In this clip, when the students realize that their initial work is wrong, they have an impulse to correct it.
TRACY LEWIS: Two, one. Eyes up. Thank you Diamond, thank you D'wone. Thank you, London. Shivani, sit on your bottom, please. Okay, so.
TRACY LEWIS: You have your papers back. This is a photocopy of your work, because I know, I already see some of you have your pencils out, you are ready to make some changes.
TRACY LEWIS: You're ready to improve your thinking and make your thinking a little bit clearer. So here's what we're going to do. Ms. Lewis is going to shift gears a little bit.
TRACY LEWIS: Because I still see that our schema is a little fuzzy about what process we're supposed to do. What operation are we supposed to. What words are important, what words are not important.
TRACY LEWIS: So here's what I'm going to do. You are going to get a colored pen, so put your pencils away. Put your pencils away. I'm going to give you a pen. And if you would like, I also have a blank task somewhere that Ms. Lewis put down. I have blank copies also.
TRACY LEWIS: You can either write the information on a blank copy, or you can change your information right on your work.
TRACY LEWIS: If you want to add something, how many people see something that they need to add to their work, to make their thinking clearer.
TRACY LEWIS: Maybe you didn't tell us that you added the tens first. Okay? Or maybe you didn't tell us how you added the numbers together. How many of you would actually like to change something?
TRACY LEWIS: Okay. So if you're going to change something, I want to know why you're changing it. If you change something, after our discussion on the rug, tell me why you changed it.
TRACY LEWIS: What are we going to do? I need somebody to be the teacher. What are we supposed to do right now? I need someone to be the teacher. What are we going to do? Giovanni.
STUDENT: We're gonna, we're gonna use, we're either gonna use our paper, for our work, what we did, or we're gonna use a blank photocopy, and if you think you have to, you could use a pen, so we can make our thinking more clear.
TRACY LEWIS: Okay. So Ms. Lewis is coming around with pens and blank ...
TRACY LEWIS: I want you to actually work on the back side. Let's take a look at numbers 3 and 4. Because we've gone over numbers 1 and 2. See if you would like to change something or add something to numbers 3 and 4.
TRACY LEWIS: So turn your papers over, and Ms. Lewis is coming around with a pen. And... yes? Just take one.
STUDENT: 26, 63, to.... Are going on the field trip. 19 persons will... how many people are...
TRACY LEWIS: She wants to buy an apple pen. So if she sees an apple pen, is that important?
TRACY LEWIS: Okay. She sees a sparkle pen for 65 cents. How much more does the sparkle apple pen cost? What do you think you're supposed to do?
TRACY LEWIS: Yes? Go grab them.
STUDENT: I think you're supposed to... add them. 48 and 65.
TRACY LEWIS: Uh huh? Why do you think you're supposed to add?
STUDENT: �Cause she wants an (inaudible) pen and an apple pen.
TRACY LEWIS: Okay, so here we go. So Ms. Lewis wants a green pen. I want a green pen and, let's say that this is a special green pen. So this one costs 48 cents. Right? This one costs, how much? This is the special one, this is the sparkle one. How much does this one cost?
TRACY LEWIS: 65 cents. So, here's the question. How much more does the sparkle pen cost? First of all, which one costs more?
STUDENT: The sparkle pen.
TRACY LEWIS: The sparkle pen. Show me how much the sparkle pen costs. Show me.
TRACY LEWIS: What's confusing you? So take a look at this. Molly wants to buy an apple pen. She sees a red apple pen that costs, how much?
TRACY LEWIS: She sees a sparkle pen for..
TRACY LEWIS: How much more does the sparkle apple pen cost? I hear you thinking about something. What do you think you should do?
TRACY LEWIS: Which one costs the most? Right. Which one costs the least? Right. Do you need that? Is that 8? Or is that more than 8.
Here, I want students to examine their process. I photocopied their work on purpose and gave them a choice about how to revisit their work. While they have a photocopy, I also provided them with a blank sheet. With some kids, they can mark up their original work; for others, they need to reformulate their thinking on a new page. I asked the question: "How many of you would like to change something?" I was pleased to see the students' willingness to say what they would change/add. When students looked around the room, they could see that they were not the only ones to want to change their work. It had been challenging getting this group to see an alternative way of working, but through this process it opened up many of them to examine how to reflect on their own work. I still had a challenge with several students who continued to be confused in applying that learning to a new problem. Through this process, students are encouraged to slow down and consider: What should I do first? What words are important? What words are not so important? Students could identify or compare the cost of the two items ($.65 and $.45); it was challenging for students to get past the desire to get both items and identify the difference. Their answer to the problem was "buy both," which is a typical second grade answer! But mathematically, I was trying to impress upon them why that didn't make sense if you were going to buy just one.