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 Thanh Heiser, and today I'm talking with Maggie Rathaus Nasrin changez. Phillips in ng cribs, and we will be discussing the article promoting equitable pre service teacher participation in mathematical discourse, rough drafts on an asynchronous discussion board, published in February 2023 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 their successes and challenges, and how these lessons relate to their other work. Maggie and Angie, can you each briefly introduce yourselves? Speaker 2 0:57 Yes, hi, I'm Maggie Rathaus. And I am an associate professor of mathematics education in the department of math and statistics at the University of Michigan Dearborn. And I teach mostly classes for future elementary and middle school teachers, although we have branched out and teaching more, some of the developmental math classes and some of the first year just gen ed, Math classes, trying to really use what we know about what works with adult learners to help those learners learn math. Speaker 3 1:32 Hi, I'm Angie crabs. I'm a colleague of Maggie's, at the University of Michigan Dearborn. I'm also in the math department, we've been continuing to work with pre service teachers, elementary, middle school and secondary teachers. We've recently been revising our program based on the our new state state standards or state. Thank you. Yeah, state certification standards. And that's been most of our work right now. Eva 1:59 Well, welcome to the podcast. And let's jump right in. Can you give us a brief summary of the article, Speaker 2 2:06 I guess I'll start out with that I was lucky enough to get a sabbatical in sort of the second year of the pandemic, the beginning of the second year of the pandemic. And we were really curious about what was going on with things that we were trying to do in the real life classroom and how they translated into the Zoom classroom that we were kind of all forced to use, or most of us were forced to use, and our particular population is of students. They're mostly commuter students, so not a big on campus presence. Anyway, so they're kind of stuck at home living, mostly living at home or living, not on campus. And so they had lots of variety of different issues with joining the Zoom meetings. At the same time, we were also had been thinking a lot about having getting greater participation in discussions in the in person classes. And one of the things that we've been playing around with was Mandy Janssens, it's not just hers, but, and Ava as well, has done work with rough draft thinking and rough draft using encouraging rough draft thinking and rough draft representations, a Rough Draft Draft, talk in the mathematics discussions to kind of get more voices out there, get more ideas out there and have students feel more confident more or more comfortable just sharing on processed ideas, or, you know, in process ideas, I guess we'd say. So pandemic, that one thing that pendant pandemic comes along, and we realized that many of our students were going to be at a disadvantage in terms of the the Zoom meetings, either because they had challenges just with the, with the electronics and having their Wi Fi be reliable, or they're going to be taking care of kids at home, or taking care of somebody else's kids or they're going to have to be, you know, working out in the thing and could actually get sick. Many of our students got sick that first year, themselves, and we're, you know, kind of just trying to do a lot of things and not able to actively participate. So one of the things that we decided to incorporate and play around with was an online discussion board or written discussion board, where ideas that came up in the Zoom meetings could be rehashed, or even started in the Zoom meeting. And then further ideas could come out in those prompts in on the discussion board. And we decided to start each one with kind of a, like, what's your rough draft thinking about this? And then we would often have another one that would be on the same topic that would follow up on that and be what is your revised thinking after talking and interacting with others? For the discussion boards, they were very low. They're very Hands off. From my perspective, I was the instructor for this class. Angie has since taught the class in person but still uses the discussion boards. Because of all let her say a little bit about about that as well. One other thing I wanted to say is that we became really interested in how these changes were perhaps impacting more equitable, or at least more participation. It was sort of just an experiment in like, Okay, we're gonna do this, and let's just see what happens. And then the data that we collected, were the actual student voices that were there written work. And I think there were a lot of surprises, which we can get into later. But I don't know. Angie, do you want to add anything else about in the summary part? I don't know. Maybe that was too much. Speaker 3 5:43 Well, I guess I'll just say, as you as you mentioned, is I used it then in future classes in in person classes, I've actually used it to inch two of these, the same class that we're talking about here. And it wasn't something that we did in our in person classes prior to, to the pandemic, it was something that you know, you tried first in the, in the, in the online, eight, online synchronous course and had success with so it was kind of exciting to try it in in person and see some of the things that you noticed, we noticed continued in the in person classes. That was kind of nice, too. Eva 6:19 Well, thanks to this introduction. Our second question is usually who should read this article? Who did you write this for? One of Speaker 2 6:27 the things that I noticed we started looking at Rochelle Gutierrez is work on equity. And when I was reading her descriptions of the like different components that she sees a inequity in mathematics education, or maybe it's just education in general, the access, I don't know if I can remember all four of them. But access helped me out Angie Speaker 3 6:49 identity, identity, Hauer and achievement, Speaker 2 6:52 power and achievement. They seem to be written for K 12 students, I learners. And I felt like some of the same things should apply to our learners and our, you know, future teachers. And I don't know if you would agree with me, or if I have not seen all of the work on this, I probably haven't seen all the work on it. But when I was thinking about it, in terms of, you know, our students have these, you know, have mathematical identities, they have access issues that may be different from access issues in K 12, that we're talking about a totally different population of students, ones that actually make it into, you know, college and want to pursue teaching. So I thought that was kind of a little bit that was interesting to me to think about in terms of recruiting and retaining teachers, a diverse teachers, and then hearing those diverse voices in the conversations, which I feel like is an important part, that equity aspect of participating in a mathematical discussion. So I'd say mathematics educators that are trying to supplement their supplement and or get more voices in their discussions out there. should read the article, Angie, any other people that I would add to that, I Speaker 3 8:12 would say teacher educators primarily based on what we've been here. Okay, Eva 8:17 so what is the important problem or issue that you are addressing? And I think you already got into this a little bit, Maggie. But let's just summarize it. I'm wondering, Angie, if you want to kind of build on what Maggie said in the last question. Speaker 3 8:34 One of the things that I think is interesting, it's, you know, we're doing this through a mathematical task. And I think to set the context of where we're doing this, this is in the second course, that are pre service teachers second content course these pre service teachers are taken, taking in Maggie's course, when she did it the first year during the pandemic, these are students who had not necessarily met each other. So this idea of identity became much more important that they were able to share their thinking without preconceived ideas of each other. I think that was an important aspect of this. I think the mathematical task we were using was really important too, because it was something that all students could feel all students were unsure of. It wasn't something that you knew some students had the answer to some students did it. All students had this kind of uncertainty with it that they were able to address in their thinking so that when they were sharing their thinking they felt very comfortable. I'm not sure what I'm not sure. I don't know, there wasn't one student who had all the answers. And I think that was a big part of it. So the task, the task that we're using, just as should they say what the task is again. Okay, so we were using this mystery number. The idea is that it's a mystery number. I don't remember what it was was, too. It's such a mystery. It's something like two to 13 times three to the 12. Oh, Speaker 2 9:53 so it was it wasn't that it was to desert four to the fourth, fourth times three to the no to two The fifth times three to the fourth. Sorry, it's my favorite number I'm sure Speaker 3 10:03 it is. So the idea is that they have a prime factorization, a number and a prime factorization of a number. And we're asking them to tell us some things about the number. Is it prime? Is it even or an odd number? Is it a perfect square? Where some of the things that they were addressing Eva 10:19 is the problem you're addressing that you want more participation from students to engage in problem solving? Or do you want more equitable participation in problem like, what is I'm trying to figure out? Right, Unknown Speaker 10:39 right. What's the problem? Eva 10:41 Why are you doing this? What's the Speaker 2 10:44 I think the initial problem was initial problem, even before the pandemic was getting more people involved in the discussion. So more students involved in the discussion, not just superficially saying, Yeah, I agree with that person, or I did it the same way. But really engaging a little bit more deeply in whatever the problem is. That was one thing. And then on top of that, thinking about the equity aspect of it, were our students going to be able to participate in this zoom discussion. And if not, then this was another opportunity for them to to participate, even if they couldn't actually attend the class. She they could watch the video and then join in the discussion. I mean, he was kind of going on to into more of like, what we actually found that were sort of additional benefits to the whole thing. But I think setting it up, setting up the the prompts was really key and setting up the way the discussion board went in, ensued, not in zoom, but in Canvas was important so that they had to post first and then then reply. But yeah, I think the main thing was to get more voices and get everybody's voices out Speaker 3 12:00 there. And I think one of the things I want to add to is this idea that it gave students time, it gave them time to think about it. So often, when we have an in class discussion, the ideas are you need to respond right away, you don't really have that luxury of thinking about it. One of the things that the discussion board did is it gave students that opportunity of time, that luxury of time to be able to respond, they could post and of course, we set it up so that they had to post before they could read somebody else's post. So they would they would think about it, they could respond on their own time. And then they could respond to their colleague to their peers. Eva 12:34 You already talked a little bit about Rachelle Gutierrez work, and Mandy Jensen's work. So one of the rush hours work is the axes, equity, right? And then Mandy dancers work is the rough draft talk. So what else are you building on? Or what aspects of those are you building your article on? Well, I Speaker 2 12:57 feel like the rough draft stuff, we were really thinking a lot about, like, my whole, I don't know, my whole math education career. That's kind of been we were just doing this today, parsing the language that students use about us when they're talking about mathematics and learning mathematics. And I feel like that rough draft aspect is so key, like I did a paper about ambiguity and how that kind of can help get the conversation started. So I don't know work from Oh, Tim Rowland. And I've tried to think of other the knowledge Cortez the nudge Cortez, I was thinking more of like use of pronouns and like just this, this very rough draft idea. But lots of the language stuff with the rough draft thinking what has been important, like for me to think about, what about not only the prompts, but the other participants in the discussions, their language that they're using, is encouraging others to, like, join in, and you see this, like, kind of in that hedging language where they're like, I'm not really sure but and that will help somebody like, oh, yeah, you're I think you're on the right track, because I was thinking the same thing, and they might start to build on that. So using you, I feel like it's not just us your own rough draft, but everybody's rough drafting kind of together. And so we're kinda Eva 14:25 Yeah, me try to summarize, see if I understand correctly. So you found yourself in a pandemic, which gave you a way to examine something that would increase participation. And one way you were trying to do that is through an online discussion format, where for example, you posed I think the tasks to two fifths times three to the fourth and asked whether that's even or odd, I think was one of the questions. Then everybody had think time right because before they Post they can think then they posted and they posted a rough draft. So I'm trying to pull together because there's a lot of bits and pieces in there, right? So there is that everybody gets to share their thinking which, in those discussions, you don't see the discussion before you posted something, right. So everybody has to post something to participate, which means, and also it means you have to participate before you saw anybody else's. And is that why the rough draft piece was highlighted so that I feel better about posting like something before anybody else sees it? Or how does the rough draft come into this? Speaker 2 15:36 That was kind of the interesting part about it, because a lot of students, we saw about half the students kind of posted with a rough draft language. And others just like said, it has to be this way, because so they were a little bit like us more well, we called confident language. And we weren't sure quite why that was, but that was of more interest to me. So then like, Okay, who are these people that are confident are these the students that maybe our transfers, and they didn't do the first class with us, so maybe they think that they're supposed to know something, and they're doing a more like complete or not a rough draft thing. But we saw that a lot of those students then backed off. And once they read the posts of other students in the class, they would back off and kind of turn into this more rough draft language. So it allowed them to reexamine, sometimes they're incorrect thinking at first, and go back and say, oh, okay, we're really supposed to rough draft this. And I've seen other people doing other things. So you know, I think it freed them up a little bit. At the same time. Eva 16:44 Why you chose the you have to post before you see others feature? Speaker 2 16:49 I don't know, it seemed like a good time. I don't think it was something that we I mean, I definitely wanted that to be a thing. It seemed like it would work better for the rough draft and for the everybody has to post? I don't know, Speaker 3 17:05 I think we're trying to avoid the I agree. Just I agree with you kind of comments. We wanted their initial thinking. And I don't think when this started, we weren't necessarily thinking of all of the equity issues that we would find we would find this as being a more equitable situation. Speaker 2 17:22 Just trying to have everybody have a champion, but But then we started seeing that Oh, wow. Okay, this is actually, you know, helps them in terms of their time that they can join in and things like that. But Speaker 3 17:34 we did have, they were they were sharing in smaller groups, too. So when they were reading the discussion groups, they weren't really reading the responses from everybody in the class, they were small groups of like four or five, I think, maybe six. So I'm Eva 17:47 gonna summarize again, because I feel like we're going in different directions in our conversation, the intervention that you're studying, was this discussion post on whatever online framework, where each person had to post the answer first, and then they got to kind of talk about it. And so now, my next question is, what is the research question that you studied? Or What question did you examine, to kind of figure out whether this intervention worked or not? Speaker 2 18:23 Well, I'm gonna, we didn't really think that this was necessarily going to be a big study, it was more that things came out of it later. But what I would say we what we found was that way more like 100% of the students participated, rather than three or four students on which was, you know, in the passion in each discussion. Yeah. Surprisingly, I was not a big proponent of written discussions, I thought, you have to have like face to face, you have to have verbal language discussions, even for rough drafts. I thought it would work better. If it's more on the, you know, not on the spot, but on, you know, in process, I thought it would be it would be too formalized. But it didn't turn out that way. I feel like we started noticing things and then we kind of asked these questions is does the data support this? So is it the is it supported that when you ask them to do a rough draft thing, that rough draft response to this task? Do they try to get a complete answer right off because they have so much time? Not really, they mostly offered very thought out but also still very, you know, rough responses, then they they thought about it, they revise, they reflected on their revisions. So there were things that we noticed after kind of after the fact that supported it wasn't like we set up this intervention. And that happened. It was like we did this thing because we had to sort of And we've noticed some of the some of the benefits from it. Eva 20:04 And so one of the benefits, I think, that you just talked about is that everybody participated, at least with a starter post, Speaker 2 20:11 everybody. Yeah. And nearly everybody did a response post to up here in their group. And this wasn't just like, once in a while, this was pretty much probably like 25 posts throughout the semester. So it was it was a lot. In fact, my students now that I had this past semester, they said, it's too much, it's too I'm thinking that they're like, we're, we're face to face. Now, we don't need this much discussion board. And I just, I'm not sure that they really fully embrace what's going on yet. But so I might have to tweak things a little bit with this new group. This reminds Eva 20:50 me a lot. My students, Simon Han, and I did a similar study to this also somewhat facilitated by COVID. And the switch to online, where we did number talks, and it was asynchronous online. Because same issues, we couldn't even figure out how to have zoom meetings at right at the beginning of the pandemic. And we found similar things. But what like blew our mind was, we asked them like to post like you guys did, and then we asked them to find one that was like the same as theirs, and one that was different. And what I they identify the same didn't align with what we identified, because they a huge and then made us question when they do that sign for same, you know, like they do in the number talks. Like, how do we know whether like what they see as the same, right? Like, sometimes they thought it was the same? Because it started out the same way. But it didn't finish or it was a different kinds of categories. And so I thought it was a really seemed like you Maggie it like convinced me of the advantages of being asynchronous online, because you do have, you know, the time and you can let them share. And then in their responses I liked in your article, how you said, some of their language changed, right? They were very confident. And then somebody else said, I'm not sure. And then they were like, maybe they were like, Oh, wait, maybe I'm not as sure as I thought I was right. Speaker 2 22:21 Yeah, it was almost like, almost like they were talking to each other a lot more than I thought it would be, you know, when we first put these out there, I'm like, Oh, this is what online, this was what written discussions are going to look like, you know, they're going to be very much like writing a letter or something rather than having a conversation. And you can see the transcript, the transcripts, I mean, there are almost like they're having a conversation, which was planned, I Speaker 3 22:47 think, I mean, the idea. So this was over a couple of classes, a couple days of classes. So we would have the discussion, the first discussion, then we'd have class, and then they had another discussion, but it also prepared them for the discussion during class time, I think that they could, they were more comfortable sharing their thinking because they had a chance to try it out in the discussion, I had much better participation in my discussions during class time. And then they started to wrap it up, but they still hadn't, you know, they still didn't resolve things. And then the second day discussion, they were able to really put some more time into it. So it took it takes some time for them to work through this. And I think that's one of the things I really learned is the importance of time just giving them time to think Eva 23:30 Yeah, and it does spread out participation. So it's not just who is willing to speak up in class and put themselves out there, right. But it gives you different forms of being able to participate in now that you said that it doesn't seem surprising that after I was able to read through everybody's thinking online that I might be more comfortable sharing in class, right? Because I know where I am in relationship to everybody. Speaker 2 23:59 Right? When you just said I, you were talking about a student, but or a pre service teachers. But we also felt like we got a lot more insight into, like, when you have six small group discussions going on in class, it's nice because you can read the room and you can kind of like, Oh, they're not getting this or they are getting this or these guys are off task or whatever. But on these like going to the Zoom breakout rooms, you can't visit them all at the same time. You can visit a few maybe in a in that amount of time. But with the discussion boards, you can actually go in there and read all of the discussions if you want. And you can even pick a few themes out that you want to highlight or a few like questionable ones without grading them. And they are posted on the slides for the next meeting. So like okay, what do you guys think about this? And a lot of times the students will say, well, that's kind of like mine. That one is my, you know, like they would self identify, but I I think that got the conversation rolling in a, in a more anonymous way. But even if they outed themselves later, Eva 25:06 but it brought up the topic inboards Anonymous, Speaker 2 25:10 they weren't anonymous to each other, although many of them hadn't actually met each other face to face. And even in the, you know, in the Zoom meetings, they wouldn't usually have their, they would often have their their video muted, or what even their audio muted. So they didn't really get to know each other and they weren't living on campus together, because they're not on campus. For the most part. Eva 25:33 It was just a weird time all together. All right, so let's wrap up our last questions usually, what is the new contribution that you are making to the field? And or what else would you like to add? Speaker 3 25:48 I think one of the biggest thing is just the importance of this kind of asynchronous discussion group giving students this time I've said that the importance of students to have the opportunity to share their thinking in a way that gives them a chance to try it out and practice what they're thinking. So the importance of kind of continuing this idea of this rough draft thinking and giving them time to work through that, do you want to add to that, Speaker 2 26:13 I think for for math teacher educators as well, or for any college educators, ones that I talked to were like, Oh, I could never do this, that's so much grading, like to follow all this stuff, and to make sure that they're saying the right things, and they're not a but you don't have to do all that you can really be very hands off, and it can kind of run itself. I mean, we did this even with with the courses for the developmental math and, you know, gen ed, Math classes where they're not going to like this, you know, but they did and they participated really well. And you didn't have you could just check off, did they do it, they post and reply, and then you can pick the ones that you want to focus on in class, you know, for a little bit more. Eva 26:55 Yeah. And I want to add, so I've been doing this also for years. And it gives you a better insight for teaching the next day, because you know where they're at, you know what they're thinking, right? It's like this luxurious way of being able to see where everybody is, and what pieces you want to pull out and addressing class. Speaker 2 27:17 Along with this whole time aspect. There is a limit like to how much you can ask of them to do outside of class, I feel like we had a special, it was an awful time, but also a special time at the beginning of the pandemic when people had some obligations, and everything was weird. But everything was weird for everybody. And now that we're in this kind of like post pandemic thing. It's still weird for a lot of people. And still people are getting sick. But not everything that worked really well, because everyone was kind of a captive audience. And we're all in the same boat together. Now works in the same way students are kind of starting to say like, we've got other things to do, we can't just be doing these posts every now it's Speaker 3 28:05 I want to add to that make though I think the importance, and this is one of the things we're finding is that we have really good prompts for them. They're not just telling me you're thinking, but they're really specific questions. What can you tell me about this number? Is it even or odd? Is this number of perfect squares? Getting them to a specific question that they need to respond to, is really, I think, important in this type of discussion. Eva 28:27 So for example, what kind of prompt will you give, Speaker 2 28:30 just to get out of the number theory realm for a second, we, I've had prompts that have them play a game, like, like they played the quadrilateral game on the geoboard on the virtual geoboard. And then they had to like, talk about a good move, and then not so good move like something where they can briefly reply and describe something but not I felt like even the shortest prompts, they would give a longer response than I anticipated, like, just these choices, like even or odd. They all they really had to say was, you know, it's odd, or it's even whatever, and but they would go further into it if they realize, oh, that's, that's all I have to do. Well, I better say a little bit about why I think that so trying to think of another content area measurement. And for that class, we've also used them for like reading responses in more in the methods classes or watching a brief video clip and talking about a particular aspect of that. But I feel like those are a little bit different types of prompts to answer to but they still have some I know Angie's taught taught the methods class more recently, but those were pretty well to don't they Speaker 3 29:46 were but the responses are very different. I mean, it's just because they're like they are kind of responses the these are still substantial responses to these questions, which would be in in surprise. I thought I was always surprised at how much they responded happily surprised. happily surprised, though. Eva 30:06 Yeah, that's it sounds like a really cool way to get access to your students thinking, whether you're in class or online or whatever, to kind of offer these posts, at least every now and then maybe not every class session to kind of get a sense for where is everybody and how do we move? All right. Well, I want to thank you both for coming on. Unknown Speaker 30:30 Thank you. Thank you for the opportunity. Yeah, it's Unknown Speaker 30:32 been fun. And for Eva 30:33 further information on this topic, you can find the article on the mathematics teacher educator website. This has been your host, Eva Anheuser. Thank you for listening and goodbye. Transcribed by https://otter.ai