# How I’m Teaching Remotely during this Crisis

Once a week, back in February, a small group of juniors and seniors would bring bag lunches into Room 133. Every Tuesday. They’d take out their lunches. I’d take out mine. I’d pass out a snack – often Croatian wafers with mocha or hazelnut filling (no allergies in the room). And then we would start.

The class? I was calling it Axiomatic Arithmetic. Goal? To construct the real number system, using, for high school, fairly formal language. I wanted to make sure they got a big gulp of history along the way. And proof. I wanted to walk away with all 12 students better at understanding proof, and with some experience constructing proofs. We did some history. Learned about Peano. Picked a least bad text (doesn’t really do what I wanted, but first few chapters are heavy on proof for the naturals, integers, and rationals, and almost within their grasp). Started. Paused to relearn arithmetic (base 4, but using four strange symbols, to make it strange and make them think). Worked through Peano’s axioms. Paused to do some easier (advanced high school) proofs by induction. Now we have defined addition, and are proving associativity and commutativity tomorrow…. Yes, March 19 I wrote, and asked who wanted to continue, lunch time class, so completely voluntary. Eleven of twelve signed back up. We are down to ten now. And the live class once a week? Not so different from sitting in Room 133, except not being in 133. Great group, by the way.

Once a week, back in February, a smaller group of juniors and seniors… Same idea, different day. Set Theory, using the primary source-heavy MAA intro to Set Theory. And lunch time, Monday, just like we were in school, we meet and have a live discussion as we carefully move through the text, dwell on the language and notation, and attempt exercises and proofs.

But those are extra classes for me. My primary teaching this term is precalculus. Four sections. 101 dalma.., er, students. Before the crisis I had an interesting set-up. Homework assigned four days a week. Graded for completeness, not correctness. It was their job to correct (by asking others, by putting on the board). A few projects. And quizzes once or twice a week. The quizzes only counted if they were at least 80% right (no major errors), but could be retaken, for full credit, as many times as necessary. Could be taken? Nah. I required it.

Cool system, crushed by Corona.

So what now?

Each Monday I post reading from the text, with exercises. I attempted to provide additional notes, the kind that I would supply during a real lesson. But they are much easier to put on the board than on paper. To cover for me not being there, I needed to supply the kind of detail that I would only offer if I saw a kid with “that look” that told me they needed more. And trying to cover every question, they were just taking me a long time to write. A 20 minute lesson I might scratch out in 4-5 minutes, was taking me an hour and a half to write. I couldn’t keep up. And dropped the attempt.

Each Friday I announce which of the problems from the week I will collect for grading. And then the homework comes in. Slowly. Two-thirds exactly when due. More over the weekend. But I take everything – no idea what is going on in their real lives. And then, grading on line! How many clicks to open? Math handwriting can be bad on paper. But try reading on a screen! Why does Google Classroom have a defective zoom in feature? Comments are typed for each error or defect, whether or not it led to a deduction. Send the comment. Record the grade. Return the assignment. If the grade is low, assign replacement problems. A stack of 100 (ok, 101), should take me 20-30 minutes. Now? 3 – 4 hours.

During the week I was running office hours, 8 – 10 each morning. Coffee with me. Over “vacation” I broke the time up into half-hour activities. I am continuing that. Each student should show up at least once a week, for at least 15 minutes. As a minimum I can check in, listen to how they are doing – life, school work. I ask about food and sunlight and exercise. Not sure why, but they seem like good questions. Here’s my “office hours” schedule for this week:

Those requizzes are left overs from before the crisis. They are awkward to run, but there’s a few kids with older quizzes, and if they want to make them up (which they should) I feel an obligation to allow them. “Current Data” is just what it sounds like. I share and we review some source data, and talk about mathematical models, and politics or next steps, if that’s the direction they want to go in. “Complex” is an extra topic, for students who want a little more math. DeMoivre, if you wanted to know. Puzzles are logic, Games are probably anagrams of student names. One of my students can rearrange her letters into Magic Lit Zone, which is a pretty cool anagram. And the graphing covers this week’s material. I’ll give instructions for anyone who needs them, and run little mini-lessons to get them started.

I am trying hard. But I am not getting very much done – certainly less than in a live class.

There are things I cannot do. I can’t watch a student, and understand they are getting stuck. I can’t listen to a wrong answer, and diagnose the misunderstanding on the spot, and help the child repair it themselves. The stuff I am best at, not available.

What I can do goes slower. I am collecting very little, and am overwhelmed by the time grading it. Tracking attendance live is far, far easier (I count the kids in each class, and conclude “all here!” or “two out – who is missing?” My little mini-lessons take more time than full lessons, and cover a fraction of the ground.

I do NOT have this figured out. I am not sure that this is even sustainable – I may need to slow it down a bit more.

Set Theory and Arithmetic, with tiny groups of highly motivated students – no issue. Live class, once a week. Doing nearly the work we would have done live. Kids absolutely are earning their quarter credits.

But precalculus? I’ll strip out some topics – and we will go to late June – and it still will be a shadow of the real course.

I am not figuring out “remote teaching” – I’m learning to cope with it. And know what? If I had to do a full term of this, I would need to sit down and think really, really hard, and talk to a bunch of really smart people. Not close to there yet. But at least next time, if there is one, we would be planning in advance.

The experience of my colleagues and friends at the college level is similar: small, engaged groups of students translate easily, as do groups of students with a very strong rapport; more mature students translate better than less. But larger groups of less-motivated students? It seems impossible, really smart people or no :(