Meditations on a Cogen (No. 24) • Thursday, May 5, 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 24th post in the series.

Lesson, Lesson, Lesson
The focus of today’s cogen is our lesson. Last week, I realized that I failed to think through how much effort would be needed to teach the students about rational exponents, talk pedagogy with them, and then plan the lesson. As the students arrive around the table after school and one helps with the tablecloth, I gain some confidence. We can do this.

The issue that’s staring us in the face is the content. Last week, I did an abysmal job of scaffolding the examples. Instead of varying consecutive problems slightly to gradually build complexity, I found myself bouncing around from problem to problem like a mad man. There were similarities between the problems (i.e., converting between rational exponents and radicals), but the jumps from one problem to another were too big. In fact, they weren’t even jumps — they were leaps. It was the exact opposite of how I would actually teach the topic.

Anyways. We settle in and I ask everyone how they’re doing. Five students are present, one was absent from school. I hear crickets, so I poke fun at a kid by drilling into the specifics of their day. We laugh at something that I can no longer remember. The ice is broken.

We recap what we covered last week and dive into a few more examples. I give them independent think time between problems and, man, it’s quiet. The kids are into it, but I hoped they would be more collaborative. On top of this, all of the examples from this week and last are so different that I feel the math is tugging and pulling us in lots of different directions. If I feel this way, the students probably do, too. They just don’t know it yet.

With about 10 minutes left, we shift gears to discuss pedagogy. How do we want to teach this?

A couple of the kids give me blank stares and another looks down with uncertainty. At this point in the year, I figured the cogen would be firing on all cylinders, but I’m wrong. I have to remember: they’re NOT teachers. Advice on my teaching? Sure. Guidance on how to make a lesson more student-friendly? Definitely. Teaching? Not so fast.

I throw out some ideas, and we eventually land on some structures for the lesson. The kids organize the examples we did by difficulty so we can scaffold the examples for the class. (I promise to bring similar examples next week for us to peruse.) We agree to combine tables in the classroom so that each cogen student has one large table for small group instruction. The cogen students will use direct instruction and wait time to facilitate a discussion of the scaffolded examples. We end in a good place.

Left wondering
After today’s cogen, I’m left wondering: is this my last cogen cohort? It’ll be past mid-May by the time we teach this lesson and the last day of classes is June 14. I have had side conversations with a few other students about the cogen and think they would make great end-of-year additions, but what would we work on? What projects could we adopt for 2-3 weeks?

Including the students from today, I’ve had a total of 22 students from three different classes be part of my cogen this year. If nothing else, I will invite all of them to an end-of-year shindig to thank them for their service to our class. The odds of everyone being able to attend is low, but it would be fun to order pizza and get them all in one place.


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