Student Coteachers Part 3: Introducing Rational Exponents

Over the last three months, my cogen has grown from a place where we generate insights into our class to one where we co-plan lessons together. So far, we’ve co-planned and co-taught two lessons. The first was a Bingo review and the second involved an original board game we created called Infinite Levels. I shouldn’t have been surprised with how much planning was needed to pull them off, but somehow I was.

For the third and final cogen-inspired lesson of the year, today my students and I used it to introduce rational exponents. In contrast to the the previous two lessons, this one required us to delve into the pedagogy behind a particular mathematical concept. For Bingo and Infinite Levels, we got away with glossing over content because the class wasn’t learning anything new. This time was different. I had to teach the cogen students about rational exponents and then, based on how they saw it playing out in class, sit with them and figure out how we were going to teach it. In all, we spent the good part of five cogens to accomplish this, with a several of the sessions running over our allotted time of 30 minutes. I reflected on the planning process in my Meditations on a Cogen series (those posts can be found here, here, here, here, and here).

As for the lesson itself, we set up the room in two large groups, each led by one cogen student. Groups faced 2-3 large whiteboards. At the start of class, I introduced the cogen students as my coteachers for the day and gave them the reigns. They designed an opening slide to acquaint their peers with the conversion between rational exponents and radicals. They used it as the warm up.

The cogen-designed opening slide

After they tag-teamed the opening, which included a short mini-lesson on the missing index for #2, my cogen students varied greatly in their instructional approaches. In 1st period, both students took a more traditional teacher role and used the large whiteboards to walk their groups through various examples we planned beforehand. In 3rd, one coteacher took a similar stance, but mixed in getting kids out of their seat to explain work to each other using the large whiteboards. The other coteacher in 3rd floated around to various clusters of students and engaged in small group instruction. In 7th period, both coteachers mainly used small group instruction.

Other than having to step into a demonstration when a coteacher made a mistake in her example during 1st period and two instances where I had to encourage my coteachers to check-in with other members of their group, my coteachers held it down wonderfully. I floated between groups to provide scaffolding to individual students, but my responsibilities were reduced significantly in support of the cogen students. Exit Ticket data was solid.

Something I wish I would have paid more attention to during the lesson was the explanations my coteachers offered the class. The pedagogy we decided upon wasn’t anything out of the ordinary: modeling, direct instruction, small group instruction, etc. Where the magic happened, I think, is how my coteachers chose to relay key ideas to their peers in the moment. It was in their less technical, more student-friendly language. It was in their informal phrases and idioms. This is one of the most intriguing and useful aspects of learning in a student-led lesson such as this one.

Adding to this, other than a 2-minute conversation after the lesson, there won’t be any time for my coteachers and I to reflect on how they think it went. Considering that 70% of students reported on a post-lesson survey that they “definitely want to do this again,” not finding time to debrief with the cogen students is a missed opportunity.

One of the less visible outcomes of the lesson was how it placed some quieter, low-performing, and math-resistant students in positions to teach their peers. This is a direct consequence of the make-up of the cogen since, by its very nature, it includes a diverse cross-section of students. What a beautiful thing it was to witness students of all ability levels and dispositions moving the class forward. A teacher’s dream!

The lesson took a lot to pull off, but was totally worth the time investment. It’s these types of lessons that help me reimagine what my classroom can be, empower my students, and maximize the potential they walk in with. It’s not the only way to accomplish these goals, but through my cogen, it’s the one way I’ve discovered works for me.

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