Meditations on a Cogen (No. 16) • Thursday, February 10, 2022

During the 2021-22 school year, I’m having weekly co-generative dialogues (or cogens) with my students. In an effort to help me process these talks and document progress, I summarize and write reflections after each cogen. This is the 16th post in the series.

Some opening reflections
Today’s cogen includes 8 students. Six are from my Regents-bound classes (the current cohort) and two are cogen alumni that just keep coming back week after week. I refuse to turn them away. I remind of a couple of them today during class, but most arrive on completely their own. This is encouraging.

We lift off with two quick talking points: today’s exam and DeltaMath Day from last week. The exam had mixed reviews. A couple of students mention that it was harder than they thought it would be, while others say it was just right. Other comments highlight specific problems, but there’s nothing noteworthy to hitch our idea train to. Our first DeltaMath Day was on Friday, a day I allowed students to work on their DeltaMath during class. Looking back, I thought we might have spent too much time discussing the opening problem (the “Do Now”) before transitioning to DeltaMath, but the cogen doesn’t think so. The students say it was enough time. In the end, I think DeltaMath Day helped because 2 of my 3 classes achieved their DeltaMath goal this week. Choice quizzes all around!

Math Journal Problems
Back in December, I assigned my math journal assignment. It’s a metacognitive writing task that asks students to choose a problem and explore their thinking around it. I’ve done it for years and am assigning it twice this year. It’s been largely unedited for a long time, but my first cohort of cogen students helped me heavily revise it. After submission of the first one, the second cohort offered several great suggestions to improve the assignment for the second go-around. One of their recommendations was to allow the cogen to choose which problems are featured in the next journal. This is a goal for today.

I provide this context (which involves me talking a lot — a mistake) and then hand the students 10 problems. I curated them based on how and what we have been learning. I want the cogen to choose five of the problems. These five will be the options for the class; each student will select one to write about in their journal. Almost all of the 10 problems we’ve either discussed in class or have been on exams (that was also based on the cogen’s feedback). Four of them include student work. As the students look over the problems, I find something to do away from the table. I want to give them time to think without me.

When I return, they pretty much have their five. This takes surprisingly less time than I thought it would. After they lock in their selections, we dabble here and there (one student voiced the lone Open Middle problem I included looked “scary”), but don’t spend enough time discussing why the students chose the problems they did — or at least why they eliminated some and not others. Looking back, this was a mistake on my end. Getting into their heads would have been valuable. What are the similarities of the five problems they chose? Why were the students drawn to them? What didn’t they like about the other five problems?

We could have spent all of our time today responding to these types of questions; it would have afforded us a rich discussion and given me some lovely insights into the mathematical minds of my students. Inquiring further into their mathematical leanings would have revealed how their thinking has been shaped by our class and even opened the door to activities like problem posing. Alas, despite being pressed for time, I feel that I missed an opportunity.

Co-designing a board game
We’re about halfway through today’s session when I ask the squad about our lesson. Last week we brainstormed and this week I wanted to lock in our decision so we can begin coplanning. Playing a board game with the class drew attention last week and it doesn’t take long before we decide to throw our collective weight behind it. We run with the idea.

We discuss details. Will the game run asynchronously in groups or as a whole class? How will players move on the board? What will the board look like? What special spaces will there be? These are fun questions to explore, but it’s clear that there is a lot of work to be done.

We flip-flop a few times, but tentatively decide to run to the game synchronously as a whole class. We conclude that, on their turn, players will pick up a Level 1, Level 2, or Level 3 card. Each card will have a math problem on it and also specify how many spaces they will move if answered correctly (a Level 1 problem will move less than a Level 3 problem, for example). We also consider having solutions on a table in the middle of the room so students/players can check their answers.

We depart with action steps. I commit to prep the problems and the students agree to design a gameboard. When we reconvene next week, we will merge our ideas and start finalizing the game. We plan on playing Friday, March 4. This will allow us to use the Thursday, March 3 cogen to create the gameboard(s) and make final preparations for the game.

Cogens = student empowerment
A recent Friday Letter from a student at today’s cogen reminded me that while cogens serve a definitive purpose of improving the classroom, that purpose comes with an important corollary: student empowerment. In his letter, he underscored the cogen’s role in helping him find his voice, step out of his comfort zone, and be a student leader. On Mondays, he’s part of the two-student team that announces the DeltaMath percentages and goals for the week in front of the whole class. It’s a role he inherited when he became a member of the cogen. It’s a simple job, but one that, when coupled with our weekly meetings, has boosted his confidence a lot. (Ironically, he is also a member of the Student Voice in Curriculum (SViC) initiative through the superintendent’s office, which is similar in spirit to our cogen.)

I’m glad that our cogen has reinforced his self-pride while also making him feel that he is an asset to our classroom, which he is. Though he is grateful to our cogen for how it has contributed to personal growth, his belief in and dedication to the cogen are equally outstanding. Without students like him, the space literally wouldn’t exist. The final words of his letter capture his allegiance to the cogen and hit home with me. They make my week.

“I’m really looking forward to continuing to work and helping in the cogen — especially the activity we’re planning. Like, I really think it has great potential and can be really, really fun if executed well, so I gotta start doing some board game research.”


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