My two cents (Week of Feb 22, 2021)

For each school day of the 2020-21 school year, I will be writing two sentences to capture some of the impressions, feelings, experiences, or thoughts I had that day. This is the 20th post in the series.

Monday (Feb 22)
After checking in on everyone’s break, I used a Desmos activity on inverse functions to ease us into the week. It went well.

Tuesday (Feb 23)
My 8th period needed a mental health day. We talked about oranges, recipes involving oranges, what makes an orange part of the citrus family, the color orange itself; it was quite fun…and, dare I say, philosophical.

Wednesday (Feb 24)
This has been a revengeful week; it’s like it knew that we had a week off for mid-winter break and wanted to get even by making us all suffer. Thankfully, I felt productive doing lots of small tasks, creating lots of opportunities for small victories.

Thursday (Feb 25)
For Black History Month, I had my students research a Black mathematician of their choosing and write a short profile of them. Today, after one of my students emailed their mathematician to see if she would be a guest speaker in our class, one of these mathematicians (Dr. Lauren L. Thomas) visited my fifth period class and shared her story with us.

Friday (Feb 26)
Had two colleagues join me for the cogen today, who have showed interest in starting their own (we talked a lot about videos). In the racial and social justice staff workshop after school, I shared (for the first time publicly) a harmful experience that a black, female school colleague had when she was dismissed from our school because of a “white privilege” shirt she was wearing; I was nervous.


Narratives in the classroom

I like to think of the relationships I have with students as stories. Each story — just like each student — is unique, having its share slow starts, funny moments, ups and downs, and dramatic pauses. Some are less eventful than others, or take a longer time to evolve, but they are stories nonetheless.

Unless I’ve taught a student before, their story usually, but not always, begins in September. It’s then when our relationship consists of nothing more than my name on their schedule. We’re strangers. But over the course of the next 10 months, a lot changes. Histories and passions and fears and hopes and interests are revealed, all expressed (or not) in myriad ways both during the 45 minutes we are granted each day and after it.

How and when these things develop over time determines the shape of the arc of each relationship. Some arcs are wide and far-reaching, others are more straight and direct. There are those that bend only through content, which is fine, but the good ones veer and loop through the many crevasses of life. Many arcs come to a solemn end at the close of the school year. A few persistent ones continue to curl and twist long after June.

For me, because teaching is so relational, each of these mostly 10-month arcs makeup one of the most important aspects of teaching. When I think about this, questions emerge. For example, how am I thinking about the bonds I create with students, both personal and academic, as something that matures, little by little, over the course of the school year — and beyond? Instead of focusing on distinct moments I share with them, how can I view my relationships with students longitudinally, where these moments come together to tell the bigger story of our work together? Over the course of many months, how I can strategically piece together and, dare I say, sequence conversations and other shared experiences that enable me to connect with a given student in effective and affective ways?

Suppose today I learn, somewhat randomly, that one of my students made breakfast for their sister. Let’s say it was eggs and bacon. Let’s also say that learning this was the consequence of a 5-minute conversation at the end of class in which I asked them about their day. Maybe a couple of days later I ask if they’ve made breakfast since then. If so, was it the same thing or something different? Why? Was it good? Maybe after a week or two of casual moments discussing food and their chef-life nature, I learn how they’ve been watching cooking shows since they were nine. Or maybe in a Friday Letter I share that I made eggs and bacon for my wife and it reminded me of them and their sister. As we laugh, one of their responses leads to something deeper, like how when the student doesn’t eat breakfast, they get headaches.

Then, after seeing how disengaged they are during class one day, they tell me they have a headache…and I guess right that it’s because they didn’t eat that morning. They were running late and almost missed the bus. We talk a week later, in the middle of class, while everyone else is working, and learn that their headaches sometimes trigger migraines. These migraines can be crippling and even keep them from attending school, which explains why they missed school the day before. During a few of our tutoring sessions after school, we chat about other causes for their migraines. Every couple of weeks I informally check in on them and if they’ve experienced any migraines, and while doing so, we branch out to other areas of their life, like their love of softball, which helps them cope with the ongoing stress that their migraines cause them. I make it known that I want attend one of their upcoming softball games…and eventually do. That opens up a world new talking points for us, like how they want to study sports journalism after high school.

I could go on here, but I won’t. It’s but one simplified, somewhat exaggerated example, but it’s how narratives can be created in the classroom and how I tend to nurture them. They’re not always rich with detail or result in frequent check ins, but they do require my inside-out, intentional pursuit for them to materialize. Framing each relationship as an ongoing set of daisy-chained exchanges like the one above sets me up to deliberately and continually see each story through to its conclusion. As they mature, I become part of and invested in each narrative. I have buy in. Each one is a thread that when picked up, followed, and woven together with the 25 others in the class, creates a fabric of humanity that makes it possible for me teach my students mathematics. Steeped in a system that too often reduces my students to test scores and accommodations, knowing their stories leads me to knowing how to teach them. For me, it comes down to stories over statistics. I don’t always live out this creed, but I try.

Because remote learning — and its endless Zoom links — has made it impossibly hard to have meaningful interactions with my students, their stories have largely gone unwritten this year. I wonder sometimes about all the moments I’m missing because of the pandemic, all the 5-minute conversations at the end of class about eggs and bacon that lead to so much more. I wonder who my students actually are.

I sit in despair when I think about these things. I struggle to accept how the arcs of their stories, of our relationships, are unmistakably flat, linear, and uneventful. There are implications buried in this struggle for me and my teaching, the affects of which I probably won’t comprehend for a long, long time.


Group quizzes for remote learning

Much of my teaching boils down to a handful of trusted, go-to activities and structures. Group quizzes (and exams) are one of them. When we were in-person, I did them all the time. The set up I had worked really well to get students talking about math and hold them accountable to the their group. But when remote learning hit last spring, I forgot about them (just like I did with traditional exams, of which I haven’t given one). They just didn’t seem feasible.

That changed in the fall when I asked my cogen about their other classes. I was interested in what things their other teachers were doing that worked well for them as students. One of the members mentioned a group quiz that their physics teacher did. Intrigued, and remembering my love affair with group quizzes, I followed up with a series of questions. I also asked the rest of the cogen what their thoughts were. I gave my two cents and, in the end, we decided that it would be a good fit for our class. I had to make it happen.

It took a couple of weeks — and another conversation with my cogen — but we uncovered a structure that we liked. Fundamentally, it’s very similar to how I structured my in-person group quizzes. Here’s how it works.

It involves Desmos Activity Builder.

Compared to options like Peardeck, which a lot of other teachers are using these days, Desmos is a great platform for my group quizzes because of the mathematical backdrop it provides. It hosts a suite of mathematical tools that are priceless when it comes to helping kids learn and also helping me to assess where they are. And, as any teacher who uses it knows, Activity Builder goes well beyond graphing. I can ask students to annotate a given graph or worked example to highlight a particular part of it, for instance, or I can have them type out an explanation of why secϴ<0 in quadrants III and IV. I can see all of their work in real-time and capture particular responses to showcase. I haven’t even fully tapped into Desmos’s capabilities, but there’s no way I would use any other platform.

Probably the most important aspect of the quizzes is how I grade them (which is the same way I graded them when we were in-person). For the quiz, each student receives two grades: a math grade and a teamwork grade. It is this dual-grade system that really makes the group quizzes come to life and promotes engagement.

The math grade is pretty obvious, but there’s a wrinkle to it. At the end of the quiz, I only grade one random student’s quiz from each group. The score that person receives on the quiz is the score that everyone receives. The kids don’t know who that is until after the quiz is over. To “end” the quiz, I use the pause feature in Desmos Activity Builder (which is incredibly smooth, I must say). I typically end the quiz with 5 minutes left in class so students will have time to complete the teamwork grade.

For their teamwork grade, each member of the group gives every other member of the group a grade from 1-4 based on how engaged they were, their communication, and how much they contributed during the quiz. Each student does this using a google form.

On the form, each student chooses their group members’ names from a dropdown and assigns each of them a teamwork grade (they complete the form separately for each group member). Along with a grade, they must also provide written feedback to each group member. After class, I average all the teamwork grades a student received and that becomes their overall teamwork grade for the quiz. I also copy and paste all the feedback a student received from their group and email it to them. The feedback remains anonymous, of course.

[Side note: I think placing on an explicit grade on teamwork sends a message to students that it’s not just about understanding the math. It shows that the ability to work together is valuable — or at least valuable to their teacher. Our grades reveal what we think is important. Our students discern this.]

Let me tell you, my breakout rooms are usually dreadfully quiet. I suppose they’ve gotten better in the 5 months since the school started, but they’ll still not great. But anytime I do a group quiz, they’re buzzing. Almost everyone is unmuted, there’s always a screen being shared, and some groups even use group texts to communicate. Not knowing whose quiz will count for everyone’s grade while also getting graded by their peers for participation creates a culture of collaboration — at least for a day. I hide it when I visit their breakouts during the quiz, but I’m blown away with giddiness at how much they’re activated and helping each other. It’s really something.

I’m grateful to my cogen for helping group quizzes manifest in a remote setting. Without their ideas, confidence, and encouragement, I’m not sure I would have worked to find a way to make this useful assessment a reality.


My two cents (Week of Feb 8, 2021)

For each school day of the 2020-21 school year, I will be writing two sentences to capture some of the impressions, feelings, experiences, or thoughts I had that day. This is the 19th post in the series.

Monday (Feb 8)
During the first 10 minutes of ninth period, 11/15 of students participated in some way (over the mic or in the chat) within the first 13 minutes of class. Considering that I have had so much silence in their class (so much so that at one point I actually started reading my current book aloud on Zoom), I was absolutely thrilled; today was a good day.

Tuesday (Feb 9)
Fifth period may have decided on a new class theme: snacks and es hora de comer. I scrambled to prep and distribute the second mathematical penpal letters for eighth period and somehow managed to pull it off.

Wednesday (Feb 10)
I sent a former student, MC, an email wishing her happy birthday, which made waking up today totally worth it. In first period, the roles were switched and instead of the class voting on the top they wanted me to wear today, a student volunteered and we voted on her top (the winner was a tie-dye hoodie).

Thursday (Feb 11)
A low-key day full of flex time to complete the week’s assignments. In ninth period, it made me happy to drop two close friends in the same breakout so they could talk to one another; given how foreign my students have been to me this year, the fact that I knew they were close friends and was able to act on it was an unusual feeling that I appreciated so much.

Friday (Feb 12)
No Classes — Lunar New Year