Meditations on a Cogen (No. 13) • Thursday, January 20, 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 13th post in the series.

Today’s cogen came at the end of the first semester. With grades due, and many of my students struggling to say afloat, my mood these last few days has been somber. I needed this week’s cogen to give me hope.

Yesterday and today I spoke to most of the students and reminded them about today’s session. I was pleasantly surprised when most of them nodded and said they remembered. The result today is solid: five students. This includes one student from the previous cohort who wanted to come back again. There was one new member from 3rd period. Another from period 7 couldn’t make it because of basketball.

There’s one empty seat from 1st period that I need to fill. I have my prospects, including a student who came after school today to take an exam. He walked into the room, saw me setting up our table, and asked, “Mister, what’s this?” I sensed his intrigue and satisfied his curiosity with some playful statement about it being a tablecloth, and then gave him the exam. After he finished, the cogen was long over. I gave him my cogen elevator pitch and he seemed interested.

Post-exam: a surprise and a revision
For the last couple of months, I’ve been asking about specifics of the class that I’ve needed their support on. This week, with mostly new students around the table, I wanted something different. I decide to cast my net out and see what I catch. So, after I oriented our new member to the cogen, I opened by asking simply, how was class the week?

We are studying complex numbers this week and the first four students mention it directly. I’m using Michael Pershan and Max Ray’s geometric approach, like I have for the last few years. The kids like it. They say playing Simon Says in the hallway was fun. I thank them for their praise, but get that feeling again. It’s the annoying feeling that the students — mainly because they’re new — aren’t able to supply ample critiques of what they’re experiencing. To them, as long as the classroom isn’t burning to the ground, everything is “fine.” I can’t blame them for this, however. How often are students asked to be critical of their teacher and then actively heard out?

I figured this might happen, so I wait and listen. I’m ready to pounce on the smallest hint of dissonance that I hear. When the last student shares, I get my chance. Interestingly, she breaks rank with the rest of the group doesn’t mention complex numbers at all. Instead, it’s her performance on the most recent exam that’s weighing on her. She is the most soft-spoken of the group, so I literally have to lean in to hear what she says. I invite her to tell me more and she goes on to ask about my retake policy. Why can’t students merely submit corrections for an exam instead of having to retake it altogether?

Some context in her question: I’ve been allowing students to retake exams — with their new score replacing their original — for a while now. It’s my meager effort to have students’ grades reflect what they actually know about Algebra 2, even if it takes them a little more time to know it. For a lot of reasons, correcting an exam after the fact doesn’t do that for me. Corrections, in my experiences, give an inflated sense of what students know — especially when the student does poorly on an exam. Hence, my policy: any student who scores less than 85% on an exam can retake it without penalty. Before this year, fearing abuse of the policy, I only allowed two retakes per semester. This year, after reading Joe Feldman’s Grading for Equity, I removed my constraint and allowed unlimited retakes to any student scoring below 85%. To be eligible for the retake, students must attend tutoring after school and earn at least 65% on the corresponding DeltaMath assignment.

For the record, students who scored above 85% have no way of showing me they understand more mathematics after an exam; they have no way to improve their grades. I know this is a flawed policy, but my reasoning for it aligned with my sanity: I feared that so many kids would retake that it would be unmanageable. The policy also helped to ensure that my attention would be given to the students who needed me the most. If I had a bunch of students retaking to improve their grade from an 87% to a 95%, for example, that would take away from me helping students who score 53% and are in desperate need of my reteaching.

Anyway, back to the cogen. We discuss these policies and something fascinating happens: the students say that they didn’t know that the retake replaces their original grade. What?! It’s January — how do they not know this? I preach about it after every exam. I’m shocked.

After my astonishment fades, I realize that the student who asked the question about retakes vs. corrections thought that I treated them the same way. I also realized that I need to do a much better job explaining retakes to my students, which I vow to do in front of the cogen today. Some of my students for sure know about it, but given this conversation, it’s probably not the majority.

As for the retake policy itself, the kids like it but opine that there should be an option for those who score above 85%. I hear them out. As we chat, they help me see that corrections can indeed work for 85%+ students. Our reasoning is that if you perform that well on an exam, you probably don’t have huge gaps in your understanding. Submitting corrected work with an analysis of your mistakes is sufficient to show that you’ve relearned the content (these students will receive 1/4 missed credit back don’t their grade). I agree to change the policy for semester two.

DeltaMath Day
We have less than 10 minutes remaining and I revisit something that was mentioned last week: using class time for DeltaMath. I share that I love this idea as a way to help everyone get some in-class practice. We coin it “DeltaMath Day” and discuss possible structures. Should students just come in and work? Can we have co-teachers (students who are finished) float around the room and help others? What about using stations? We don’t leave with answers to these questions, but do decide that DeltaMath Day should occur during the second half of each unit. It will lead up to the exam and serve as review.

Before we close, I reiterate the DeltaMath goal that we’ve started using in class. It was developed by the previous cohort of cogen students and want to ask if these students are on board with unveiling the final percentage to the class on Mondays. They’re good with this responsibility.

I appreciate how a student’s disappointment about her grade triggered a collective deep dive into one of my grading policies today. By centering her experience, it afforded us the opportunity to interrogate my retake policy and help me see how poorly I was advocating for it, which eventually led us to revise it. The student who spoke up is one of the quietest students I teach and this fact only magnifies my appreciation for our dialogue. Without the cogen, would I have made space to act on her feedback? Would I have otherwise known about my blindspot? I hope she sees how valuable her comment was to me and other students.

As I remove the tablecloth and tuck away my snacks, my mind lingers back to the closing of the first semester and all of my struggling students. A few of them were present today at the cogen. Two of them are failing. If I’m not careful, this might discourage me from engaging with them at the cogen. Besides, they’re failing. Shouldn’t I be lecturing them on what they’re not doing, creating a plan of action for their individual success? Shouldn’t I be spending this time tutoring them?

Despite their struggle — and probably because of it — it’s vital that I stay proximate to these students and get their feedback. I need them close to me. Their experience in my class has been less than ideal and they can help me explore why. It’s through their eyes that I can find a way forward.


Meditations on a Cogen (No. 12) • Thursday, January 13, 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 12th post in the series.

New faces, new energy
This week’s cogen brought new faces! As the 2nd cohort transitions out and the third transitions in, several members brought their successors with them today. In all, there were 8 students: 5 were veterans and 3 were newbies. As we settle in around the table, and I dump the snacks and water in the middle of it, fresh energy and a feeling of newness envelop us. The kids are laughing. There’s a lot of chatter. The mood is affable. It’s refreshing.

I open the cogen with introductions. Everyone goes around and says their name and grade. I explain the formal name of our space, write it on a nearby whiteboard and explain the term “cogen,” and then ask the veterans to share the purpose of our weekly dialogue. Just like the first time this happened back in November, it is pleasant hearing the students speak of the cogen from direct experience.

As the vets finish, I remember to hit record on my phone and drop it in the middle of the table to capture today’s audio. I hurriedly ask a non-cogen student who is in the room waiting for their friend to snap a few photos of us while we talk. She agrees and says that she’ll email them to me later. Before moving on, I give my two cents to further illuminate the what, why, when, and how of the cogen for the new students. I ask someone to take notes. We’re off and running.

Journal reflections
Eager to know how the math journal went, I ask them about it. How was writing it? What aspects did you like? What can be improved? I inform the group that the assignment was co-designed by me and the first cohort and that the next iteration of the assignment will be assigned in the coming weeks. The students’ feedback today will shape what it will look like. It’s worth noting that a couple of students at the cogen didn’t submit the journal. I assure them that this is not a place or time for me to indict them on their incomplete work. Rather, I want to learn from them, too. Is there something about the design or implementation of the assignment that might help them be more proactive next time?

After I serve up my questions and talking points, they return with several really good critiques and suggestions. I plan to use them all.

  • Add sentence starters to the assignment. I love this idea mainly because I recently saw an English teacher at my school do this for a writing assignment of hers. I underline it in my notes.
  • Make it due on Sunday. This way, the students get the weekend to work on it before it’s due. We recently adopted this approach with DeltaMath and someone notes how it helped her get more of it done.
  • Allot at least one day in class to work on the journal. This is good idea, which I should have thought of myself.
  • Use the cogen to determine the problems featured in the journal. This last recommendation is the most intriguing — at least from a cogen standpoint. I ask the students about the problems I included in the journal; they had to choose one to write about. A few students say the problems were fine, but I suspect that there’s more to uncover, so I probe further. After a few more of my questions, one student asks, “Mister, what if we chose the problems?” I immediately love this idea and nearly hug the student. My vision for her suggestion entails me presenting the cogen 10 problems and then us deciding which 5 end up in the final assignment. We agree that some of the problems should come from the in-class problem set.

Math bingo
Last week, after I asked the cogen to think of an assignment or class activity that they wanted to plan and enact, the students mentioned Math Bingo. So, after we finalize plans for the next journal, I show the group a Math Bingo activity that I found in my Dropbox archives. With some minor edits, it aligns well with the specifications we decided upon last week. The students glance through the handouts that detail the game and like what they see. I remind the crew that they will be co-teaching this activity with me. Next week, we’ll begin our study of complex numbers and the Bingo game — which is based on complex numbers — will take place late in the week, possibly Friday. We field a few logistical questions about gameplay and agree to touch base next week to finalize.

Ideas for Semester 2
A few minutes remain. With all the new members here today, I’m reminded that these students are going to help launch me and our class into the second semester. I decide to do some priming and ask them — I’m specifically looking at the new cogen students, but open it up to everyone — if they want to change anything about the class as we move into semester two.

Any time I ask far-reaching questions like this, I don’t usually get anything of substance from students. These types of queries — how I frame them, at least — are too vague and inexact of requests for students to get into particulars, which is want I want. This time, however, the students prove me wrong! They have two very specific proposals:

  • Given one day per unit to work on DeltaMath in class. I think this was bridged from our discussion about the journal. It is a great suggestion. I should allocate class time for what I value most, right? This is a major takeaway from today.
  • Use the start of class to relearn quiz content in a breakout group. The start of class usually looks the same for us (whole class dicussion). But why? This suggestion is aimed at helping only the students who stuggled with the previous day’s quiz. This means I could use the first 10 minutes of class to reteach these students in a small group while the rest of the class works on something different. We would reconvene as a class after.

After the students leave, I stop my phone from recording and plop down at my desk to gather my thoughts on the last 30 minutes. I play two minutes of the audio, but know I won’t have time today to listen to it. Was I talking too much? Did I tap into 1 or 2 quieter students enough to ensure their voices and ideas were heard? The presence of the outgoing cogen students was so bright today. They were wonderful and engaged and unhesitant in their feedback. The demographics of the group stand out to me as well and I note how balanced they were. There was a nice mix of grade levels, genders, races, achievement levels, and special needs around the table today. I’m grateful for the perspective they offered me and to each other.

At this point, I’ve been alone in my room for 45 minutes. As I get up to leave, I remember that I’m still wearing my mask. I unhinge it from my ears and breathe deep. I smile warmly. My body and mind delight in the fact that, for the last 75 minutes, my cogen made me forget where I was. It transported me out of pandemic school year and into a normal one. We laughed, debated, and planned. There was no mention of Covid or remote learning. Both were banned from our dialogue and subtracted from our planning. At least for today, I feel far removed from reality.

I grab my things and leave satisfied.


Meditations on a Cogen (No. 11) • Thursday, January 6, 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 11th post in the series.

Starting with Gratitude
After a week of remote learning and another week of winter break, we were back. Learning from my mistakes, on Monday I reminded my cogen students about today’s session. I wasn’t going to back myself into another 5-minute cogen that is squeezed in on a Friday afternoon. By Tuesday, 5 of the 6 kids confirmed their availability (one is out with Covid). I supply another gentle reminder today during class.

With one student not able to make it last minute, four mask-covered faces accompany me around our table at 2:45pm. Not bad! Despite all that is eating us alive at the current moment, we manage to meet again. I couldn’t help but express gratitude to the students as we open today. I thank everyone for their time and commitment — especially now. I tell them that examining my teaching alongside students is different — and often times more productive — than when I do it with colleagues. Instead of talking above those who I’m serving, cogens bring me to the source.

Finding successors
The second cohort of cogen members is in its 5th week. A couple of meetings back I asked the group to begin thinking about their replacements. Today, I take a more formal stance and ask them to drop names. We go around the table and each of them chooses a replacement along with a back-up. I explain the changeover process and ask that they start reaching out to their person. Hopefully this time next week we have everyone’s successor locked in. (Today in class I helped one member secure their replacement already, which was nice.)

Earlier today, I finally finished my “Cogen Exit Survey.” The survey is 10 questions; I plan to give it to students when they “graduate” from the cogen. My hope is that it will help me measure impact and better understand my students’ cogen experience. Tomorrow I’m sending it out to cohort 1. This cohort will complete it in a few weeks.

Math Journal
I wanted to use part of today to collect my students’ early impressions of the math journal assignment. The previous cogen students co-designed it with me. It was assigned before the break and is due tomorrow. When I ask if anyone has started it, they gracefully shake their heads. With the week we’ve been having, I kind of expect this. We bookmark the discussion and place it on next week’s agenda.

Crafting their own assignment
After my last cogen, I had an epiphany: Why not have each cohort co-design an assignment with me and help implement it? Maybe my cogen ambitions are growing (or maybe I’m getting bored), but I want the responsibilities of the cogen students to extend beyond our 30-minute weekly dialogues and move into things like co-teaching. For the first cohort, it was the math journal. What could it be for cohort 2? What’s an activity, assignment, or lesson that they want to do with the class?

I don’t know why, but after I ask, a student immediately blurts out, “Math Bingo!” I’m surprised, expecting something more complex. After I think about it, however, it makes sense. We never play games. Years ago, I used to play them all the time, but along the way I have become stilted and set in my ways, I think. His blurting out Math Bingo is a sign: let’s have fun.

The group latches on and we talk logistics. They really surprise me with their planning skills. Some of them are talking like teachers! They walk me through their vision for the game; I request they co-teach it with me and they have no qualms about it. I promise to piece together the problems and create some gameboards. I’ll present this to the kids at next week’s cogen. Win!

DeltaMath Goals
We’ve been discussing DeltaMath completion goals for the last several cogens. This week in class I displayed completion percentages and we set a goal to maintain what they achieved on the previous assignment. The next DeltaMath is due Sunday. At the start of class on Monday, I want the cogen students to reveal the final percentages in a fun way. Since there are two members of the cogen in each class period, they want one student to have the real percentage and the other a fake one. The class would vote on who they think who represents the actual percentage and the cogen students would be reveal it. Going back to my earlier point, this activity extends the reach of the cogen students beyond the cogen itself and into class. It’s not a lot, but it’s something.

And the reward has been decided: me including two problems on next week’s quizzes (instead of one) and the students choosing which of the two they want me to grade. I like this because it avoids awarding bonus points outright, like we had previously discussed. The reward would only apply to students who met the DeltaMath goal individually.

I fill the remainder of the cogen with smaller questions that we don’t have time to fully explore. The first was, would the students attend the cogen if I offered no extra credit? I’ve been thinking about this a lot since September. I don’t love giving extra credit, but I’ve committed to it. What do the students think? Most said they would attend without it. In fact, three of them said they forgot all about the extra credit and have been coming simply because they like it. They admit, however, that the appeal of extra credit convinced them to be part of the group in the first place. As one student said, “It might be hard to get students to come without offering them extra credit, but once they’re here, they will see the purpose and kind of forget about it.”

I also ask the students what advice they have for me when teaching the class at 75% attendance? This has been a reality for the last week and its growing increasingly more difficult to manage. How do I keep absent kids in the loop? How do I approach the students who are present? The unpredictable nature of this phenomenon makes it even more tricky. The students give me little insight into what I should do, but do tell me what I shouldn’t: mandate Zoom for absent students. They are vehement about this! They do not like mandating absent students to Zoom during the in-person lesson. Doing this hasn’t seriously crossed my mind, but another teacher is doing it, so that’s why they mention it to me. If they’re absent, the students much prefer to be given the work to complete asynchronously. I’m still processing how I will adjust my instruction to account for so many missing students, but their feedback is a great place to begin formulating my plan.

Notes to self:

  • I usually take informal notes/minutes during cogens on paper, but in an effort to transfer more power to the students, today I asked a student to do this. It was a small act, but one that I hope to make routine each week.
  • I want to start recording the audio of the cogens. I should start next week by placing my phone in the middle of the table at the start, turn on the audio recording app, and hit record. There’s nothing to lose. It would be interesting to listen to these — especially in the company of other teachers.
  • At a future cogen, I need to grab someone from the hallway and have them take a photo of me and my students around the table. I need at least one!


Meditations on a Cogen (No. 10) • Wednesday, December 22, 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 tenth post in the series.

Back to Zoom
The last week has been chaotic. After having few students in class on both Friday and Monday because of Covid protocols, it was decided that we transition to remote learning for the three days leading up to winter break. Like anyone else at my school with a pulse, I anticipated this and last week asked my cogen students if they were good to meet on Zoom. I emailed them yesterday and 4 out of 6 confirmed that they could make it. We were on.

So, this afternoon, after a wild couple of days, my cogen found itself back on Zoom. I say “back” on Zoom because the memories of last year’s all-online cogens showed up immediately in my mind when I logged in today. I held 24 cogens last year, all of which were on Zoom. Participating in a cogen online triggered mixed emotions for me. Obviously, I’d much rather be in person. The conversation is more dynamic and nuanced. Not to mention the snacks! At the same time, last year’s cogens were my first and made me an adamant believer in them. In this sense, holding them online today felt strangely natural and, dare I say, homey.

I opened Zoom ten minutes early and caught up with a student who showed up before our scheduled meeting time of 2:45 p.m. I asked him how the transition has been for him these last few days. Like a lot of students, he lamented about his boredom and yearning to get back into school. We chatted about our upcoming break. He was going to Rhode Island to spend time with family. At one point he asked me for advice on a personal matter that I vowed to follow-up on.

Our non-academic chatter served as a reminder for me that cogens aren’t just a place for teachers and students discuss classroom matters. They’re for getting to know each other, too. At cogens, teacher-student relations can be nourished without the demands of curricula and instruction.

When the other three cogen students arrived, he and I were in the middle of a playful discussion around the ethics of napping (smile). Feeling encouraged by our banter, I invited the rest of the crew to give their two cents on the napping debate. It was fun. I mentioned that I took a 10-minute power nap before 7th period today and the kids were rendered speechless. How is that possible? Why would you even want to do such a thing to your body? The only naps they know of are the multiple-hour variety and those that result in unintentionally waking up the next morning wondering what happened. One student, speaking as if it were part of his religion, said point-blankly, “Mister, I don’t believe in 10-naps.” I laughed harder than I did all week.

In Limbo
Given the whirlwind of this week, I was curious how classes were going for them. How are their teachers going about things? What have my colleagues done so far that the students have liked? I was transparent about my desire to steal ideas and adapt them for our class. I also wondered if the students could give me any advice on how to approach our new in-person/remote dilemma. If we remain in limbo — teetering between the classroom and Zoom based on Covid numbers — what are some tips they can offer me?

Above all else, the kids stressed the importance of checking in with my students. Many teachers, from their perspective, have a singular focus: work getting done. This was true of the last two years, but also this week. Disappointingly, the students struggled to offer me examples of things they enjoyed from their class over the last few days. The lone highlight came from a teacher who played Christmas songs for the class and did fun trivia based on them. I appreciated their honesty, but I was left wanting more examples of what the students saw as exemplary teaching moves. Maybe I need to be more specific? Perhaps next time I ask something like, What’s something you did in Chemistry this week that you liked? What about ELA?

Curious what “checking in” meant to them, I asked the students if they could illustrate their point with some examples. What does it look like when a teacher checks in? I did a few Zoom polls today in class to catch the mood of the room and the kids were in agreement that those were a great example of how to do it. One student commented that ours was one of her liveliest classes because of the polls. They also liked how I used the chatbox to refocus the class and grab their attention. I did this by asking 10 students, say, to respond to a given question. Both the polls and the call-and-response in the chat added an interactive component to our time together that they enjoyed.

In terms of the big picture, one student suggested that on certain days I assign the class independent work and use my time to conference with individual students. I liked this because it could work whether we’re online or in person. An idea that added more structure to it was to have a 4-day work week. The students said that the 5th day could be used for more intensive check ins and independent work. This made me think of Shraddha Shirude and how she modified her curriculum to make this structure work for her.

Dreaming and thank you
Wishing I had spent more time discussing this, I closed today’s talk by asking the group to complete the upcoming math journal assignment with a critical eye. I co-created this assignment with the first cohort of cogen students back in November and formally assigned this week. It’s due January 7. I told the cogen that after we come back from break I’m going to need their feedback on it. I want to use their experience completing it to make it better and more relevant for all of my students. I asked the cogen that they dream big, as all recommendations on editing it will be welcomed.

Asking the students to dream got me thinking of my own: How great would it be if I co-designed an assignment with each cohort of cogen students? If it’s not an original assignment, maybe we co-design a new version of a past assignment? If we can pull something like that off, each cohort would be in a position to critique their predecessors’ assignment and then go on to make their own.

Before we left, I profusely thanked the students for their time. Part of me can’t believe we actually made this week’s cogen happen. All I can say is that I’m seriously blessed with some amazing students.