Monday, December 9, 2013

"Many people enjoy readings cut-and-pasted from reflective emails."

I'm betting that Danielson is wrong on his cut-and-paste theory, but I figure we'll give him a shot.

Earlier this year, I tried to implement Prof. Danielson's hexagon sequence in my Geometry class, and it basically failed. I tried again in my 4th Grade class this past week, and it's been going really well. Part of that is the age difference, but the other part is what I wrote to the kindly Professor about.

I sent him this email tonight. Enjoy, and keep the fantastic comments coming.*

* Kudos to the crew responsible for a great conversation on the last two posts. I'm looking at you, Denise, Chris Painter, mrdardy, Sue, Gregory, Megan, Justin, Christopher, Mike, EdRealist, David and Teresa. You guys rock.


Hey Professor, this email is too long, but I wanted to share some exciting hexagon moments with you.

Another fun day of hexagons today. After a slow start last week, things have been clicking with the 4th graders over the past few days. In particular, I was surprised by a bunch of coolness that happened today, and I wanted to share it with Prof.

Teresa called her shape "Squashed" because it looked like a squashed hexagon. Cool. Rather than directly ask students to clarify their thinking, I asked them to make little "What's My Rule?" puzzles and had the class try to discover and express the rule. Someone articulated a version of the "squashed" definition, so I turned a squashed shape on its side (so that it was now very narrow), and asked whether it was squashed.

Unanimously, no.

Today I cut out a bunch of shapes (squares, triangles, various hexagons) and got all of the students sitting in a circle on the floor. The idea was to force them to observe the shapes from different perspectives, and to build the notion that our classifications ought to be invariant of viewing perspective.

I put down the shapes in the middle of the circle, one at a time, and asked them to speak up if we already had a name for this shape, or if it was a new one. I accidentally stumbled onto a really great question, because the hexagons that I presented were all similar, but non-identical to, some of your hexagon pieces.*

* I put those to good use as well. Each student got one hexagon piece handed to them, and that was their shape. I was eager to make this more about individual perspective than anything mediated by the group, so I wanted each kid to own a different hexagon.

This, more than anything else, helped drive us to some clarity in our terminology.

I meant to cut a shape that looked a lot like the three-pronged shape from your set, but I accidentally altered it a bit. When I put it in front of the kids, a lot of them started giving it a new name. I asked whether any of our old names applied to it. Someone said it looked like a rocket. Others said it didn't. Then a bunch of stuff clicked for me.

I realized that Lily, who gave us the "rocket" in the first place, owned the shape. I asked her, as the originator of the term, whether this new guy was also a rocket. She said that it also had three points, and then I realized that this was our data. This was the fact, end of the story. So I turned to the rest of the class and said, "Hey, that's really interesting. We weren't sure whether it was a rocket, but Lily said that it counted because it had three points." Then -- thank god for this -- a kid pointed out that my shape had four points. So then this became our puzzle. "Yeah, you're totally right. This does have another point. So how come it looks like a rocket to Lily?"

The big, big reason why this flopped so hard for me earlier was because I was completely unable to find the constraints on the problems involved in this context. If the kids have complete ownership over all these observations and terminology, where's the reality pushing back on their views? What are the problems to solve?

Over the past two sessions I feel as if I've had a breakthrough. The move is to make the particular visions of individual students into problems that the rest of us have to solve. We become students of our various ways of seeing things. The way our friends see the world is non-negotiable, and it's the constraints that push our language to more precision.


  1. So I see that the professor has already tweeted out what I think is the KEY passage here. Your last two sentences are knockouts and IMPORTANT reminders. Whenever we can make the students the teachers instead, whenever we can give their ideas some primacy instead of our ideas being at the center, whenever we can incite them to work hard at making their own thought process more explicit, well then we're on our way to helping them grow and learn in a meaningful way.

    Thanks for the reminder!

    1. No doubt the core idea is in those last two sentences. But I'm not sure I agree that this is a case of making students the teachers. Their ideas are being put at the center of class in a different sense. It's more that their way of seeing the world is the problem: How do we find a way to make sense of Lily's way of seeing things?

      Because it's her subjective vision, it's valid and uncontestable. So we're stuck with it. What we're trying to do is find a language for that vision, whether it comes from her or some other student.

      In these sort of openish student-centered explorations, I've struggled to understand how we get interesting constraints and problems to work on. I mean, there's only so far you can go with "Here's how I see it" and "No, actually I see it this way."

      What I realize here is that a technique for creating problems out of particular visions is to bounce a particular vision back to the class, and ask them to explain it. So we get to keep the subjective, individual perspective, but we also get a problem that is much more amenable to group discussion.

  2. Some of the best discussions have occurred when I have been willing to allow the conversation to go a direction I may not have anticipated or planned. When I intervene, students may feel they are "wrong" or don't have anything of value to contribute. When I allow them to challenge each other, or add there thoughts even if I had a different agenda, it is amazing what ideas will emerge, and the learning that occurs. Periodically I may draw it back in with a question if things seem to be going way off track, but I'm learning to be comfortable with a change in plan so to speak. Thanks for this post, great reminder to be aware of learning taking place, rather than sticking to the lesson plan.

  3. This reminds me of theatre improv games. We have to accept fully what others say and then build on it.

    1. Yeah, that's actually a great way to put it.

  4. "If the kids have complete ownership over all these observations and terminology, where's the reality pushing back on their views? What are the problems to solve?"

    Fwiw, I tried to adapt the hierarchy of hexagons a few weeks ago as well (with high schoolers) and I'd say that this pretty much sums up my frustrations too.

    I think its a great idea to give each kid their own personal shape. I wish you had posted this a few weeks ago.

    1. You and I will have to check in with each other when we try this with our high-schoolers next year. Hopefully it will go better for both of us!