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Hello and thank you for listening to the teaching math teaching podcast. The teaching math teaching podcast is sponsored by the Association of mathematics teacher educators. The hosts are a with Anheuser me, dusty Jones, and Joel Amidon. today. We have a real treat for you. We're sharing a conversation from the method podcast hosted by Sam Otten method podcast is available on most podcast apps and also at math Ed podcast.com. Sam's guests for this episode are Michelle Cirillo, and Kristin Beata, they'll be talking about their recent article about alternative field experiences for prospective secondary math teachers. We hope you enjoy this episode.

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Welcome to the math Ed podcast. My name is Sam Martin from the University of Missouri. And in this episode, we're going to be talking about field experiences for pre service teachers. field experiences are when people who want to become teachers get the chance to go out into the field, go to schools, maybe shadow a teacher work with real students or real children, and start to get some first hand experience in the teaching profession. This is an important part of any teacher preparation program. But in the era of the pandemic, and COVID, there have been disruptions to school systems and therefore also disruptions to the field experiences that college students pre service teachers can have in schools. And a lot of people are also thinking about what the field experiences are going to look like for this fall semester, as the United States is still really in the thick of this pandemic. What is it that pre service teachers can do when schools are either under state social distancing guidelines, maybe not as open to outside visitors, or when schools might not be meeting in session at all, but being entirely online? I know here at the University of Missouri, we've been getting a lot of questions from college students, but also from the parents, also from the schools and from even journalists asking about what can field experiences be during this pandemic? So it's an important question that I'm sure a lot of people, a lot of universities, a lot of teacher educators are thinking about right now. And so I'm very happy to be joined by two people who have been thinking and writing about this particular issue. Michel Cirillo is from the University of Delaware. Michelle, thanks for being here. Thanks for having us, Sam. And Kristin v. Ada is from Michigan State University. Kristen, thanks for being here as well. Thanks, Sam.

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They have an article that they've written with Ray larochelle and Fran arbab. That was published just now in the Journal of technology and teacher education. That's volume 28. And that article is entitled an innovative early field experience for pre service secondary teachers, early results from shifting to an online model. So this involves field experience for people who are earlier on in their pre service teacher career, so maybe sophomores or juniors, for example. And this article involves a field experience that is already somewhat different than the normal thing of going out in the schools. It's a field experience that involves pre service teachers working in college level mathematic classes. So Kristen, I want to start with you. And I was wondering if you could tell us a little bit about the model for this alternative, early field experience that you have at the university level? And what was it like in that model of field experiences before the pandemic happened? Yeah, so this models, we started working on this back in I think 2012, because I had as a teacher educator had really felt like, they needed some opportunities to experience a lot of the theory that they had been learning in the pre service teachers have been learning in their methods courses, before they went out into schools, and and did that work with actual students. And we wanted it to be more authentic experience for them. So we decided to partner with a college algebra course on campus. Actually, we started with developmental math course on campus, which Michigan State no longer offers. But we started there. And we devised a model that's really a it's a mediated assisted teaching experience for them in their very first methods course. So they have opportunities to work directly with students one on one in small groups. They observe students things thinking in those small groups, and so that gives them a sense of the challenges that students may face as they're learning mathematics. Then they graduate into taking on some teaching responsibility in that class, leading lessons that are guided and facilitated by both the mentor teacher of the course who is a mathematics instructor, as well as the mathematics teacher educator who's the instructor of their methods course. And as they're teaching, they're receiving in the moment feedback from their mentors to help them be successful in teaching this class, but it really immerses them in the work of teaching and trying out

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Some of the things from their methods course and realizing, yeah, this is tough stuff, this is hard work. And it gives them a sense of what it's like to try to do it. But then also this reality of Okay, this is why engaging students with these talk moves makes a difference in getting students to participate. And that really is planting a seed, I think, for their work throughout the program. So this kind of experience in a college classroom is really designed as an early field experience that they refer back to as they go through their teacher preparation so that they're better prepared for that student teaching experience or their early years in the classroom. So the student teaching still is in the school setting. And actually here at the University of Missouri, we do have approval from schools to have the student teachers be in schools, and they'll kind of follow the same safety guidelines as the schools. But the earlier students like the sophomores, the juniors, they are not allowed in schools in our area. So this would be exactly the kind of alternative that might make sense to be like, Where can we find people who are learning mathematics and have a way to authentically interact with math students, even if it's at a college setting? Exactly. Same situation at Michigan State. And so I felt really, I was somewhat relieved, because we had this already set up. And so we don't lose the field expect early field experience for our students. We already had that in place. So and Kristen, you've been talking about Michigan State University, but you've also been expanding this early University based field experience to other institutions. Could you just say a little bit about that? Thanks to funding by the National Science Foundation, we have expanded the development and research of the model now it to other teacher preparation institutions, University of Delaware, where Michelle is elite, as well as Penn State University under the direction of Fran Arbol.

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Now, Michelle, I want to turn to you and just hear a little bit about what happened in spring of 2020. So as this alternative field experience was in place at the university settings and at various universities, what happened in spring 2020? And how did the adjustment get made? Yeah, so University of Delaware, we have our our juniors who are enrolled in the in a first methods course, essentially, I like to describe it as adopting a precalculus course on campus. So Kristin mentioned that they do college algebra, we do precalculus at university delver. And that course, is taught by one of our core math teaching faculty, who are already we have in place for our introductory math courses, a really nice active learning model of instruction. So it really matches very well with the kind of pedagogy that we want our pre service teachers to be experiencing, both as observers and as teachers in that classroom. So that for the first few weeks, the pre service teachers are observing, getting to the students sitting in groups and helping to support facilitation of discussion. And they're also preparing to teach their lessons. And so they initially they UD, they teach about 15 to 15 minute activity, and they spend hours preparing to teach for 15 minutes. And they're very surprised at how much time it takes to prepare to do it well, especially for the first time. And so when the pandemic hit, we did just had the first teaching pair, so only one one pair had gotten to teach and everybody else was in the middle of their lesson planning. Interestingly, when one of the things that that was mentioned by the pre service teachers was that the wind kind of got knocked out of their sales when they had to do the lesson planning, knowing that they weren't going to teach it Anyway, after all, so that that was interesting. But anyway, so with the precalculus instructors, and it's a coordinated, coordinated teaching, they decided that they were going to produce some asynchronous videos for students to watch independently. And then they were going to offer synchronous workshops. And so our pre service teachers just essentially joined those workshops. And in the workshops, they would do what they typically would do in class, which was at least a portion of class, which would be to work on some kind of problem solving activity groups. And what they did was they worked in zoom breakout groups when they when they shifted into group work. So the pre service teachers ended up joining a zoom breakout group each day that they were there so what one of the I've become familiar recently with a term called the two worlds pitfall of preparing teachers where you are trying to navigate different worlds the K 12 world as well as the university world. And one thing that was really nice was that we did not have to navigate that when you d shifted online, sort of the field experience, and in that sense, it was seamless. Another way that it was sort of seamless was the idea of the UT model is that it all happens in one city.

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single core. So you're not dealing with a whole bunch of different field placements in different schools with different teachers. So in that way, it made it really pretty seamless as well. So then, because those videos were being created, we had to determine, well, what what do we do now with the, with the pre service teachers to give them some kind of a field experience, right? So the SEC, the co author, Ray larochelle, was actually teaching the course at the time. And he, he's a postdoc on on this research project. And he and I brainstormed and so he decided that he was going to have the pre service teachers work on just working on different discourse moves, and attending to student thinking in the zoom breakouts and the zoom breakouts, let them easily record their own sessions individually. So they were able to reflect on the teaching and the moves that they did, and maybe missed opportunities. And then they still were able to run the debrief session after each of these workshops, where the student teachers could ask questions about something that didn't go as they planned, or something that happened during the zoom breakout that they didn't know what to do. So the debriefs that are in the style of Lesson Study, we're still able to happen as well. And was it just one pre service teacher that was in each of the small groups? And then like, how big of the small groups are we talking about in the course? Yeah, so So one thing that occurred, and that math instructors are thinking trying to think about how to do that differently is because they didn't require attendance in those breakouts. So they didn't always have equal attendance. And so initially, it was one preset procedure in the breakout, and then sometimes there would need to because there were enough groups, but that was just a sort of a logistical challenge, because of the kind of, you know, setting things up on the fly. So students, in moving forward, those students will be required to attend workshops as well.

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So you then the summer with everything else going on, you decided to really kind of look closely at how this transition to the fully online kind of experience worked. And so that's kind of the focus of the article in the Journal of technology and teacher education. And so you conducted interviews with six of the pre service teachers. So they're the ones who are in this kind of early field experience trend on the trajectory of becoming a teacher, you also talk to the instructor. And then you also had interviews with seven of the precalculus students, the students who were actually learning the mathematics at the university. So just tell us a little bit about what were some of the main ideas that came out in your findings, when you did those interviews? Yeah, so the what we thought was that this was a really interesting opportunity to learn some things about the benefits or the you know, the features of this, this university teaching experience, we call it UTP model. Because it was just such a neat, unique opportunity in the sense that the students experience it with the same, you know, methods instructor in the same course, with the same precalculus students. And then it was taken away, right and shifted to online. So we thought that having them you know, you don't usually get to compare online versus face to face in that way. Usually, you'd have a control and experimental group and make comparisons. But we thought that the students would be able to articulate some things that they were missing once we shifted to online, or we were open to finding that there were things that they liked better about it being online, right. Yeah, so that was what we did. And so we were interested in basically, what benefits were articulated by the stakeholders of this online experience. Basically, when we think about the stakeholders, we were thinking about the precalculus math students who are trying to learn math content, and then the precalculus instructor who's was navigating this online teaching world, you know, for the first time herself. And then, of course, wanting the pre service teachers to have a good experience. One thing that I was really impressed by was all of the students who we interviewed pre service teachers, math students, who were so resilient about this whole thing. I mean, all of them would talk about things that they liked, and things that they've missed, but they'd always say almost every single person we interviewed said, but under the circumstances, you know, went really well, I made the best of the situation. And so I was really impressed basically, by this group of, you know, 20 somethings, who just had this really great attitude about the whole thing in general. But anyway, that wasn't a finding. But it was something something interesting that I was impressed by, in doing these interviews. And the precalculus students, we it was, so let me back up. We actually interviewed the students. As soon as we got IRB approval as soon as we came back from our extended spring break for when we just started the shift online. And then at the end of the semester, so we were initially asking, What are you concerned about with the shift online and then sort of had an echo and the preset was the sort of precalculus students

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They were so relieved when they saw that the pre service teachers were still there, because they really appreciated having them in their groups, they liked having someone they like to say, like my age. So you can, you can ask a question to that you wouldn't ask the teacher that you could kind of just ask privately and not in front of the whole class. So they were very happy to have them there. And they all spoke about benefits of having them there. The precalculus instructor also really appreciated having the pre service teachers there, because she was teaching other sections online. And she said that, you know, I put them in breakout groups. And when I would pop in and visit the breakout groups, there'd be nobody talking except in like, in the section with the pre service teachers. So she said, You know, I pop in, and they didn't even have their microphones on, let alone their cameras. So obviously, there was no discussion going on. While there were, you know, that while the while they were supposed to be engaged in group work, and then the pre service teachers, they articulated multiple benefits, including the opportunity to help the precalculus students sort out difficulties that they felt like they weren't able to really engage with student thinking to do that. And they have lots of opportunities to observe the student thinking. And then thirdly, this idea of attending to precision with their language came up as a theme, because they didn't have access to a lot of the resources that they didn't even realize that they use to communicate mathematics, including just being able to glance at the students papers quickly to diagnose an error, or to, to do an assessment of their work, for example. And so that required from the pre service teachers being more clear with their language and the way they ask questions or the way that they respond to students, because the visual medium wasn't as as available to them. So those are the three main things that came out for benefits from this, from the pre service teachers. I mean, they, they were so positive about all that they learned, like they almost didn't even seem to realize what they missed in terms of the opportunities to teach they did to teach the whole class, they did say that talk about how that would have been great. But they said what we what we experienced was so good, I learned a lot. Yeah, that's kind of how I think about it as well is that, especially since it's early field experiences, that there are so many things, there's so many complexities to teaching, that you can easily just use that part of the semester to work on some other aspects of teaching, you can't actually address all of it at all times anyway. So you might as well just hone in on the ones that are sort of well suited to the small group zoom kind of online setting, and really try to gain some experience and reflect on those. And then hopefully, in the future, have a chance to do some of the other things like whole class management, whole class discussions, like that sort of thing. I'm also just curious, since you, you know, did this analysis over the summer and trying to kind of share it with the community, as we're all sort of thinking about how online, what online options there are for us and things. But are there other parts of the analysis that you're kind of curious about or that you're still working on? Or that were kind of piqued your interest while you started to look at these data? Yeah, I mentioned to two things in particular. So I was especially intrigued by the the challenges described about doing active learning in math online. And I've done a preliminary review of the literature. And while there's lots on learning math online, and on active learning, of course, trying to do active learning online, is doesn't seem like there's been much work done in that area. And so one of the one thing that I found in literature, for example, was a some frustrations with the platforms like the canvas or whatever the learning platform is that the online courses are run that they don't have, you can't use mathtype, for example, in the in the web chat, but that's different even than trying even being on zoom. And so you have this great technology where you can put people in breakout groups, but both the students learning the math and the students trying to work on teaching the math, articulated a lot of challenges that were really interesting with the things that even I and as someone who studied classroom discourse for a long time I took for granted in terms of just the visual and the multi modal ways that we communicate mathematics being able, they the pre service teachers, for example, would have asked the students to explain their answers. And the math students sometimes struggled with doing something like describing what their graphs look like. So not being able to sort of describe their work mathematically. And the pre service teachers missed being able to like I said before, just glance at their paper and see what they did, or do to just do a quick, you know, assessment of how the whole group did and they talked about how they, almost every person that we interviewed use the phrase, I became the teacher in the room, and when I believe they meant by that was that instead of just helping to facilitate

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The discussion amongst the students, it shifted to that everything went through them, because they described it that the students, the precalculus, students, were no longer talking to one another, which they did in the face to face, but they said it was just much more uncomfortable. And then the nation time shifted to like, I'm learning, I'm taking math class myself, and it's just really different online. So that was one interesting thing that's making me think too, about just authority dynamics of a Zoom Room versus authority dynamics of a physical space, it sounds like there might be some differences there that I have not seen explored, really in their full potential.

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And then the other thing that's related and also related to authority, there's I've seen on social media, lots of discussions and advice about requiring students to turn on webcams in class and people, you know, talking about how that's, we shouldn't be doing it. And it's, it's an equity issue. And, and I and I understand all those arguments, the presence or not of the webcam was such a dominant player, I'd say, in how well, the the pre service teachers describe the functionality of the groups that I wonder if we just blanket say, it's fine. If you don't turn your webcam on, what do we lose in engagement? And what are students missing out on in terms of engagement, because everybody described that when we could all see each other and we'd use sometimes we'd show our work, we'd hold our work up to our web camera. And that was the only way that they had sometimes to just share their thinking. So what do we lose? So so you know, I've been thinking about, you know, a potential solution would be to encourage and invite students to have their cameras on rather than requiring them, but to talk to them about how class could potentially be more engaging, when we can all see each other. And we can communicate more easily and talk to each other. So. So you know, I have some concerns. It's like a delicate balance, right? Because I do think we lose something if we just heard Paul looking at a bunch of black boxes on zoom. And I'll chime in to say that I think this pandemic situation, as Michelle was saying, there's so many opportunities here, not only for research, but also just really looking at ourselves and saying the existing digital tools are really designed to be supplements to face to face instruction, not designed to carry the full instructional load. So like zoom obviously was not created for work students working in math classrooms, it's great for meetings. But it's really limited when we think about what we want math classrooms to be, which are spaces where students are collaborating to solve problems, and that those problems are highly, they involve highly inscriptional work. So I'm on another project where we're working on a new kind of digital curriculum for the connected map project, where we designed a platform where students can see each other's in progress work in real time. So even if you weren't in a Zoom Room, or didn't have your webcam on, other students could see each other's work and use it and watch it evolve. And, you know, in real time, so this is really, it's an opportunity, it's huge opportunity, kind of three things, what we know is necessary for the kind of like collaborative ambitious math instruction and see how digital tools can help us achieve that. But we're all I think, right now we're in this interim period, where we're trying to come up these tools that really don't quite work as well as we'd like. And it's just, I think, making us realize what what is so important about face to face. And that's a starting point then for digital design. So I guess sir Michelle Cirillo from University of Delaware and Kristin via from Michigan State University. And I do have one more question I want to ask and just there's like you're you're talking about here, there's so many things to be thinking about to be investigating to be just troubleshooting. But if we focus in on teacher preparation, and thinking about those people who are at universities trying to move forward towards becoming, you know, having a career as a teacher, what is it that's really on your mind for this fall semester, when we're still in the United States still in like, you know, the high points of the pandemic? Yeah, so we're going to be implementing the UT model in the fall at Michigan State with a new cohort, a pre service teachers. We are in a unique position that our campus is opening for classes, but largely many of the classes are either hybrid or online. And so we that the math class that we're partnering with, which is the color

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algebra course is an online course. And so we are facing a similar situation that Michelle faced in the spring at University of Delaware. And, you know, now we have somewhat headstart and thinking about what we could do. And we're going to be looking at a situation of working with this online math class for the entire semester. So what's on my mind are how can we utilize digital technologies to help our pre service teachers get to know students in the same way that we, you know, the luxury that we had in face to face settings. And it's also on my mind, that part of the getting to know process is also making some space for the pre service teachers I work with, as well as the math students to feel comfortable sharing when things are getting hard. I mean, I think that the mental health impact of this kind of situation, especially for think some of the math students are going to be freshmen, this is their very first semester in college. And this is the kind of impoverished sort of social setting of online course taking, I think, is going to take a toll for their motivation, engagement. So we're going to be working a lot with a pre service teachers about how when we engage in zoom, how do we kind of create more of a community and do that quickly, so that we feel like we can help their engagement and motivation to, to stick with this online format, and this online course. So that's really I think, the center of it. And then we're kind of exploring right now, different options for ways that they can experience some of the aspects of teaching, as Michelle mentioned, things like discourse moves, you know, ways to launch a task, we want them to experience that. But we also want to be sensitive to the nature of online teaching, and that there are some limitations that we face with the tools and curriculum that we have. So we don't want to be setting expectations that are unrealistic for the online environment. At the same time, we want them to face some of the difficulties of teaching. So we're exploring a couple of options with that one of them, as Michelle was saying, you know, definitely having them work in small groups. But I've also toyed around with know that it's very common for a lot of programs to be designing videos that can be watched, asynchronously. I've used an assignment in the past. And I may kind of reconstitute it, I think, for this semester, which is to critique existing asynchronous math videos, and then create their own that incorporate more active learning strategies. So we may be trying something like that for the fall. Yeah. And I'm, I am scheduled to teach our methods course in the fall. And it's the second and final methods course that our seniors end up taking, prior to student teaching, but their field experiences such that they are in their student teaching placement in the fall, so that they get to know the kids in the setting prior to going in the spring. And so, you know, what is the balance in terms of what you do in the methods course? So are you preparing them for real teaching, which is hopefully what's going to happen for most of their career? Are you? Are you preparing them for COVID? teaching, which is what they're going to have to do immediately in the in the spring, right? And so do you favor the COVID teaching? Because that's most immediately of concern? How heavily right and how much do you do preparation for the face to face that, like I said, they'll mostly be engaged in throughout their career, hopefully. So I've been thinking about that. At the same time. One of the things that I've become aware of is a is a some interest in interesting city by Kennedy, an Archon ball to in 2012 argued that there are 50 states in the US offering k 12 online learning opportunities, and that pre service teachers should have all kinds of opportunities and field experiences learning how to teach in different setting, and that the importance is that they get to interact with students. They have mentioned in 2012, that online learning has grown exponentially, and that we're actually denying our students opportunities if we don't actually give them some kind of experience like that. So I'm kind of intrigued that our pre service teachers are going to learn lots of different strategies that will probably carry through

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Beyond COVID, in terms of different technologies, like one of the pre service teachers said, I imagine we're never going to have a snow day again. Because why would we need to write we know how to do this online now. So I think there's lots of it's challenging, of course, as Kristen mentioned, really challenging, especially for students of that age group right now. But there's so many interesting opportunities and things that they get to learn that are different from what we normally would be doing. All right. Well, thank you so much for doing this work. And especially now in this time, when we're all having to be kind of flexible. We're all having to have some out of the box ideas about how to still, you know, prepare teachers the best ways we can and help students in learning mathematics. So really appreciate sharing the ideas and again, the articles in the Journal of technology and teacher education. shaylen. Kristen, thanks so much for being here. Thank you, Sam. Thanks.

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