August 18, 2012 by ray_emily
Last year, I purchased some big whiteboards. I had read about how giddy folks were about this supposedly-super-awesome, still-completely-foreign-to-me modeling stuff, and figured I’d give it a whirl.
Unfortunately, I didn’t integrate whiteboarding into my classroom routine/culture very successfully – or really hardly at all. Maybe this was because I didn’t purchase the whiteboards until halfway through the year, or maybe it was because I hadn’t quite wrapped my mind around the potential that they hold. (I’m still working on that second piece, as I attempt to integrate whiteboarding into not just a math context, but a middle school math context.) I made some real progress, yesterday, though! In fact, am so pleased that I want to tell you all about it. (Lots of questions still loom about how to make this work best for my teeny tiny kids. Will certainly write more about those in the future.)
Here’s a preview:
And, a note before I jump in: Trying new stuff is scary. I didn’t have much faith in my lesson design at the outset of this activity, largely due to my inexperience in this arena. I was feeling tentative, and started the school day with the most meager of hopes. There were no bold-faced, confident “SWBATs” at the forefront of my mind; rather, my objectives had question marks hanging uncomfortably at their ends. For instance: Students will recognize that there are many methods of solving a single problem… maybe? Students will consider that there is an infinite number of ways to represent mathematical solutions… I hope? Students will begin to think critically and creatively about what makes a model compelling… if this isn’t an utter disaster? Students will engage in an authentic conversation about each other’s solutions, thereby sharpening their perceptions of effective communication (visual/oral) in math class… if I’m lucky?
I am a little (okay, a lot) in shock that these hopes were fulfilled – and my students were willing, capable, and enthusiastic participants, every step of the way. (Concrete evidence that my hopes were fulfilled is pending. Next week, my students will write about this activity in their soon-to-be-launched blogs. My fingers are crossed that they will have brilliant things to say about CCSS Standards of Mathematical Practice #1, #3, and #4.)
Okay, okay. Enough rambling, already! Here’s what happened: I presented the class with this classic river-crossing puzzle that you’ve heard a million times. (Yep, the set-up was super simple – almost embarrassingly so, hence my lack of confidence. I think this was best, however, given that the idea of setting kids free with markers and whiteboards and rags made me a nervous.) I let them think through the problem, independently, and jot down some notes on loose leaf. After this independent think-time, I released students to work with their small groups on three separate tasks: (1) agree on a solution (or a few) and ensure that everyone in your group understands and can explain the solution; (2) talk to the people in your group to develop a way (the best way) to illustrate / chart / explain your solution; and (3) transfer the solution to your group’s whiteboard, revising and improving as needed.
After every group had come up with something they liked, they shared their models with the rest of the class. The ‘audience’ responded by sharing a compliment or two (what worked well? why?) and then offering constructive criticism (if you could change or add one thing, what would it be?). I also let students revise / improve their whiteboards, after getting their feedback. (OMG, they all received soooo much awesome feedback.)
I took photos of all 18 whiteboards. Enjoy! (I’m pretty sure that if you click on any image, you can see it a little bit bigger.)
I dig how each of the solutions is unique in a fun, quirky (and sometimes slightly ridiculous) way.
Facilitating this activity (and seeing my kids totally get into it) was a strong reminder for me to step back and think more deeply and more often about process. I want to work on engaging kids in communicating with each other as a method of cementing and internalizing their just-formed understandings.
Key takeaway (which I think I already knew, but sometimes I need reteaching, too): When I direct students to focus explicitly and deliberately on their journey, rather than on the final destination (whiteboarding does this, by default), the atmosphere in my classroom shifts dramatically. In other words: If I want more energy, more inclusion, and more conversation, I must veer sharply away from the pervasive, solutions-obsessed, joy-killing, test-driven culture.
Oh. At the end of class, I did a general share-out (what did you learn? what’s on your mind?). Along with the numerous remarks expressing disbelief at the variety in their solutions, one student stated (I kid not), “I’ve never seen so many kids working so hard on just one math problem!”