Staying in sync (Murd Letter #8)

My school colleague Stephanie Murdock and I are writing letters to each other and publishing them on our blogs. We are both white math teachers leaning on one another to improve the antiracist stance that we take in our lives, classrooms, and school. This is the eighth post in the series.

Hey Murdock,

Thanks for your letter! Let me start by saying that it’s crazy to think that, no matter what happens with school, I won’t be able to physically see you until maybe next year. It’s obviously best for you, and I’m happy that you will have peace of mind and body, but that is wild…and also kind of fitting at the same time. I guess we’ll have to double-down on our letter writing to stay somewhat in sync, won’t we! That makes me think…in our summer letters, we talked about reading a book together and using our letters to discuss it. What do you say? If things are too hectic, maybe we start with an article?

And on the idea of reading books, have you read anything good lately? No lie, I kind of miss the book updates that you used to give me in your early letters. I know they were for keeping yourself accountable, but they still filled me with ideas. At a recent meeting, I overheard you mention that you have come to appreciate James Baldwin, but haven’t had the chance to dive into his thinking or writings so much. Ironically, as you were saying that, I had just finished Begin Again by Eddie S. Glaude, which is a kind of intellectual biography of Baldwin. Towards the end of the book, I feel like Glaude trailed away from the Baldwin more than I would have liked, but it was still an insightful book when it comes to understanding Baldwin’s message…and also to gain some inspiration in these trying times that we live in today. I’ve previously read Fire Next Time, which I now want to reread, and also hope to read No Name in the Street in the coming months as a result of Glaude.

I think adopting the title “A Mathematician and Me” stemmed from my desire to include a mathematical “identifier” in its title. It’s probably a mundane detail, but I wanted the title to have a direct tie to math. I haven’t done the task yet with my kids, but it’s in the works. I have, on the other hand, started my Mathematicians Beyond White Dudes project with my students. I’m feeling that some of the mathematicians’ profiles may get a facelift this year. That will be refreshing, but it does feel strange not being able to hang up the posters around the room and in the hallway.

Oh, this is exciting. In an effort to capture all that’s happening and help humanize my kids’ mathematical experiences this year, I’ve connected with another math teacher from Indian River, Michigan…and together our students will be mathematical penpals this year. There are a lot of cool dynamics that could result of this project. My partner teacher teaches in a rural setting with mostly white students. I don’t. The pandemic. Writing about math. There’s a lot we could do. In addition to using the assignment to have students do some identity work and connect with potential real-world mathematicians, I would like the A Mathematician and Me task to be a focus of a future letter or series of letters with their penpal.

Shifting gears, you mentioned, “My tools of measurement is the feedback from a handful of students that propel me forward.” When I read that, I could not help but think about the cogenerative dialogues that I’ve been having with students this year and how useful they’ve been for me and my virtual classroom. I feel like I mentioned cogenerative dialogues to you in a previous letter, which have been pioneered by Dr. Chris Emdin. Are you also doing them? If so, I would love to chat about how it’s going. Since I’m the only I know who is doing them, I have no one else to talk to about them. I would love a thought partner.

I’m inspired to read how you’ve been able to find small ways to keep your classes current and tap into the present moment. The electoral college and positivity rate examples were fascinating. I can’t say that I’ve been doing the same, but reading about you and BD’s successes may be exactly what I need to get the ball rolling.

It’s crazy that you feel that some of your biases might be getting erased in the virtual setting because, after a recent conversation with a colleague of ours, that exact thought been running through my mind for a few weeks. She compared not being able to see students with losing one of her senses and how this has “heightened” some of her other senses. How is my reading of students different now that I can’t see them — or, in some instances, even hear them? How are students’ behavior changed now that they know I can’t see them? Implicit bias is a huge component of how I might respond to these questions, I think, and it’s utterly fascinating to think about them. I have, have, have to excavate this for myself through a future blogpost.

One last thing I wanted to share with you. This summer, after attending one of their many workshops, I was talking with MfA about creating a white, antiracist affinity group for the spring. They’ve never had a place where white people can come together in solidarity and unpack their privilege and share how we’ve been been complicit in racist systems. There was another MfA teacher who I connected who helped me pitch the idea, which was accepted by MfA. I’ve never planned for this type of workshop before and I am eager to see how it plays out. Though it will be through MfA, I am heading into the affinity group hoping that what I learn from the experience can help me create white affinity groups at our school next year.

My last letter concluded with me being disheartened. Despite some of what I said in this letter, I can’t say that I’ve been doing any better. For me, acknowledging the uncertainty of everything hasn’t seemed to help with how disconnected I am to our school, my students, our colleagues. I can’t shake it. And for the last couple of weeks, the colleagues aspect of my struggle has been particularly challenging. Attempting to do any work — let alone equity work — in isolation from colleagues that I trust has been exhausting and demoralizing. You may or may not have noticed this in my demeanor as of late. Having already been dealt the piercing blow of being in a long-distance relationship with my students, now that schools have closed and I cannot feed off of the trickle of energy that I was getting from in-person relations with colleagues, I’m not sure where to turn. Alas, the work must get done.

Thanks again for your letter, Murd. Writing these letters helps me forge connections that go beyond the shallow zoom links that I’ve become so dependent on.

Mr. P

My Two Cents (Week of Nov 23, 2020)

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 tenth post in the series.

Monday (November 23, 2020)
I think racial and social justice may be slowly becoming a priority at my school. It appears as if our institutional priorities may be changing to help us dismantle white supremacy culture, but there’s still a long way to go.

Tuesday (November 24, 2020)
Another roller coaster. I barely taught in eighth period today before realizing that they needed a mental health day; I wish I had the answers they needed.

Wednesday (November 25, 2020)
I played math pictionary today. It was fun, interesting, and useful to see how students think about and represent the various concepts we’ve learned through informal sketches.

Thursday (November 25, 2020)
No classes — Thanksgiving Recess

Friday (November 25, 2020)
No classes — Thanksgiving Recess


Math Pictionary

I did an interesting activity with my students this week: math pictionary. I used the site, which enables you to upload custom words to be used in the game. For ours, I used some common math terms as well as some key terms that we’ve used so far in Algebra 2 like end behavior, difference of cubes, and cosecant. Like many good ideas, math pictionary came to me five minutes before class started. Luckily, it was simple to set up and pretty much ran itself after I inputted the custom word list.

Aside from being really fun and engaging, playing the game in a math context also got me thinking about how students are visualizing what we’re learning. What does their pictorial representation of a given term say about how they’re thinking about it? Plus, when it’s their turn to draw, they’re given mere seconds to determine how they want it to look. What they elect to draw and how they do it may also speak to their “first impressions” of the term, which can be revealing in its own right. Each of their drawings were a sudden, in-the-moment representation of a mathematical idea. This could also go for the students who are guessing. Based on what is drawn, the terms that students are guessing may be indicative of how students have oriented themselves to those terms. (Through all of this talk of math and drawings, I can’t help but smile and think of Ben Orlin. His warm-hearted and funny book Math with Bad Drawings is an absolute gem.)

There are definitely implications for my teaching here. Students capturing ideas through quick drawings can be a useful alternative for them to communicate their mathematical thinking…and for me to get some glimpses into how they’re understanding content. It invites in students’ creativity and perspective. Interpreting their sketches — however loose and informal they are — is a unique and worthwhile form of assessment. And in a remote setting, everything helps! For example, when given the term tangent, a kid drew a right triangle that was intended to be in the first quadrant of the unit circle (I think). They labeled the horizontal leg of the triangle “cos,” the vertical side “sin,” and the hypotenuse “tan.” Because tangent = sine/cosine, I took this to be a possible error in the student’s knowledge of tangent.

During the game, while managing zoom and gauging interest in my last-minute choice of an activity, I only caught a few of those types of interesting sketches. If I played again, I think I could pick up more. Plus, when I do this again, I’m wondering if there would be a way that I could get creative with the word list so my assessment targets the nuances of a specific concept. For instance, could I get them to draw and guess specific cases of end behavior?

Here are several of my students’ sketches and the terms they were attempting to represent.

end behavior
vertical line test


Instructional routines for remote learning

Remote learning has sucked the life out of me this fall. With schools closing this week, there appears to be no end in sight. It’s been hard for me to find bright spots, but I have landed on a few instructional routines that I like. To help me cope and take my mind off everything else on this sinking ship, I want to write about them.

Ungraded Student work
Since my curriculum problem-centered, I have my students scan their handwritten work to 1-3 problems per day and upload it to Google Classroom. The next day, I carefully select a few pieces of anonymous work and place them in our “Work Analysis” Google Doc that is shared with students. The bulk of our time together on Zoom is spent discussing the work from this doc in our breakouts. What’s cool is that the doc has correct (and incorrect) work from every problem we’ve ever discussed. As a running total of what we’ve learned, it’s a resource that kids are beginning to rely on more and more.

2. Feedback
When students scan and upload their handwritten solutions to Classroom, I give feedback on specific parts of their work using the comments feature. It creates a box around the area of the image that I need to provide feedback on and opens up a comment box. This effectively allows me to annotate student work like I would in-person. I have yet to see another solution for commenting of student work that is this efficient or precise. A screenshot:

3. Revisions and Resubmissions of Graded Work
Instead of administering traditional exams, which I’m struggling to see the point of in this context, I am assigning students 2-3 problems on Monday which are due Friday on Classroom. (These are the exact problems I would give on an exam. Students scan and upload their work, just like the daily problems.) Though they are due on Friday, if students submit their solutions before Thursday, I will give them feedback on their work with a grade and return it. If they didn’t earn full credit on the problems, they can revise their solutions and resubmit them as many times as they want for a higher grade. I like this because it builds in revision as a core component of our class that is far more meaningful than “test corrections.” It also opens up a line of communication between individual students and myself that is always buzzing. Plus, there is a steady stream of work I’m receiving throughout the week instead of one lump sum that can take forever to get through.

4. Self-Assessment
Instead of creating some complex system of accountability when it comes to participation and engagement, like tallying how many times a kids speaks, shares their screen, or even submits the daily homework problems, I let the kids do it. They decide their grade. I have a rubric that the kids use to assess themselves on Fridays based on how active they were in class that week. I glance through their self-reported grades, but I extend trust to them and find that the students are overwhelmingly honest.

5. Google Forms Self-Graded Quizzes
In the spring, I wrote about my love for this assessment tool and I appreciate them even more now.

6. DeltaMath
A priceless commodity even before remote learning. I post one assignment every Monday that aligns with the problems that we’ll be studying that week. It’s always due Friday.

7. Desmos
Desmos Activity Builder is an invaluable tool, but I don’t think I use it nearly as much as other math teachers I know. For many, they use it to format and structure all of their lessons and content. Even with it’s souped-up features, I’m more strategic when I opt for it. The Desmos grapher gets used all the time in class, but I prefer Activity Builder for only specific concepts.

8. Zoom Polls
Maybe it’s just me, but these have been getting far less attention than they should be from teachers. They’re built right into zoom, quick to set up, and provide me a quick, real-time check in whenever I need it. Sure, not every student responds to them, but I usually get enough data to pass judgement. All of the polls I set up are generic and designed for kids to respond to whatever question I have on the current slide, which often pertains to a piece of their scanned work.

9. Pre-assigned breakout rooms
In Zoom, there’s an ability to place students in breakout rooms before the session begins. When we were in person, I used to change my students’ seats every Monday. I loved doing this to inject fresh energy into discussions every week. With remote learning, because there’s so much missing, I think having consistent groups for long periods of time is important if I want students having meaningful interactions with each other. (I keep students in the same breakouts for six weeks.) It helps kids get comfortable with one another and establish informal roles — like who is going to screen share or annotate. In some cases, I strategically put friends together to help ease the awkwardness. Kids have to sign into Zoom for this feature to work seamlessly, but even when they don’t, I spend a few minutes at the start of class to put kids in their rooms. Many of my breakouts are still deathly silent, but I have noticed positive changes as a result of doing this.