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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 today I'm talking with Don woods, who is an assistant professor of elementary math education at Oakland University, in the teacher development and Educational Studies Department in the School of Education and Human Services, and within a Wilhelm, who is an associate professor in the Department of teaching and learning. In the Simmons School of Education and Human Development at Southern Methodist University, we will be discussing the article learning to launch complex tasks, how instructional visions influenced the exploration of the practice, published in the June 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. Done. Annie, thank you for joining us.
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Thank you for inviting us.
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So can you just start us off with quickly describing the innovation.
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So in this study, we investigated how the exploration phase of the teacher learning cycle really works to support novice teachers to learn how to set up or to launch a complex task in a way that really helps their students to engage in the task
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and to learn the math. First thing you said, is that teacher learning cycle, is that right?
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Yes.
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Could you describe what that is? Yes,
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the teacher learning cycle is really a way that guides the development of novice teachers by introducing them to the high leverage practices through units of exploration, then we work to prepare them to enact those practices. And that could be requiring them or having them, rehearse them, and then enacting them within the classroom. And then finally giving them an opportunity to reflect on the accident, after they have gone through that process.
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So it's exploring it, trying it out in the safety of the teacher education group, like rehearsing or something, implementing it, and then reflecting Yes, that right. And then you said that your innovation takes place in the exploring part of this.
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So we really focused for the purpose of this paper just on that one small piece to see what kinds of things that teachers were thinking about, as they were learning about the high leverage practice.
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Awesome. I think I understand now where that's situated. So it's, it's right at the very beginning of the cycle. Yes. Okay. So can you give us a brief summary of what you said in the paper. And the idea here is to we're going to go into all of the pieces more in depth later. But
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let's just quickly summarize, we looked at how 11 first year in service teachers, so they were taking coursework at the same time as they were learning how to teach and teaching in the classroom, how they took up the idea of launching complex task. And again, in the exploration phase of the learning cycle, the first phase, one thing that we found that was pretty interesting was how critical it was to consider their instructional visions, when thinking about how they took up and interpreted aspects of launching complex tasks. I don't know if you want now as quick preview, but in particular, teachers who had more traditional instructional visions tended to view the notion of launching complex tasks unproblematically, yet, somewhat superficially, and on the other hand, teachers with more reform oriented instructional visions tended to note congruence with their vision. So like, Oh, yeah, I do this. And they also highlighted challenges that they might face and implementation. So from our perspective, the use of the teacher learning cycle enabled those novice teachers to explore, reflect on and interpret through the lens of their instructional vision, the fit of the focal practices with their instructional practice.
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And so there's two pieces that you mentioned, that I think would be worthwhile to explore a little bit. Instructional vision, if you can give us a tight, tiny, brief summary and complex tasks.
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Sure. So instructional vision, we're borrowing from the work of hammer Enos and also more recently, Chuck munter. In his work on teachers visions of high quality math instruction, and using that as a way to think about the way teacher what teachers are aiming for instructionally. So not necessarily what they currently do in their practice, but what they perceive to be the goal, or what they're striving to do in their classroom. And then the other one was launching complex tasks and that draws on the word of Cara Jackson, and her colleagues, including myself. And we found that launching complex the ways in which teachers launched complex tasks, meaning they set up the tasks so that teachers could students could engage with the mathematics and the context of tasks when appropriate, in meaningful ways, they seem to be related to different types of discussions following work on the task. So we're borrowed, we borrowed from that work to think about to both in the instructional design and in our analysis.
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So in just a few words, what is a complex task,
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I'll take a stab. And then Don, you can add on if you want, I would say it is a challenging cognitively demanding task. And that's the way that we we have been taking it on. So if it is something rigorous, that requires students to think a little bit more conceptually, in a mathematics classroom. That wasn't just a few words, though. Sorry.
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That's okay.
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But I also think it has an entry point that gives has a low enough entry point where all students have access to the task, so they can answer it conceptually, in many ways. And then you can just really build a layer on the mathematics learning from there.
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All right, thank you so much, who should read this article,
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math teacher, educators, maybe even instructional coaches, and or teacher mentors, who are supporting novice teachers to take a pile of rich practices may be interested in the article?
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And this, I'm assuming is k 16. applicable article? Or is there a grade level bands that you were targeting?
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I think it works across the grade bands in that it's really, it's more of a pedagogical piece. So a lot of it is thinking about instructional design, rather than necessarily any one group like content area, or great age of kids that you might be working with.
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Okay, so now let's dig a little deeper, we got kind of an overview of what you did, and who should read it. So now we get to take a little bit of time to dig into this. What is the important problem or issue that your article addresses?
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The important problem, or issue that it's addressing is the shared math teacher, and how to support novice teachers to take at the highest leverage practices? So one of our solutions for this was to draw on the teacher learning cycle in ways that guide teachers to integrate student thinking,
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content, knowledge and equity? That's a lot of stuff. I'm just I took a minute to think so You said students thinking, content, knowledge and equity. Okay. So how do we build? Or how do you build on existing work in the field, particularly in particular, and you mentioned that a little bit already, but I was wondering if we could go a little bit more in depth, like when you talk about the instructional visions Could you tell us what those might be and how they might align with things
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built in really unchecked mentors work? We were looking at what the their visions of high quality mathematics instruction were. So before we even began working with the teacher learning cycle, we had an opportunity to have them, you know, tell us about how they saw their instructional practices, what kinds of things how did they see the math talk within their classrooms? How did they design tasks, and other qualities that really help understand, you know, where they were coming from, or where they are wanting to go within their mathematic? attics classroom,
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I was gonna sort of characterize a difference in how we used it compared to how Chuck and others initially used it. So originally, Chuck monitors measure uses an interview protocol, where you would ask teachers, if you were asked to observe another math teacher's classroom, what would you look for to determine if the instruction was high quality? And we instead used a written protocol that instead of asking about observing and other teachers classroom, we asked if you had to describe high quality math instruction to someone who's not in education? How would you describe it? And then we add, there were some sub questions that included things about what types of tasks or problems you would use, or what's the role of the teacher in the classroom. And that's pretty parallel to how Chuck has used it, but we in this case, we used a written prompt instead of an interview protocol, which might be worth noting
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and your focus in the paper was on figuring out whether they were looking at a delivery versus other kinds of instruction.
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In the instructional vision rubrics there are essentially five levels and they range from at the bottom Describing the like, sort of at the most detailed level as really just the teacher being a motivator at the second level, the deliver of knowledge, which is what we would consider sort of a pretty traditional model. And then at the top, and really somebody who acts as a facilitator, or sort of a more knowledgeable other, but as in a sort of a more sharing the authority in the classroom. So that was one dimension, the the role of the teacher that we really focused on.
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Okay, yet, I remember that from reading the article that you use that to kind of match other things. What else were you paying attention to in this area? In the area of instructional vision? Yes,
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we also looked at the types of tasks specifically and looked to see if they talked about the launch to see if they might say that there were specific things that a teacher should do to launch. But this was ahead of them hearing about the or, you know, participating in the exploration phase. And so we didn't, that we didn't end up hearing anything about what would characterize or what's important to attend to within the launch.
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So if I'm trying to summarize what theories you drew on it's one was just instructional vision, and then the other one was to teacher education preparation cycle. Was there anything else you were drawing on? That a pretty good summary of what you do? I'm
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I'm trying to see if Dawn's gonna chime in. It's hard without video. The other one is the work from Carrie Jackson and launching complex tasks. So we mentioned that earlier, but that was pretty central to the design, and even the artifacts that we use that were directly from that work that work Central.
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Okay. So if we go back to what is the problem you were addressing, then one would say the problem you're addressing is how to launch complex tasks. Now, let's talk a little bit about how does innovation that you create it helps address that problem. So describe the innovation and then tell us how it addresses the problem.
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So the innovation was really in designing the coursework around the high leverage practice. So around the launch, then use the coursework time, or the time that we were in class, the teachers for the novice teachers could like workshop, how to launch the task during their coursework, activities, and they had the support of their peers and myself, within our community of practice. So during that explore phase, they came in having thought about this article some, so we were able to take it a little bit deeper and really think about how could they use this tool? How can they launch a task to really support the content and the content of their work with students?
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So you refer to an article that they read what article is that?
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That was the the work by Kara Jackson, it was launching complex tasks it was in I think, mathematics teacher, nap mathematics teacher educator.
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It wasn't a middle school one, right?
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Yes. The Middle School one?
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Yes. So they read that article, and that there's one task that's described in there, right? Can you describe that task really quickly, so
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we can get a vision for what that look like. So it involves a teacher whose pseudonym is Mr. Smith. And the task itself was a task that he created, called dollars for dancing involved a dance marathon. And students were asked to think about different ways that they would raise like that several other students within the task, were proposing different ways to raise money. And within the task, student tunes in the math classroom, were asked to consider how those different ways of raising money would work. And some of the big ideas were around a pledge, which was sort of a one time gift versus something that accumulated for each hour of dancing, and things. And so it was all related to ideas of linear equations with sort of nonzero Y intercepts.
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So that's the task. You guys today read this article. And they read about this task, and then what happened in your classroom.
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So within the classroom, we watched Mr. Smith, we had a video of him actually launching this task. So we were able to go through and we watched the video kind of as a whole, and then we will come back through and discuss the different parts, looking for opportunity or looking for when he did something that really supported students access to the task.
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So you as a class analyze this teacher's launch of a task. Yes. Okay. And I think in the appendix of the article, there is a whole like layout of how this lesson could be implemented in teacher education, correct? Yes.
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There's also a QR code that will take them to the video of Mr. Smith and his launch tasks. So
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people who download the article will also have access to this other article and the video and all those. This is kind of an example, right? Where you looked at a teacher and you discuss launching the task with your students in your classroom, then what was the next step
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outside the purpose of this article, but for the innovation, they had opportunities to think about what they were going to be teaching in the future. So they have thought about a task that they are wanting to teach. And then we look to see how it could be launched. So they had some time to workshop it, some of them taught the same grade. So they worked on this together, how could they actually take this task that they were planning to do? And how could they launch it? So it made sense to the students and give the students that access to the task to be successful?
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Let's come back to the motivation. What made you guys want to create this launching complex tasks? innovation? Well, the
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teachers that we were working with were alternatively certified teachers, and they were so they were still really learning about instructional design and pedagogy that really supported the development of mathematical sense making. So we felt that we could really connect our coursework to the work that they were doing in schools, so that they would have the opportunity to really make those connections from theory to practice, in ways that were meaningful for them and their students. So it's very practice based, and teacher oriented.
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What research questions did you study to figure out whether this innovation worked or not? And what did you find?
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So the research question that we studied, there were two, how does the exploration phase of the teacher learning cycle provide opportunities for novice teachers to reflect on launching complex tasks? And how is this reflection related to their instructional vision? And then specifically, what insights and challenges arise as teachers instructional visions filter their learning?
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And what did we find?
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Well, one of the things that sort of piggybacks on what Don was saying earlier is that we were really interested in understanding how the instructional design supported their learning. And in a perfect world, we would have collected video data, and been able to triangulate that because that's one really amazing affordance of working with inservice teachers is that they have, they can take it directly into their classrooms. But the research office at the district level would not allow us to collect that data for research purposes. So we were limited there. And so that's why we drew on their instructional visions and their reflections to try to unpack a little bit more about what they were taking up. I'll let Don tell you a little bit more about what we actually found.
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So what we actually found was that really a lot depends on their instructional vision. So if they, if our, if the teachers were more used to a teacher directed type of classroom, and focus there, they were like, Oh, I can do this. And I can do this, or I can do that. But it was very superficial. So they were trying these things. And it wasn't really that they, they didn't learn about launching a task, they just connected to where they were at in their practice at that moment. So there were still some like things that they took up from it. But it may not have been as ambitious way as if their instructional visions were at the other end of the scale. So if they had that more reformed oriented view of the classroom, they're like, Oh, I am doing these things. So they had this like validation moment. They're like, I am trying to implement this practice this way. But they also are able to see that they had some challenges and some other things that they had to negotiate. In order for these practices to
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be successful. The
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students,
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a takeaway could potentially be that we really need to pay attention to their instructional vision,
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right. And I think there was, because they have such variation in these visions. It even speaks to how in teacher education, it's not, we can't just have a one size fit all innovation or professional development or anything like that. We need to really think about these broader issues of supporting teachers to realize that mathematics is a place where all students can find success when they have these opportunities to enter with a complex task at their own level of understanding. So it's really thinking about how we can find these opportunities for our pre service or in service teachers to I don't know if it's challenge or to really go deeper about what their visions are? And what does that mean for working with the students within their context?
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I'm going to add one thing on to that too, which I think is, I spent a lot of time thinking about the sort of the implications of this. It doesn't mean that only certain teachers who have certain instructional visions are ready to learn certain things. I don't think it means that or I don't think, but I think cuz I think what we saw just scratching the surface is that all of these teachers, sort of, were able to make small or great or larger shifts in sort of the ways that we're thinking about instruction just in this one tiny exploration piece. But it might be that the teachers who started with more traditional instructional visions might need more more more opportunities to think about it and reflect on it then other teachers who are might need other supplementary experiences to really help them wrestle and grapple like maybe they need more videos to give them concrete opportunities to take it up. I don't think we have the answer. But I think we definitely aren't trying to say that it's like, only certain teachers are ready to do certain things. It's just it's, it seems to by adding this piece of information about teachers, instructional visions, it gives you a slightly more complete picture of how you might support those teachers and or not how but where these teachers are coming from instructionally.
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Yeah, that makes sense. And that you if you knew something about their instructional vision that could inform potentially, what kinds of experiences you want to present.
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Exactly.
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All right. So let's wrap up slowly and just summarize what is the contribution of this particular paper to the math teacher education community.
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So one critical finding is just really that importance of attending to novice teachers, instructional visions, and the design of mathematics teacher learning, since there was so much variation in their instructional visions, and maybe necessary to address some broader issues, so that we can help them find success in their teaching and learning of mathematics. And really, this is why the learning to launch a task is so important. It really helps to support teachers in eliciting student understanding, and then responding in the moment to the needs of the students. by clarifying the content and the context of the mathematical task.
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There were also two other big takeaways that were sort of, again, more on the pedagogical side of things. One of those was how important these opportunities for reflection were within the context of the exploration phase, sort of this sort of the juxtaposing of the actual, like digging in and new information with sort of reflecting and thinking about how that fits with what they already know, or have experienced. And then, and both in individual settings and in a whole group setting. And then also, our hypothesis is that if we could have if we could have engaged in multiple cycles of the enactment and investigation around this one particular practice with could it would have been even more influential. So that would be another takeaway is, we think it's pretty important to do these. Oh, like the iteration is a really important feature of the design.
23:29
Sounds like you have a follow up study right there. Sounds like so I just pulled up the paper, just to quickly in your appendix, you have a description of the instructional visions. And then you have the launching a complex task lesson plan. So if anybody is interested in trying out what you guys did, then all the pieces are there. And there's also that QR code. One piece of advice, you want to give people who are like me and want to go ahead and try this out in their own classroom.
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I think over the last few semesters as I've gone through, and I have tried this, I have found out that I really need to have my, my teachers have a good idea of what tasks that they want to launch before they do this launching piece. So that tasks that that complex task has to be well designed. And then it's really easier to think about how they're going to launch it.
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So potentially, it's easier to go with a Val established task at the beginning, rather than trying to create your own
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Yes, depending on the experience that teachers have had with with tasks.
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Sure. I just wanted to chime in with the QR code again, because I think like Also, I'd encourage people to take that QR code, the stuff in the QR code and the QR code itself and do something else with it or like I think they're what we need more of in our field is examples. practice that we can use with teachers in a teacher education setting, I think that there's a lot to be capitalized on and just having that do something different, like try it a different way. And maybe we can add to the field in terms of what we know about how to support teachers to learn new things, or incorporate new practices in their existing practice.
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That's actually a really nice concluding comment, because I agree that we need to know more and learn more from each other, which is exactly what the focus of the math teacher educator is. So let me wrap up by thanking both of you to take the time to talk with us and to take the time to do the study and write it up and publish it. For further information on this topic. You can find this article on the math teacher educator website. This has been your host, Eva Anheuser. Thank you for listening and goodbye.