Story: Creating a Discourse-Focused Class Culture

After working collaboratively with colleagues, her administrator, and researchers for two years, Trish—a second-grade teacher in Auburn, Maine—sat down with project partners to reflect on her experiences exploring evidence-based practices in early mathematics education with digital tools to enhance her own classroom practice. The text below is a summary of the longer conversation.

Setting Clear Targets

Q: How do you set up your lessons to promote communication and critique among second graders during mathematics lessons?

A: One of the first things I do is I take a target that we’re working on, that’s a required part of our curriculum, and I print off the target goals. Then I make it into an “I can” statement, which I make sure is in student-friendly language. Each target has a proficiency scale that we review so students understand what we are working on together.

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Q: Can you provide an example?

A: “I can solve a word problem by adding or subtracting.” “I can use tools and equations to solve my problem.”

Open Tasks

Q: What else do you do?

A: I make an open-ended problem, usually something related to our school community that is personal for the students.

One problem that I made last year was related to Mrs. H—she’s our physical education teacher. Students had played a game in physical education made up of stations with groups of balls of different sizes. So I made up a problem that asked how many could she have of each size if she needed a certain total number of balls—let’s say 91. What are the three quantities you could have if some are small, some are medium-sized, and some are large?

I created two open-ended problems when we were getting ready for our yearly Art and Music Show. One was about displaying students’ clay sculptures from art class. Mrs. S had to set up a display for kindergarten, first grade, and second grade. If she had 69 sculptures total, how many could be on three tables, or on four tables? Another open problem was about the musical portion of the show. This time the focus was on the possible combinations of drums and xylophones if we needed 72 for our performance. We had conversations about how 70 drums + 2 xylophones would not make the best performance. Students approached these problems as real-life situations to solve because they were part of our daily life at school.

Listen to a second-grade student who had previously been non-verbal with all teachers during grades K–2. The audio of the screencast was the first time any public school teacher had heard his voice. With the support of his teacher and aided by the creation of screencasts, he began to communicate regularly with his teacher and in front of his class to explain his mathematical thinking as well as his ideas in other subjects.

Q: So, I hear you say that while working toward these learning targets you like to create an open problem with a context to which students relate. When do students work independently and when do they have opportunities to talk with others? How do you create a discourse-rich classroom culture?

A: First we review the open problem as a group to clarify the target and the task. Often, I give students some time to think about a strategy themselves and then they work with a partner. It may look like this: If Sarah and I were partners, Sarah would share her strategy with me and then I’d have a conversation with her about my strategy. Next we would take turns making our video or screencast explaining how we would each solve the problem. First one student would make the video, with some support from his/her partner. For example, Sarah would be sitting beside me when I made my video helping me work through the process so I didn’t forget a step. She may be talking me through it, saying, “Oh, don’t forget to start recording,” or “Don’t forget to save it”, giving me a little tip. She might also ask me to explain my thinking more, possibly saying, “How do those numbers go together?” ” Is that a friendly number?” Especially when students first start to make screencasts or videos, it can be hard to remember all the technical steps. A partner helps with the management pieces by encouraging, giving tips and asking questions. I also provided a screen recording checklist for students to use as they create and revise their videos. The checklist was shared from another second grade colleague in Auburn during our monthly meetings as part of the research project.

Q: What else, if anything, do you hope to achieve by having students work in pairs when making their videos?

A: When students work in pairs it helps give clarity to the videos. Each student makes a video and saves it. Then students watch one video at a time together. Students know that they can ask questions about their videos. Sometimes students make a simple addition or subtraction mistake and a partner will say, “Is that really how that works?” or “Are you sure that this is right?” Students know that they can go back and edit videos. They help each other go back and self-correct their videos. This can happen during the video as it is being made or students can decide to go back into their video and make some changes. This kind of self correction encourages students to explain and check their thinking. They are working on solving the problem by talking through it. The conversation is fluid and promotes self correction as part of the conversation between partners.

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Strategies for Problem Solving

Q: What strategies do students draw on when solving mathematics problems for their videos?

A: We usually brainstorm strategies together as a class before they work in pairs. Before we do problem solving, I introduce the strategies in the morning message. My morning message every day is related to a math strategy that I want students to learn or practice. First, I give them a hint about how it works and then I start to propose open-ended problems related to that strategy, and we practice together using that strategy before I have them go try it on their own—and over time, they have a bank of strategies to pull from.

Q: Do you have a list of those strategies?

A: I do. I keep a list on my easel in my classroom, and we add to it as we start a new strategy. Students can see the list while they work, so it can remind them of ways they might approach a problem.

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This is a photo of the first few strategies listed on the easel while students worked on the Art and Music Show task.

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Scaffolding Peer Discussions with Classroom Routines

Q: How do you support students in discussing their videos?

A: When the students make the video, they have the problem and they have sentence starters or sentence frames to help them with their explanation. For example, they can use sentence starters like these:

  • “The math problem I’m going to solve is…”
  • “The strategy I used was…”
  • “I checked my answer. I know it’s correct because…”

This is something that I added after I first started doing open problem solving videos—after I realized it wasn’t really clear what I expected students to do. At first students didn’t know how to talk about their work. Once students realized that they could explain the steps used for their solution, the opportunity to give details about different strategies started to emerge.

Q: So, after they make and review the video with a partner, what happens next during a typical lesson with an open problem they are recording?

A: After students share their video with a partner, I reorganize them into small groups—usually three students. The students in these groups do not include the partners, so it’s a completely different set of students. Then students share their videos one at a time.

Q: Do you have a sharing protocol for students to use in small groups?

A: Yes, we made a list in the beginning of the year. We discuss how to work with a partner and also how to work in a small group. When you’re in a small group, one person shares a video at a time, everyone else has their devices screen-down, and everyone who isn’t sharing is using the five magic rules of listening. Students watch the video together, then they ask each other questions, give a compliment or make a connection about their understanding of the video.

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The Five Magic Rules of Listening.

Q: That sounds like routines you create with them, an expectation for behavior that you keep the same over time. How did you establish routines around the use of the tablets during sharing?

A: When we first introduced tablets in our district in kindergarten, a list was made about how to safely handle tablets. For example: “No Running.” “Two thumbs on the top.” In my school, we have what we call SOPs—standard operating procedures. These are the procedures and routines in a classroom. Teachers introduce this idea in kindergarten, and I use them also. The students know what SOPs are and that they are a part of how the classroom works. I created SOPs for the tablets that are specific to how we use them in my class. The “turn it upside-down” procedure came from watching students as they shared with each other in groups. I realized that what I wanted my students to do was watch a video and have a conversation about it, but that can’t really happen if students are all looking at their own tablets. I was observing a group and thinking: “My, you’re not even looking at his video.” I asked myself: “What is it that I want students to do? Why do I want them to do it? What can I do to help students focus on one video at a time when a peer is sharing?” These questions came about because our focus during the research project was to support student dialogue around their own problem solving.

Watch three grade 2 students discuss math work made on a tablet.

Q: Did you prompt them with the types of questions they could ask each other?

A: Yes. I gave them a list of possible question starters, but they could also ask their own questions. For example, I gave them starters such as: “Did you use (friendly numbers)…” “Did you try…” “I noticed that you used…” After students say one of these starters, the rest of what they say is usually related to one or more of the strategies that we have on our list. The conversation continues as students make connections to the problem solving in the video that they are watching.

Q: Have you thought about what types of questions will lead to the most productive student discussions? Are there some questions that work better than others?

A: A good starting question is, “What do you notice?” Once the conversation gets rolling, I’ll say, “Oh. How did you figure that out?” or, “What does that look like? Can you explain how you did that? Can you come up and show us how you did that?” or “What made you think that?” Another question I ask students a lot is: “How do you know that?” “How does that work?” It will lead you down the path to understand students’ thinking and the connections that they are making.

Q: In what way do you see interactive technology playing a helpful role in supporting students’ mathematical discussions?

A: Students really want to see their friends’ videos because they want to be able to talk about what they saw. Kids naturally love to talk about the stuff that they know. They notice something in a peer’s video and they make a connection to it because they may have used a similar strategy, it may clarify a strategy for them, or give them a new idea. Writing about strategies can be isolating because students do not have anyone to bounce ideas off of. While writing is valuable, it is often an independent activity. Videos are all inclusive because peers can share their videos and have a conversation right away. The feedback is immediate. It also helps that the videos are short enough to keep students engaged and focused. Students’ videos are usually no more than three minutes or so.

Q: What else do you do to promote students’ mathematical discussions?

A: I put open-ended math equations in the morning message. I usually write out problems with blanks and we come up with the numbers as we go. I start simple. Here are a few examples: 1.) ___+ ___= 12.  2.) ___-___=9.   3.) ___+___- 10=____ .  4.)  ____-(___+___)=____ . 5.)  ____= (___-___) X2 . Sometimes we’ll work on solving word problems. What I say to my students is: “Does somebody have a strategy that they think they could explain and show us?”

In the beginning of the year, I’ll say, “Does anybody have another idea?” Students become comfortable with sharing their ideas because it’s part of what happens daily. After the start of the school year, once we are into our routines, a student will solve a problem and another student will say, “Well, I thought of another way.” The conversation continues as students keep asking questions or pointing out something that they know. My role is to keep the focus on the task and ask clarifying questions, if needed, to support the problem solving. Sometimes a student has an idea of how to start but needs support to finish a solution so we talk it through. Sometimes students will solve a problem in a way that I never thought of, but if it works for them, I say, “OK! A different way.”

Q: So you started by prompting [students] with questions such as “Does someone have a strategy for solving this problem? Does anyone else have another idea?” And you’re saying by now, at this point in the year, they’re prompting each other?

A: Yes, students feel comfortable with each other and they know that, as a class, we are going to listen to each other. They begin to realize that answers have multiple pathways and solutions and we can talk and think things through. We talk this way every day, all year.

Q: Just in math class?

A: No, I do it all the time. I have a large set of colorful letters in my classroom that spell out the word: “THINK.” It is right on the wall in our classroom meeting area. We see it every day! Students know at the beginning of the year, the biggest job they’re going to do when they come into our classroom is THINK! I set that tone in the greeting of our morning message each day. “Dear Math Maniacs,” “Dear Lucky Learners,” “Dear Problem Solvers” or “Dear Wonderful Workers” are a few examples.” I expect everyone to work, think, talk, and have fun learning together.

Q: Can you give another example of the kind of problem you would ask students to solve during the morning message?

A: Some problems I get from my teacher’s edition of our math series. We have sections called Mental Math and Math Reflexes. If it’s a closed problem, I usually take that problem and leave out some numbers to make it more open and interesting, depending on the skill that I’m teaching. We could be learning about how addition and multiplication are connected and how do we use that information. We may be working on geometry and the problem might be, “What do we know about parallel lines and how can we prove what we know about parallel lines?” We might be trying to show how to make change with different coin combinations. Sometimes I ask a question, and depending on a student’s response, it will help other students think of another strategy or idea. Students start to share their thinking and sometimes we will continue in the large group, sometimes we continue in small groups, sometimes in pairs. Students know that we are thinking and learning together.

Q: What gives you the courage and willingness to take these kinds of risks in the classroom and open things up for unexpected turns?

A: The reason I can do it is because we have SOPs (standard operating procedures), and students know exactly what it means to be sitting in the meeting area and how to focus and listen, and that something important is going to happen. We create our SOPs together so students are invested in what they need to make learning happen. They already know the five magic rules of listening from first grade. We have routines and the expectations are clear. We practice these routines so they are automatic. Students know they can make mistakes and try again and they know we are at school to learn and have fun! Establishing a culture where students and their ideas are valued is a critical first step in a classroom where students are expected to think, learn and grow.

I also think that being part of the Research + Practice Collaboratory gave me the tools to work with to open students’ thinking. We looked at what an open problem is and we had conversations in our monthly meetings about how to promote mathematical discourse with children. I had a supportive atmosphere to explore my own thinking and have conversations with my colleagues and found it helpful. This is what learning is for everyone both adults and children.

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High Expectations for All while Attending to Individuals

Q: So returning to students working in small groups with their tablets. You have given them prompts to help them understand what to say when they’re reacting to a video, correct?

A: Yes. They say, “I noticed…” and they look at the list of strategies. They might say, “I noticed you used friendly numbers” or “I noticed that you used an open number line,” or “Oh, I get what you did. You added this and this together.” So they make some kind of connection based on what they see in the video.

 When students say “I noticed…” the critical piece is that what children are noticing is what they own and know in their own learning. Every child is going to come at that problem from his/her perspective. One child might say, “Oh, I noticed that three plus three is six and that’s a double.” Another child might really expand on that. It depends on where each individual student is in his/her learning and thinking. They feel free to state what they notice and know that it’s going to have value.

Q: How did you foster these expectations? Did you make them explicit at some point?

A: I believe in students as individuals and I believe every child can learn! At the beginning of the year, if we’re in the morning meeting and I pose a basic question such as 3 + ___ = 7, I choose a student and I don’t let someone else answer the question. I have the student come up to me at the easel. We find a way to answer the problem. I’ll ask: “How do you think we could figure this out? What do we know about this?” And the whole class watches and then we figure it out. When the student gets the answer, I say, “You got it! I knew you could do that kind of thinking.” I want to build their confidence. I don’t let someone else take away a student’s ability to answer a question. Another student can’t jump in and answer for someone else. I tell them: “I’m going to call on you if you raise your hand or not, because I know you are already thinking about what you know!”

Q: How do you support students who have difficulty solving a problem?

A: Usually I ask: “What is the part about this problem that we know? How can we use what we know to help us figure out the part that we don’t know yet?” I look for the seed, the little piece that I know that student has, to get started. And if the student has completely no idea, I’ll give them a hint – the hint will depend on the child. I might even say, “Do you think you could ask a friend? Do you have somebody that might give you a hint?” It depends on the student and what I think will help him or her be successful with the problem.

Q: How do you find out what might work for individual kids and what might not work?

A: At the beginning of the year, I spend a lot of time watching how students interact with their peers and how they might approach me if they have a question. Or if I ask a question, I pay attention to what they do. Are they a child that has to sit and think? Are they a child that has to watch what’s happening in the classroom to feel comfortable? Are they a child that comes in and starts sharing something they figured out and want me to know right away? Are they a child that comes in and starts asking me questions as they hit the classroom door? Or are they the child that needs a personal connection to start their day? I want to know my students as individuals.

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Additional Strategies

Q: So how do you help students get to a place over time where they’re sharing as a whole class and you’re essentially hardly involved?

A: At the beginning of the school year I start with the simple question: “What do you notice?” It’s very open-ended and it’s in all areas of the curriculum. It could be after I finish reading the class a story. “Do you notice anything about the characters in the story? Do you notice anything about the illustrations?” I always start with: “Do you notice anything?” Students get used to this question as a way to share information and have a conversation. We also practice active listening with the 5 Magic Rules of Listening chart.

We have to have a lot of time noticing; how long depends on the group of children. It could be one week of noticing; it could be two weeks, a month. The goal is to have all students engaged, hooked into what is going on in the classroom.

After we are good at noticing, then I can ask: “Do you have a question?” “Can you explain it in another way?” “Does this remind you of something else?” We move forward from there.

Q: What’s the next thing you think is important to do to build a classroom culture where students are having discourse that’s real?

A: I introduce a term very early on in the year in my class: the concept of prior knowledge. We talk about, “What do you think that might be?” We begin to have a conversation about things that we already know. I want students to realize that they all have this prior knowledge. I want them to know that they’re going to take what they know right now and use it to learn something new.

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Wait Time

Q: If you think about the work you do over time to get to whole classroom discourse that students themselves are leading, what else is really important?

A: I think it’s important that when you ask students a question to make sure that you give them wait time. When you’re talking to children there is a give and take back and forth. When you ask a question, students may have to think about the answer for a minute and you must wait while they think. It’s a natural thing to do. You are providing students with a model that you value what they have to say. That value helps students become risk takers and owners of their learning! This is how we help create thinkers and problem solvers. Learning every day is a lifelong skill!

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