Eva  0:00  
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 Anheuser and today I'm talking with Travis Weiland of the University of Houston and Lisa poling of Appalachian State University. We will be discussing the article taking a spatial turn in mathematics teacher education, published in the September 2022 issue of the mathematics teacher educator journal. We will begin by summarizing the main points of the article, and then discuss it in more detail. Travis and Lisa, can you each briefly introduce yourselves? 

Travis Weiland  0:45  
Sure, my name is Travis Weiland, and I'm at the University of Houston. I'm an assistant professor in the College of Education. And a lot of my work revolves around thinking about statistics education, and how to get that more into the K 12. environment but with a critical lens. 

Lisa Poling  1:00  
Hi, my name is Lisa poling. And I'm at Appalachian State University. I am a full professor. And I'm also the chair of the learning teaching and curriculum department in the right college of education. Other than the work with the spatial justice or spatial work, a lot of my research is done within social justice in mathematics and how to use those two in a meaningful way in the undergraduate classroom. 

Eva  1:26  
Excellent. Thank you so much for those introductions. So as I was preparing for this podcast, I realized that this is a non standard, or I shouldn't say non standard, it is a standard form, but not the most typical we've had. So the article is a theory to practice article, can you briefly explain what that means? 

Lisa Poling  1:46  
I just wanted to start out by saying Travis and I worked together at Appalachian State for a number of years, and we both came together with these ideas related to how space is infecting our, the learning and the abilities and the opportunities of students. So that became the impetus that started all of this work. And this is one of the pieces that has come out of that work. So when we're thinking about the research piece, this has been a lot of thought put into this, but this is just one of the trajectories that we took from the research, but grounding in how we can make opportunities better educationally for students that may not have the same affordances as other students in in different locations or different areas. placements. Travis, I don't know if there's something that you would like to add, just, you know, we, we started with a practice approach, right, we wanted to do this stuff in our classes, but we got really interested in kind of the theory that was driving what we were doing. And so there is a fair bit of empirical work that is behind what we kind of described here, it just doesn't really come out in the article. And so we've certainly though I forget how many times how many iterations this we've done, we've probably done this and 15 or so content and methods, courses in various different ways. Over the years, we just haven't really kind of published that aspect of the work. 

Eva  3:02  
Okay, thank you so much. So I think what if I, you know, it's been like a whole 12 hours since I read the paper. But if I remember correctly, you're taking this theory of space. And like how to integrate space in you particularly are bringing it into mathematics, teacher education. Is that correct? 

Travis Weiland  3:27  
Yeah. And part of the reason why teacher education is because the folks have already pulled it into kind of mathematics education research. So I mean, I think what, at least sparked my interest in some of this is reading a lot of Laurie rebels work that she was doing in in New York City, and kind of the lenses that she was developing with spatial justice, and then kind of jumped to other theoretical lenses from there. So thinking about, you know, Foucault and how that speaks to this or from So John, in critical geography and in those folks. And so, I think that that is part of kind of where the theoretical ideas were coming from. But what Lisa and I both noticed is that a lot of this stuff is done in more urban settings, right, like in major cities. And so, I mean, I'm in a major city now. But at the time, you know, Lisa and I were working in a very rural setting Appalachian State. And so we were trying to think about what what does this theory look like in a rural space, and we're starting to see a lot of connections, but also things that maybe weren't highlighted as much like the environmental aspect, you know, you're much more immersed in kind of your, the environment in some regards, when you're in a rural space, because you're sort of you, you constantly have seen trees and mountains and like, that's just a part of your daily experience versus when you're in an urban space. There's a little more artificial nests, that you're kind of experiencing the sense that more concrete and steel and things like that, and so thinking of some of those differences, but also how did they relate to teacher ed, so, you know, like we talked about some of the schools that we go to are super small in the Appalachian space and take a really long time to drive to it.

Unknown Speaker  5:00  
Throughout the middle of nowhere, and so what does it look like to do some of this spatial justice stuff in those spaces? Well into in the population that Travis and I were working with at Appalachian State two, we had students that were coming into our university, from urban areas, Charlotte, Raleigh, bigger areas thinking, you know, not understanding the challenges, or the the situation of the schools that Travis just was talking about, you know, the smaller schools further out, you know, students not having the same opportunities to be in extracurriculars or participate in different ways in their educational experience. So, you know, we wanted to make sure that we were sharing a lens that allowed our students to see more of what was going on in the space that we were in. Okay, so let's come to like a very brief summary of the article, if you had to summarize briefly what the article is about, what would you say, I think the two big takeaways that we're kind of trying to present here is one kind of building off, rebels were thinking about these different levels of scale, but thinking about it in the context of teacher education, there's kind of some specific levels of space that are really important to consider, because of kind of the the socio political nature of it. So like the state level is really important. I mean, we can look across the legislatures right now. And what state your school is located in has a huge impact on what counts as mathematics or what counts is, you know, acceptable conversation or knowledge to be presented in the classroom. And I think that's an important thing for pre service teachers to be aware of and attune to, but then also kind of drilling down to the idea of like, the school building itself is a space that creates different kinds of affordances, but also constrains things. I mean, we've all walked into schools, where it's like, is this a prison? Or is this a school. And that's a different feeling than when you walk into a school that's, you know, bright and open. And there's spaces that are naturally lit, and there's students murals on the walls, and things like that. And so kind of a tuning students to some of those things, as they're thinking about how the space changes. And then even in the classroom space, I mean, when I go into observe a class, one of the first things I do is I sketch out a floorplan of the room, because that helps me then right field notes, right, but getting students to start to think about, hey, you rent the way that desks are organized, or what's on the walls, all that stuff influences how you're going to interact in the classroom. And so we theoretically kind of added those levels to the framework, and then tried to connect it to some of the, like practical things that we're doing. And then the other thing that we were trying to highlight a little bit more is that the ecological side, so pulling a little bit more from, like place based education, where your interaction with the natural world is important to to highlight some of those kind of aspects that we're seeing coming out a little bit more in, in rural education settings. Well, also, just to add on to again, going back to the human piece, the students making sure that when we're working with our students, that they're noticing what the life, the day to day activities are of the individual students sitting in front of them, too, because oftentimes, with undergraduate, pre service teachers unit, they believe something that isn't always true when it comes to what those experiences of the students are. So we just wanted to make sure that we were sharing that lens too. So who would you say should read this article, teacher educators,

Unknown Speaker  8:30  
best teacher educators across all levels, I think it relates to all levels. So you know, I was in the content department when I was there. And so I was thinking about this in content classes for elementary teachers, but also in the statistics courses, I was teaching with undergraduates and for pre service, high school teachers. And I found that it was relevant at all of those levels. So I do think that it's not, what we talked about is a great band specific, it's more of the general kind of practice of teaching, but we tried to contextualize it within mathematics education, because I think Mathematics provides different practices and tools that you can look at space in different ways in the space, I think, shapes the epistemological Foundations of Mathematics in different ways to and so I think those things kind of dialogue back and forth. So yeah, I mean, I think it kind of spans the great bands, but um, at least if you think differently, no, I agree. 100%. Let me interrupt quickly, because sometimes I think it's hard for me to follow when you say, the shape, I forget what you said exactly, but something about episomal mythology and, and space. Could you explain a little bit what you mean by that? Yeah. So like, when you think about, like, what is mathematics if you asked a student that and their experiences are shaping what they kind of define as mathematics or what it means to do mathematics? And I think that space very much is related to that. And so, when I think of talking with pre service, high school teachers, for example, a lot of

Unknown Speaker  10:00  
them when they think about what they want to do as a mathematics teacher is drawing upon what their experiences were in their high school mathematics classrooms. And so those might involve like our desks where in rows, we got lectured from a chalkboard or an overhead projector, there's ti 84 is hanging in like a shoe holder on the site like that physical space kind of shapes, the experiences they've had, and also then what they're thinking about doing with their students. And so that's a different way about thinking about mathematics that might make it more individualistic, right? Like, you sit at your desk by yourself, and you work individually on mathematics. And so that's, it's a solo endeavor versus if I walk into a classroom, and kids are at tables, and they're intentionally kind of placed there in ways that are creating interactional spaces for them. That creates mathematics and more of a collaborative sense. And so I think that space then leads to what they construct as mathematics in what they're learning, and the way they see themselves as a mathematician. Exactly. That's really helpful. Thank you so much for that explanation. And potentially, we already touched on this, but I'll ask the question anyway. And we can kind of just jump in, what is the important problem or issue that your article addresses, I will just reiterate, what I've already said is that we need to make sure that we're giving a more broad lens, when we're working with our pre service teachers to understand that community isn't what they imagine, it's really thinking about the different aspects and how those different influences are changing the perceptions of what mathematics is, again, as I said, Before, the student as a mathematician, again, those opportunities are afforded in different ways based on the spatial characteristics. So I just think it's about broadening the lens in which our students are looking at their world. And I think to it allows students to maybe have better language for thinking more about assets and systemic issues, because, you know, oftentimes, the refrain can kind of fall into this. Well, these students can't do whatever kind of deficit language and so kind of trying to use this as a perspective or reframing, well, maybe these students don't have access to some of these things, because of just, you know, the nature of the system that's in place around them the space that's around them, but they also leveraging, like, what do they bring to this, though, that, you know, you might not otherwise expect, like, what understandings do they have based on their space that we can leverage and work from, because students usually know their communities and very, like visceral ways, because they've lived there. And so they likely know that community far better than a lot of the teachers, because oftentimes, teachers aren't necessarily living in the communities that they teach. And, and so kind of really like trying to get them to think more about like, what are the assets in this community? And how could we draw upon them in the classroom? Versus like, what is this community lacking? I'm wondering if you could give an example of what you're talking about. One that came to mind, and I know we would touch upon it in the article is this idea of data. But one thing that, you know, Travis, one of the first activities we brought into the class setting was this idea of how school systems are using report cards to differentiate between individuals, right, or individual schools. But what they haven't taken into account is the space that they're operating in, right? They've they've taken them, and they've put them all on the same kind of criteria and basing them and then giving them this letter grade. So in one of the activities that Travis and I did when we were sharing a course, is having the students think about what that where the school was situated, what kinds of opportunities, all the pieces like Travis was saying, you know, what the school look like, what, and putting more of a context around what that grade card was sharing. That's one of the main ways that we considered it and to like, pointing out that these report cards are missing things. So like, what are the numbers tell us? But also, what are the numbers missing about like this school in general, but to some of the things that we played with too, is just like the idea of have access to resources? So, you know, like, do you have after school programs? Well, maybe not. Because the busing, it takes two hours, because it's a rural district, and there's no such thing as a straight road. And so, you know, some of those things about like, maybe, you know, the solutions need to be different in the settings or thinking about what your students are bringing into the classroom are different in some of these settings. I know one of the things that I've poked on is like when you look at the contextualization of standardized assessment questions, you know, if you're in a rural setting, what context it makes sense to you that you've had lived experiences with are different than if you're in an urban setting, and vice versa. So problematizing some of that and how you're thinking about relevancy to students to Yeah, one example that comes to my mind is we're working locally with an elementary school, and there's a double decker bus in the problem and none of the kids have seen a double decker bus

Unknown Speaker  15:00  
So before, right, that's one of the interesting and the other one that comes up constantly is bunk beds, and sleepovers. Which, especially now after COVID, is something that kids haven't necessarily experienced coming into first grade. And so it was just interesting when you talk about how, you know, like contacts that we think would make sense for everybody. Don't always make sense for everybody. Okay, so let's jump into you already mentioned that you are working a little bit based on Laurie rebels work. The next question is, how does this article build on existing work in the field? And what do you ground your work on? And then how do you build on it? So I think we grounded it certainly in a lot of Lori's work. I know also, Erica Bullock, and it was learn how was the other person that she wrote with kind of did some very theoretical conceptualization of the idea. But all that was very kind of mathematics education, broadly, thinking about how it brings in new lenses there. And so what we were trying to do is kind of think about, specifically in teacher education, how do these lenses help maybe communicate to some of the things that we're doing? And so that's why we tried to kind of present three different examples of typical activities that you think of and methods courses are that are done, but thinking about, how can you kind of tweak them, so to speak, to kind of add this spatial lens into them? And what does that perhaps provide? And so I think it really is the theory to practice part that is one of the main contributions is that we're really thinking about, first off, how does the theory maybe a little different? Or maybe there's certain things that we need to foreground a little differently in teacher education? But then also, what does that mean, in terms of how might we change some of the activities that we use so that students have experiences with these things in the classroom as well? Well, I think the thing that has been apparent in all the articles that Travis and I have worked on is this idea of this scale, right? That instead of looking at everything top down and saying, Oh, look at all these things that are wrong or missing, or, you know, what they're not doing is but continue to think about, and that was all through so Joe's work, but coming down and looking, you know, to that micro level, and really getting in deeply into that piece. Because like we mentioned earlier, you know, the the great cards for whatever reason, it does seem to be very top down that you see it, but you don't really drill down into what it means. But everybody regards the you know, a great card is being the driving force in that educational setting, which is unfortunate. And there's just more to it. So, so there is this cone shaped figure in your I don't know if it's cone or try one of the levels, I wonder if you could talk us through, because I thought that was really helpful to kind of think of what the different levels might be. So I mean, I have to credit Lori's work for that, because that really comes from her, we, we basically just took that and then added some levels, right? So this idea that, like Lisa said, the you know, the the person has kind of the the most concrete kind of form of these different levels of space. Again, that's coming from rebels work. But then what we were trying to think about is, alright, so, you know, Laura's work was kind of looking at, like how kids are interacting, and these different levels of like the home versus the street, the neighborhood, the city, the region, what we're trying to think about is, what about the teacher education side of those things, like what levels are really important for us to consider. So this idea of the classroom itself, and the school and the district and the state, because you also have that kind of like political dimension of this too, right? Like, there's all these policies that impact what's going on, which then impacts based on where your schools physically located, and then impacts what you can even teach in those settings. I mean, we've Florida is a prime example right now, of some of those issues, and what can be taught as you know, about race or you know, in that impacts mathematics to like, what how we can teach mathematics. And so that's kind of the big thing that we were kind of trying to add to that figure is for grounding more of the the important elements for mathematics teacher educators to maybe consider and these different levels of scale. Yeah. And that also made me think of Kathy's book, reimagining the math classroom has a whole chapter on space and the layout of classrooms like you got you talked about earlier as well. Okay, let's kind of go through the three examples. Because what you did is you shared three examples of what you say are activities that are typically done. And then you talked about how you adjust them a little bit to address the spatial spatial turn. So could you talk us through those community walks event come fairly popular, I feel like in the past five or six years in a lot of different settings for you know, trying to get pre service teachers out to actually learn about the community that their students are coming

Unknown Speaker  20:00  
hang from. So to get a little bit more knowledge of their students in that setting. And so essentially what we're doing with that is kind of adding on some additional questions that you might ask them to get them to, to prime their thinking more towards some of the spatial sides. So like one of the things that I often have my students do is not only walk the community but like, actually start with the classroom that their student teaching in described that and thinking about how it impacts mathematics, now walk around the school itself, walk around the outside of the school, and then kind of go into the community. Because to that kind of primes, the different like levels thinking to that they're doing. And then another thing we tried to highlight was the fact that, you know, in, at least when I was at Appalachian State, a walk through the community isn't necessarily the most practical thing, because the communities are super rural. So they're like, super vast. And so perhaps a drive with some purposeful stops is a better approach to think about it in the settings versus like in an urban setting. So that was one of the things we looked at. Lisa, did you want to talk about one of the other ones? Well, the the one that I would say, Travis and I have spent a lot of time working in and again, it's not all in this article, but the data investigations, we spent a lot of time working with large data sets and thinking about what the community looks like, and having our students engaged in that. So they could pick and choose what data they wanted to look at. But just that piece, and, you know, one of the things that in Travis already mentioned it, you know, in Appalachian, we're in the mountains. So, you know, a drive into school is could take a half an hour, 45 minutes. So you know, there's always the question, well, why does so and so come back in for whatever, fill in the blank, you know, why are they a part of this community? Well, there's reasons right? There's these spatial reasons that we started having students explore, you know, we have places in Boone, where there's water is an issue like electricity, Wi Fi, you know, all those things. So why is that? And what does the community look like? Because I think oftentimes individuals think it is the straight road out to wherever you're going. Like Travis said, they don't exist in our, in our world, it's very curvy, you can only drive 25 minutes. So there's reasons why kids aren't coming back and aren't being engaged in the school setting. But we had to find a way to bring that in. And and that's where that data investigations is thinking about what aspects we should be looking at, you know, one of our very first conversations, Travis, I don't know if you remember this, but we talked about, you know, to be able to come into the library, you know, there's this expectation that every student should be able to go to the library whenever they want. In our community, that's not true. Especially if there's only one vehicle in your household, your parents are working two jobs, right, all the issues that we always think about or should be thinking about. But in a rural setting, it's just compounded because we have this terrain that is not easy to navigate. And to have that data investigation, some of the other things that we played with were, there's just so many online digital kind of applets out there now that can allow you to explore kind of different data layers, spatially. So like, food deserts are an interesting way to explore that, like there's an online applet through I forget, I think it's a department that you can layer on different definitions of food deserts, and see where those are. And then you can go to Google Maps and see, okay, well, what's actually there, like what grocery stores are? So food sources, so to speak, are there how far is it to travel between these things? And then you can go to like the opportunity Atlas, and then start to look at, you know, what's the median income in this area, or, you know, other kind of opportunity indicators that are there, too. And so, I think that there's technology is allowing us to delve into some of these spatial dimensions in ways that we couldn't do before. And I think that ties into the levels of scale, right, like, we can zoom in and zoom out in ways we never could before. You know, like, I just think a Google Maps alone, right? So I can like, look at this huge, like map of the world. And then I can zoom down to like street view and see, read the numbers off the front door, somebody's house, right. And so I think because we have these technological advances, it means we can think about things in different ways. And I think that's important for pre service teachers to to be thinking about in terms of like, these different levels of scale, and how, you know, they can think about this data at these different levels. And what does that tell them about these places and spaces in different ways? Right, because when with our work with the data, you know, it was amazing when you would look at it at at the more macro level, you thought you had one interpretation of what you thought was going on with the community. And as we continue to drill down looking at the different variables that we were able to select from it told a very different story. And that's again, going back to what I had said originally, you know, we just need to get a more broad lens first, when we're working with our pre service teachers to consider because they may be coming from a very different investment

Unknown Speaker  25:00  
I'm in different socioeconomic as lifestyle. So it's just making sure we we broaden that lens for them or help to broaden it. So one of the questions that has been rolling around in my head while we were doing this podcast, was how would you? What would you describe mathematics is? And what I'm trying to ask is, why are these things important? With respect to mathematics? I don't know that there is one definition of mathematics, right. Like, I think it's a socially constructed idea. I mean, that's at least my kind of philosophical positioning. And so I think, having students have opportunities to see different ways that mathematics could be defined or could be constructed, maybe helps open their minds to those perspectives. So that when they're working with students, and students are talking about mathematics in different ways are shaping and defining it in different ways, they're able to still recognize that as mathematical thinking, like, I always tell my students like, Don't shut down a student just because you don't understand what they're doing. Because they can be doing very meaningful, complex mathematical reasoning. Just because you don't can't make sense of it right, then doesn't mean that it's not valid thinking, though. And so, you know, that idea of kind of just opening people's minds to there's more ways to think about mathematics. And it's not just this objective thing, like handed down from above, that we're, you know, using, it's, it's, we were building it in our daily social interactions, seeing those things that oftentimes are seen as deficits in mathematics as an asset. And being able to recognize, like Travis was saying, this idea of thinking and, you know, engaging in problem solving, maybe they're not doing a computation, right, but the engagement and the problem solving in those pieces become the asset. And that's what the the pre service teachers or whomever is focused on and not the deficit, well, they can't do this, they can't, but thinking about and not limiting students based on their location, their their opportunities, right, because I think oftentimes,

Unknown Speaker  27:15  
if you come to where we where I am in North Carolina, there's this idea, well, because they live in this space, they're not as capable as this person in a different location. And again, just thinking about what it means to be a mathematical thinker, and applauding their work in that. Okay, I'm sorry, I through such a hard question I do. It's a question that's in my head constantly, as I go through the world. Do you have a definition? I actually have a whole paper that I can send you. Okay. I just published a paper that is titled, What is the math in mathematics education, where I'm tackling these like different ways you could look at it? And the reason I asked that question is because if somebody is concerned, as a teacher, for their students to pass the standardized tests, sometimes it's hard to envision a broader view of mathematics. And to understand why space might be important. That's just where the question came from, like, how are we thinking about math, that makes space an essential element? I like what you all started with is that even the environment you're in already shapes who you are, and what you can do, right? Like the classroom, you walk in the setup of the tables, all of those things? Play in there. All right. Our last question is usually what new contribution to our field of math teacher education does your article make? Other than, you know, what we've been saying is this idea of just there's this additional aspect that we haven't considered? And I think just bringing that focus into the idea of space, because often mathematics education has what they're able to do the standardized test, you know, the curriculum that's purchased for the school system, whatever fill in, you know, whatever you want to say. But I think that oftentimes, the physical space is not part of that equation. Sorry for that little time. But do you know that and we see it Travis and I see it as being so influential in the experience overall, and how those individuals are being acknowledged, represented, and applauded for what they're able to do you ask the question, like, what is mathematics? And I think, in educational space, too, we have to math teacher educators and math educators in general, have kind of do roles with that content, knowledge, there's the content knowledge for thinking about teaching the mathematics, but there's also that content knowledge that we use as professionals to I mean, we're constantly hearing these

Unknown Speaker  30:00  
discourses around, you know, data driven assessment or interventions or things like that. And so I think that our content learning more about I mean, I focus a lot of statistics, right. So that's the thing that gets me so excited. But that's a lot of this assessment data that we deal with. And so thinking about, well, how do we take the tools that we're teaching our students? And also look at those in the context of our profession? And what can we do with some of these things? And so I think it also opens a little bit of space of thinking about as professionals, like, when we get the question, like, where's the mathematics in what you're doing? Because somebody might argue, I mean, really, this speaks to just teacher education in general, like what makes it specific to mathematics education. And I think part of what makes it more specific to math education is that we have different spatial tools as doers of mathematics that might be different than other professions. There's different kinds of connectivity that we can do between our content and our practice, and some regards with that. And so I think we kind of play with that a little bit in this article, as well of those connections. Yeah, if I remember correctly, I really like the your interweaving the notion that space is really one element of what everybody would consider to be part of mathematics, undeniably right geometry, but also really links nicely to, you know, social justice and visualizing issues. Like I'm just imagining that tutored classrooms do you described earlier, right, where one was like a warm, welcoming environment, and the other one was less so. So that I thought was really kind of extra cool that it's like, we're taking a piece of what we all agree on is mathematics, right? And then kind of go from there. Yeah, I really, really, really appreciated your article and loved reading it. And it made me think about my own assignments. I liked how you're, you took some assignments we're all familiar with and talked us through how to adapt them. And in that case, I feel like this article is in line with like, typical MTE articles, right? It's like, here's an innovation like, look, we're like modifying something to be more spatial. And you can do that with almost everything. Yeah, yeah. No, thank you so much. We appreciate that. And we had a lot of fun writing the article. It's always hard to show like all the work that goes into an article because I mean, Lisa, how many iterations of this thing did we have before this got published? I want to say 10, maybe, at least, and a lot of work that has gone into this same work in different ways. I mean, we have been thinking about this for

Unknown Speaker  32:41  
six years, Travis travels, I don't know. While in, you know, and we're still new at all of this and still thinking it through and what it can look like and how it how it needs to be interwoven even more into our mathematics classrooms. I think there's so many more connections that we didn't even have space to talk about with different activities. And and I'd love to see what other people end up doing with it. Yeah, one of the things that hit home to me in reading this was this, the levels right, like how your body is like the first piece in space, but then also, I think we talk about home and school and community, if we're in critical math, and that those are the places we often talk about. But the street, like I was like, Wait, there's other levels, right. And so I thought that was really cool to lay out the intermediate levels that are potentially in there. And it just made me think more about, you know, space is space, but space can transcend space, too, right? So there's all kinds of anyway, thank you so much for writing this article is on the empty website. There's very well described articles. And we didn't really talk about one example that you have in there, where you overlaid a map, a topological map to kind of make a case for I think this is in line with some of your rural rural

Unknown Speaker  34:13  
Germans have trouble with the Rs. We're all like layout. So it's definitely an amazing article. And I just wanted to thank you for coming on the podcast. Thank you for having us. Yeah, thank you so much, really appreciate it and love to conversation. Absolutely. For further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host Eva fan Heiser. Thank you for listening and goodbye.

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