Tutita Casa, Anna Strauss, Jenna Waggoner & Mhret Wondmagegne, Developing Student Agency: The Strategy Showcase ROUNDING UP: SEASON 4 | EPISODE 7

When students aren't sure how to approach a problem, many of them default to asking the teacher for help. This tendency is one of the central challenges of teaching: walking the fine line between offering support and inadvertently cultivating dependence.

In this episode, we're talking with a team of educators about a practice called the strategy showcase, designed to foster collaboration and help students engage with their peers' ideas.

BIOGRAPHIES

Tutita Casa is an associate professor of elementary mathematics education at the Neag School of Education at the University of Connecticut.

Mhret Wondmagegne, Anna Strauss, and Jenna Waggoner are all recent graduates of the University of Connecticut School of Education and early career elementary educators who recently completed their first years of teaching.

RESOURCE

National Council of Teachers of Mathematics

TRANSCRIPT

Mike Wallus: Well, we have a full show today and I want to welcome all of our guests. So Anna, Mhret, Jenna, Tutita, welcome to the podcast. I'm really excited to be talking with you all about the strategy showcase.

Jenna Waggoner: Thank you.

Tutita Casa: It's our pleasure.

Anna Strauss: Thanks.

Mhret Wondmagegne: Thank you.

Mike: So for listeners who've not read your article, Anna, could you briefly describe a strategy showcase? So what is it and what could it look like in an elementary classroom?

Anna: So the main idea of the strategy showcase is to have students' work displayed either on a bulletin board—I know Mhret and Jenna, some of them use posters or whiteboards. It's a place where students can display work that they've either started or that they've completed, and to become a resource for other students to use. It has different strategies that either students identified or you identified that serves as a place for students to go and reference if they need help on a problem or they're stuck, and it's just a good way to have student work up in the classroom and give students confidence to have their work be used as a resource for others.

Mike: That was really helpful. I have a picture in my mind of what you're talking about, and I think for a lot of educators that's a really important starting point.

Something that really stood out for me in what you said just now, but even in our preparation for the interview, is the idea that this strategy showcase grew out of a common problem of practice that you all and many teachers face. And I'm wondering if we can explore that a little bit. So Tutita, I'm wondering if you could talk about what Anna and Jenna and Mhret were seeing and maybe set the stage for the problem of practice that they were working on and the things that may have led into the design of the strategy showcase.

Tutita: Yeah. I had the pleasure of teaching my coauthors when they were master's students, and a lot of what we talk about in our teacher prep program is how can we get our students to express their own reasoning? And that's been a problem of practice for decades now. The National Council of Teachers of Mathematics has led that work. And to me, [what] I see is that idea of letting go and really being curious about where students are coming from. So that reasoning is really theirs. So the question is what can teachers do? And I think at the core of that is really trying to find out what might be limiting students in that work. And so Anna, Jenna, and Mhret, one of the issues that they kept bringing back to our university classroom is just being bothered by the fact that their students across the elementary grades were just lacking the confidence, and they knew that their students were more than capable.

Mike: Jenna, I wonder if you could talk a little bit about, what did that actually look like? I'm trying to imagine what that lack of confidence translated into. What you were seeing potentially or what you and Anna and Mhret were seeing in classrooms that led you to this work.

Jenna: Yeah, I know definitely we were reflecting, we were all in upper elementary, but we were also across grade levels anywhere from fourth to fifth grade all the way to sixth and seventh. And across all of those places, when we would give students especially a word problem or something that didn't feel like it had one definite answer or one way to solve it or something that could be more open-ended, we a lot of times saw students either looking to teachers. "I'm not sure what to do. Can you help me?" Or just sitting there looking at the problem and not even approaching it or putting something on their paper, or trying to think, "What do I know?" A lot of times if they didn't feel like there was one concrete approach to start the problem, they would shut down and feel like they weren't doing what they were supposed to or they didn't know what the right way to solve it was. And then that felt like kind of a halting thing to them. So we would see a lot of hesitancy and not that courage to just kind of be productively struggling. They wanted to either feel like there was something to do or they would kind of wait for teacher guidance on what to do.

Mike: So we're doing this interview and I can see Jenna and the audience who's listening, obviously Jenna, they can't see you, but when you said "the right way," you used a set of air quotes around that. And I'm wondering if you or Anna or Mhret would like to talk about this notion of the right way and how when students imagined there was a right way, that had an effect on what you saw in the classroom.

Jenna: I think it can be definitely, even if you're working on a concept like multiplication or division, whatever they've been currently learning, depending on how they're presented instruction, if they're shown one way how to do something but they don't understand it, they feel like that's how they're supposed to understand to solve the problem. But if it doesn't make sense for them or they can't see how it connects to the problem and the overall concept, if they don't understand the concept for multiplication, but they've been taught one strategy that they don't understand, they feel like they don't know how to approach it. So I think a lot of it comes down to they're not being taught how to understand the concept, but they're more just being given one direct way to do something. And if that doesn't make sense to them or they don't understand the concepts through that, then they have a really difficult time of being able to approach something independently.

Mike: Mhret, I think Jenna offered a really nice segue here because you all were dealing with this question of confidence and with kids who, when they didn't see a clear path or they didn't see something that they could replicate, just got stuck, or for lack of a better word, they kind of turned to the teacher or imagined that that was the next step. And I was really excited about the fact that you all had designed some really specific features into the strategy showcase that addressed that problem of practice. So I'm wondering if you could just talk about the particular features or the practices that you all thought were important in setting up the strategy showcase and trying to take up this practice of a strategy showcase.

Mhret: Yeah, so we had three components in this strategy showcase. The first one, we saw it being really important, being open-ended tasks, and that combats what Jenna was saying of "the right way." The questions that we asked didn't ask them to use a specific strategy. It was open-ended in a way that it asked them if they agreed or disagreed with a way that someone found an answer, and it just was open to see whatever came to their mind and how they wanted to start the task. So that was very important as being the first component.

And the second one was the student work displayed, which Anna was talking about earlier. The root of this being we want students' confidence to grow and have their voices heard. And so their work being displayed was very important—not teacher work or not an example being given to them, but what they had in their mind. And so we did that intentionally with having their names covered up in the beginning because we didn't want the focus to be on who did it, but just seeing their work displayed—being worth it to be displayed and to learn from—and so their names were covered up in the beginning and it was on one side of the board.

And then the third component was the students' co-identified strategies. So that's when after they have displayed their individual work, we would come up as a group and talk about what similarities did we see, what differences in what the students have used. And they start naming strategies out of that. They start giving names to the strategies that they see their peers using, and we co-identify and create this strategy that they are owning. So those are the three important components.

Mike: OK. Wow. There's a lot there. And I want to spend a little bit of time digging into each one of these and I'm going to invite all four of you to feel free to jump in and just let us know who's talking so that everybody has a sense of that.

I wonder if you could talk about this whole idea that, when you say open-ended tasks, I think that's really important because it's important that we build a common definition. So when you all describe open-ended tasks, let's make sure that we're talking the same language. What does that mean? And Tutita, I wonder if you want to just jump in on that one.

Tutita: Sure. Yeah. An open-ended task, as it suggests, it's not a direct line where, for example, you can prompt students to say, "You must use 'blank' strategy to solve this particular problem." To me, it's just mathematical. That's what a really good rich problem is, is that it really allows for that problem solving, that reasoning. You want to be able to showcase and really gauge where your students are. Which, as a side benefit, is really beneficial to teachers because you can formatively assess where they're even starting with a problem and what approaches they try, which might not work out at first—which is OK, that's part of the reasoning process—and they might try something else. So what's in their toolbox and what tool do they reach for first and how do they use it?

Mike: I want to name another one that really jumped out for me. I really—this was a big deal that everybody's strategy goes up. And Anna, I wonder if you can talk about the value and the importance of everybody's strategy going up. Why did that matter so much?

Anna: I think it really helps, the main thing, for confidence. I had a lot of students who in the beginning of starting the strategy showcase would start kind of like at least with a couple ideas, maybe a drawing, maybe they outlined all of the numbers, and it helps to see all of the strategies because even if you are a student who started out with maybe one simple idea and didn't get too far in the problem, seeing up on the board maybe, "Oh, I have the same beginning as someone else who got farther into the problem." And really using that to be like, "I can start a problem and I can start with different ideas, and it's something that can potentially lead to a solution." So there is a lot of value in having all of the work that everyone did because even something that is just the beginning of a solution, someone can jump in and be like, "Oh, I love the way that you outlined that," or "You picked those numbers first to work on. Let's see what we can use from the way that you started the problem to begin to work on a solution."

So in that way, everyone's voice and everyone's decisions have value. And even if you just start off with something small, it can lead to something that can grow into a bigger solution.

Mike: Mhret, can I ask you about another feature that you mentioned? You talked about the importance, at least initially, of having names removed from the work. And I wonder if you could just expand on why that was important and maybe just the practical ways that you managed withholding the names, at least for some of the time when the strategy showcase was being set up. Can you talk about both of those please?

Mhret: Yes, yeah. I think all three of us when we were implementing this, we—all kids are different. Some of them are very eager to share their work and have their name on it. But we had those kids that maybe they just started with a picture or whatever it may be. And so we saw their nerves with that, and we didn't want that to just mask that whole experience. And so it was very important for us that everybody felt safe. And later we'll talk about group norms and how we made it a safe space for everyone to try different strategies. But I think not having their names attached to it helped them focus not on who did it, but just the process of reasoning and doing the work.

And so we did that practically I think in different ways, but I just use tape, masking tape to cover up their names. I know some of—I think maybe Jenna, you wrote their names on the back of the paper instead of the front. But I think a way to not make the name the focus is very important. And then hopefully by the end of it, our hope is that they would gain more confidence and want to name their strategy and say that that is who did it.

Mike: I want to ask a follow up about this because it feels like one of the things that this very simple, but I think really important, idea of withholding who created the strategy or who did the work. I mean, I think I can say during my time in classrooms when I was teaching, there are kids that classmates kind of saw as really competent or strong in math. And I also know that there were kids who didn't think they were good at math or perhaps their classmates didn't think were good at math. And it feels like by withholding the names that would have a real impact on the extent to which work would be considered as valuable. Because you don't know who created it, you're really looking at the work as opposed to looking at who did the work and then deciding whether it's worth taking up. Did you see any effects like that as you were doing this?

Jenna: This is Jenna. I was going to say, I know for me, even once the names were removed, you would still see kids sometimes want to be like, "Oh, who did this?" You could tell they still are almost very fixated on that idea of who is doing the work. So I think by removing it, it still was definitely good too. With time, they started to less focus on "Who did this?" And like you said, it's more taking ownership if they feel comfortable later down the road. But sometimes you would have, several students would choose one approach, kind of what they've seen in classrooms, and then you might have a few other slightly different, of maybe drawing a picture or using division and connecting it to multiplication. And then you never wanted those kids to feel like what they were doing was wrong. Even if they chose the wrong operation, there was still value in seeing how that was connected to the problem or why they got confused. So we never wanted one or two students also to feel individually focused on if maybe what they did initially—not [that it] wasn't correct, but maybe was leading them in the wrong direction, but still had value to understand why they chose to do that. So I think just helping, again, all the strategies work that they did feel valuable and not having any one particular person feel like they were being focused on when we were reflecting on what we put up on display.

Mike: I want to go back to one other thing that, Mhret, you mentioned, and I'm going to invite any of you, again, to jump in and talk about this, but this whole idea that part of the prompting that you did when you invited kids to examine the strategies was this question of do you agree or do you disagree? And I think that's a really interesting way to kind of initiate students' reflections. I wonder if you can talk about why this idea of, "Do you agree or do you disagree" was something that you chose to engage with when you were prompting kids? And again, any of you all are welcome to jump in and address this,

Anna: It's Anna. I think one of the reasons that we chose to [have them] agree or disagree is because students are starting to look for different ways to address the problem at hand. Instead of being like, "I need to find this final number" or "I need to find this final solution," it's kind of looking [at], "How did this person go about solving the problem? What did they use?" And it gives them more of an opportunity to really think about what they would do and how what they're looking at helps in any way.

Jenna: And then this is Jenna. I was also going to add on that I think by being "agree or disagree" versus being like, "yes, I got the same answer," and I feel like the conversation just kind of ends at that point. But they could even be like, "I agree with the solution that was reached, but I would've solved it this way, or my approach was different." So I think by having "agree or disagree," it wasn't just focusing on, "yes, this is the correct number, this is the correct solution," and more focused on, again, that approach and the different strategies that could be used to reach one specific solution that was the answer or the correct thing that you're looking for.

Tutita: And this is Tutita, and I agree with all of that. And I can't help but going back just to the word "strategy," which really reflects students' reasoning, their problem solving, argumentation. It's really not a noun; it's a verb. It's a very active process. And sometimes we, as teachers, we're so excited to have our students get the right answer that we forget the fun in mathematics is trying to figure it out.

And I can't help but think of an analogy. So many people love to watch sports. I know Jenna's a huge UConn women's basketball…

Jenna: Woohoo!

Tutita: …fan, big time. Or if you're into football, whatever it might be, that there's always that goal. You're trying to get as many more points, and as many as you can, more points than the other team. And there are a lot of different strategies to get there, but we appreciate the fact that the team is trying to move forward and individuals are trying to move forward. So it's that idea with the strategy, we need to as teachers really open up that space to allow that to come out and progressively—in the end, we're moving forward even though within a particular time frame, it might not look like we are quite yet. I like the word "yet." But it's really giving students the time that they need to figure it out themselves to deepen their understanding.

Mike: Well, I will say as a former Twin Cities resident, I've watched Paige Bueckers for a long time, and…

Tutita: There we go.

Mike: …in addition to being a great shooter, she's a pretty darn good passer and moves the ball.

And in some ways that kind of connects with what you all are doing with kids, which is that—moving ideas around a space is really not that different from moving the ball in basketball. And that you have the same goal in scoring a basket or reaching understanding, but it's the exchange that are actually the things that sometimes makes that happen.

Jenna: I love it. Thank you.

Tutita: Nice job.

Mike: Mhret, I wanted to go back to this notion that you were talking about, which is co-naming the strategies as you were going through and reflecting on them. I wonder if you could talk a little bit about, what does co-naming mean and why was it important as a part of the process?

Mhret: Mm-hmm. Yeah. So, I think the idea of co-naming and co-identifying the strategies was important. Just to add on to the idea, we wanted it all to be about the students and their voice, and it's their strategy and they're discussing and coming up with everything. And we know of the standard names of strategies like standard algorithm or whatever, but I think it gave them an extra confidence when it was like, "Oh, we want to call it—" I forgot the different names that they would come up with for strategies.

Jenna: I think they had said maybe "stacking numbers," something like that. They would put their own words. It wasn't standard algorithm, but like, "We're going to stack the numbers on top of each other," I think was maybe one they had said.

Mhret: Mm-hmm. So I think it added to that collaboration within the group that they were in and also just them owning their strategy. And so, yeah.

Mike: That leads really nicely into my next question. And Anna, this is one I was going to pose to you, but everyone else is certainly welcome to contribute.

I'm wondering if you could talk a little bit about what happened when you all started to implement this strategy showcase in your classroom. So what impacts did you see on students' efficacy, their confidence, the ways that they collaborated? Could you talk a little bit about that?

Anna: So I think one of the biggest things that I saw that I was very proud of was there was less of a need for me to become part of the conversation as the teacher because students were more confident to build off of each other's ideas instead of me having to jump in and be like, "Alright, what do we think about what this person did?" Students, because their work became more anonymous and because everyone was kind of working together and had different strategies, they were more open to discussing with each other or working off of each other's ideas because it wasn't just, "I don't know how to do this strategy." It was working together to really put the pieces together and come to a final agree or disagree.

So it really helped me almost figure out where students are, and it brought the confidence into the students without me having to step in and really officiate the conversation. So that was the really big thing that I saw at least in some of my groups, was that huge confidence and more communication happening.

Mhret: Yeah. This is Mhret. I think it was very exciting too, like Anna was saying, that—them getting excited about their work, and everything up on the board is their work. And so seeing them with a sticky note, trying to find the similarities and differences between strategies, and getting excited about what someone is doing, I think that was a very good experience and feeling for me because of the confidence that I saw grow through the process of the kids, but also the collaboration of, "It's OK to use what other people know to build upon the things that I need to build upon." And so I think it just increased collaboration, which I think is really important when we talk about reasoning and strategies.

Mike: Which actually brings me to my next question, and Jenna, I was wondering if you could talk a little bit about: What did you see in the ways that students were reasoning around the mathematics or engaging in problem solving?

Jenna: Yeah, I know one specific example that stood out was—again, that initial thing of when we gave a student a problem, they would look to the teacher and a little bit later on in the process when giving a problem, we had done putting the strategies up, we'd cocreated the names, and then they were trying a similar problem independently. And one of my students right off the bat had that initial reaction that we would've seen a few weeks ago of being like, "I don't know what to do." And she put a question mark on the paper. So I gave her a minute and then she looked at me and I said, "Look at this strategy. Look at what you and your classmates have done to come together." And then she got a little redirection, but it wasn't me telling her what to do. And from there I stepped away and let her just reference that tool that was being displayed. And from there, she was able to show her work, she was able to choose a strategy she wanted to do, and she was able to give her answer of whether she agreed or disagreed on what she had seen. So I think it was just again, that moment of realizing that what I needed to step in and do was a lot smaller than it had previously been, and she could use this tool that we had created together and that she had created with her peers to help her answer that question.

Anna: I think to add onto that, it's Anna, there was a huge spike in efficiency as well because all these different strategies were being discovered and brought to light and put onto the strategy showcase. Maybe if we're talking about multiplication, if some student had repeated addition in the beginning and they're repeatedly adding numbers together to find a multiplication product, they're realizing, "Oh my goodness, I can do this so much more efficiently if I use this person's strategy or if I try this one instead." And it gives them the confidence to try different things. Instead of getting stuck in the rut of saying, "This is my strategy and this is the way that I'm going to do it," they became a little more explorative, and they wanted to try different things out or maybe draw a picture and use that resource to differentiate their math experience.

Mike: I want to mark something here that seems meaningful, which is this whole notion that you saw this spike. But the part that I'm really contemplating is when you said kids were less attached to, "This is my strategy" and more willing to adopt some of the ideas that they saw coming out of the group. That feels really, really significant, both in terms of how we want kids to engage in problem solving and also in terms of efficacy. That really I think is one to ponder for folks who are listening to the podcast, is the effect on students' ability to be more flexible in adopting ideas that may not have been theirs to begin with. Thank you for sharing that. Anna.

I wonder if you could also spend a bit of time talking about some of the ways that you held onto or preserve the insights and the strategies that emerged during a showcase. Are there artifacts or ways that a teacher might save what came from a strategy showcase for future reference?

Anna: So, I think the biggest thing as a takeaway and something to hold onto as a teacher who uses the strategy showcase is the ability to take a step back and allow students to utilize the resources that they created. And I think something that I used is I had a lot of intervention time and time where students were able to work in small groups and work together in teams and that sort of thing, keeping their strategies and utilizing them in groups. Remember when this person brought up this strategy, maybe we can build off of that and really utilizing their work and carrying it through instead of just putting it up and taking it down and putting up another one. Really bringing it through. And any student work is valuable. Anything that a student can bring to the table that can be used in the future, like holding onto that and re-giving them that confidence. "Remember when this person brought up that we can use a picture to help solve this problem?" Bringing that back in and recycling those ideas and bringing back in not just something that the teacher came up with, but what another student came up with, really helps any student's confidence in the classroom.

Mike: So I want to ask a question, and Tutita and Mhret, I'm hoping you all can weigh in on this. If an educator wanted to implement the strategy showcase in their classroom, I want to explore a bit about how we could help them get started. And Tutita, I think I want to start with you and just say from a foundational perspective of building the understanding that helps support something like a strategy showcase, what do you think is important?

Tutita: I actually think there are two critical things. The first is considering the social aspect and just building off of what Anna was saying is, if you've listened carefully, she's really honoring the individual. So instead of saying, "Look," that there was this paper up there—as teachers, we have a lot on our walls—it's actually naming the student and honoring that student, even though it's something that as a teacher, you're like, "Yes, someone said it! I want them to actually think more about that." But it's so much more powerful by giving students the credit for the thinking that they're doing to continue to advance that. And all that starts with assuming that students can. And oftentimes at the elementary level, we tend to overlook that. They're so cute—especially those kindergartens, pre-K, kindergarten—but it's amazing what they can do. So if you start with assuming that they can and waiting for their response, then following up and nurturing that, I think you as teachers will get so much more from our students and starting with that confidence.

And that brings me to the next point that I think listeners who teach in the upper elementary grades or maybe middle school or high school might be like, "Oh, this sounds great. I'll start with them." But I want to caution that those students might be even more reticent because they might think that to be a good math student, you're supposed to know the answer, you're supposed to know it quickly, and there's one strategy you're supposed to use. And so, in fact, I would argue that probably those really cute pre-K and kindergartners will probably be more open because if anyone has asked a primary student to explain what they have down on paper, 83 minutes later, the story will be done.

And so it might take time. You have to start with that belief and just really going with where your class and individuals are socially. Some of them might not care that you use their name. Others might, and that might take time. So taking the time and finding different ways to stay with that belief and make sure that you're transferring it to students once they have it. As you can hear, a lot of what my coauthors mentioned, then they take it from there. But you have to start with that belief at the beginning that elementary students can.

Mike: Mhret, I wonder if you'd be willing to pick up on that, because I find myself thinking that the belief aspect of this is absolutely critical, and then there's the work that a teacher does to build a set of norms or routines that actually bring that belief to life, not only for yourself but for students. I wonder if you could talk about some of the ways that a teacher might set up norms, set up routines, maybe even just set up their classroom in ways that support the showcase.

Mhret: Yeah. So practically, I think for the strategy showcase, an important aspect is finding a space that's accessible to students because we wanted them to be going back to it to use it as a resource. So some of us used a poster board, a whiteboard, but a vertical space in the room where students can go and see their work up I think is really important so that the classroom can feel like theirs. And then we also did a group norm during our first meeting with the kids where we co-constructed group norms with the kids of like, "What does it look like to disagree with one another?" "If you see a strategy that you haven't used, how can you be kind with our words and how we talk about different strategies that we see up there?" I think that's really important for all grades in elementary because some kids can be quick to their opinions or comments, and then providing resources that students can use to share their idea or have their idea on paper I think is important. If that's sticky notes, a blank piece of paper, pencils, just practical things like that where students have access to resources where they can be thinking through their ideas.

And then, yeah, I think just constantly affirming their ideas that, as a teacher, I think—I teach second grade this year and [they are] very different from the fourth graders that I student taught—but I think just knowing that every kid can do it. They are able, they have a lot in their mind. And I think affirming what you see and building their confidence does a lot for them. And so I think always being positive in what you see and starting with what you see them doing and not the mistakes or problems that are not important.

Mike: Jenna, before we go, I wanted to ask you one final question. I wonder if you could talk about the resources that you drew on when you were developing the strategy showcase. Are there any particular recommendations you would have for someone who's listening to the podcast and wants to learn a little bit more about the practices or the foundations that would be important? Or anything else that you think it would be worth someone reading if they wanted to try to take up your ideas?

Jenna: I know, in general, when we were developing this project—a lot of it again came from our seminar class that we did at UConn with Tutita—and we had a lot of great resources that she provided us. But I know one thing that we would see a lot that we referenced throughout our article is the National Council of Teachers of Mathematics. I think it's just really important that when you're building ideas to, one, look at research and projects that other people are doing to see connections that you can build on from your own classroom, and then also talking with your colleagues. A lot of this came from us talking and seeing what we saw in our classrooms and commonalities that we realized that we're in very different districts, we're in very different grades and what classrooms look like. Some of us were helping, pushing into a general ed classroom. Some of us were taking kids for small groups. But even across all those differences, there were so many similarities that we saw rooted in how kids approach problems or how kids thought about math. So I think also it's just really important to talk with the people that you work with and see how can you best support the students. And I think that was one really important thing for us, that collaboration along with the research that's already out there that people have done.

Mike: Well, I think this is a good place to stop, but I just want to say thank you again. I really appreciate the way that you unpack the features of the strategy showcase, the way that you brought it to life in this interview. And I'm really hopeful that for folks who are listening, we've offered a spark and other people will start to take up some of the ideas and the features that you described. Thanks so much to all of you for joining us. It really has been a pleasure talking with all of you.

Jenna: Thank you.

Anna: Thank you

Mhret: Thank you.

Tutita: Thank you so much.

Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability.

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