In this clip, Linda Fisher, Carolyn Dobson, and Hillary Lewis-Wolfsen discuss the idea of a "think sheet" for students to record their thoughts and observations during the lesson.
LINDA FISHER: One of the features that you were putting in there is you have a “think sheet”. Can you tell me a little bit about the think sheet and why you think that’s important, and what it is, exactly?
HILLARY LEWIS-WOLFSEN: Well, it’s just a blank piece of paper that we hand out, right in the beginning of the lessons. It serves a couple of purposes. First, it has their name on the top—we don’t know the students, and that helps us to see their name. And second of all, it’s a blank canvas for them to do whatever thinking that they need to do. There’s no structure to it, we’re not helping them. We’re not handing them a structure to organize their thinking. So it’s pretty open.
LINDA FISHER: So it’s very open-ended. So why do you think that you don’t want them to have a pre-imposed structure on their thinking, like we typically would see in a worksheet?
CAROLYN DOBSON: We’re not trying to lead them anywhere! We’re trying to see where they will go, they’re the mathematicians, and let them discuss between themselves!
LINDA FISHER: One of the questions today is going to involve students using some tiles, and I know that we have three or four opposing ideas about why we should use tiles, why we shouldn’t use tiles, why we should make tiles optional. Can you give us some of the reasoning behind both sides of using tiles? We really want the observers to look and see what the effect of the tiles is on the student thinking.
HILLARY LEWIS-WOLFSEN: Well, I think for not using the tiles, a couple of the reasons were that we wanted to move away from having that manipulative and being able to think through the problem at a more advanced level, a more…
CAROLYN DOBSON: Abstract..
HILLARY LEWIS-WOLFSEN: abstract level, thank you.
LINDA FISHER: Efficient, I think, was the word?
HILLARY LEWIS-WOLFSEN: Yeah. Also, none of the other examples had used tiles per se, and so, would we be… did we need, at the end of a lesson, to add the tiles too?
LINDA FISHER: Yeah, so it was one more way of thinking about it without being one too many.
HILLARY LEWIS-WOLFSEN: Right.
LINDA FISHER: Okay, and Carolyn, I think you had quite a different opinion about the use of the tiles?
CAROLYN DOBSON: Yeah, I feel that you have a different perspective on a problem when you’re actually manipulating it. If you’re a person that usually manipulates numbers, when you manipulate things, or you’re forced into a diagram, you look at the problem, you see the problem differently, structurally. It’s like using a spatial kind of thinking instead of a logical-mathematical type of thinking. You get a more rounded view.
HILLARY LEWIS-WOLFSEN: In my own class, I do a lot of pair-sharing, I do a lot of allowing the kids think-time. I didn’t want this lesson to be so different from my style that I was uncomfortable. It had to be delivered in a way that I was comfortable. To establish the norms for doing math in my own classroom, it’s a process. We start off without, we don’t open a textbook for a couple of weeks. We start off with games and puzzles that they do collaboratively in groups, the focus is on working together, listening to each other. That sets the climate. We also do things like commend students who raise their hand and say, “I don’t know the answer, but this is what I’m thinking. “ I draw attention to those students and talk about how brave they are. We do a lot of number talk, so that the students can hear how other kids are thinking about numbers, so hopefully more and more other kids will share how they thought about the numbers. I also make sure that there is think time. There can’t always be think time. They always need quiet think time to process for themselves what’s going on with the problem.