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.


Future Educator Club

For years I’ve wanted to start an after-school club for students who are thinking about being teachers. Because I love it so much, I have always low-key promoted teaching while I’m actually teaching…so why not do it in a more formal setting? I was part of Future Educators of America when I was in high school, and while I don’t recall us doing a whole lot as part of the club, I do remember feeling affirmed because of it. Most of my friends thought that wanting to be a teacher was crazy. Being part of that club gave me an early sense belonging within the field of education.

Well, in the midst of a pandemic, I finally got a “Future Educator Club” off the ground at my school. We met this week for the first time. We were a small but mighty group which I hope will grow in both vigor and in numbers. I can’t deny the strangeness of a virtual after-school club, though. It’s weird. But everything is weird these days, so meh.

What pushed me over the edge? What finally helped me create a space for students to explore teaching as a viable and important career path? I think internalizing over the last several months how overwhelmingly White teachers are in the U.S. played a big role. Practically all of my students are Black or Brown and I’ve had more than a few through the years tell me that they thinking about perusing teaching. When that happens, I want to do more than smile and encourage them — I want to provide institutional support. And then follow up. It’s a humble dream, but I believe this club could help plant the seeds to get more Black and Brown teachers into the classroom. At least that’s what I keep telling myself.

We have to recruit heavily, but exactly what do I do when students come to the club? Outside of surveying this kids who came this week, I don’t have any good ideas right now. We’ll see. I’ve really only found Educators Rising, which is promising, but communicating with them and navigating their site has been wonky and slow.

I could be looking in all the wrong places, but there doesn’t seem to be a ton of resources out there for structuring a space like this for high school students. Part of me finds this odd. And problematic. I also wonder if it contributes to the low status that teaching has in our country. As part of a field whose mission is to educate, shouldn’t we be doing more to produce folks who do the educating?


Rethinking the mathography

I’ve had my students write a mathography at the start of each year for the last three years. While they do take time to read and digest, I’ve found them to be an invaluable part of how I reach and connect with my students. They establish personal mathematical narratives in the classroom, give me a mathematical context for the young people I’m serving, and help students explore their own mathematical identities.

Because the mathography has become such a key element of my teaching, I wonder what it would look like if teachers, instead of approaching the mathography individually with their own classes, thought about the assignment more comprehensively. For example, what if high school math departments, like mine, designed a four-year mathography? What would that look like? Could kids write one “chapter” of their math autobiography each year of high school? Could each year have a different theme or have kids reflect on at their relationship with math through a different lens? What would these themes or lenses be?

As more and more math teachers turn to the mathography to raise the social consciousness of their classroom (especially those who teach at the same school), we will need to transform it from a stand-alone classroom activity to one that develops over time between classes, grade levels, and teachers. I imagine us sharing the students’ mathographies with each other from year to year, and using this collaboration to help students to discover and tell their bigger mathematical story while allowing us to gain unique insights into students that weren’t possible before. Using the mathography in this way could be a small but systematic solution to the lack of humanity and social awareness that exists in so many of our classes and curricula.