In this clip, Hillary Lewis-Wolfsen introduces herself to the fifth grade class and orients them to the day's tasks. She hands out “Think Sheets” and asks them to think as mathematicians.

5th Grade Math - Proportions & Ratios*Hillary Lewis-Wolfsen, Forest Park Elementary School, Fremont Unified School District, Fremont, California*

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HILLARY LEWIS-WOLFSEN: Okay, fifth graders, I need you to quiet down now…I am Ms. LEWIS-Wolfsen, some of you may know me. I know I know some of you. And I’d also like to introduce Mrs. Dobson, she’s going to be helping me out today. We’re going to be looking at that candies assessment. Remember that candies assessment you did, I think, on Monday? We’re going to be looking at different ways that students used to solve some of the problems. Okay? Before we do that, I’m going to pass out a blank piece of paper. I’m going to call this your “think sheet.” What I’d like to do with this is put your name kind of big at the top, as you, that way those of us, there are visitors in the room here, can know what your name is, and I might even be able to call you by name. (Three, four, six, eight) Pass that down?

Oh! Thank you, Mrs. Dobson. And you’re welcome to do, to write on this, go ahead and put your name on this. And as we think about the math today at any time, if you want to write anything down to keep track of anything, you can use this for this. You can use both sides, if you need more, we have plenty. Okay? So there you go, I’m going to hand this back to you.

First I want to talk about—I talked about how we’re going to be looking at how different students approached the problems in that candies assessment. We’re going to talk like we’re mathematicians. We’re going to discuss as mathematicians do, about how the different approaches and strategies make sense. Okay? What I need you to do is listen really carefully to the other students who are talking and see if you can hear something that they say that makes you change your mind. Okay?

As you look around, you are very aware of the visitors in your classroom, you recognize some of the teachers in here, and you see the camera in here. I want you to know, they are curious about how you learn, and they’re here to think about, or look at how you think, and how you learn about math. So could you please make sure you speak loudly and clearly when we are talking? There will be times when you will be talking in front of the whole class, and times when you’ll be talking in your pairs, so if you can do your best to speak loudly enough that we can hear you, so we can learn about how you’re thinking about the problems. Is your hand up, did you have a question? Oh, okay. (laughter) Okay.

HILLARY LEWIS-WOLFSEN: Background information about this class: This class is a Mandarin Language Enrichment Program. It is a voluntary program offered to all children at our school who are either fluent in English or have some Mandarin knowledge. Many of the children have been together in the program since kindergarten. By fifth grade, they know each other well and are comfortable working together. A day or two prior to this lesson, the students were given the “Candies” task. They had not seen it since, and had no feedback as to their success with it. I was not their regular classroom teacher, so I needed to set up my expectations and address the unusual situation we were in with having so many observers. It was also a deliberate decision to not hand back their original work. I wanted them to think through the problems again, not worry about what they did right or wrong initially.

LINDA FISHER: The students were asked to think like mathematicians. This had been an important discussion point when planning the lesson. Hillary and Carolyn wanted the class to be able to have discussions about the logic of the mathematics and confront their misconceptions.