In this clip, Linda Fisher, Carolyn Dobson, and Hillary Lewis-Wolfsen discuss how they decided to introduce the re-engagement lesson.
LINDA FISHER: so when I was listening to you plan the lesson, you spent a lot of time thinking about how to introduce the lesson, to get students really excited about talking about the problem. Can you talk about that a little?
HILLARY LEWIS-WOLFSEN: This was something that you brought up.
CAROLYN DOBSON: Yes. I think it’s very important that the kids feel like, that the kids get a chance to discuss like mathematicians! We’re trying to teach mathematics, what do mathematicians do? Well, they discuss interesting problems, and they argue back and forth, to discuss what makes sense! They find the pieces in the logic that they confront—they find these misconceptions and confront them head-on. That’s the experience we want the children to have.
HILLARY LEWIS-WOLFSEN: and that will be part of our introduction is to ask them to think and discuss as mathematicians.
LINDA FISHER: I think when we were discussing it, we were sort of talking about—when they’re doing the procedures or working the problem, they’re using about this much of their brain, but then when they go back in for that mathematician piece, that developing justification, they’re like using more of their brain, or sort of having a higher cognitive demand about how much of their brain is engaged in the activity. We want to look for that increased level of thinking.
CAROLYN DOBSON: I also want to say that I think there’s a difference, when you take a task, and you feel like it’s like a test, you’re more concerned, a little bit, with “right” and “wrong”, and that’s really different than thinking about the interest of this problem. Then much more of you is completely engaged in it.
LINDA FISHER: So, I know when you were developing this idea of reengagement, you sort of added a piece where you had a follow-up to the reengagement level where you added the red pens. Can you talk about the response of students to the use of the red pens, and even what that process is?
HILLARY LEWIS-WOLFSEN: Well, at the end of the lesson, we close the lesson by telling the students that we’re giving their teacher their original assessments back, with red pens for the students to go back and edit their work. That anything that they’ve learned from our lesson today, they can add, and make changes, and improve their work. The assessments haven’t been scored, so as far as they’re concerned we haven’t even looked at them.
CAROLYN DOBSON: Yes, that’s what I would say.
LINDA FISHER: What I remember was like when they wrote their little notes back to you, a lot of the students said how nice it was to get a chance to go back and fix their work, and how much they really enjoyed the opportunity to like change their answers and show new things that they knew.
CAROLYN DOBSON: They showed a lot of appreciation for that experience.
HILLARY LEWIS-WOLFSEN: Because we had done this lesson a few times before with other groups of students, we had anticipated what kinds of errors we might see. It was very similar, so that worked out well. The first time, we didn’t have that, so we based our whole lesson on the exact errors and interesting answers we got the first time around. Each of the classes have had very similar “interesting answers.” We started off reading through all the assessments, making notes of the interesting answers and categorizing them: What was the answer? If it was wrong, how was it wrong? If it was right, was there a diagram that went with it? What made it interesting? We tallied a lot of these to see what was common. Even some of the interesting things that weren’t common were valuable enough that we might still include it. I’m sure there were some that we wouldn’t have used. There was a time consideration. We needed to “tell the story” of the problem: How do we want the kids to think about it, what do we want them to get out of the problem? If an interesting answer doesn’t help, then we don’t use it.