Month: February 2022

This is the first post of a four-part series where I explore planning and implementing a social justice-themed activity in Algebra 2. In addition to traditional collaboration with colleagues, my use of three cogenerative dialogues to develop and reflect on the activity were critical to its design and execution.

Part 1: Preplanning

For years, I’ve been in search of meaningful ways to bring social justice into my Algebra 2 class. I haven’t had much success, but there is hope. It comes in the form of the math department at my school as well as my students — namely my cogenerative dialogue.

Last year, the Geometry teacher at my school designed a project based on the 1619 Project podcast. It was a highly creative endeavor that focused on the historic discrimination in the farming industry. He used excerpts from the last two episodes which profile a Black family, the Provosts, and their experiences with their farm.

For his project, he presented students with fictional data of many plots of land. The data included info on plot sizes, bank loan information, and the demographics of the loan recipients. The goal was for the students to determine if discrimination was involved in handing out the bank loans. It was part of his triangle congruency unit (all plots of land were triangular). If two plots were equal in size and location, for example, are the two people of equal qualifications applying for loans given the same amount? Are there patterns of discrimination? Could students prove it in court?

He first ran the project last year during remote learning. He did it again this year. Intrigued by his creativity and willingness to embrace the intersection of social justice and mathematics, I’ve decided to build on what he started. More specifically, I see a throughline between his project’s focus on farm loans and how compound interest is explored in Algebra 2. Could I continue what he started — but instead of exploring plot sizes, could I anchor my activity on interest rates? Or extend it to discuss something like predatory lending and its impact on urban communities?

I brought this idea to the rest of the math department. We brainstormed. Our wealth of experience fueled my idea with momentum. In our talks, however, I wondered: what do my students think? If there’s anything that I’ve learned these last few years, it’s to make space to listen to students. Talking my head off with fellow teachers absent student voice is not something I want to do anymore. I pump the brakes on my planning to seek out some student perspectives. I want to hear what they think.

To do this, I begin planning for a series of three cogenerative dialogues (or cogens). The first cogen will be used to gather baseline info from students that will shape my planning. I’ll use the second cogen to present students with the activity itself, make space to receive their feedback, and then modify the activity based on what they say. The third and final cogen will occur after the activity’s conclusion and will be used to hear from the students how it went.

I identify students for the cogens by asking my Geometry colleague for recommendations. Who was active last year and can supply me insights into his project? He drops five students’ names. I also pinpoint four other students who are currently in Geometry and just experienced his project this year (they’re doubling up on Geo and Alg 2). I check all of their schedules and determine that lunch is a viable meeting time. I find them a few days later and explain that I want their feedback on an upcoming class activity. They agree to meet during lunch this past week.

Because of scheduling, I’m unable to meet with all of the students in a single session, so I hold two separate cogens. The first cogen has 7 students and the second has 3. I sketch out a few questions ahead of time to ask the students. I also consult my Geometry colleague for his input on what to ask. My questioning went a lot of different places during the cogen based on student responses, but here’s what I entered with:

• What are your first impressions of the farming project you did in Geometry?
• Was the project worth your while?
• What advice can you give me as I plan a similar activity?
• What did you think of the social justice aspect of the project? Is there social issue you want to explore?
• Does me being a white man affect how comfortable you are exploring issues such as racism and sexism?

On the day of the first cogen, two students whom I didn’t invite were curiously hanging around the room. Noticing their inquisitiveness, I explained what we were doing. They seemed loosely interested and, before I know it, they are sitting down with us. Right place, right time. (One of them was part of my weekly cogen at one point this year, so she kind of knew what was happening.)

What follows is a synthesis of my students’ feedback from our cogen, which I will use to begin designing the activity.

• Find balance. Most students commented that I need to strike the right balance between learning math and exploring social justice. This means possibly frontloading the mathematics and rolling out the social justice aspect of the project slower than I would have previously anticipated. There is genuine concern in the group about not understanding the mathematics before being asked to apply it.
• Choose different launching point. Because of remote learning, last year’s students struggled on the Geometry project. They found it confusing and frustrating and struggled to say it was worth the time investment. For this reason, they recommend that I don’t use the Geometry project as a launcing point for our activity. If I do, it’ll probably cause dred and angst to sweep over our class on day 1 (many of these students rolled their eyes when I first mentioned the project to them). Instead, the kids suggest that I don’t even bring up the Geometry project — at least not initally. This was valuable insight.
• Interest rates are relevent. From what I gauged, there was interest amongst the students in studying interest rates and how they could be used in things like predatory lending. The students offered up no other particular topics that they’d like to see us study. To their defense, I did put them on the spot with this question.
• Don’t overcomplicated it. Students suggested that I be careful not to make the activity too complex. Social issues are inherently thorny and multilayered. I need to honor their complexity, but making it digestable for students is also important. Students don’t want their heads to be spinning because there’s so many factors to take into account.
• Presentations should focus on different issues. If I ask the students to present their findings at the end of the activity, each group should have a different focus. This way, students can learn something new from each presenting group.
• Be mindful of my teacher moves. The Geometry teacher is a white man — so is 60% of the math department (we’re 80% white overall). Almost all students in the cogen expressed no discomfort with exploring racism or sexism with him in the context of the 1619 project. They appreciated the need for social change and saw the project as a means to that end. That said, one young lady did wonder whether another teacher (of color?) could have led her through the activity, but did understand its purpose. I’m glad she said that because it spoke to the tension I feel exploring these sensative isssues given that I will never experience them firsthand. Another student said plainly, “Mister, it’s what you do that makes a difference.” His words were pointed and would stay with me for a long time.

As I move out of my information-gathering phase and begin planning, Gholdy Muhammad is in my head. In addition to her four pillars of identity, skills, intellect, and criticality — which I will try to address in my activity — one of her guiding principles is to start with joy. It’s terribly easy to see injustice and center it completely in activities involving social issues. Besides, what joy is there to find in predatory lending and payday loans and how they eat away at one’s finances? That said, I’ll need to ensure I make room to cultivate joy and love in whatever my activity asks students to do.

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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 17th post in the series.

A full house with no reminders
This was the first cogen of the year that wasn’t preceded with an in-person reminder from me. I didn’t pull up to any of my cogen students at any this week before, during, or after class and ask them if they could make it today (also: there were no classes yesterday). The way things have been going these last several weeks, I was confident that they didn’t need me to do that. The one move I did make, however, was to email them yesterday to remind them about bringing in a blueprint for our board game. No one responded, so I couldn’t be sure if they read it or not.

It’s no matter because my students don’t disappoint today: everyone shows up. Even the newest member who couldn’t make it last week because of tutoring surprises me by coming through. One cogen alumnus also comes — he actually reminded the newest member about today. I shout him out both during and after the cogen for his act of community.

As we settle in around the table, my cogen family has me on a high. Though they’re no different than usual, the snacks taste better today. The air is light. I breathe in deeply and smile.

Successors
This week we have a singular focus: planning our board game lesson. It will be the second coteaching experience for the cogen. We left last week with plans to move forward with the idea and have a lot of work to do.

Before we start planning, I remember something a student asked me about this week: cogen replacements. I’ve been so wonderfully engrossed in the cogen’s progress these last few weeks that I didn’t even realize that the current cohort’s six-week tenure is coming to an end. Because of this, a hint of melancholy is present in my voice when I ask the students about their successors today. They have been so productive and willing, it is bittersweet for them to leave. Half of the group has a replacement in mind and drops names. I ask them to reach out to these folks and offer my support in breaking the ice.

Creating a board game
When we left last week, I asked the students to make a prototype of our gameboard. (I took on the responsibility of creating some makeshift problem cards.) This was really interesting because it was the first time all year that the cogen students left our meeting with “homework.” I was unsure of what to expect. But if coteaching is the next phase of the cogen, then it’s natural to presume students will have some work to do outside of the allotted 30 minutes we meet each week. Besides, the buy-in was strong last week from the kids. It felt right.

Did I mention already that the students have me on a high today? Well, they do. They bring three different hand-drawn gameboards! I do my best to contain my excitement in front of them. I’m thrilled. The boards varied in shape and orientation but were similar in that they all had a starting point and ending point. Think Shoots and Ladders. I ask the students to share what went into making their boards. One student shares her vision for using mathematicians during the game. Another has neat ideas for special spaces on the board. Their ideas are clever.

After I share my improvised problem cards, we get into the nitty-gritty of the game. There’s a lot of back-and-forth action for the rest of our time together as we hash out details of the board and gameplay. Here are some highlights and key takeaways of our dialogue:

• Player movement. We originally decided (last week) that the problem cards would determine how players would move on the board. Each player would get to choose the problem level they wanted (by picking a card) and, if they got the problem on the card correct, they would move that number of spaces. Well, it doesn’t take long for the students to squash this idea. Instead, players will roll a die to move. The problem levels will be scattered randomly all over the board. Whatever level a player/team lands on, they pick up that card and solve the problem. We agree that this is fairer, more equitable, and more balanced.
• Using points. By changing how how players move (random), we conclude that our game cannot be won by reaching a specific location on the board. There can be no “end” space. Instead, the game should be point-based. When players get problems correct (whose levels are also random), they will earn points based on the difficulty of the problem. Whoever has the most points at the end of the game, wins.
• Infinity-shaped gameboard. Because the game is no longer based on a players’ positions, a student quickly suggests the board be made into the shape of an infinity symbol (∞). Everyone loves it.

• Group gameplay. Throughout our talk, we flip-flop on whether to play the game synchronously (whole class) or asynchonrounsly (small groups). There are pros and cons to each, both for gameplay dynamics and logistics, but in the end agree to play the game in small groups. This means that each group plays its own game I have 4 groups in my classroom with 5-8 students each, so each player in the game will consist of 2-3 students.
• Table vs. Table. In addtion to having individual winners from each group, we also want to have a winning group. To do this, at the end of gameplay we can have all players in each group sum their points. Whichever group has the largest sum wins that award. This way, players have an incentive to support other players in their group.
• Coteachers checking answers. As players move around the gameboard solving problems, the cogen students (and myself) will float around the room with an answer key. After a player solves a problem, they will signal one of us by raising their hand. A coteacher will come over and check their work and final answer (all problems will be numbered for quick reference). This provides immediate feedback to the players. If the player gets it correct, they will earn the points for that problem. Incorrect solutions do not result in a penalty. (When I proposed that a key be left in each group so players/tables can self-check, the cogen said outright: “Mister, we’re going to cheat if you do that.” This was surprising and hilarious.)
• Lockers. I have lots of empty lockers in my classroom (we used to be an elemenatry school). While we ultimately didn’t adopt it, there was a fascinating suggestion to use the lockers during our game. This spoke to me because it uses the physical environment to enhance the game. The idea to use them proved unwieldy for our game, but I pocket it for future use.
• Point stealing. When a player lands on a “Level 2” space and begins working on the problem, all other players will work on the same problem. If the player who chose the card gets the problem wrong, another player will have a chance to steal the points for that problem. We didn’t determine yet who gets to steal.
• Special Spaces. The majority of spaces on the board will have a problem level (1-3) on them. To add to the fun, we also want to have “special” spaces. These will be different and add some spice to gameplay. Some possibilities include: (a) challenge space (hard problem worth more points), (b) nothing space (no problem, no points), (c) steal points from other players (all players give another player 1 or 2 points), (d) donate points to others (player “gives” all other players 1 or 2 points), (e) earn a second chance card (if a player gets a problem wrong, they can exchange this card for a second chance at getting it correct before another player can steal)
• Homework. At the end of our discussion, I ask if someone can make a sketch of the board that includes what we talked about today. Next week (or the week after, if we need more time to finialize), we will use our cogen to redraw the boards on large chart paper for each group. The chart papers will be placed at the center of each group for gameplay. The quietest student of the cogen agrees to take on this task. I promise to email her — and the rest of the team — our notes.
• Game name. After we leave, it hits me that we don’t have a name for the game. We have to think of somethign catchy.

Excitement all around
A lot happened today. The energy was high, ideas were flowing, and everyone was present in body and mind. There was plenty of debate about our game/lesson. It’s really taking shape. Everyone contributed and is feeling good about it. I even overheard a student say at the end, “Today was really productive.” I couldn’t agree more.

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In For White Folks Who Teach in the Hood…, my man Chris Emdin writes:

Coteaching is a natural outgrowth of the educational cypher. Ideally, coteaching is implemented in the classroom after a cycle of cogen sessions has taken place with a group of students….Cogen participants are more amenable to putting themselves out on a limb fot the sake of further improving classroom instruction. (p. 93)

I have more or less adopted Emdin’s model for cogenerative dialogues these last two years. In doing so, coteaching with students has always been on my mind. It’s a natural progression for students to go from discussing and critiquing the class to taking the helm and being the change they wish to see. Positioning myself as a coteacher alongside my students has been a primary goal for my cogens since I started them. I achieved that goal for the first time this week.

I played around with the idea last year during remote learning, but I think I planted the seed a couple of months ago with this year’s first cohort of cogen students. I was preparing one of my hallmark assignments and they helped me revise it. It was an interesting and worthwhile venture, but I noticed afterward that the students had merely helped me plan the assignment — I didn’t get out of the way and let them enact it. Don’t get me wrong, their planning was new and critical in the development of the cogen’s work. But it would have been better if, instead of me, the students rolled out the assignment to the class. They knew the assignment well and could speak to it, but I gave them no airtime to present it to the class. Noticing this, I was encouraged to go a step further with the next cohort of students: design a lesson with them and coteach it.

When I approached the students about the idea of coteaching, they were on board. As Emdin suggests, I think their willingness to boldly engage in coteaching was a direct consequence of their involvement in the cogen and how it has positioned them as change agents. Having never cotaught with students before and wanting to privilege their ideas, I encouraged them to decide the topic and format of the lesson.

What did they choose? Math Bingo.

A game! I was excited. So were they. We spent the next few cogen sessions planning it out. I showed them a Bingo template and sample problems. We discussed flow and logistics and consulted on timing. I was nervous, but we were ready.

The game was originally planned for one day, but ended up needing two. We finished it this week. Five cogen students cotaught my three Regents classes. Overall, it went smoothly. My coteachers led the class through the game — they floated to assist students, called on students to respond, and kept everything organized. I stayed mostly in the background, anchoring myself to some of my most struggling students. I would occasionally nod to my coteachers indicating that I thought it was time to move on to the next problem. Without even knowing it, I guess you can say we adopted the “One teach, one assist” coteaching model. We played off each other well.

On the exit ticket, there was plenty of positive feedback. When asked about one aspect of the activity they liked, students wrote things such as, “It was something to have fun with and learn at the same time,” “We worked together,” and “It was fun competing with one another.” The constructive feedback came in the form of things like, “Maybe try and fit more problems,” “It felt kind of slow,” and “Give us more time for the problems.”

My cogen met two days after the lesson and we spent the majority of our time reflecting on how the lesson went. I asked my coteachers to attend, if they were able (they had already selected their replacements for the cogen). Three of my five coteachers joined us.

We agreed that Bingo was a nice escape from what we usually do — the break from the norm was appreciated by all. The students liked the diversity of the problems too; they got to review many key ideas from the current unit in a game format. I heralded the time I spent helping weaker students as a major achievement of the lesson; having coteachers freed me up to work closely with those who needed me most.

While there was copious amounts of positive energy about the lesson, we knew it could be improved. To help with timing, which was highlighted on the exit tickets, the cogen agreed that we should have paid more attention to the details of the game (some problems needed less time than others, for example, and we didn’t have rewards for winners). We also admitted that I should have helped my coteachers gain a deeper understanding of the problems before we played. This would have equipped the coteachers to better help their peers during the game. It would have also helped with pacing. In the end, when I asked if they would want to play again, the cogen’s answer was unanimous and enthusiastic: YES!

In the days leading up to the lesson, I went back and reread the “Coteaching” chapter in White Folks, from which the above quote was taken. Despite a year and a half of cogening, relinquishing my status and upending my classroom’s power dynamic would be hard. I needed to steal some of Emdin’s confidence. Interestingly, when I first read the chapter many years ago, it felt unnatural and impractical. The idea of coteaching with students was ambitious, but too much so. Looking back now, I simply wasn’t ready. This week, I found myself reading it with a fine-tooth comb. I pocketed advice and identified personal weaknesses that might prevent me from embodying my new role as coteacher. It couldn’t have been more useful.

All my previous cogens and my rereading must have worked because during the lesson I felt something shift and click into place. It was magical. Coteaching with my students felt organic and necessary. It felt like a practice that should have been happening all along.



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