Square peg in an octagonal hole

Interview with Ari Nieh, with commentary from Yvonne Lai

Like many of us, I began teaching online this Spring. Unlike many of us, I began doing so at the start of the semester. I am co-teaching a class at Michigan State, and I live in Nebraska. One of the most useful conversations I had in preparation for this assignment happened in 2013, well before the current coronavirus epidemic. The math department at the University of Nebraska-Lincoln had been considering a synchronous online version of a mathematics course, for rural teachers. I chatted with Ari Nieh, then an instructor for Art of Problem Solving, about what it would take to teach online, especially via chat forum technology. (Ari then became a lecturer in Writing, Rhetoric, and Professional Communication at MIT; and now he is a game designer at Wizards of the Coast.) In the end, that course was run asynchronously (and in many ways consistent with the advice given in a previous post). Nonetheless, much of the advice I received 7 years ago aged well. With Ari’s permission, I share snippets of our conversation in this post, edited for readability, and with commentary from present-day me.

First, here is a summary of the key pieces of advice I took from the conversation.

Key pieces of advice for teaching online using chat technology

  1. Tools for making students feel comfortable in class and that their input is being valued– careful choice of words to maintain a welcoming tone; consistently responding to questions, whether publicly or privately; and using a fair bit of humor at the beginning of class and during transitions.
  2. Opening a class – it’s kind of like face-to-face, but word choice is perhaps even more important, because you don’t have tone/body language.
  3. Lectures – don’t really translate. Make sure to have questions for students. This can take the form of closed questions (e.g., multiple-choice questions or ones where there is one right answer) or open-ended questions.
  4. Whole group discussion – There are some ways that this is easier, because students can see each others’ thoughts for longer. Also, questions can be answered privately as well as publicly. Giving instructions is perhaps easier than in person, because of persistent text: whatever you say hangs in the air and they keep reading it.
  5. Whole group discussion, continued – In general, the biggest skill that doesn’t translate is improvisation. You can’t improvise spoken words, so you want to develop skill at improvising written words.
  6. Wrapping up discussions/class – this is a place where it would be good to have some prepared draft/default text.
  7. Diagrams – should be prepared ahead of time when possible.

Now for our conversation.

Yvonne (2013): So, let’s talk online teaching. The context is this. There’s a class we offer that is 2.5 hours long, that alternates between lecture and working time and discussion, and some time to work on homework problems. We want to translate this online. How should or can this work?

Ari: I see. What is the format of the online classroom?

Y2013: That is a good question. It hasn’t been determined, but there will be an online chat place for teachers and students to interact.

Ari: Our online classroom platform [at Art of Problem Solving] has a setup where everything the students type goes to the teacher first, who has the option of showing it to the whole class or not. In any case, there’s probably some form of moderation?

Y2013: Let’s assume that for now.

Present-day Yvonne (2020): This kind of moderation is available on Zoom, and potentially on other platforms as well.

Ari: Right. Working on shorter-length problems in class works fine online.

Lecturing is actually the hard part. The reason it’s difficult is that it’s much less interactive. If the instructor is just typing stuff which gradually appears on the screen, there’s not much incentive for the student to pay attention instead of deciding, “I’ll just read the whole transcript later.” So lectures must be liberally sprinkled with questions to evaluate comprehension or points for discussion by students.

What’s the topic of the class?

Y2013: Geometry from a transformation perspective.

Which brings up another question: How do you handle discussions about diagrams?

Ari: We have prepared diagrams for geometry classes.

But if the students want to do something that we haven’t prepared in advance, it doesn’t work too well. You want some sort of interactive blackboard thing for that, I would think.

Y2013: Hmm … okay. I’m thinking about a question that we often open the course with: Given two rectangles in the plane, show that there is always a line that bisects both rectangles simultaneously.

Should I maybe look for a separate program that students can be logged onto at the same time to draw?

Ari: Possibly. Prepared diagrams actually work most of the time. If your chat system supports them sending images, that might be good, too.

But it’s also okay for them to express some idea in words, and then you provide the diagrams which demonstrate it. For instance, suppose some student says, “The lines that bisect a rectangle all have to go through the middle.”

You say, “You mean, like this?” (DIAGRAM)

It’s partly a question of whether they’ll be able to make good diagrams on the fly, which students may or may not be able to.

Y2020: In 2013, virtual shared drawing spaces didn’t exist the way they do now, and certainly webcam technology wasn’t as prevalent. All that said, there’s still something nice about being able to ask students to articulate, in words, what they are imagining. There’s an entire literature on how connecting diagrams with the logical constraints behind them may be key to learning geometry (e.g., Duval, 2006; Fischbein, 1993; Jones, 1998; Mesquita, 1998; Presmeg, 2007). In the class that I’m co-teaching currently, which uses Zoom, I swap between making diagrams based on what students are saying and asking students to make drawings and shove them up against the webcam. I find both useful, and the latter especially useful for getting a read on the class as a whole.

Y2013: How much have you found that your face-to-face teaching skills translate to online teaching? For instance, we’ve been talking about diagrams and discussions; what about building rapport with students on the first day and throughout, or how to give instructions for what would otherwise have been a handout or slide?

Ari: Good question!

So, obviously one can’t build rapport via eye contact, body language, tone of voice, etc. Some tools for making students feel comfortable in class and that their input is being valued include: Careful choice of words to maintain a welcoming tone. Consistently responding to questions, whether publicly or privately. And using a fair bit of humor at the beginning of class and during transitions.

On answering questions. When students ask a question, the teacher gets the question ‘privately’. The teacher can then choose to pass the question to the whole class, or answer it privately. This allows the class to proceed without those questions, which might distract. At the same time, it allows student to get answers to individual questions.

Giving instructions is perhaps easier than in person, because of persistent text: whatever you say hangs in the air and they keep reading it.

In general, the biggest skill that doesn’t translate is improvisation. Instead of improvising spoken words, you need to get good at improvising written words very quickly.

Of course, one can always stick to a script, but it’s nice to have the option of exploring tangents, finding teachable moments within alternate solutions or mistakes, etc.

That said, for lecturing, I strongly recommend having the remarks prepared and using some amount of copy-pasting rather than writing them on the fly.

Y2013: Wrapping up discussions and summarizing key points – are those also places where generating some draft or default text ahead of time would be a good idea?

Ari: Yes, definitely. Teaching online can be pretty tiring because you have to produce cogent text on the fly. Delegating some of it to your past self is a good idea.

Y2020: As one of my friends recently commented, “How is it that talking at students for 20 minutes on Zoom is more tiring than jumping around a classroom for 2 hours?!”

I have also found online teaching to be similarly or more tiring than physical teaching because I’m limited to primarily one mode of interaction: words. Even though there is some facial interaction on Zoom, I haven’t found it to work with my intuition in quite the same way.

Ari: One other thing I should mention about your class plan: I’m not sure that giving students in-class homework time will work. When you do that in person, you can circulate and watch them and there’s lots of direct social pressure to actually work during that time. But if an instructor did that to me online, I feel like I’d probably get up and eat. This is a gut feeling and not based on any particular experience.

Y2020: This is perhaps the hardest thing for any instructor seasoned in discussion-based teaching: that in-person social contracts differ from online ones! Social pressure works in different ways, and circulating also feels different. When I teach in person, I often can make in-the-moment changes to my discussion plans based on what I am seeing from students, and how they respond to my questions just to their group. Although I can do this in breakout rooms, it requires a different kind of concentration than visually scanning the room and making connections between different students’ work. As well, in-person, I often send delegates from one group to meet with another group to compare strategies. This doesn’t translate as easily or well, especially as one function of this technique is to give students a physical break by having them walk instead of sitting.

Y2013: Thanks so much. I think these are all the questions I have for now.

Ari: You’re welcome.

Y2020: Reading this over again now, there are some parts that seem charmingly quaint, such as our implicit question about whether there might even exist accessible platforms where people can simultaneously share images. But there are other pieces that ring true: that carefully chosen words are key to helping students feel welcomed. That teaching online can be tiring in its own way, and one way to mitigate that is to have some prepared text. And also that teaching online, though different from physical teaching, can have its perks. A great affordance of online teaching, that you don’t necessarily get so much in physical teaching, is the capacity for students to ask questions privately, and for you and the student to choose between private and public answering. And personally, I’ve found that having students work collaboratively on google docs is far easier than using a document camera to show multiple solutions.

Because I have a toddler at home, I spend a lot of time looking at her shape sorter, and how she will still sometimes put the square peg in the round hole (and it doesn’t fit). On the other hand, the square peg does fit in the octagonal hole, with appropriate rotation (at least in her set). To some degree, I think my difficulties in online teaching are in part due to fitting a square peg of physical teaching into a round role of online teaching. The times that it’s gone best are when I see online teaching not as a lesser version of physical teaching, but as its own kind of teaching with its own special opportunities.

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