My Discovery-Based Math Elective: Modifying for Distance Learning (Part 10)

This is part 10, of a 15-part series of posts detailing how I developed and piloted a discovery-based high school math elective. The first, introductory, blog post for this series can be found here [Introductions]. The goal of this post is to describe how I modified the class once we had transitioned to distance learning as a result of the COVID-19 pandemic.

I can't say the "distance learning" version of this class did everything I wanted it to do. But this class made the transition to distance learning better than my Math 1 class. So after trying a few things, here's what I settled on.

• Platforms I Used
• Google Classroom
• Google Voice: for weekly phone calls/texts with students, checking in with them, and answering quick questions
• Google Hangouts, Zoom: for conferencing/tutoring
• Awwapp.com: an online collaborative whiteboard during conferencing/tutoring
• Desmos.com/geometry: a canvas upon which to record videos
• Typical "Week"
• ~Sunday Night: I posted PSets at the beginning of each week.
• In addition to posting the PSet, I found it helped to post a very quick (~2 min) video explaining the Big Problem, and doing a couple quick examples to get them started. A little bit of extra support, early on, can do a lot for facilitating student entry into a task. This was crucial, because students were doing PSets mostly on their own.
• Thursday/Friday: text/call each kid to check in about the work, school, life, etc.
• ~Sunday Morning: Post the end-of-PSet notes video
• Compiling PSets
• I kept this super wide open. Google Classroom is pretty effective, in that it allows students to basically upload anything into an assignment. Most kids uploaded the pictures directly. Some made a Google Doc and uploaded pictures in there, along with some descriptions typed in the document. Others made Google Slides, doing a similar thing. I even had one student submit a video demonstrating their solution to a problem. Another student opted to use the Awwapp online whiteboard, and they just uploaded the link to their work.
• With Google Classroom keeping everything together, it really didn't matter what the format of their submissions were. As long as I am able to make comments on the product somehow, anything goes. This is a place where I can remain flexible, hoping to make distance learning more accessible for students.
• The Architecture of a PSet
• Students were going to be completing these PSets mostly independently. During a regular PSet, the general philosophy is to provide scaffolds "just-in-time," so that students only get the minimum degree and kind of scaffold that they need. However, this is basically impossible to do with distance learning. So I erred on the side of including a bunch more scaffolding questions.
• These more developed scaffolding questions looked like smaller questions, more "easy" questions, and some questions that provide more explicit directions with how to do some of the work. They also included more examples and diagrams.
• I also included more "self-checking" questions. For example, if I wanted kids to convert numbers to binary, I could add a small question before that: "Show that 12 in binary is 1100." Thusly, the question provides an answer key with which they can double-check their process.
• With all the extra scaffolding questions and additional pictures, the PSets got longer. Back in the Normal Times, I would restrict each PSet to a single two-sided page (albeit with very narrow margins). Once we got online, with these added design principles, the average PSet was closer to four pages. I further justified this by including more, different questions, in an effort to really amp up the degree of choice and flexibility students had.
• There were some things that were actually better about the PSets, because students were accessing the PSets digitally. I was able to include more links to online math tools and videos. I was also able to include little animations directly in the PSet, by copying in GIFs. I also hoped that more students would comment on the PSets, asking clarifying questions, because I think that would have been helpful for other students as well. Next time I might advocate for this more directly?
• Grading, Standards, and Assessment
• Each PSet is graded 0, 1, or 2 points.
• 0 = no work submitted
• 1 = some work submitted, PSet off to a good start, but not "done"
• Most first submissions of PSets got a 1, so it was more like I was recognizing that the student had submitted a 1st draft of the PSet.
• I would then return the PSet to them, with comments on where they could go from there, feedback on the work they'd done, or just recommendations for other problems that build well on the work they'd done.
• I will say, this mechanism was the closest I ever got to a system for meaningful revision, in any version of this class.
• 2 = solid PSet, lots of problems done well enough, or a couple problems done really well
• In order to pass the class, students needed a certain number of points. In an effort to minimize the privilege filter that is student performance during a global pandemic and national crisis, I ran the class Pass/Incomplete.
• This is about as far from standards-based as grading gets, which is not great. But at a time when students need maximum flexibility in their work and assessment, this felt respectful. It is pretty subjective, and really requires the teacher to understand the students, both as a mathematician and person in the middle of a pandemic.
• To balance the subjectivity, it helped that I had most of the students for the time before distance learning, and I had everyone for in-person school for at least a month. So I had get an understanding of where they were going into this. I also had weekly individual text/call conversations with each kid, just so I could keep up with how they're doing. I would then take all that into account when reading PSets.
• No late penalty for PSets. I had a "due date" so that they'd get regular reminders, but I would grade a student's PSet whenever they turned it in. All-in on asynchronous learning.
• End-of-PSet Discussion Notes
• The end-of-PSet notes were much more "level to the objective." Students did different PSets at different times, so it was not possible to get a feel for which ceilings which students hit, and level to them. So I basically just leveled to the objective, and erred on the side of spoiling the Big Problem as little as possible.
• I tried to keep the videos to 10 minutes, but they often were closer to 15 minutes. 
• I originally recorded videos using my phone like a document camera. But uploading videos was a pain. So instead I made the videos on my computer, typically using desmos.com/geometry. I would record just a section of my computer screen, and then have all the objects/labels I needed just off the edge of what was being recorded, so I could bring them in quickly. The Desmos Geometry app is definitely rudimentary, and if I were to do it again, I might consider GeoGebra instead. But I didn't need that much from it, so Desmos Geometry did the trick.
• For Graph Theory: PSet 23: Bridges, the Big Problem was the classic Seven Bridges of Konigsberg problem. Instead of recording my own video, I posted Numberphile's video on the problem, which did a better job than I ever could have. I would do this as often as I could, though rarely could I find a video that did what I needed it to do.
• Exhibitions (?)
• I technically offered an option for an end-of-semester exhibition. You can see the memo I gave them, detailing all the options, here. It was worth up to 6 points (3x as much as a PSet). All but one student said they'd rather just do more PSets, and revise more PSets. Which was totally okay with me. I can't totally blame them--exhibitions are a lot of work! If I were to do this again, I would need to reconsider the weight, or potentially make it mandatory if it was that important to me.
• The biggest issue with this class, I felt, was that it didn't support students in collaboration. It was certainly possible for two students to call each other up, pull up the PSet, and do the work together. But it's pretty difficult. I need to do a lot more learning about what remote math collaboration can look like.