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 Sennheiser. And today I'm talking with Corey from the University of Missouri, and sing Young from the University of Alabama, we will be discussing the article developing skills for exploring children's thinking from extensive one on one work with students published in September 2021 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 work. But you both take a minute to introduce yourselves full names where you're from what you do paid nothing.

Corey Webel  0:56  
And my name is Corey webull. And I'm an Associate Professor of Mathematics Education at the University of Missouri in the College of Education and Human Development. And it's, I think, my ninth year here. Hello, thanks

Sheunghyun Yeo  1:06  
for having us. I'm Singhania. And I, assistant professor at the University Alabama, I'm teaching a Master's course for elementary math education.

Eva  1:16  
Also in an education department, I'm assuming

Sheunghyun Yeo  1:19  
Yeah, in the College of Education. Let's get

Eva  1:22  
started. Can you guys give us a brief summary of the article, including the results?

Corey Webbel  1:28  
Sure. So this was a project that grew out of our work as teacher educators. So in our methods courses, we do kind of a hybrid at the University of Missouri. And this project stems from when singin was a graduate student. So he was working in this course with me. And so we do a hybrid where we do content and methods kind of together. And like a lot of methods courses, we try to hook into the field placements that students are in as a part of their program. And we've done a lot of assignments over the years where we try to have our pre service teachers engage with students in conversations about their mathematical thinking, and we just happened to have a school reach out to us and say, you know, we'd love to have you host your methods class on our campus and have your students really be engaged in a daily basis within the processes of the school and students that, you know, their mathematical students that we're kind of needing opportunities to, to work on their mathematics more. So we had some reservations about that. But we decided that, you know, the, the opportunity to really have our students work with our pre service teachers worked with students in a kind of an immersed way, an extensive way, where they really meaning was doing this, basically, they were meeting five days a week with these with these will be ended up calling math buddies. And we just thought that'd be a really good opportunity for them to develop their skills for interacting with students. And that's what we did. And the paper talks about the kind of structure we put around that those interactions and how we set that up. And then we basically had them record screencasts, with iPads devices, where as they enter interacted with students, and then we analyze those interactions over time. And so while we'd one thing we did in the paper was we looked at their first interaction with the students, and then their interactions at the end of the semester with the math buddies, and we analyze those for what we called Exploring student thinking, which is kind of a subset of what my colleague Susan Empson and Vicki Jacobs have developed within their kind of responsive teaching model. So within that as a exploring student thinking, so we wanted to see whether preserves, teachers got better at exploring student thinking over the course of the semester. And so in the paper, we kind of give some holistic results, when we showed that there was there was some improvements. We also saw some students who, for a variety of reasons that we talked about in the paper either didn't really show much improvement, or some of them showed, you know, stronger interactions at the beginning of the semester, and not as strong towards the end. But overall, we saw some nice growth amongst all of the students in the course, that was saying you don't want to add anything to that.

Eva  3:57  
That sounds really interesting. And I can't wait to dig into it to it in more detail. First, who do you think should read your paper? Like? Who's your audience?

Corey Webbel  4:07  
I think the audience is mostly teacher educators, folks who teach methods courses who are thinking about especially thinking about this, I think there's always a perpetual challenge between these two. So we call it the two worlds Pitfall, you've got this world of the university where you're engaging students in trying to learn some skills or learning some mathematical ideas. They're learning how to interpret kids thinking, noticing a lot of things we're trying to do, and then they're often placements. And I as a teacher, educator, I've always, one, I always never had a good sense of what they were learning in their field placement and to what extent does it interact with the kinds of things we're talking about in our methods classes, and once they graduate, once they leave and go off? Is the stuff that we do in our methods, classes are going to have an impact on what they do, and what's the influence of that of that context. So this gave us a chance to be in the school and kind of understand a little bit about what that context was, and I think especially these cases where you have folks who seem to demonstrate some of the skills that we were talking about, or they could they had the capacity to do that. But in some interactions didn't do that, like we saw them in some interactions, they were capable of exploring students thinking, but they, they kind of chose not to in certain contexts. And that was really interesting for thinking about in the future in the future, if they, if we develop these skills, and they go out into schools, will there be reasons why they will choose? Or maybe it's not even a conscious choice, but they just don't use those skills for contextual reasons or for for other kinds of reasons. And so that that's something I think I want to get thinking about in terms of research, but it helps also love other math educators were also kind of exploring those questions as well.

Sheunghyun Yeo  5:41  
Yeah, I can learn something according to my own teaching or so elementary math methods course. But it was really difficult to find enough room for connecting methods of course, where to place month on there, the many limited conditions, our students have a two days to fill the placement every week. So but um, one thing I'm doing is like a, providing a task with a three step interview with an actual student, but it is just like one student and then two story problems way to interview. So it is like a steel barrier limited. But as a like a novice, teacher educator, after reading, rereading this paper, I got an idea that my current assignment might be extended to a series of interview assignments, for them to provide a more continuous continuous exercise where practices for pre service teacher, that's why I think on other novice or experienced teacher educator, and also like with the Office of field placement, or school administrator can also have a good insight from this paper. In addition, I experience my teacher education program as South Korea, we exactly have to work this issue between the local schools and the university, because we just like to keep our principal teacher to local school. And they handle all the situation about the placement during the two weeks or four weeks like that. But I think this kind of model can be implement to other countries, as well, to make a supporting partnership and relationship and make our precipitate teacher prepare, prepared better. So they're there for international mathematics, teachers care can be also audience or this article.

Corey Webbel  7:32  
That's a great point. One, just one other thing I'll add is the use of the screencast, I think that was really a great way to get insight, it was easy. I mean, it was a little bit tricky to kind of set up in the beginning. But once they got used to the technology and got used to putting these screencasts on, we just had this amazing resource to really understand what was happening in those interactions. And then we would be able to get feedback directly on those. So here, we saw this interaction, and we, they could submit it through our learning management system. And we could give feedback right directly after that, after the screencast. So that was a tool that's a tool, I think, other teachers

Eva  8:08  
tell us a little bit more about what a screencast is,

Corey Webbel  8:11  
it's basically just a whiteboard on a screen. So you can do it on any kind of tablet device. There's a variety of different ones we've played with different ones, but it records audio, and then anything they write anything anyone writes on the screen. So as our reserves, users were interacting with students, the students will be drawing a picture of the you know, to represent the task they're trying to solve, and then you would hear the question and answer and the explanations and so you got a really good sense of what this interaction looked like. And you can see kind of the drawing to as it got created and how and you know, it's interesting cuz in the paper, we talked about a time where the preset procedure kind of takes over the drawing for the student and you can you can see it because the handwriting changes it gets a lot neater and so you can tell you know, when that kind of take over move happened because you can actually see that screencast as it's happening in real time. Yeah, there's

Sheunghyun Yeo  8:57  
a additional feature of the this kind of digital whiteboard whiteboard app. So there's various similar apps but as you creation we use has also another feature which is to manage it the online classroom with this tool, so you can share your video your students and also your students can unload or share any videos with an instructor. So this Allah to kind of a fleet learning or like a process basis like evaluations so this is how we collected our main data for this study. So they create a problem serving interview videos with their memories and they all know that those education videos so those are free so the teacher this these clip provide like a PV the memories for reflecting what they were their students based on the video. And for researcher we can also access how each is preserved a teacher actually use a teacher moves in the moment in terms of like a takeover, spring extending, and we can also analyze Legos, actress children's responses, they're struggling or they're easily solve the problem like that. So it is a really dynamic tool.

Eva  10:14  
So it sounds like there's three things happening. One is the connection between the university and the schools. One is the Making Sense of kids thinking. And then one is the screencast thing. So there's really like a whole bunch, which leads me nicely into my next question, which, I guess focuses does, what is the problem of practice that you are addressing? In your article,

Corey Webbel  10:40  
like I mentioned this, the more holistic vision is a responsive teaching kind of set of skills. And I mean, most folks who teach these kinds of courses are familiar with incoming students have a idea what mathematics teaching looks like, and feels like from their own experiences, it's often very different than that kind of responsive teaching vision that we're kind of hoping to expose them to, and help them develop those skills. And so, you know, there's kind of an instinctive, you know, a student solves a problem and they get the wrong answer. And so there's a very instinctive like, Okay, well, I will tell them what they did wrong and have them practice it again and try to get it it's like the instinctive thing to do. And so we're trying to kind of almost reprogram like, or at least, like give other options. So that's one thing you could do. But some of the things you could do is ask the student to explain some more ask the student to tell you how they got the answer, or to say whether they how strongly they believe that answer is correct, or justify the reasoning they got to that answer. And so we're trying to give them some other options for what to do when students do various things. One of the interesting findings we found was that we saw kind of improvements in how these pre service teachers explored students thinking more in cases where students got incorrect solutions. So we saw more improvement in that case, but when students kind of solved the problem easily and got the answer, we saw basically the same distribution of whether you know, they were kind of exploring their thinking or not exploring the thing, we see a lot of a lot of like overall improvement in those cases, which raises some questions about like, maybe it's just harder to know what to do. When students get the answer, right. It's like, Oh, they got the answer, right, I guess we'll move on. And we tried to talk about things like extending questions, and how do you get them to still go back and kind of explain why they think that's true, or maybe even asking a different task that's related to the one that they did that kind of pushes the thinking a little bit more, that may just be a harder thing to do? Or maybe like, we just didn't focus on that as much, that kind of raising questions for us that we didn't see. So like a different pattern than those cases that we saw when students struggled. But we were encouraged that they did seem to have a bigger repertoire of things to do when students struggled,

Sheunghyun Yeo  12:44  
and from a press of a teacher's perspective, like, they can't anticipate like, oh, how solve this problems? And then they also get the answer. But it is really difficult. If your students say, I don't know, like, they never thought about like, oh, how can I solve this problem like that? Maybe they can think about that. So it is really important to keep in such kind of experience for them more like actual review these peers. So as you saw, in this paper, we reported like, if your student is trouble, in the beginning of the video, there's a no exploring. But in the end of the video, there's a Lyco more a lot of student change it though their responsiveness. So we believe in like this responsiveness can be taught, however, what if they want to really change their like mindset word disposition, then it means like, some required like experience like that. So that's kind of the another key part why we provide like, these volume over the interactions and times for where the keys like a thing that's without experience, even might be really difficult to develop.

Eva  14:02  
So let's talk a little bit. I think when we started, you mentioned Susan Empson and Vicki Jacobs, let's talk a little bit more about what literature you built on as you developed your intervention. We've also been

Corey Webbel  14:15  
pretty influenced. So there's kind of this noticing literature in this responsive teaching literature that really kind of decomposes practice into some various things. And especially they have some Yun was mentioning, supporting and extending moves. So like supporting is before the student gets the correct answer and extending his aptitude to get the correct answer. And because this thing of I think questioning kinds of, you know, eliciting thinking that, you know, tell me more about how you're thinking, and again, I think I think is really about a repertoire, like instead of having only one thing you can do. Now I have four things I can do. And I could think about what would be the most productive do in this situation, or also, I think, provides the idea that I can learn from what I'm asking students to do, like I'm actually learning when I'm talking to students, as opposed to I'm just telling students what to do. I'm actually learning it So you're being like kind of a curiosity about student thinking as well. Another sort of body of literature that's influenced us a lie doesn't show up as much in this particular paper, but it's kind of the literature on on rehearsals, and like a cycle of shoot, I'm gonna forget the exact terminology, a cycle of enactment, I think, within this like rehearsal process. So we did incorporate that with these these math buddies. So we did some initial interactions, you know, one on one interactions with each other, you know, one person playing the role of a student, one person playing role of the teacher and kind of playing out different possibilities, what if the student can start the problem? What would you do then? What if the student does some work, but then gets stuck? Now? How are you going to respond with the students solves it easily and tried to have them rehearse some of those scenarios and have developed this repertoire in kind of a safer environment where they had to actually work with kids. And so we had them record those as well. And then we actually shared some of those with the whole class, let's talk about this interaction. Let's talk about the responses. And what are, you know, how did the what did the what was the effect of this response? How did this draw more thinking out of the student? How did this continue to position the student as competent? So that's another kind of body of literature that's informed some of this some of the work that we did practice

Sheunghyun Yeo  16:07  
basis, teacher education?

Eva  16:09  
Yeah, let's jump into the innovation a little bit more. And I'm assuming that the innovation, there's like, again, a bunch of things that we could think that what is your innovation, but there's one on one in depth work is really heard of what is new about what you're publishing, right, combined with screencasting. So tell us a little bit more about how did this work,

Corey Webbel  16:38  
it was a really kind of exciting opportunity that just fell into our laps where a principal reached out and said, you know, we'd love it, he was kind of on the lines of like, we need more he'd come from like a title one building with the title or building, he was used to having more math sort of specialists around and more kind of, you know, people to work with students who were struggling, we didn't necessarily just want to work with with students who were designated as struggling, but we just thought, you know, if we can work with kids more, get more. And especially along the lines of these, like practice spacing will get more practice, or feedback, more engagement, this will feel more authentic, right, it won't be just this kind of artificial assignment, go out and talk to one kid one time, just I like to think he was mentioning as a very limited kind of opportunity. So we had our methods class on campus on this at the school, we met every day at the school. So they would come to school, there was a little stuff in the beginning of the day, and then they meet with their math buddy for 30 minutes. And we were usually there on those days, or at least the days when we had class, we had class two days a week. And we would kind of just meander around as they're working with their math buddies, we would sit in and some have some, you know, conversations with the students and with the pre service teachers, as they're having these conversations, we actually evolved over the course of the project, we started off pretty rigid about what they were going to do with those math buddies, like we're going to do story problems, you need to do a story problem. And here's, you know, because we were really building the course around numbered operations. So this kind of like story problems that involved you know, addition, subtraction, multiplication, division. And then over the course of time we loosened up a bit, especially in that spring semester, we really let them kind of have some say the pre service teachers have some saying, because they were in the classes to with these students, the students were drawn from the classes they were observing. So they knew what the teachers was working on. They knew that, you know, if we were covering, and there were some frustration expressed in the first semester, where, you know, our students or our students are really struggling with this concept, but you're making me do a story problem. And I'd really love to help them with this other concept that they're working on in class. So we ended up loosening up that a bit. As far as the structure goes, they would work with their math buddies for about a half hour, and then they would come to our class.

Eva  18:34  
That's two days a week that you had class, right? And then what about the other two days?

Corey Webel  18:42  
So the other days they were they still did their math buddies, and then they would, they would also they have their, you know, other methods, classes. Were also on site. All of the all of their classes were on site at

Eva  18:51  
that school. So they would spend all day every day at the school.

Corey Webbel  18:55  
Basically, I think we negotiate it was a lot. So that second semester, that spring semester, we negotiated that we will be on Fridays, I think they're Friday class was back on campus. And they didn't come to the elementary school on Fridays, but yeah, Monday through Thursday, they were at the school from basically eight to two.

Eva  19:10  
And so if I'm one pre service teacher, I'm assigned to one teacher to kind of spend my time in one teacher's class or do I rotate around?

Corey Webbel  19:19  
They were mostly with one teacher. So they actually have paired this with a reason they did math buddies, they had reading buddies, and so they didn't. I can't remember exactly if they had the I don't think they had the same because they had their reading Buddy was a different grade level, their math buddies, math buddies, were all third through fifth grade and reading buddies were all hated too. So they did spend some time in the other teachers class from there. Were there other buddy was coming from just that sense of what that that,

Eva  19:42  
that and who chose the students that they worked with?

Corey Webbel  19:46  
The teachers did. This was again a point of negotiation. We didn't want to be seen as like, you know, tutoring, the intervention, the remediation for students who teachers that were struggling, and we wanted to be supportive. We wanted to be for the teachers to feel like we were there to support what they were trying to accomplish as well. And so we gave the teacher per teacher pretty broad, a pretty broad criteria, we just said, a student who you think would benefit from some additional conversations about mathematics. And so some students that did math buddies were students who, you know, I don't, I don't actually know how that teachers thought about it. I think some students, teachers thought, this is a student who's who's pretty advanced and just kind of not getting good could benefit from like, some additional, like more more challenging or extensions on what we're doing in class. And some students, you know, it was tough to figure out how to advise teachers on how to how to pick those students who didn't want to reinforce kind of the ability, grouping kinds of things that have happened in a lot of schools, where you're separating out kids based on you know, their achievements stuff.

Eva  20:47  
So for this study, their students were in your math methods class two days a week, and they talked with the same third through fifth grade student, every day for 30 minutes, four days a week throughout the semester. That's right. And that's the data you you used for the study. Right?

Corey Webel  21:08  
So those conversations, and some they had to submit a few. And then we they often they just recorded, we encourage them to just record any conversations that they were having.

Eva  21:19  
Was your research question

Corey Webbel  21:21  
and move on paper to get the exact wording. But basically, we wanted to know, if they showed improvement in their response to teacher their, their, their use of exploring, teaching, or sorry, exploring student thinking over the course of the semester. That was kind of the main thing for this paper that that we looked at. And then we also wanted to know kind of what would explain some of those patterns, if there were patterns or people showed improvement will may explain that if there were patterns where they kind of just stayed in this superficial exploration was one of our categories? What were some explanations for that?

Eva  21:52  
And so you already hinted at the fact that some there was some change. So can you respond to how you use the data that you collected to answer this research question?

Sheunghyun Yeo  22:05  
After we collect the data, we transcribe their videos based on Lyco initial video and the final video to see their level is to change over their responsiveness. So we use a categories or there are three categories. The first one is not exploring stored student thinking. The second one is a sufficient exploration of children's thinking. The last one is the Explorer chiller thinking, so we, so they're like, Well, we're we're changing between iniciar and the final video, then we got the number. And more generally, most of our students have improvement for explore responsiveness. And then we choose like some representative cases it from like, some implemented cases, or some person or teacher has some implement about their responsiveness versus like some student has still very limited responsiveness for with children. So we made us we use like Jacob Stan embryos, the coding scheme from 2018 paper. So if they have like a struggle today, yeah, if they get prior to student getting the correct answer, what kind of a supporting moves they can do, such as like ensuring the child understand the problems or changing the mathematic and the problem to match you, students level, or exploring what they've done so far, something like that. And then we also analyze the if they the child to get the right answer, how the preceptor teacher can extend, such as like promoting the faction about their strategies, or encouraging a child have to explore multiple strategy, or sometimes the connecting to the other students and rotation like that. So these are some like more specific teaching moves they do, we analyze that. And we choose like one case of a piece of a teacher each further implement and the sustaining. And we analyze Lyco their first video and the last video and then the a series of videos, the bell amo data on the education. So that's how we analyze the data.

Corey Webbel  24:30  
One of the things that you know, Seung Hoon is mentioning where we analyze for some of those cases we look really like coated every single move that they made in their interaction. And then in the paper we have these we use Max Q da as our software and they have like a camera with a term for it but a way of representing the coding with these like time maps. And so we have this like you see like their first one and we coded you know Green was the exploring moves or extending moves and the red was takeover move And I think there was another category Blue was like a neutral category. And you just saw this, here's a depiction of this with all that, it just kind of started to describe you to yeah, look at the paper, but it's got like, you know, the time of the kind of a timeline of the whole interaction. And you put these next to each other. You see, this one's just got all this red, and this one's got mostly green and a little bit of blue. And you really see a nice contrast.

Eva  25:20  
Yeah, those images are pretty amazing. Yeah, that was a

Corey Webbel  25:24  
pretty cool feature that we discovered in Max Q da to you just look at those MSA Oh, wow, this really looks like a different interaction. You can read all the text, you can see that too. But just, it was kind of nice.

Eva  25:34  
So what if you had to sum up? What is the contribution that you are making to our field with this paper,

Corey Webbel  25:43  
I would say on the positive side, this kind of exploring student thinking is a teachable skill. I think there's a lot of literature to back that up, in that, you know, these opportunities to engage with kids and get feedback on these interactions is one way to develop that skill, some of the caveat that I that I want to keep thinking about, they were with these students a lot minutes like it was, you know, these like four times a week, and so like, there was almost a sense of week, it was hard for us to keep up with the feedback in trying to, you know, we would see things happening, and you can't comment on everything that's happening. If something's you're concerned about, you're like, Well, that was heavy takeover that I saw. And then like, we want to really unpack that, but you're like you're doing this every day. So they kind of build up. And I think in a in a future iteration of this, I might want to actually, maybe we did, there was too much too much interaction, it was really nice to have it. But did we have enough time to really thoughtfully plan what this interaction was going to be about really, like, take it apart and debrief it and think about all the things that happened, and we had so much it was just like going on to the next one. So I think that was that was challenging. I think another one is we really thought about this interaction between the contexts that we were there. And we wrote about this in a in a conference paper, where this has to do with like the students and what they you know, what their capability of doing is, and what they actually chose to do. And so, you know, we would watch and there's, there's one of the cases in the in the paper where there's like a pretty heavy takeover towards the end of the semester. And wondering, like, why is the student choosing to do this? One reason could be, you know, they are under some constraints, because they're, they're in the school all the time. And the school has expectations for what they're supposed to do and what students are supposed to learn. And you know, there's testing pressures, and all these other pressures that we don't have to worry about and the university world, but they do have to worry about there. And so they may choose to engage in a set of moves that we would not think of as exporting thinking. But there might be really reasonable reasons why they're doing that. They know there's a test on that coming up, or they know there's a they know, that's what the teacher in their host class was really emphasizing that they learn this procedure, and then they put the answer in final form that looks like a mixed number. And they don't leave it as an improper fraction. And we were thinking about, like those competing tensions. And what our project did, I think, is take a situation in which a typical field placement, you know, a student might be able to do their exploring student thinking stuff with us, they might be able to go to their house placement, do something totally differently, and not really experienced much cognitive dissonance, because they just kind of get enculturated into that world. This is what I do in this context is what I do in this context, and not even realize that those are competing. I think that in our project, because they had to do that same work in the same space, where they were doing work, where they're like, Okay, Dr. Webber wants me to do this, these exploring moves with these kids, I'm going to try to do that. But at the same time, my teacher wants me to do this other thing. Now that complex, Lana, like, right in their face is very present and with the work that they're doing. So I think that's why, especially in the fall semester, which we don't talk as much about in this paper. There were concerns expressed about that, like, I'm concerned that I'm teaching my kids, or I'm, you know, working with my kids. And I feel like I'm not really teaching them because I'm just asking them all these open ended questions and like, when do I get to tell them how to actually solve these problems. And so they felt that tension in a really salient way. And I feel like maybe that it needs to happen at some point. And maybe in our old way of doing this things that tension never even got raised. So maybe that tension needs to get raised. And then we need to really walk students through and think about, okay, well, what is the pressure that you're facing? And why is that pressure there? And who's putting that pressure on? And let's think think a little bit more critically about that. And I don't know that we got there in this project, but it is raise a lot of questions of how do we help our pre service teachers who are going to go out and be in this world where there are pressures and all those pressures exist? And are we helping them really navigate and negotiate those pressures before they get into them? So that's the question that kind of this is leaving me thinking about for just future any classes that we that we have not just ones where we get this opportunity to be embedded in a school?

Sheunghyun Yeo  29:35  
Yeah, I believe our principal teacher will is a school teacher as well as their lifelong learner lipu long like a mathematic learner. So in mathematics course, we might focus on and cover a variety of pedagogical content, knowledge and practices. Of course we value one of the Five was translatable mathematical properties, and C, which is a productive disposition, that leafers to the heavy chair inclination to see math as useful and worthwhile. However, it will be difficult to develop it without actual experiences and reflections. In this study, we did not measure their change of this position to teach mathematics. But I do think the extensive in interaction have a potential to change it substantially, which evidence by their course evaluations. So because to change it belief takes time, when they experience a small successful teaching, from the iteration of methodologies, day by day, they can experience invisible things such as self reflection, or with their teaching, and the relationship where the keys and teacher and their belief and attitudes about to teaching math. So based on these findings, I think these are my takeaways and contribution, and the next step I can take in the future.

Eva  31:07  
So it sounds like that anybody who's interested in some form, or another way of doing math buddies, whether it's as intense as you did, or even just once a week kind of thing could benefit from reading this paper and adapting some of those ideas. Any concluding thoughts,

Corey Webbel  31:29  
there's one other pieces that I mentioned is like kind of the feedback piece. And we did talk about in the paper, we talked a little bit about we did when they submitted their screencasting, it was two or three times over the semester where they submitted a screencast. And we would give like direct feedback on that. That's another piece of thing. I know that the feedback is really important, what we noted in the two cases that one of the pieces of feedback was more about the critique is too hard of a word. But like, let's talk about the moves that you made in this particular interaction. And another one was like, let's, here's a way that you could extend this, or here's some other other things you could do. And it wasn't as much like a critique of what the what the reason was that your head done? And so we're trying to think about, like, what's the best way? I guess the general question is, how do you give feedback on this in a way that, you know, is supportive of what they're trying to do, and but still also, you know, gives them some vision for what this could look like. So we're still thinking about what kind of feedback really

Eva  32:24  
seems to me that you should sit down with them and screencast your feedback, and then analyze.

Corey Webbel  32:31  
We did do an analysis of the feedback that we gave, but it was just written feedback, right? In the in our learning management system. So we do have a sense of like, and one of these acredita was really, really specific. So here's the thing you said, here's another option for what you could have said, or one thing I like to do at the end of a problem like this is change the problem a little bit so that it makes the see if they can use the structure of the problem in a different way, or like extend their thinking in this particular way. But yes, that'd be really, really interesting to sort of record that as well. You know, another thing that was fun about this, like, it was so fun to just be there in the school, and like just kind of meandering around and sitting down with these interactions. And, you know, I was pretty liberal with I would just jump in, and like as soon as some questions, that's the teacher questions, and then like, debrief afterwards, it was just like, that was one thing like it just the joy of like exploring kids thinking, that's what I really wanted to impart as much as anything else. And like this is really fun to well, how did you get that answer? What did you do like that was kind of amazing, an amazing solution, and took us a while to unpack and understand what you were saying. But once we understood it was it was amazing. Those interactions were I jumped in, we have those some of those on tape, hey, we have those, we recorded some of those because the screencast is going. So that'd be interesting to this to just take a look at some of those ones where it was not just the preserve a teacher and the student, but the pre service teacher, the teacher, educator and the student all talking together, again, so you see kind of the mentoring and the modeling and that kind of thing happening at the same time, just interacting with the student.

Eva  33:53  
Well, thank you so much for coming on today.

Corey Webbel  33:57  
Thank you. It's been it's been fun.

Sheunghyun Yeo  33:58  
Thank you for having us.

Eva  34:00  
And for further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host, Eva Sennheiser. Thanks for listening and goodbye.

Transcribed by https://otter.ai