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WHAT WORKS IN EDUCATION The George Lucas Educational Foundation

How to Teach Math as a Social Activity

A master math teacher in Anchorage, Alaska, establishes a cooperative-learning environment in an upper-elementary classroom. More to this story.
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How to Teach Math as a Social Activity (Transcript)

Chris: Oftentimes we have private think time before we share our visual models in math, Matthew.

Narrator: Chris Opitz is a master teacher at Bowman Elementary School in Anchorage, Alaska. He views math as a social activity, and believes taking time to impart the skills required for cooperative learning can lead to calmer classrooms and more rigorous studies.

Chris: Why is private think time important before we have our discussions? Sadie, what are you thinking?

Narrator: This fifth grade math class was recorded during the first month of the school year.

Chris: At the beginning of the year, we establish a set of working agreements that I provide four categories, I provided speaking, listening, thinking and behavior, and that's really, social emotional learning. Then we did an exercise where the kids thought about, and kind of imagined a great classroom, like, the best place where they could possibly be learning, and what would that look like in each of those categories? And so we took all of those ideas and we developed what's called our working agreement. And then kids look at that consistently and set goals from that, and then they rate themselves. You know, today I did a great job, and they provide an explanation and evidence of their rating in terms of those goals. Also we do a lot of discussion, and that's another area. Kids did the same thing, they worked together, and thought of what a great discussion is. It wasn't kids raising their hands, it was kids bouncing ideas off each other. I personally believe, when kids have some say in making those rules and those routines, and those working agreements, they're going to own them more.

So I'm going to give you your first model. We're probably going to go around and do a fish bowl, where we stand around the outside, and we're going to watch and really think about what a good discussion looks like, how we talk and how we listen, how we ask questions, all of those good things that you guys do very, very well. So here's your first model. Please honor the private think time. Want me to read it with you? Mike has eight dollars, Kelly has twice as much as Mike. Do you know what that word twice as much means? Hey, Riley, could you and Laura work together as a team on this one? Would that be okay with you?

Riley: Sure.

Chris: Okay.

Riley: So Mike has eight dollars. Is this Mike?

Laura: Yeah.

Chris: In any classroom, anywhere you go, you're going to have an incredibly broad range of kids, socially, academically, all across the spectrum, and so how does a single person, as a teacher, as a manager, teach, you know, 20 to 30 kids in a single classroom, when that ability range is so wide? I personally believe that the social skills and more importantly, students building social skills to help them work together, to talk about math, to explain their thinking, to offer help when another student is struggling, and just as importantly, for that child to be able to accept help. That's a really difficult part of that equation. All of those skills are part of the social arena that we're working in, and without them, I don't know how you could teach a classroom with such a broad range of abilities.

Riley: How do you want to make this model?

Chris: Kids' ideas matter.

Thank you for sharing your idea.

When we pay attention to their ideas, not necessarily saying, that's a good idea, or that's a bad idea, but we say, thank you for your idea. They're more willing to share it, they probably care a little bit more, it probably feels a little bit safer to share that idea, because no matter what I say or try to push, unless kids own it, it's not going to matter.

I took your ideas about discussions, what makes a really great discussion, and I wrote them on the board for today. And so when we go to fish bowl, we're going to choose a team like we do. We're going to go around and we're going to make these observations, and your job as an audience, is to listen very closely to see if every voice is heard at that table. I want you to listen for thoughtful questions, and look for this evidence. You ready? Okay, remember, give them space. Give them space, and if you're in front, what can you do to let everybody see? Audience, our voices are off, we're just going to look for evidence of a really great discussion, and then we're going to talk about that afterwards.

I began using the fish bowl, having kids really closely observe other kids in discussion, identifying particular types of language, ways to ask questions, how to use manners when disagreeing, how to choose-- as simply as how to choose who speaks first.

Student: I'll start.

Chris: In a fifth and sixth grade classroom, we wouldn't expect that, but boy, it can derail a classroom instantly, if they don't have those basic skills and once that foundation is built, then the academics can be so much more thoughtful, so much more intense, and that's what we're shooting for.

Student: So Mike started with eight, Kelly had twice as much as Mike, and Joe had half as much as Kelly.

Chris: Every teacher out there has probably said, at some point in time, turn to your neighbor and talk about this idea. Look at your teammates and talk about this idea.

Student: Actually, I'm not quite getting, why did you do those shapes?

Student: Because it looked cool.

Chris: And really watch, and if they are talking about the topic that you've asked them to talk about, if they're actually listening to each other, and using that language and those social skills, then all of a sudden, you have an environment where 30 kids are all learning at the same time.

Student: And how would you get three, even if you did the half of eight? That's four.

Student: Is that right?

Student: I don't know how I got three.

Chris: It's not going to happen at the beginning of the year, but in my opinion, the efficiencies that you'll gain later, by far outweigh the time you spend at the beginning, teaching those basics.

Caleigh, I was standing behind you, and I kept hearing a lot of questions coming your way. How did that make you feel?

Caleigh: I don't know.

Chris: I mean, sometimes when people ask me a lot of questions fast in a row, I get kind of nervous. Do you know what I mean, and I can't-- my thoughts, I kind of lose my own thinking. Does that happen to anybody else, when somebody says, Hey, Riley, hey, Riley, did you-- what's the answer? But do you know what I mean?

Riley: Yeah.

Chris: Yeah. And you get a little nervous but that's all right, that's part of our learning. And so I want you to feel comfortable with that. That's okay to feel that way.

Right now, we're going to have-- the observers are going to discuss a little bit and make some comments. Audience, what are some things that you noticed, okay?

Riley: I kind of have a comment, but I think next time, Braden, because maybe you should spread it out, because when you first had, like the red right there, and then the green right there, it kind of looked like it was just 32.

Braden: Well, I was thinking of it, from, like, a side view, so if you're like down-- but I mean, if-- still, you can kind of somewhat see from my angle.

Chris: Say we provide a math problem. Many students can find the answer very quickly, but can they explain the process that was happening in their mind? Can they explain it to somebody that doesn't understand it? You take a really gifted kid, for example, and you have them try to explain a multiplication problem, a very basic one. They know the answer like that. And try having them explain it to somebody that it doesn't come so quickly to. It's an amazing activity to watch, to see them think through the process, oh, well I know that three times four is three groups of four, or four groups of three, and here's how I see it, and here's what it looks like visually, and that's how I get to this answer. It's an entirely different skill to be in tune with your own thinking, and so, in order to do that in the classroom, those social skills need to be in place.

Okay, for closing today, you're going to go to your math journals, and you're going to write--

By spending some time developing these routines, and helping kids learn social and emotional skills, where they can manage themselves and their interactions with others, the classroom will be a better place to be, and the academics will also be-- have the opportunity to be more rigorous, and thoughtful. And I've seen it work in my classroom, and I believe it can work in other classrooms.

Narrator: For more information on, What Works in Public Education, go to

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Video Credits

Produced, Written, and Directed by

  • Ken Ellis

Associate Producer:

  • Amy Erin Borovoy


  • Karen Sutherland

Camera Crew:

  • Rob Weller
  • Cal Coleman


  • Karen Sutherland

Comments (70)Sign in or register to postSubscribe to comments via RSS

Carla Golden's picture

Excellent video. This way of teaching or guiding the students to teach themselves and each other is a fundamental of the Montessori Method which is becoming increasingly more popular in the public school arena. Teachers may want to look into Montessori Methods to see this collaborative teaching applied to other subject matters. Thanks for this inspiring work!!

JAnne's picture
Special education, science-math teacher, instructional coach

I especially like your discussion goals, Chris. Nice work! However, as a veteran teacher of 30 years, having taught math with cooperative learning in affluent schools (class size 20-24) and currently in the inner city (class size 28-32), I can share that it's a whole new level of challenge with a larger, inner-city class. I'm not giving up (valuing discourse more than ever), and I admire your classroom climate, but it's a MUCH more daunting task with many more and varied classroom management issues that are not captured in this video. Fortunately, I've had the opportunity to observe an amazing master teacher at work with our students this year -- it took him half a year to facilitate student work successfully in partners! Sadly, most of our teachers do not utilize cooperative learning methods and strategies, so when one teacher is successful, the benefits are especially evident. Kudos, Chris, for valuing mathematical thinking and reasoning above a "rush to the right answer" (coverage of content for a high-stakes test at the expense of deep understanding) that is still evident in so many math classes.

Summer Dunsmore's picture
Summer Dunsmore
Intern at Sundt Memorial Foundation

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Mandy's picture

Thank you for all of the ideas. I teach 3rd grade but I still believe that my students would be able to do some of this. Like he said in the video, you have to teach them how in the beginning of the year but continueing with this type of teaching will have great advantages in the end.

Wendy Zahrn's picture
Wendy Zahrn
Fourth Grade Teacher, Michigan

Excellent video - I like the way it is broken down into steps. How much time is spent on each problem? Are there regular workbooks?

Mytfinn's picture

I want to be as thoughtful about my teaching as Chris is. I hope to use some of these ideas in my math class this year. Fantastic video.

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