Meditations on a Cogen (No. 17) • Thursday, February 17, 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 17th post in the series.

A full house with no reminders
This was the first cogen of the year that wasn’t preceded with an in-person reminder from me. I didn’t pull up to any of my cogen students at any this week before, during, or after class and ask them if they could make it today (also: there were no classes yesterday). The way things have been going these last several weeks, I was confident that they didn’t need me to do that. The one move I did make, however, was to email them yesterday to remind them about bringing in a blueprint for our board game. No one responded, so I couldn’t be sure if they read it or not.

It’s no matter because my students don’t disappoint today: everyone shows up. Even the newest member who couldn’t make it last week because of tutoring surprises me by coming through. One cogen alumnus also comes — he actually reminded the newest member about today. I shout him out both during and after the cogen for his act of community.

As we settle in around the table, my cogen family has me on a high. Though they’re no different than usual, the snacks taste better today. The air is light. I breathe in deeply and smile.

This week we have a singular focus: planning our board game lesson. It will be the second coteaching experience for the cogen. We left last week with plans to move forward with the idea and have a lot of work to do.

Before we start planning, I remember something a student asked me about this week: cogen replacements. I’ve been so wonderfully engrossed in the cogen’s progress these last few weeks that I didn’t even realize that the current cohort’s six-week tenure is coming to an end. Because of this, a hint of melancholy is present in my voice when I ask the students about their successors today. They have been so productive and willing, it is bittersweet for them to leave. Half of the group has a replacement in mind and drops names. I ask them to reach out to these folks and offer my support in breaking the ice.

Creating a board game
When we left last week, I asked the students to make a prototype of our gameboard. (I took on the responsibility of creating some makeshift problem cards.) This was really interesting because it was the first time all year that the cogen students left our meeting with “homework.” I was unsure of what to expect. But if coteaching is the next phase of the cogen, then it’s natural to presume students will have some work to do outside of the allotted 30 minutes we meet each week. Besides, the buy-in was strong last week from the kids. It felt right.

Did I mention already that the students have me on a high today? Well, they do. They bring three different hand-drawn gameboards! I do my best to contain my excitement in front of them. I’m thrilled. The boards varied in shape and orientation but were similar in that they all had a starting point and ending point. Think Shoots and Ladders. I ask the students to share what went into making their boards. One student shares her vision for using mathematicians during the game. Another has neat ideas for special spaces on the board. Their ideas are clever.

After I share my improvised problem cards, we get into the nitty-gritty of the game. There’s a lot of back-and-forth action for the rest of our time together as we hash out details of the board and gameplay. Here are some highlights and key takeaways of our dialogue:

  • Player movement. We originally decided (last week) that the problem cards would determine how players would move on the board. Each player would get to choose the problem level they wanted (by picking a card) and, if they got the problem on the card correct, they would move that number of spaces. Well, it doesn’t take long for the students to squash this idea. Instead, players will roll a die to move. The problem levels will be scattered randomly all over the board. Whatever level a player/team lands on, they pick up that card and solve the problem. We agree that this is fairer, more equitable, and more balanced.
  • Using points. By changing how how players move (random), we conclude that our game cannot be won by reaching a specific location on the board. There can be no “end” space. Instead, the game should be point-based. When players get problems correct (whose levels are also random), they will earn points based on the difficulty of the problem. Whoever has the most points at the end of the game, wins.
  • Infinity-shaped gameboard. Because the game is no longer based on a players’ positions, a student quickly suggests the board be made into the shape of an infinity symbol (∞). Everyone loves it.
an infinity-shaped game we sketch out during the cogen
  • Group gameplay. Throughout our talk, we flip-flop on whether to play the game synchronously (whole class) or asynchonrounsly (small groups). There are pros and cons to each, both for gameplay dynamics and logistics, but in the end agree to play the game in small groups. This means that each group plays its own game I have 4 groups in my classroom with 5-8 students each, so each player in the game will consist of 2-3 students.
  • Table vs. Table. In addtion to having individual winners from each group, we also want to have a winning group. To do this, at the end of gameplay we can have all players in each group sum their points. Whichever group has the largest sum wins that award. This way, players have an incentive to support other players in their group.
  • Coteachers checking answers. As players move around the gameboard solving problems, the cogen students (and myself) will float around the room with an answer key. After a player solves a problem, they will signal one of us by raising their hand. A coteacher will come over and check their work and final answer (all problems will be numbered for quick reference). This provides immediate feedback to the players. If the player gets it correct, they will earn the points for that problem. Incorrect solutions do not result in a penalty. (When I proposed that a key be left in each group so players/tables can self-check, the cogen said outright: “Mister, we’re going to cheat if you do that.” This was surprising and hilarious.)
  • Lockers. I have lots of empty lockers in my classroom (we used to be an elemenatry school). While we ultimately didn’t adopt it, there was a fascinating suggestion to use the lockers during our game. This spoke to me because it uses the physical environment to enhance the game. The idea to use them proved unwieldy for our game, but I pocket it for future use.
  • Point stealing. When a player lands on a “Level 2” space and begins working on the problem, all other players will work on the same problem. If the player who chose the card gets the problem wrong, another player will have a chance to steal the points for that problem. We didn’t determine yet who gets to steal.
  • Special Spaces. The majority of spaces on the board will have a problem level (1-3) on them. To add to the fun, we also want to have “special” spaces. These will be different and add some spice to gameplay. Some possibilities include: (a) challenge space (hard problem worth more points), (b) nothing space (no problem, no points), (c) steal points from other players (all players give another player 1 or 2 points), (d) donate points to others (player “gives” all other players 1 or 2 points), (e) earn a second chance card (if a player gets a problem wrong, they can exchange this card for a second chance at getting it correct before another player can steal)
  • Homework. At the end of our discussion, I ask if someone can make a sketch of the board that includes what we talked about today. Next week (or the week after, if we need more time to finialize), we will use our cogen to redraw the boards on large chart paper for each group. The chart papers will be placed at the center of each group for gameplay. The quietest student of the cogen agrees to take on this task. I promise to email her — and the rest of the team — our notes.
  • Game name. After we leave, it hits me that we don’t have a name for the game. We have to think of somethign catchy.

Excitement all around
A lot happened today. The energy was high, ideas were flowing, and everyone was present in body and mind. There was plenty of debate about our game/lesson. It’s really taking shape. Everyone contributed and is feeling good about it. I even overheard a student say at the end, “Today was really productive.” I couldn’t agree more.


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