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Hello, and thank you for listening to the mathematics teacher educator journal podcast. The mathematics teacher educator journal is co sponsored by the Association of mathematics teacher educators and the National Council of Teachers of Mathematics. My name is Eva Sennheiser, and I'm talking with Jen Monson, who is an assistant professor in the learning sciences in the school of education and social policy at Northwestern University. We will be discussing the article noticing aloud uncovering mathematics teacher noticing in the moment, published in the march 2020, issue of the mathematics teacher educator journal, we will begin by summarizing the main points of the article and discuss in more depth the lessons they shared in the article, their successes and challenges and how these lessons relate to their other work. Jen, thank you so much for joining us.
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Thanks for having me.
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So let's jump right in. Can you just briefly describe your innovation?
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In this study, I was looking at the ways that side by side coaching, where a coach is positioned with a teacher during instruction to support their decisions and their learning can uncover teacher noticing in the moment and support that teacher noticing as it unfolds.
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Okay, so can you give us a brief summary of the article, including the results?
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In this study, I had three teachers who are participating in side by side coaching with me, I was the coach. And they were aiming to learn how to navigate those complex interactions that we have with kids in the midst of problem solving. They wanted to grow their ability to do that. And so what I did was work with them side by side during those interactions, to listen to student thinking with them, and to figure out how we might respond to that student thinking in the moment, during the course of all of that I video and audio recorded all the interactions. And occasionally I asked teachers what they noticed, I asked them what kinds of features they were paying attention to, and how they were interpreting those features. And the goal was to support them in their decision making. And at times, asking them those questions made a lot of sense to support the decisions that they might make about how to respond. Later, I went back and I analyzed all of those instances in which I asked teachers to share their noticing in the moment, or they did so spontaneously. And I looked for what patterns there were in what they shared, I found that teachers shared six different types of noticing that could be clustered into three different categories, depending on how they express their noticings, either with confidence, with some sense of struggle, or with wonder,
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okay, so who should be reading this paper,
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I see a couple of audiences for this work. First coaches and teacher educators who are looking to support teacher learning, always benefit from having access to what teachers are noticing about their classroom experiences, because the decisions that they make about practice hinge on what they actually notice in their work. And oftentimes, we don't have access to what teachers are noticing in the moment. So positioning a teacher educator side by side in the classroom to ask those kinds of questions can reveal things that will support the ways that we decide how to support our teachers and their own learning about practice. So this paper offers some insight for those people who are trying to do that kind of work. Second, for researchers who are interested in the field of teacher noticing, and the relationship between what gets noticed and controlled settings after instruction, and the kinds of noticing that happens in the classroom in the moment, this paper offers some interest.
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Okay, so let's kind of dig into what is the important problem or issue that you're addressing
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prior research has identified the value of exploring teacher noticing what teachers attend to and how they interpret the details that they see. But uncovering teacher noticing in real time is very challenging. Researchers have used a lot of different tools to examine teacher noticing, most of which occur outside of the classroom and after instruction, or in more hypothetical settings, where we give teachers samples of student work that are not their own. And we ask them to notice and to consider the decisions that they might make.
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But
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we don't always know how those relate back to what teachers notice in real time and their own classrooms and the decisions that they're making, under the pressure of needing to respond to student thinking in the moment. So this study identifies an avenue for uncovering that kind of noticing in the moment.
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And this kind of leads nicely into the next question you already hinted to is what literature Are you building on or what prior theories and I think you just mentioned that you're building on the noticing work, but a lot of that has been done kind of in laboratory settings.
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Yes, so the field of teacher noticing has proliferated over the last two decades. Building on the initial work of Charles Goodwin and professional vision. Researchers like my colleague, Miriam, Sharon, and others, Beth Venice, Vicki Jacobs, Randy Phillips, others have focused a lot on trying to uncover the cognitive work of teachers as they look at the artifacts of classrooms. And they've looked at student work, sometimes their own students work, sometimes hypothetical students work, they looked at videos both of their own students and of other people, students, and asked teachers questions about what it is that they've noticed, thinking that these features of what we are noticing as professionals determine how we act as professionals in our field,
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Jacob lamb and Philip in particular have been thinking about the connection between what gets noticed in the decisions that we make, as professionals, particularly about how to provide students the kinds of work like selecting problems that they might investigate or responding to students in the moment, even through discussion, this connection between what gets noticed and what we do in the classroom has received quite a lot of attention. But the methods for investigating and intervening on noticing in the moment, have yet to really be developed. Most of this work is built on more controlled settings like sort of laboratory style studies, or work in video clubs, where teachers notice videos have their own classrooms or their colleagues classrooms after instruction, with the goal of supporting learning to notice through discourse with other professionals. And these studies have all shown great promise in the fact that learning to notice is something that all teachers can do that we can learn to notice socially with one another. And that using artifacts from our own classrooms was really supportive. However, the rubber hits the road in the classroom, and we don't yet know the relationship between what teachers can notice in the Remove of pressure, when you have the opportunity to slow the video down and take a long pause or return to the work later on after your stomach is full. And you're not rushing to get the kids off to PE the real pressures in the classroom may change fundamentally what it is we notice and the decisions that we make as professionals. And so this study is trying to extend the both the methods for uncovering those kinds of noticings. But also the opportunities that coaches or teacher educators have to intervene on noticing in the moment to support it right when teachers need support in learning what to notice the sense they can make out of it and how to respond
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give us a little bit more of a vision. If let's assume somebody does not know what side by side coaching is, how would we imagine this would look like the side by side coaching for noticing
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it looks very much like it sounds. As a coach, you move side by side with the teacher in instruction. Many models for coaching include features like observation and feedback or modeling for the teacher to observe, in which case one person is positioned to lead instruction and the other is an observational role. those roles are typically assigned for the duration of the lesson. And side by side coaching. However, the coach and teacher work together, literally positioned physically side by side to co teach and to exchange roles back and forth for leading and observing the interaction. And they have the opportunity to problem solve in the moment around the issues of practice that emerged from talking with students, for instance, oftentimes what would happen in our work together is that we might get to a point in an interaction with students where the teacher just didn't know how to proceed. And she might turn to me and say, Can we pause? And we would pause the interaction with our students step back for about 30 seconds, talk about the conundrum the teacher was facing, typically not knowing what to ask next, or how to make sense out of what the students were trying. And we would think about the next move and then dive back into the interaction.
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Could you give us an example of what this might look like?
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Sure.
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There was one instance in which a teacher and I were kneeling on the floor next to pair of students who were trying to solve the problem from a context for learning lesson about a vending machine. And the students had tried to figure out how to distribute, I think it was 176 bottles into six columns of that vending machine. And they needed to figure out if they were distributed equally, how many would be in each column. And there were many numbers. There were many drawings. The student work was rather sprawling across multiple pages and two different students work and the students were using lots of words To describe their thinking, but the teacher was getting lost in the numbers, students would often say things like, I took the five, and then I put it with the 25. And then I found that there were 30. And so then there were this many. And it became difficult to follow oftentimes, because things were out of sequence and not linked to the picture. So the teacher said, pause and step back with me just we moved back about a foot and she's just said, Do you know what he's doing? He's doing something.
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And I can't tell what he's doing. Where did that five come from? And so we sat for a moment and thought about how I was interpreting his thinking. And we identified a place where neither of us knew what was going on. And so we went back with that very specific question to the student and said, Tell us where this five came from? Can you show us in your picture? So by identifying the point where our understanding was collectively breaking down, we could go back with a better question to the students to elicit the exact thinking that we needed to better understand what they were trying because we knew that they were making sense. We just couldn't follow that sense ourselves.
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And you alluded earlier, and I'm sure we'll talk about this later, a little bit more, that you had three different kinds of noticings. So this one would be a confusion. Yes, I don't remember the exact words you used.
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Yeah. So at times, teachers struggle to notice. And I found that they struggled each one of the stages of noticing that's been identified in the literature, Jacob's lamb and Philip outline, attending to student thinking, interpreting student thinking and deciding how to respond to it as three components that are intertwined to noticing. And I found instances where teachers struggled, and expressed struggle in each one of those stages. This would be an example of a place where the teacher was struggling, had attended to student thinking, and was able to tell me what it was that she was noticing what features of the work she saw, that was struggling to interpret that thinking to come up with an idea of what it meant, and understand the strategy the students were using. And so I found that there were examples of struggling to attend, attending but struggling to interpret, attending and interpreting but struggling how to respond. And that at any one of the points and noticing teachers can face challenges.
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In your paper, you have this nice chart where you organize the six different kinds of noticing, could you just summarize quickly what those are.
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So one category was the one that I just described, where there was struggle in those three different layers. I also found times when teachers expressed confidence in their noticing, and they would either do so by telling me what they attended to and how they interpreted it, or attending and interpreting the student thinking and then telling me exactly how they plan to respond. In both of those cases, they felt very comfortable and expressed no doubt in what it was that they saw, and how they were making sense out of the details whether or not they were responding to it or not. And then I found one final category of teacher noticing allowed, which was to notice with wonder. And this was a rather unexpected finding in the data. It wasn't something that was informed by the literature, but entirely emergent, from what I found, in these cases, the teachers would attend to or interpret instances they saw in their classroom, but then move on to use those to ask a larger question about practice. In these instances, they were using the what they saw in the student worker in their classroom as a case of a larger question about practice that they wanted to propose to me, or to pose out loud and wonder about collectively. For instance, at one point, a teacher paused and looked around at the classroom, and noticed aloud the ways that students were using different kinds of tools, and described how she was interpreting that, but then use that then to jump off into this problem of practice around how much precision should we expect out of our students, when they're using particular kinds of tools? Do we need them to measure? Should they be making these things with rulers at all? Is it okay? If they're mere sketches? When do we press on precision? And when do we let sort of the natural messiness of thinking unfold? These were things that were inspired by this specific case, but they weren't tied to it. She wasn't trying to respond in the moment, but rather to ask this larger question, and I found these particularly interesting cases of the ways that noticing can actually move beyond responding in the moment to inspiring something larger around teacher learning.
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That is really cool. What is the problem of practice that you were addressing in this paper,
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the problem of practice for the teachers was simply how to respond In the moment to their student thinking that as a researcher, the problem of practice is more about how do we understand what our teachers are noticing in the moment. So we can support them in making those decisions, we often don't have access to that kind of noticing in the moment, or we only have access in the aftermath, where our support isn't terribly supportive, it's not very helpful to tell a teacher what they should have seen, could have responded when they've lost the opportunity to do so. So in this case, as teacher educators standing side by side with teachers noticing together and gives us a an opportunity to intervene on that kind of noticing, and support teachers and moving through their struggles with noticing so that we can help them to learn how to respond in the moment when that response is needed.
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So I think we tackled some of this already. But let's just explicate again, what was the research question that you looked at in this paper? And then follow it up with? What evidence Did you look at to answer your research question?
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So I explored this question of how side by side coaching can reveal teacher noticing in the moment, and I asked what types of teacher noticing, can it reveal in the moment, so that I use the data set of all of the teacher noticing instances during the side by side coaching sessions of three teachers. And these were just instances that emerged naturally during the course of that coaching, in order to create that topology?
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So your research question was, what kinds of noticing happens, and then you your framework, which is actually so beautiful, with the colors and the circles? is kind of the response. And you basted? I think I remember that you said that there was 23 instances of coaching that you looked at,
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yes, I had three teachers. And the goal was to coach to do eight sessions of side by side coaching each but of course, schedules create issues. So we had eight, eight, and seven. So 23, coaching sessions, and 21 instances of noticing allowed happened, just naturally, it was not an intentional component of
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it side by side coaching. So it sounds like it's almost like there was about one per session is that about what it was like, or was there like a lot in a few of them, and none and some others,
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they were a little more clustered in moments when particularly at the beginning of the units that the teachers were engaged in, they tended to struggle somewhat more with interpreting and attending to students thinking at the beginning of a unit when there was great heterogeneity in what students were doing. And that often sort of defied their expectations.
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So the evidence that you present in your article is,
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I share some excerpts of the noticing a lot of the six types that that occurred during these 21 instances of noticing aloud,
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let's wrap up by kind of reflecting. So I'm a math teacher, educator or a coach and I read your paper, and I have this beautiful framework, what contributions did you make? And how can I as a math teacher, educator, use those in my own practice?
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So for math teacher educators, in particular, those who work with teachers, in their own buildings in their own practice, I think what this offers is a window into what kinds of things we can expect teachers to express to us if we ask them to share their noticing. I think what's most fascinating to me, the first time I asked one of my teacher partners, what she noticed, she paused and looked at me and said, no one's ever asked me what I noticed before. Wow. And I was fairly stunned. And then it also struck me as quite obvious because we're often alone in our rooms, and there isn't anyone to ask that question. I think collectively, as math teacher educators, we can work to change that, that we can be present in the classroom, we can be asking, What do you notice? What do you see, teachers bring an extraordinary amount of expertise and contextual knowledge to what it is that they're observing in the classroom, and we don't see it the same way that they do. And we need to tap into their expertise and uncover what it is that they're seeing. And then use our own expertise to support the growing of teacher noticing. And then we can do that in the moment. So as a teacher educator, we can think of responding to these kinds of notices in a couple of different ways. If teachers are confident in their noticing, we might use it as formative assessment. data for us to simply learn about what teachers notice. But it also might be an opportunity for us to challenge what they see to offer alternative interpretations or to point out things that they may not have noticed in forming their interpretations. And we can be critical partners that way. When teachers struggle, we can pull back with them. And we can model what we see. Or we can press them to consider alternatives for how to respond and be brainstorming partners in the moment to think about what are some ways we could respond to what would be the consequences of those moves, let's quickly choose. And then if teachers are noticing aloud with wonder, then we can consider that an invitation to larger work together. Those are questions that can inform future coaching. And they can also be an opportunity to be the kind of reflective professional partner that teachers rarely have standing in their classrooms with them, and give them an opportunity to explore practice in deeper ways. So as teacher educators, I think what this framework does is it lets us know what it is we might be able to expect if we ask and some ideas about how we might use what we learn to support teacher learning.
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Well, thank you so much, I'd like to close out a giving you a chance to talk a little bit about how this work in this article fits with your larger work in just before we started recording, you shared with me that you recorded an audio book on conferring, which I thought was really exciting. So I was just curious, like, how does this work fit with your larger work?
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I think at the heart of it, my research is concerned with the ways that interactions support learning. And I think about interactions between teachers and students and how those interactions can support learning, like the kinds that we were working on here, which were conferring interactions. And the ways that coach or teacher, educator and teacher interactions can support teacher learning, and how we might intersect those as we were doing here and side by side coaching where student and teacher and coach for all interacting together to support the learning of teachers and students simultaneously. So this work is just one example of how all of those intersections of interactions and learning can be happening in one place at one time. And I have also worked on thinking about these conferring interactions that teachers have with their students and how they can support making just incremental progress on student thinking that it's not about the answer. And it's not about accomplishing some stupendous leap and learning in three minutes of an interaction. But how those interactions can just incrementally move student thinking forward.
22:41
So that's what the book was that I
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wrote and recorded the audiobook for.
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And the title of that was
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in the moment conferring in my elementary math classroom,
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okay, I'm also very
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interested in these coaching interactions, and how teacher educators interact with teacher learners, and how we structure things like debriefing after the bar work together, so that we can make meaning out of those things that we shared experiences around. So this is one case of these kinds of interactions where they're happening, right in practice, but we have interactions in lots of different layers around our work around teacher learning. And I'm I'm interested in exploring how we structure those to make meaning, particularly when so much of our work is improvisational, and we can't plan for it in advance.
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Isn't that just choice? Well, thank you so much for joining us on the podcast. And for further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host Eva Energizer, thank you for listening and goodbye.