Meditations on a Cogen (No. 5) • Friday, November 12, 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 fifth post in the series.

Lunch and a debate
We usually meet on Thursdays, but because of Veteran’s Day, that couldn’t happen this week. I remembered that we all have lunch 4th period and asked my cogen students if they could do Friday during lunch. They said ok. I don’t like sandwiching the cogen between classes like this, but I had to take it over not meeting at all. I spiritedly promised to bring the students Slim Jims for their flexibility, but ended up forgetting them. I now owe them double next week.

As I began dumping all the snacks onto the table, the kids trickled in. Two forgot that we were meeting today, but someone ran down to the cafeteria to get them. After a few minutes, we were all sitting around the table again. This was our 5th session together. I was unexpectedly comforted by this.

We checked in on how everyone was feeling. As a means of breaking the ice, I like picking up on whatever energy, vibe, or idea reveals itself in a given moment. I tend to be pretty observant, so it’s not that hard. I do this in class, too. It’s my way of staying present, acknowledging one another, and warming up to dialogue. Today, one of the students brought a cup of water they got from the cafeteria. For whatever reason, something spoke to me about that cup and we spent the next few minutes airly debating water dispensers vs. water fountains. It was fun.

Collective brainpower
We opened the formal dialogue by recapping what we discussed last week. I mentioned the feedback quiz that I tried last Friday (the day after our last cogen), and how that led to Monday’s lesson on trig ratios in the coordinate plane. I used VNPS and VRG for that lesson — which is the structure the students told me they learned a lot from. We ended up spending two days this week using it as well, which the students confirmed were effective. Last Friday the cogen also persuaded me to bring out the dry erase sleeves for worked examples and practice problems in small groups. I botched the timing so it wasn’t the best lesson, but it was cool. I don’t think the cogen students even realize it, but I often use worked examples at the start of class now. I didn’t mention this last point at the cogen today, but it’s interesting how our talks are impacting class in unforeseeable ways. Our ideas are helping me rethink areas of the class that we don’t explicitly touch on in our dialogues.

At one point during our recap, one student pointed out how another student was responsible for a couple of the ideas. “That was from her…” the student said casually a couple of times. I was proud that the student vividly remembered our last talk, but commented that those ideas, though one person may have said them, were the direct result of our dialogue. Our collective brainpower, problem solving abilities, and creativity birthed them; through our dialogue, we co-created the context that enabled the solutions to emerge. The students nodded.

Making journals relevant
I left last week’s cogen desperately wanting to discuss metacognitive math journals with the group, so that’s what we did for the remainder of today’s talk. I’ve done metacognitive journaling with my students for the last several years and have even used editorial boards to peer-review them, but the journals themselves tend to be fairly dull. They need some sprucing up.

I overviewed the journal process to the cogen and asked for their suggestions. I told them I was looking for ways to make it more meaningful, but also for ways to make it fun and engaging. After some clarifying questions, they let loose. One recommendation was that students turn the journal into a written dialogue between two people. If this is the case, maybe students should be permitted to work in pairs to do the journal? This is a fascinating idea! Other ideas were allowing the journal to be a letter to self or even a short story. The journal requires a student to reflect on their solution pathway to a problem, but could they integrate drawings or other art to do this? Instead of students choosing any problem (what I have always done), one student commented that they should have to choose between a handful of challenging problems that I curate for them. In years past, I have required that the journal entries come from our standard problem set, but why can’t it be one from an exam that the entire class struggled with? Or an entirely new problem they haven’t seen yet? Our recent usage of worked examples even made me think about students using one for the journal. Why not? Given the right problem and work, it could make for juicy reflections.

An assumption throughout our dialogue and their recommendations was choice. In my three years of doing journaling, crazily enough, I never considered giving students a choice in the matter. But why not? Reflecting on one’s mathematical thinking should not be uniform. Putting their ideas in a box is probably why the journals have failed to come alive for my students these last few years. I need to throw out the box. As we wrapped up, I thanked the students and them that I would use the ideas we generated today to create an updated version of the journal assignment. I would present it to the cogen next week to get their feedback before I assigned it to all my classes.

During our discussion, I noticed one student in the group was kind of quiet and I encouraged him to share what he was thinking. He remarked that he didn’t really like writing. I sensed that he wasn’t looking forward to this assignment and withdrew from giving me feedback on it. I respected this, but told him this is precisely why I wanted him to give his opinion. What could make the journal worthwhile for him? At a minimum, what could make it less annoying for him to do? Of all the students sitting around the table, his opinion mattered a lot because of his overall disdain for writing. I even followed up with him after the cogen to reiterate this message and hear his thoughts.

I got the feeling that, for the cogen students, they felt they didn’t do much today. They were just offering up their opinion on some writing assignment. This was true, they were. But I shared that I never considered any of these types of ideas in past years. There have been hundreds of students who have written journals in the past — and all of them were confined to one way of expressing their metacognitive reflections. Our conversation today changed that. As a result of our talk today, I hope more students will find meaning in the assignment.

After the students left, I noticed a colleague in the room. I believe she was there the entire time. I explained to her what it was. She remarked that she really liked the idea and wished she was “at the point” where she could do something like it in the future. We chatted briefly about the difference between giving kids a survey to gather their feedback and being in dialogue with them. One provides real-time opportunities for follow-up questions, divergent thinking, and adjacent ideas, and the other one doesn’t. Our exchange reminded of me last year when I asked a few colleagues to join the cogen to provide me with an outsider’s point of view.

Last two things. Our meeting today felt a tad rushed and it caused me to forget to inform the students that they need to choose their replacement next week. I emailed them afterward about this. All good things must come to an end. Secondly, I realized that we had an exam this week and didn’t revisit the DeltaMath review/exam score correlation idea that was brought up a couple weeks back. Today would have been the perfect time to discuss it, but I had to prioritize the journals. So much to discuss, so little time.


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