Theorem of Calculus. I use my colleague Matt Boelkins' Active Calculus text and we work with the first four chapters. I am teaching two sections of this in the Fall.

Before the pivot to online, both sections of the class were scheduled for face-to-face meetings on Monday/Tuesday/Wednesday/Thursday (MTWR) for 50 minutes each, in a standard classroom that holds about 35-40 students; the class size is typically capped at 30 but I've admitted as many as 34 before. However, this all changed this summer as our plans for Fall semester began to emerge. Here's the chain of events/reasoning that have altered the course:

  • Early on, our university committed to having a significant portion of course programming to be F2F. The rule of thumb that has emerged is that first- and second-year courses should have at least half of their coursework F2F. For the Calculus course, that would mean that two of the four weekly meeting days should be F2F and the rest online. (Exceptions are being made for those profs in high-risk health situations and for other reasons.)
  • Because of social distancing and because we have very few large classrooms on campus, we can't meet an entire 30-student class in the scheduled room at the same time. Most classrooms on campus can only hold about 40% of their usual capacity, meaning for me that any F2F meeting needs to have around 15 or fewer students in it.
  • Therefore, the Calculus class should follow some kind of hybrid setup that combines F2F and online work.

To modify my Fall Calculus course to fit these conditions, last week I had to think carefully, and quickly, about the model that I wanted to use for Calculus.

Three models

It turns out there are a lot of ways to potentially offer a 4-credit course in which at least 50% of the meeting time should be face-to-face – each model having its own set of pros and cons. I think this is the first major decision we all have to face when building courses for the fall, and many of you are currently thinking about this. The choices we make at this stage determine many if not most of the pedagogical choices that follow. So here was my thought process.

To think this through, I first of all acknowledged the constraints I mentioned above, and I thought about the following principles that must be in place no matter what model I went with:

  1. The course will be predicated on active learning and students being active, constructive, reflective participants in the learning process. No compromise on that, and models that make this harder should be less likely to be picked.
  2. The course will use a mastery grading setup.
  3. Students should have significant choice in how they learn and how they are assessed.
  4. The model has to be sustainable, with as low of overhead as possible for both students and myself. (I can't be put into a position to have to spend tons of time simply figuring out and maintaining the model itself, including technologies used to support the model.)
  5. The model has to be easily convertible into a 100% online format in the event of another pivot where all F2F instruction is suspended.

With those guideposts in mind and after a lot of looking and asking around, there were three models that became the finalists. Because I have zero creativity with naming things, I called these Model 1, Model 2, and Model 3.

Model 1

This was proposed by my colleague Dave Coffey who, I think, is going to use this in his math education courses in the fall.

  • First, divide the class up into groups of 4 students (roughly 8 groups in all) and give a designation to each student in the group – like a color. For example, one student is Red, one is Green, one is Blue, one is Yellow. These groups are study groups/support cohorts for the semester. (Or change them up at mid-terms, etc.)
  • Different students from each group take turns being representatives at the F2F meetings. For example, on Monday only Red students come; Tuesday, Blue students; Wednesday, Green; Thursday, Yellow.
  • Those students who are not present F2F on a given day are expected to participate remotely via a live-stream of the class on Zoom or Google Meet, and stay in contact with their representative who is present (through a breakout room, private chat space, phone call, etc.). Their representative for the day is their group spokesperson with a direct physical link to the prof and the other groups.
  • During active learning tasks in class, the group representative is responsible for managing the group's work, including communicating with and channeling questions to the professor and taking notes.
  • Otherwise the class structure is what it normally is. A flipped learning setup for example would involve students doing pre-class work just like always; active learning tasks done in class in the past can still be done unless it involves sharing physical objects; and so on.

I like this model especially because of the built-in support networks it creates, for the fact that each student shares the role of group manager regularly through the semester, and because it really leans into rather than away from the role of active learning in the class. And as the last bullet points out, while a lot of disruption of the normal flow of class will take place in the Fall regardless of model, Model 1 does not disrupt the schedule or calendar of the course, and despite the fact that only the group representatives are physically present on any given day, most everything else in the class can happen more or less when it always happens. So it ticks off several of my boxes: active learning is supported, mastery grading (while complicated by the dispersed F2F meetings – more on that in a later post) can still be done, and students can have choice built into the syllabus. Model 1 also preserves social distancing since at most 8 students will be physically present at any given time.

Model 1 as given does not meet the constraint of "50% F2F". But it does guarantee 25% F2F, and 50% can be achieved by having a more controlled schedule of who can attend. For example you can schedule permutations of pairs of students like so:

  • Monday: Red + Green
  • Tuesday: Red + Yellow
  • Wednesday: Green + Blue
  • Thursday: Blue + Yellow

The major downside of Model 1, for me, is the dependency on synchronous online meetings. Synchronous online meetings have to work every single class day on both my end and the students' end in order for Model 1 to work.

I'm not as concerned as some other people about the amount of overhead and attention needed to do online synchronous meetings. I think that a good-enough synchronous meeting can be done with a cheap webcam set up on a tripod and pointed at the front of the room and run through a laptop into a Zoom meeting, which costs about $50 (for the webcam and tripod) and maybe 5 minutes a day of setup.

My real issue with synchronous online is twofold: (1) It depends on the technology actually working the way it's supposed to all the time, and (2) it depends on students' ability to have sufficient tech on their end in the first place. I've been burned enough by technology going south at the worst possible moment to be wary about this, and I'm not sure I am ready to trust my entire course to a model with those two bottlenecks in place.

Model 2

Model 2 is a bit like Model 1, except instead of several small groups of students, we work with a small number of large groups.

  • First, divide the class up into 2 groups, each with roughly 15-16 students, and designate one group as "Red Team" and the other as "Blue Team".
  • The groups alternate attendance F2F through the week: Red Team comes on MW and Blue Team comes on TR for example.
  • Those students who are not present F2F on a given day are expected to participate remotely via a live-stream of the class on Zoom or Google Meet and stay in contact with the professor or a friend who is present (their choice – no fixed representative as in Model 1).
  • Otherwise nothing changes in the class from an ordinary F2F setup.

I liked Model 2 because as with Model 1, it doesn't disrupt the schedule or calendar of the class – I don't have to change anything from how I've taught the class in the past other than the way that I interact with students, half of whom at any time will be participating remotely. It also doesn't require any asynchronous work on course content except for perhaps pre-class work done in a flipped learning setup; everything is done synchronously. As with Model 1, Model 2 satisfies the social distancing requirements (although it pushes the limit of classroom density) and checks a number of my needed boxes for a classroom model.

Model 2 also gives a lot of flexibility. For students, if one of them is feeling sick, or is sick, or simply doesn't want to be physically present, it's OK – just put yourself on the other team for the day and participate remotely. It would be not that much extra work to turn this into a hyflex setup, either – just hit the record button at the start of class and put some additional work on the active learning tasks that the synchronous students are doing. And from my standpoint, it would be trivial to move this 100% online if needed – just drop the F2F meetings.

However, Model 2 has the same issue that Model 1 has: the dependency on synchronous meetings, and the bottlenecks that this brings with it. And it lacks the built-in support networks that Model 1 gives us for free (although this could be arranged by having small four-person support groups set up with two Red people and two Blue people). Another downside of Model 2 is that my course modules as currently designed are four days long each; so, the Red team always sees the same parts of a module F2F, as does the Blue team, so it's not totally equitable.

Model 3

Model 3 is like Model 2 except we do away with the required synchronous activities and introduce asynchronous work.

  • First, divide the class up into 2 groups, each with roughly 15-16 students, and designate one group as "Red Team" and the other as "Blue Team", and the groups alternate attendance F2F through the week: Red Team comes on MW and Blue Team comes on TR.
  • The Monday and Tuesday classes are repeats of each other, as are the Wednesday and Thursday classes. (The inspiration here is my pastor, who celebrates Mass with the same homily three different times every Sunday.) Both meetings are aimed at active learning on basic Understand/Apply level skills on different blocks of content.
  • The work that would ordinarily be done on the other two days of the week by each team, focusing on Apply/Analyze/Evaluate tasks, is shifted to asynchronous online activities that are mediated by different tech tools (CampusWire, Desmos, Google Docs, etc.)

One major upside of Model 3 is that it does away with all the issues surrounding synchronous meetings. You could have synchronous online participation available for students in Model 3 by live-streaming the F2F meetings; this would be helpful for students who couldn't attend their team's F2F meeting, or who just want to opt into all online activity, or a Red team person who wants to see the lesson again because they didn't understand something (or Blue team person who wants a preview). But none of the synchronous meetings are required.

Another thing that's appealing about Module 3 is that it's very close in structure to the way we've done hybrid classes in the past, pre-Covid. I've taught Calculus before in a hybrid format where the entire class meets MW for F2F activities and the rest of the work is done online asynchronously. Model 3 is exactly this, only we are staggering the F2F meetings between two groups of half the usual size. Also, unlike Model 2, Model 3 is equitable in the sense that all students get the exact same lesson F2F and online each time.

Model 3 preserves social distancing and doesn't prevent active learning or mastery grading, although the reduced F2F and synchronous meetings cut into this. If we were to pivot to fully online, too, I'd have a choice to make: Make the entire course asynchronous, or replace the F2F meetings with online synchronous meetings? Both can be done but it's not clear which is better right now.

The major "con" with Model 3 is that it is really hard to sustain student engagement on asynchronous online activities. I've learned this through teaching hybrid courses and asynchronous online courses. Going with Model 3 would mean that I would trade potential issues of tech problems, time and attention requirements, and student access related to online synchronous meetings for the almost certain issues of designing engaging activities and getting students to work with each other every week. It's a serious tradeoff.

Running the scenarios: What each Model would see

To choose the model, I really needed to visualize how students in each model would experience a typical course module. I have the content in the course split up into 12 modules, each four days long (usually but not always starting on Monday and ending on Thursday) and then subdivided into an "A" part and a "B" part. To visualize the models, I picked Module 6 from the course, which is on implicit differentiation (the A part of the module, corresponding to Section 2.7 in Active Calculus) and L'Hopital's Rule (the B part, coming from Section 2.8).

Here is a high-level overview of how this module would go.

Sunday: All students regardless of model complete a Guided Practice assignment focusing on reading Section 2.7 and watching some video, then completing exercises focused on the Remember/Understand level tasks for implicit differentiation (e.g. Preview Activity 2.7.1 in Active Calculus).

Monday:

  • Model 1: All Red students are present F2F, everyone else participating remotely. Activities: Q&A over the Guided Practice, active work on basic implicit differentiation computations using Jamboard to work with teammates remotely; debrief and Q&A over the group work.
  • Model 2: Entire Red team is present F2F; Blue team participating remotely. Activities: Q&A over the Guided Practice, active work on basic implicit differentiation computations using Jamboard to work with teammates remotely; debrief and Q&A over the group work.
  • Model 3: Entire Red team is present F2F. Live stream is available optionally for Blue team. Activities: Q&A over the Guided Practice, active work on basic implicit differentiation computations using Jamboard to work with teammates remotely; debrief and Q&A over the group work, end with instructions for asynchronous work due later in the week on implicit differentiation (equivalent to group work done by Model 1 and Model 2).  

Tuesday:

  • Model 1: All Blue students are present F2F, everyone else participating remotely. Activities: Active work on more advanced implicit differentiation computations using Jamboard to work with teammates remotely; debrief and Q&A over the group work.
  • Model 2: Entire Blue team is present F2F; Red team participating remotely. Activities: Active work on more advanced implicit differentiation computations using Jamboard to work with teammates remotely; debrief and Q&A over the group work.
  • Model 3: Exact same thing as Monday, except Blue team is present and Red team has optional live stream.
  • Tuesday night: All students regardless of model complete a Guided Practice assignment focusing on reading Section 2.8 and watching some video, then completing exercises focused on the Remember/Understand level tasks for L'Hopital's Rule (e.g. Preview Activity 2.8.1 in Active Calculus).

Wednesday:

  • Model 1: All Green students are present F2F, everyone else participating remotely. Activities: Active work on identifying indeterminate forms and seeing that some exist and some don't, plus basic practice with L'Hopital's Rule; debrief and Q&A over the group work.
  • Model 2: Entire Red team is present F2F; Blue team participating remotely. Activities: Active work on identifying indeterminate forms and seeing that some exist and some don't, plus basic practice with L'Hopital's Rule; debrief and Q&A over the group work.
  • Model 3: Entire Red team is present F2F; Blue team optionally participating remotely via live stream. Activities: Active work on identifying indeterminate forms and seeing that some exist and some don't, plus basic practice with L'Hopital's Rule; debrief and Q&A over the group work; end with instructions for asynchronous work due later in the week on L'Hopital's Rule (equivalent to group work done by Model 1 and Model 2).  

Thursday:

  • Model 1: All Yellow students are present F2F, everyone else participating remotely. Activities: Group practice with L'Hopital's Rule using Jamboard; debrief and Q&A over the group work.
  • Model 2: Entire Blue team is present F2F; Red team participating remotely. Activities: Group practice with L'Hopital's Rule using Jamboard; debrief and Q&A over the group work.
  • Model 3: Exact same thing as Wednesday, except Blue team is present and Red team has optional live stream.

Later in the week:

  • All students turn in WeBWorK sets for practice.
  • Model 3 students turn in asynchronous work corresponding to the Tuesday/Thursday activities done by Model 1 and Model 2 students.

And the winner is...

I'm going with Model 3.

Although getting students to engage and stay engaged with asynchronous online work is difficult, it at least is a problem I am sure that I can predict and manage – unlike the unpredictability of the synchronous meeting technology and access issues in Models 1 and 2. That is, it's a devilishly hard pedagogical problem, but it's the devil I know.

I also think that in this fraught environment, when we're going to have to manage so much change in the Fall, there is a lot to be said for keeping it simple. And for me, Model 3 is the simplest of the three. It's essentially the same setup as I've used more than once in the past; it requires no management of synchronous meetings; and it seems like the simplest for students to keep track of (Am I a Blue person or a Yellow person? Is today Green day or Red day?). Although it will challenge students' time management and organizational skills to do the asynchronous work, that challenge is present in all three models (and the ones I didn't mention) and Model 3 seems to cut out much of the extraneous cognitive load.

As I said, I'm still going to try a low-budget synchronous live-stream setup as well – knowing that if it craps out or students can't access it, it doesn't disadvantage anybody – and tell students that if you were scheduled to be present F2F on a given day but can't or don't want to, you can participate online, no questions asked and no prior notice necessary. That is, I'm going to try making the course a kind of garage-band hyflex (garflex?) where students can just pick their modality. There are potential problems with this, but I'll think through those later.

Parting shots

  • Obviously my choice for Model 3 is just my personal selection. It's not an endorsement; it is not necessarily the best thing for all teachers and all students; and your mileage may vary. And these are not the only three ways to do it.
  • I get it that some profs simply don't get a choice because this is mandated by their institution. That's a bad situation and I'm sorry. But I would encourage creative thinking in such situations and focusing on what you can do with the cards you've been dealt.
  • I am not going to tackle the issue of the premise of all this, which is the idea that we should have F2F meetings at all, other than to say that I have definitely availed myself of my rank and privilege to engage vigorously in debates on this within my institution. I'm not going to pull that out for public view.
  • You might have a lot of questions about how Model 3 is going to actually work. If so, (1) you're not alone because I have a lot of those questions too, (2) that's what the next few posts are about, and (3) I have you right where I want you, thinking about specific tasks and what can be done rather than dwelling on the supposed impossibility of doing anything good in the Fall and what you supposedly can't do. Stay tuned.