I sat with fourth grade teacher Ms. Goldman in the back of her classroom as students cleaned up materials from the class. There were 15 minutes left in the school day: just enough time for chaos to take hold of the classroom.
“Shall we play a game?” Ms. Goldman asked with a dramatic flourish.
There are lots of games that fit into those awkward, small spaces in the day. I considered proposing one, but Ms. Goldman had already announced a better idea: a drawing contest!
Okay, I was skeptical. My mind flashed with a thousand ways in which this could end badly. However, if there’s anything I’ve learned as a math specialist (or coach), it’s that sometimes I need to observe rather than interject.
“In outstanding classrooms, teachers do more listening than talking, and students do more talking than listening. Terrific teachers often have teeth marks on their tongues.”Alfie Kohn, “A Dozen Essential Guidelines for Educators”
Ms. Goldman directed students to retrieve whiteboards and dry erase markers from their desks. Ms. Goldman walked around the table groups, and continued with directions: “you’re going to draw a snowman!”
Students started to draw nice, fat circles.
“Oops, I forgot one thing…” Ms. Goldman said. Students’ eyes lifted from their whiteboards to gaze at their teacher. She has a delicious flair for the dramatic. “You need to draw with the whiteboard balanced on your head.”
I had read Fawn Nguyen and Nat Banting talk about using “Oops, I forgot” (OIF!) as a way to introduce constraints. (Others, including Mary Bourassa and Nolan Bourassa, later wrote about it, too.) They have used it more to celebrate how we need to revise our thinking. Ms. Goldman was using it to turn everything… well, onto its head. (Apologies for the pun.)
Students immediately diverted their course. They used a balled fist to erase their carefully crafted snowmen, and balanced the whiteboards atop their heads. They were thrilled!
Many students drew a quick sketch, and then pulled down the whiteboard to admire their work. Or… maybe not admire… Several of them shook their heads, and set about a second attempt.
“Don’t forget the top hat!” Ms. Goldman called out.
They engaged in some solid geometric reasoning while doing this. How would the circles connect? Or, at least, how does one reduce the amount of overlap among the three circles? How could these circles make them as similar as possible? What does it feel like to draw the 90 deg angles of the hat?
Three of the students attempts are above. The first student thought about trying to draw the three circles with a single stroke. The second one was trying to estimate placement of the circles, but then lost track when it came to draw the hat (which looks like it’s standing in for a snowman belly button). In the third picture, you can see that Ms. Goldman asked students whether they wanted to share. This student wanted to continue to add to his picture. Students were anxious to revise and revise and revise!
The class then played a quick second round: draw a snowflake. What angles did you TRY to draw? IS it easier to draw right angles purposefully?
Students are currently wrapping up their unit on geometry: Measuring and Classifying Shapes. (TERC’s Investigations in Number, Data, and Space curriculum) One of the instructional routines used throughout the unit is called “Quick Images: 2-D.” I first learned about this routine under the name Quick Draw, via Sarah Carter (@mathequalsove) and the book Quick Draw: Developing Spatial Sense in Mathematics by Grayson Wheatley. In the routine, an image, like the one below, is flashed for only 3 seconds.
Students are then asked to draw a copy of it from memory. The teacher might then flash the image one more time, giving students a chance to revise.
Students had engaged with this routine multiple times before playing Drawing Contest, and they brought these experiences with them. They were accustomed to this framework for thinking. How we remember the parts of the image is asking students to think about how they decompose the desired image into smaller, perhaps familiar shapes. Asking what we notice about the relationship of the parts of the image ask students to think about placement, the relationship of lines, angles, etc. Having these experiences helped bring out the mathematics in Drawing Contest.
What I loved the most about this game is that it was a small, beautiful moment. It felt spontaneous and dramatic. Students were playful. The task was imbued with mathematics. It took less than 10 minutes to play the two rounds, and that seemed like enough time. There was momentum throughout.
When I left Ms. Goldman’s room, I ran into her grade level colleague, Claire. She listened to me gush about what I had just witnessed. (Claire wasn’t at all surprised to hear about her friend’s quick flash of brilliance.) I think we don’t share these sorts of things enough: the small moments. The playful moments. The moments of curiosity, of joy, of mathematical exploration. The moments that maybe can’t be replicated… and that’s okay.
I love to share when a student has a breakthrough, and when a lesson felt like it was worthy of some sort of teaching academy award. I also want to celebrate more of these tiny things. There is so much beauty when we look for it.
Here’s the original tweet, which I composed while perched atop the heater towards the back of Ms. Goldman’s class.