Meditations on a Cogen (No. 19) • Thursday, March 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 19th post in the series.

Pre-cogen recruitment
With my current cohort of cogen students transitioning out, I went hard this week on my recruitment efforts. Last week, four prospective replacements were identified by my current group. The cogen students did their part and reached out to them. They told me that most of the students they identified were hesitant about joining. That was my cue. Time for some encouragement and cogen advocacy!

I found most of the prospective students during lunch. There I pulled them out for a few minutes and gave them my elevator pitch. I managed to convince all of them that the cogen was worth their while. Two said that they would make it today and the others said they would come next week. (After today’s cogen I learned that one newbie from period 3 — who said he coming today — now cannot do the cogen because of a prior commitment. I’ll be on the hunt again next week.)

We finalized the directions and logistics of our board game last week, so today has a singular focus: prep the materials. We’re playing tomorrow and Monday. The two major tasks are: (1) create four gameboards on chart paper based on a revised blueprint and (2) label 34 problems with their respective levels (1-4). I dig through the mess inside my desk to find markers to draw the game boards and bright paper for the problems.

As we begin, I realize that I’m short two members that should be here. I find out later that both are attending an Emerging Leaders Program meeting. I have no problem at all about this, but only one of the students informs me. I’m slightly annoyed because of how much we have to do in just 30 minutes. We’ve been planning this for weeks, I say to myself. With so much prep to do for tomorrow’s kick-off, how could one of them bail on us today?

I quickly shake off my negativity and focus on who’s here. I see the new member and quickly (and poorly) orient him to cogen. Other than the snacks and water, I mention that today’s meeting will look nothing like it usually does. We will not be sitting around the table and there will be no formal dialogue. He nods willingly and unassumingly. It’s clear that he’s grateful to be here. I’m grateful he is, too. He’s dependable and eager and will be a wonderful asset to the next cohort.

We divide up the work. There’s a total of six of us. Half create the boards and the other half (which includes me) label the problems. After some scrambling to find additional staplers and staples, my half finds our rhythm. The students who are creating the gameboards work together nicely, too. Unknownst to me, they even coordinate colors on the board with the colors we’ve chosen for the different levels of problems. There’s synergy in the room.

As 3:15pm approaches and we are completing everything, a few members have to leave. I bid them farewell and thank them vigorously for their leadership. They should be proud of what they’ve created — not just today, but in the weeks leading up to today. As they pack up, I’m placing game pieces in makeshift envelopes for the tables when suddenly remember that we don’t have a name for the game. Ha! Weeks of playing and we forget the most obvious of things. The kids quickly throw out one name after another. One sticks: Infinite Levels. It’s fitting. We run with it.

Upon finalizing the name, one of the students who missed today due to Emerging Leaders flies into the room. He apologizes for his absence and asks if there’s anything he can do to help. He was actually the one who came up with the idea of playing a board game in the first place. When I see him come in, it’s clear that he feels horrible about not being here to help us today. I thank him for coming back and checking in and then ask him to look over the slides he created with the directions. The cogen students are going to use his slides to introduce the game tomorrow. Now that he sees the game in the flesh, is there anything he wants to edit? We make a few additions. I give him a huge high five. He heads home.

Let’s play
After all the students leave, I tidy up and get the tables in order for tomorrow. I place the gameboards, problems, and game pieces out. I drop some whiteboards on each group and call it a day. Infinite Levels is born.

I leave happy.


Meditations on a Cogen (No. 18) • Thursday, March 3, 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 18th post in the series.

A new tradition
We’re coming off mid-winter break and at some point during the last two weeks, I found inspiration — I forget from where — for a new tradition at the cogen. It’s pretty simple: I want to start each session with everyone answering the question, What’s something you have done for someone else in the last week? It’s a way of starting every cogen with generosity and kindness and also helps me get to know the students better.

Everyone shows up again today with no in-person reminders. I’m not surprised; this cohort has been so consistent these last several weeks. They’re great. I ask everyone how they’re feeling and then introduce our new tradition. We all go around and share our acts of generosity. The standout: earlier today, someone gave a friend a snack because they were hungry.

Finalizing Plans
I long to touch on several issues with the team today (seating arrangements, journal 2 reflections, problem presenters), but I have to push them aside and prioritize our board game. Our planning is basically complete, and we were originally scheduled to play tomorrow and Monday, but we decided to wait one more week. There are details that need to be ironed out. I’ve been super flexible on timing — there’s no need to rush.

The first item up for discussion is the gameboard. The student who was responsible for creating it emailed it to me earlier this week. I present it to the rest of the cogen. Everyone loves it.

The student-created gameboard

I show them a die that players will roll to move along the board. We agree that the center space should be a “challenge problem” and decide that it will be a Level 4. We have an interesting debate over which direction players will move and whether it matters. Can players change direction after passing through the center? This gets messy and we determine a uniform direction for all players. We figure that we will remove the word “space” should be removed in favor of an empty black space (if a player lands on it, they get no problem to answer and, hence, can earn no points on that round). A student proposes an “entry” square to the immediate left of the board where players will start play. Chess and checkers pieces are to be used for players’ game pieces.

If a player gets a problem wrong on their turn, the other players will have the opportunity to “steal” — to answer the problem correctly and earn the points. There’s going to be 3-4 teams per table, so how will the “stealing team” be determined? I’m baffled, as I usually am when it comes to simple things, when a student says, “Let them roll the die for it. Highest number wins.” It’s perfect. Because of this, we decide that the problem cards (that I’ll be creating this week) should be printed on 8.5″ x 11″ paper. This way, all teams can see and work on the problem at the same time. This will not only keep everyone engaged even when it’s not their turn, but speed up gameplay during stealing because stealing teams will have their answer ready.

We do a mini walkthrough of the game and feel good about it. I remind the students that I will be creating the answer key for the problems. They offer some pointers on its structure that will allow for easy checking as players call them over. I take note. At the end of our meeting, someone volunteers to create a couple of slides with game rules and instructions. The cogen students will use them to introduce the game to the class.

There’s nothing left to do now but play! We’ll use next week’s cogen to recreate the gameboards on four large chart papers that will be placed at the center of each table and make any other final touches. I forget to ask the group about a name for the game — but we decide that next week, too. I promise to have the problem cards and answer key ready for them to review. I tell the crew that it’s been so much fun planning the game with them that even though we haven’t even played yet, I see myself using it again next year. We’ve put a ton of thought and effort into it. Why not reuse it? One student remarks that I ask next year’s cogen to modify the game for their class — to make it even better. It’s a brilliant idea.

We depart, eager to play.

This is sixth week for the current cohort. We’ve been talking about their replacements for a few weeks now — including at the start of today’s session. All of them have identified at least one potential successor, but most of their choices have expressed little interest in joining the cogen or need to be convinced. I’ve been pretty good at helping students network cogen replacements this year, but I’ve been so absorbed with planning our game these last few weeks that I haven’t done any advocacy work for the next cohort. That needs to change next week. Time to recruit!


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.”


Meditations on a Cogen (No. 15) • Thursday, February 3, 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 15th post in the series.

A good problem
It is 2:45pm and I sit down around the table to realize that this is the largest cogen of the year. I have nine students around me as we start. This included three cogen “graduates” who came back for another round (two of them are now regulars). I successfully filled the empty seat from period 1, but the invited student brought their friend with them. An added bonus! I now have three students from period 1 and two from periods 5 and 9.

I am flattered and excited about the turnout. Kids actually want to be here! Maybe this shouldn’t come as a surprise during 15th cogen of the year, but it does. I try not to take their time for granted.

As we start, I quickly realize that with such a large group, I have another problem on my hands: too many voices. Throughout the year, worried that I wouldn’t have enough students, I have been welcoming all students — even those whose six-week commitment has passed or those who wonder into the room on a limb. But now, after today, I’m concerned about my open door policy. There are several new and reserved students in the cogen and I fear that their voices might get lost in the crowd or inadvertently silenced by more established members. The intimacy and exclusivity of the cogen is precisely why it works. Do I politely ask older members to step aside to make room for their successors? Do I turn away non-regulars who stumble upon us? Or do I remain inclusive and find a way to balance it all? This is a good problem to have.

Reflections on Bingo
The primary goal today is to debrief the Bingo lesson that I cotaught with five of the cogen students this week. It was a big deal for me and to the evolution of my cogen. We have reached the next phase.

Coteaching with the students was so rich and informative that I had to write a separate blog post about it. In addition to detailing how the lesson went, the post also captures the cogen reflections from today.

Next cogen project
After witnessing their predecessors coteach the class, I turned to the current cogen members. What lesson do they want to teach? Similar to the last group, I want them to choose. Drawing off the competitive vibes that resulted from the Bingo lesson, they mention games. Bingo was fun and the class enjoyed it. Why not try a different game?

The first student mentions one she played in her AP Spanish class that used In the game, students stood and moved forward and backward based on correct answers. It sounds fun. She provides details and we take note. A second student recommends Jeopardy. I’ve played plenty of Jeopardy-style games in the past, so I could help a lot with planning if we go that route. A third student recommends something interesting: a board game. It’s such an unexpected idea that it gains traction with the group. We imagine each of the four groups in the room playing the same game asynchronously. It’s an early favorite.

I ask the students to continue thinking about their lesson. We should commit to one and start planning it next week.

Updates and Next Steps
With about 5 minutes left, I provide the crew with some quick updates.

First, we had a quiz today in class and I ask the students if they noticed my improved timing. Acting on the cogen’s feedback from last week, I organized the lesson so that no one would have to stay after class in order to finish it. The kids noticed the improved timing on the quiz and appreciated it. I give my word to continue this.

Second, I remind them that tomorrow will be our first DeltaMath Day. We have been talking about this for a few weeks. I ask for quick suggestions on structure. Should we treat it like an independent workday? Should I set up a “help desk”? Should I simply float around the room? What would work best for them as students? They seem indifferent, but do like the help desk idea. We’ll see.

Lastly, we have an exam next week. Two cogens ago, we revised the class retake policy for exams so that anyone can take action to improve their grade (not just students who scored below 85%). We also realized that many students in the class may not know that a retake exam replaces their original grade. I vow to reannounce and place emphasis on both of these class policies next week before and after next week’s exam. I ask the students to hold me accountable for this and to also help spread the word.

After the students leave, I realize that I forgot to ask the new members about taking over the role of announcing our DeltaMath completion percentage. The cogen members have been doing this on Mondays and a routine is starting to form. I make note to follow up during class tomorrow.


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