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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

Joy Widmann's picture
Anonymous (not verified)

You and I share a pedogogical point of view. While some of your vocabulary is different from mine, our actions are similar. I'm fortunate to work in a school that encourages this type of teaching.

I agree with you 100% about the time invested at the beginning of the year. All the community building pays off as the year progresses, especially as we start our projects and cooperative learning.

I wish there were more reports in the media about teachers like us. We represent all that is good in education, and others need to know it is possible.

John McAdam, Marist College's picture
Anonymous (not verified)

"A picture is worth a thousand words." And, this video was a great model of how cooperative learning strategies can be played out in an elementary mathematics classroom. My college prospective teachers thoroughly enjoyed this math lesson where students were actively engaged in the process of learning and enjoying math in a social context!

Chris Opitz's picture
Anonymous (not verified)

I appreciate your opening quote about "a picture is worth ....". Visual models are such powerful teaching and learning tools. Just like the students in our classes need hands on models for math, they also need explicit models for building social skills. I appreciate that you point out that we as adults also need models for our learning. It's so true. Having the opportunity to watch and learn from other teachers is so important.

Chris Opitz's picture
Anonymous (not verified)

I really appreciate your comments about kids feeling "at ease to explore, discover, and build....". I couldn't agree more with the importance of students having the confidence to dive into their learning, not fearing the outcome, even when it might be unexpected. I can only hope that we strive for learning environments where kids feel ok about being confused, where kids are ok with the idea of struggling through a process, where they feel like all their learning is important; these are the places where kids make breakthroughs. These are the environments where kids stretch themselves academically.

Chris Opitz's picture
Anonymous (not verified)

Thank you Joy. I think you are right on when you call it an investment. Kids have amazing ideas, but without the social tools to share those ideas, very few people will ever understand or appreciate their insights. You're right, the particular vocabulary we use is not near as important as the fact that we think through what we expect, and spend time planning and teaching children to meet those expectations. They can absolutely live up to a high standard. Thanks for your ideas.

John McAdam's picture
Anonymous (not verified)

Hi Chris,

Teaching and learning are two sides of the same coin. And, if learning is a life-long process then we all need models. And, you and your class represened a wonderful model for all of us. Thanks for the reply and thanks for your modeling.

Baye's picture
Anonymous (not verified)

Observing classes during student teaching is, of course, helpful in gaining an understanding of real world teaching. However, having access to videos that not only show us a master in action, but give voice-over explanations of the process is ideal.

Thanks for taking the time and effort to create and share this with us. So many will benefit.

Cristi at Walden University's picture
Anonymous (not verified)

I think you have done a fabulous job teaching students to be respectful to each other. Students do not often realize that not listening to each other is a form of disrespect. It is sometimes difficult to incorporate teaching character at the same time as you are teaching content. This video has given me some great teaching tools to put into use in my own classroom.

Chris Opitz's picture
Anonymous (not verified)

I agree with you. Facilitating respectful conversation and dialogue among students can be incredibly difficult, but boy is it worth the investment. I love your comment regarding respect and disrespect. I hear those terms so often, and I've got to wonder how children interpret what respect means and what it looks like to them. I believe that by explicitly modeling and practing discussion habits (what respectful discussion does and does not look like), students are more likely to internalize and in turn, practice those expected habits. In the long run, the learning of content will benefit, and students will be more likely to engage themselves independently because they have the skills to do so. Thank you so much for your comments and insight.

Luke Benson's picture
Anonymous (not verified)

Great work! Chris, just came across this video and was thoroughly impressed with your manner. I was fortunate to teach in the same building with you at Russian Jack and your Space and Ellis Island projects continue to work their way into my instruction. Thanks for the ideas and thank you especially for allowing your students to think.

Luke Benson
Tennessee School for the Deaf

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