This past spring we had to jump into remote learning. We were all figuring it out as we went along. I happened to be teaching two very different math classes at the time, which were being taught in very different ways. As such, I was able to experiment with two very different approaches.

I wrote about what I tried and learned during remote learning here. One of my preps was Integrated Math 1 (~CPM). It went fine. My other prep was a discovery-based math elective I developed (you can read about it here). This elective seemed to make the jump to remote learning much better than Math 1. I wrote about how I modified it for remote learning here. But the big idea was using weekly

**problem sets**(PSETs). That's what I plan on doing this fall. So I want to take an opportunity here to reflect on what I think PSETs can do for remote learning specifically, and why.What is a PSET?

- Here is a model PSET I made. Here are the major features
**Big Problem**: the big complicated problem at the center of the PSET. Everyone works on it. Most of our class discussion is focused on it.**Four Sections**: Big Problem, Related Problems, "Not" Related Problems, and Going Deeper**Variety**: Different kinds of problems, of different sizes, different topics, different goals**Content Thread**: All the problems have a "Different Surface -- Same Depth". They appear different, but are all perspective on the same central Big Idea, that weaves through all the problems, like a thread.- Students are given a PSET at the beginning of the week, and they have the week to do a week's-worth of work. They upload all their work in Google Classroom at the end of the week.

PSETs Adapt Well to Remote Learning

- More Choice → More Engagement
- Except for spending a portion of their time on the Big Problem, students can spend as much or little time as they want on whichever problems they want. If I made the PSET right, and they do a week's-worth of work, they should work with the Big Idea no matter what path they choose.
- This increases the odds that students are relatively more interested in the work they do, b/c they're picking from a bunch of problems. Moreover, just the process of picking problems will inherently build commitment...b/c they chose it!
- This also allows them to remain sensitive to their own readiness to engage in more complicated discussions out of self-preservation. If I had a PSET on exponential functions, I could totally include a problem on the COVID-19 and disease spread. But that could also be super traumatic for some students. So instead I make sure there are problems that also hit the same Big Ideas, but aren't as heavy, in case they don't want to think too much about the global pandemic. And if some kids *do* want to learn more about it, if they're ready, there it is.
- Focus on fewer bigger ideas → more efficient
- Learning has a kind of "efficiency ratio." We engage in some quantity of "doing," and some smaller quantity of it sticks as "learning." The rate at which that transfer from
*doing*to*learning*is a function of a lot of factors, only some of which students and teachers can directly impact. - Stress, new technology, different learning environment, health and wellness, and change in and of itself, are all factors that are greatly impacting students' "efficiency ratios." Kids are also being asked to quickly learn a ton of non-academic stuff. They're learning about the world, health, their own hearts, how to do emails, how to sustain relationships from afar, how to manage sickness, and a million other incredibly important things. And as far as academic learning goes, even if students are able to create space for it, it's reasonable to expect that this "efficiency ratio" is lower than normal.
- As such, it's more important than ever for is to answer the question: what are we willing to trade? Assuming we were operating anywhere near the frontier of performance and capacity for learning, we are going to need to reallocate capacity away from academic content, and toward
**surviving**in These Uncertain Times. - Option 1: Distance Modulation. Go into the same depth, but get through fewer ideas, modulating the distance you get based on your community's capacity.

- Option 2: Depth Modulation. Go through all the same ideas, but don't go as deep, modulating the depth you study based on your community's capacity.

- I claim that depth modulation is the way to go here. Because U.S. math education has built itself around the idea of prerequisites, and because we
**know**the U.S. is going to push schools to push kids to get "caught up" (an oppressive and garbage expectation), it'll be a lot easier to bridge this time if kids at least have exposure. - PSETs also have a lot of other mechanisms that allow for differentiation for readiness, and I talk a bit about them in this post. But the big idea is that it's easier for a bunch of kids to be working on the same content to different depths, as opposed to working on totally different content.
- All the problems packed into one paper → increased need/flexibility in product
- A long-term goal is that students learn how to do math "anywhere." On a whiteboard, window, piece of paper, spreadsheet...wherever is convenient and appropriate for the math itself. Part of learning how to do math is learning "where" you should do the math. Is this a small problem I can scrawl on a napkin? Is this going to make a bunch of data I'll probably want to put into a spreadsheet? Am I going to need a bunch of blank paper? Grid paper? By making it impossible to do the math *where* the problems are assigned, we force students to make a decision about when/where/how to do the math. This definitely takes up cognitive energy and work time, especially if they don't make the most efficient choice. But that's an instructional trade that feels worth making.
- This becomes especially useful during remote learning for a lot of reasons. Computers are more available than ever. So math on the computer becomes accessible anew. Not everyone knew to bring their notebook home from school. My kids this fall may not have one (we tried to pass them out at orientation, but I doubt that most kids were able to pick one up).
- Do the picture on some paper, or in your notebook, and upload a picture. Did something on desmos.com/calculator? Upload a screenshot or upload the link to share it. Made something with blocks? Take a picture and upload it. Google Classroom does decent job of collecting and archiving work. It's pretty easy to leave comments on things. I push it back for revisions? Do some work and upload pictures of that! Now we have a "paper trail" for revisions--something that's not always easy to do when passing a paper assignment back and forth.
- This is definitely going to raise the demand for teaching students how to use math tools like spreadsheets, graphing calculators, and google docs. Seems worth it though.
- You've got a week to do a week's-worth of work → honor increased demand for time flexibility
- I remember video conferencing with a student about some work a few months ago. As they were talking to me, their little sibling was running around, asking for food and attention. At one point, the kid was literally climbing my student (as two year olds are wont to do). When you're at home, it's not always as easy to get a whole hour dedicated to a task, without distraction. Throw in a dash of the year 2020 and there may be entire days where you can't set much time to work. I get it. And any adult that doesn't has to seriously do some empathy building.
- The body of mathematical knowledge isn't neatly packaged into 54-minute units of knowledge. Some things take 10 minutes to learn. Some problems take 4 hours to work through. So I'm going to give you a bunch of math to do, and you do a week's-worth of work by the end of the week. Do what you can, when you can.
- As a teacher, I am professional. And that comes with the recognition that all that matters it that I get the job done, by the time it needs to get done. I think about how disrespected I feel when PD is super prescriptive with how I spend my time. It feels important to extend that opportunity to students whenever possible. In regular face-to-face school time, that's more difficult, b/c we have 500 kids to rotate through 40 teachers, spanning 6 different courses. And very few people in power are willing to invest in schools so that they can be more humane in their scheduling. So we have to make some sacrifices for large-scale efficiency.
- Some students will need a lot of support and scaffolds for how to manage that expectation. And I'm prepared to do that. I'll recommend for some kids that the set a time for 60 minutes, sit down at the kitchen table, and crush some problems till the timer goes off. Some kids I'll say set a count-down for 5 hours, and then start it whenever they're doing math, and pause it when they stop. Again, this seems worth the instructional time it will take. Through continued conversation, reflection, and experimentation, students will learn what they need to do the learning--to get the job done. And if that's not the most transferable learning objective, I don't know what is.

PSETs do a lot of things. They're also a major area of pedagogical exploration for me for the last year and a half, for a lot of reasons. So maybe they're the hammer to my remote learning nail. But they are a remarkably flexible approach to math instruction, and now is

**definitely**a time that demands flexibility.