Meditations on a Cogen (No. 6) • Thursday, November 18, 2021

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 sixth post in the series.

New members
This was an important week for the cogen: it was the last scheduled meeting for the initial members. After a six-week commitment, it was transition time. Having mentioned this to them a few weeks ago, earlier this week I reminded them individually to identify their replacement. Who would it be? Who might be a good fit? I meant to discuss this with them at last week’s session, but got too caught up with the journals. I noticed some hesitancy for two of the students when it came to picking their replacement. I want to offer them suggestions on who to choose, but also want them to own the decision. It’s their seat at the table and they need to ensure it gets filled.

I’ll be honest, all this talk of transition and finding replacements has me a little anxious. Will we have to coordinate a new meeting time? Will there be the same amount of buy-in from the new members? Just when I was getting comfortable, there’s suddenly so many variables that could derail us.

My hope for this week was that some of the new members would be able to join us for today’s cogen. I shared this with the cogen, but knew that scheduling conflicts might prevent it from happening.

Fast forward to 2:45p today and — bam! — there was two new members sitting around the table. I was pleasantly shocked. The initial members actually recruited! They care! One of the new members even had a friend with them and asked if they could stay too. The friend was a student I taught last year and I immediately said yes. How fascinating would it be to get his perspective on things after having been in my class for an entire year? I learned that the other newbie would be sacrificing 15 minutes of basketball practice every Thursday so that she could take part in the cogen. It was only her first meeting, but it already seemed worth it. I did my best to contain my excitement as we got started.

My giddiness in check, I asked everyone how they were feeling. There were casual nods and grunts of fatigue. I empathized. I was exhausted too. Poor sleep has ravaged me this week and my eyes have been burning for the last three days. But going back to last year, my cogen has been a highlight of my week for a while now. The dialogue heals and leaves me energized. So despite my tiredness, I was elated to spend 30 minutes building with them again.

As we went around sharing about our days, I sensed awkwardness in the two new members. This was to be expected. Cogens are unusual and untraditional spaces — especially if you’re new to them. To help welcome the new members, I asked the initial members to describe the cogen and share its purpose. They talked about some of the changes that were made as a result of the cogen, like the Deltamath review assignment and the after-school tutoring scaffolds. They also mentioned the time commitment and perks. Towards the end of the shareout, one student said confidently, “He actually makes changes based on our opinion — it’s not just us talking about it.”

I must say, hearing the students talk about the cogen in this way made me proud. They believed in the space we created together and in their authority as change-makers. Our dialogues activated their ideas for improving the classroom and helped their solutions manifest in concrete ways. I don’t know where things will go from here, but for now, it seems like the cogen is making a difference.

I treat quizzes as bite-sized check ins. They’re based on an individual students’ understanding of a single concept or, at most, two concepts. They’re always one problem and take around five minutes to solve. I call them “quizzes,” but other teachers would probably call them exit tickets.

Anyway, this week, somewhat spontaneously, I tried two new structures for quizzes. My students have struggled this year with collaborating, so I decided to use our quizzes to help them improve. The first thing I did, on Tuesday, was to have a “Class Quiz.” I stole this idea from another teacher at my school and it asks each group to solve a problem on a large whiteboard. The problems were from the homework and there were four of them (I had four large groups, too). After students finish and have an opportunity to revise their work, they listen in as I grade the problems in front of everyone. I choose a random problem to count as the quiz grade. The grade that problem earns is what everyone in the class receives for the quiz.

The second thing I did, today, was what I called a “Group Quiz.” For this one, I gave everyone in a given group the same quiz. The quiz was one problem, just like the regular quizzes. In a twist, at the end of the class, I asked for one random student’s paper from each group. The grade this student earned on the quiz would be the grade everyone in the group received.

I’ve never used either of these quiz formats with students before, so I was curious how my students experienced them. Were the quizzes fair? Did they serve their purpose? Which format did students’ prefer? The bulk of our time in the cogen today was spent with me picking the students’ brains with these types of questions.

Interestingly, the first comment came from one of the new members. She said that, during the class quiz, another teacher who does it asks the class to vote on whether the problems should be revised (this is the teacher I stole the idea from). For mine, I made revision mandatory. Another student commented that the revision process didn’t enable her to adequately take notes on the problems. This made sense because, after putting up their solution, each group was assigned one problem to revise. After that, I graded them. If I stay with four problems, one idea that was mentioned by the crew was to have students rotate so that every group gets a chance to visit each problem before the grading. (Ironically, after this comment, I managed to do just this in one of my co-taught classes the next day.)

The kids also gave me some quality feedback on the group quiz. What stood out most to them was how hard they worked on it. They were hovering over one another feverishly checking each others’ papers to ensure that everyone’s work was representative of the group. They felt pressure to work together and praised this aspect of the quiz. While the students appreciated being forced into collaboration of that degree, they said I should have ensured more time for them to work (many had to stay a few minutes after the bell to finish). Because I collected one random students’ paper, one cogen member pointed out that he was uncomfortable with his grade being dependent on another student. This was a fair critique.

Overall, the students appreciated the spiced-up versions of the quizzes. They recognized that the quizzes gave them a better understanding of the mathematics as compared to a traditional quiz: they got to communicate about it and compare ideas in the moment. They wanted me to use both again. We acknowledged that the students’ grades on these quizzes are not always going to be indicative of what each individual knows. This can be unfair and inequitable. From a teacher’s point of view, these quizzes also make it impossible for me to assess individual students’ understanding of the mathematics we learn. That said, I commented that my quizzes are a relatively low-stakes assessment; you have to take five of them for it to be equivalent to an exam. I reminded them how hard they worked on the quizzes; sometimes it’s worth sacrificing individual accountability if what results can promote cohesion and teamwork. In a system focused on individuality and students working in silos, our talk today evoked the “Are you responsible for the others’ learning?” conversation the cogen had a while back.

Near the end, I asked the students to choose which quiz format they preferred. The group quiz won 5-2. One students’ comment after we did this made me think: higher-performing students probably prefer the class quiz over the group quiz because they have more influence over what gets graded; they can write the correct work on the whiteboards. I left today’s cogen searching for small tweaks to make both quizzes better. The students’ criticality today definitely opened the door for that. The quizzes will surely be a topic of discussion at a future cogen.

Revisiting the math journals
At last week’s cogen, the students had a hearty discussion about the upcoming math journal assignment. They showered me with suggestions about it and I told them I would use their feedback to create a draft of the assignment. In the last 10 minutes of today’s session, I presented them with the assignment and asked for their feedback before I finalize it and assign it to my classes.

The students liked what they saw. They felt their ideas were reflected in the options students had for writing the journal. I reiterated that in previous years there was only one option for the journal and thanked them for their input in opening it up.

Saying goodbye
It was bittersweet that I had to say goodbye to some of the initial members at today’s session. I told the cogen today that these students have officially graduated and are now “cogen alumni.” The departing students asked if they could come back in the future and I replied with an enthusiastic yes. They will always be welcome; they are the founding members, where it call began. They filled me with the conviction that in-person cogens can and should happen. Truth is, these students have set the tone for an entire year of critical conversations and student-empowered decisions about our class. I couldn’t be more thankful for them. The day after today’s cogen (Friday), one of the graduating cogen students wrote me a Friday Letter that warmed my heart:

Next week is Thanksgiving break and I’ve decided that instead of holding a cogen, I will try and touch with the students individually as best I can. I’m doing something funky with next week’s exam and I’ll need their feedback.


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