Back in the Before Times, I took hundreds of photos of student work.
“What do you do with all of those photos?” students would ask.
I am a student of student thinking. I would look back at some of the photos later, either on my own or with the classroom teacher, and dig deep into how students represented their work, or how I annotated thinking during group discourse.
Because I am teaching on zoom this year, it’s easier than ever to capture photos and video. With a few keystrokes, or clicks of a button, I can save what students said, or how their thinking was represented. It all saves to my computer — like magic! Whenever I have questions about a student, or my practice, I review what I have.
Yesterday, I wrote about how students represent their own thinking during independent or partner/group time, as well as ways in which teacher bias can creep into any learning environment. Today’s post will focus on how questions about how I represent student thinking. How can I use the annotation tools to make student ideas visible? This is work that is inherently biased because it’s all filtered through my perspective and way of seeing things; how can I make certain I am accurately represent what the students say and push the math conversation forward?
How am I representing student thinking?
Looking back at how I annotated student thinking can help me reflect on the choices. How did I make that student’s thinking visible? What worked about the equation I wrote? Did the diagram help or confuse? How accurately do I think I matched the student thinking? What feedback did the student give me?
Isaac was the first to share. he shared how he saw ‘6 in the first row, and every row is 6, so then it’s 12, then 18, then 24… ” He skipped over a few multiples to land at 42. I recorded his answer above the array of half dots: 42.
Nella shared next. “I saw that you needed two of those things to make one. So I saw 2 and 2 and 2 and 2 of them…” As Nella spoke, I circled pairs of them going left to right, for 3 total pairs.
Nella stopped me: “No, not like that! More like up and down.” I erased what I had drawn, and made the image you see above. “I didn’t use the next-to-each-other dots until the last row because it didn’t have a pair.” As she spoke, I could see Isaac, who had left his camera on, seemingly have a breakthrough. He unmuted himself.
“Oh, oh! I need to change my answer!” Isaac burst out. I asked him to wait until Nella finished, and then he knew what he had to do. “Now I get why everyone else had a different answer from me! Okay so it’s 42 like I said but it should say 42 halves.” I wrote 42 halves. “Does that get me the right answer?” Isaac asked.
I smiled, and didn’t respond immediately. Instead, I wrote 42/2.
“Oh! Yeah! It does! That’s 21! It’s like division!”
I did take one final strategy, from Emory. He told me that he matched them up to make 3 x 7.
“Oh, like Nella’s…” I started.
“No, not at all like Nella’s. Because mine is 3 x 7.”
“Because you did what I had originally drawn for Nella?” I started to circle every 2 half dots.”
“No!” Emory persisted. “Like you can see the 3 x 7 array, right?” Then there’s another one next to it. There are two matching arrays and you put them together so that it’s just a 3 x 7 array.” I drew rectangles around the larger arrays.
Saving this image reminded me that I need to listen closely to students, and to ask questions.
How should I annotate student thinking?
I had never been a middle school classroom teacher until this year. Previously, I had either taught many subjects (as an upper elementary classroom teacher) or many grades levels (every grades K-8 as a math specialist/coach). I feared that teaching the same lesson multiple times would bore me. Blissfully, it doesn’t! (and it cut way down on my prep in a year when prep is a beast!)
Sometimes, I will play around with different questions, strategies for annotation, or adaptations to a lesson. Here, in a notice/wonder warm-up (using a graphic from Prime Climb) to launch a lesson, I tried writing using a stylus for one class, and typing for the next.
The typed text was much easier to read than the text I wrote using a stylus. (I swear, my handwriting can be beautiful! The delay during zoom annotation makes it impossible to employ my ‘I Taught Elementary School’ penmanship.)
Later, I switched to handwritten notes in order to highlight different pieces of the graphic, and quickly record expressions.
I have discovered that when I have a lot to write, and it can be in paragraph form, it is best to type (e.g. for notice and wonder, which one doesn’t belong). If I have less to write or it needs to be in specific places around the screen, or I need to switch easily between text and pencil tools, it seems more efficient for me to write it using a stylus.
Reflecting Later — the Importance of Screenshots
I am confident that I had some ‘a ha’ moments about when to use the stylus and when to type while I was teaching. But it’s easy for ideas about teaching to be fleeting. We are focusing on so many many things simultaneously, making dozens of decisions in the course of a single class period. Brilliant ideas can still be casualties to our short term memory. Keeping the screenshots (and videos, while I’ll share in tomorrow’s post) helps make this learning about tools ‘stickier’ for me. I can revisit it later, at a slower pace, when I’m not worried about checking in with students who are muted with cameras off, or thinking about how to make this idea accessible to my new students who missed the first three weeks of our work with ratios, or whether I should e-mail Cole’s mom about something that happened during a breakout room, or… or… or… and, wait, did Jarrid just say something unduly snarky in the chat? Gah.
Remote pandemic teaching is exhausting.
Sometimes, we just need space to think, and saving screenshots means I can return to it when I have space… whenever I am finally able to have some space.