0:00 Hello, and thank you for listening to the mathematics teacher educator journal podcast. The mathematics teacher educator journal is co sponsored by the Association of mathematics teacher educators, and the National Council of Teachers of Mathematics. My name is Eva Anheuser and I'm talking with Fran arbo, who is an associate professor at Penn State University in the College of Education. We will be discussing the article the three minute rehearsal cycle of enactment at investigation, pre service secondary mathematics teachers learning to elicit and use evidence of student thinking, published with co authors, Dwayne gray, say nursin carnac and Ben freeburn. In the September 2019, 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 their article, their successes and challenges and how those lessons relate to their other work frame. Thank you for joining us. Thank 0:58 you for having me. I really appreciate it. 1:01 Can you give us a brief summary of the article including the results? 1:05 Sure. So Ben freeburn came to me when he was in the doctoral program at Penn State and said, I've been reading about these cycles of enactment and investigation in the literature. And I think we need to talk about doing them with our pre service teachers, secondary pre service teachers. And so we designed a learning cycle, modeled after Lambert at all 2013 jte article, we have a couple of different changes. But basically, we have a learning cycle that we do with our pre service teachers that has six nodes, so do the mathematical task, individual analysis of representation of practice, node three is collective analysis of a representation of practice. Node four is planning the rehearsal lesson. Node five is rehearsal, and then node six is collective analysis of the PSTN or Herschel's, what we didn't have that Lampard at all and many other learning cycles have is them going out into the classrooms, to then do the lesson was students, this methods course that I was teaching didn't have a concurrent field experience. And so we had to figure out a way to make this cycle work without them actually ending in the schools. So we did that. And we collected data from them about what they feel like they learned as a result of participating in each of those nodes. So we had their written it was written data, and then we analyze that data. So they reflected after they did one of these rehearsal, yes. So they reflected after they did one of the one of the the whole cycle, they reflected, and about the different parts. And the cycle took us, I don't know probably two weeks in class to do by the time each of them went through this, the rehearsing. So then we took those data, those learning reflections, and using a framework that was developed by guzzini and herps. In 2016, they interpreted the framework for learning to teach from hammer Enos at all 2005 and created these dimensions of what it means to learn to teach. So the first mention is developing a professional vision. The second is developing knowledge of students. The third is knowledge, developing knowledge of mathematics content. The fourth is developing a repertoire of practices and tools. And the fifth is developing dispositions for teaching and learning. This is slightly different than guzzini. In herps work, we separated their knowledge of students and mathematics content into two separate areas to separate dimensions. So we then went through and coded the data based on those dementia reflections, their reflections. And what we present in this article is what they told us that they learned in each node. So what did you learn by doing the mathematical task? And what did you learn while doing while analyzing narrative case based on that task, and etc. You know, the article itself has a really explicit description of what we do in Yes, in the cycle, along with the 4:46 findings. I'll get to that in a second. But before we get there who should read this article? 4:51 I think anybody who is doing this kind of pedagogies of practice and their teacher education courses, A lot of people have picked up on this idea about rehearsals, but they don't do them in conjunction in a cycle like this. And I think one of the things that this this research shows is that the pre service teachers really learned something distinctly different in each node of the cycle. And so if you're kind of picking and choosing parts to do with pre service teachers, then you're not tapping into the potential of the teacher activity. So 5:33 when you're talking about cycle, you're talking about those six node Yes. Okay. And so that's one cycle that a preschool teacher would go through. And then what you said right now is that they're learning different things. And each of them so if we don't do all of them, we might be missing things. Yeah. And that's the one of the arguments we make at the end, is the study helps us see that all of the parts of the cycle are important. So people who teach methods classes would you say could use these may be coaches, 6:04 maybe coaches, but I don't see because the cycle takes so 6:10 long. So it's more like an in class? Yeah. Or city? Kind of? Yeah. Okay. What is the important problem or issue that your article addresses? Like? Usually, when mte calls for paper, they stay asked, like, what's the main problem that we're addressing with the paper? Will you say that that's a practice allowing students to practice teaching in methods course that doesn't have access to students? Yeah, 6:37 I think that's one of the things I mean, we had done peer teaching before, and methods courses. But this kind of short rehearsal, where I can do some coaching during the rehearsal. That's one of the things that happens during rehearsals that the mte can stop the action and ask them to rephrase or engage the teacher, the PSE who's teaching in a short conversation. That was one of the things that attracted me to this work to start. And so I think, overall, though, the problem that we were trying to solve was, how do we help our teachers both build knowledge and build teaching skills at the same time, and this cycle allows them to build both? 7:27 I feel like that the question comes later, but I would really like to pull it ahead. Because we keep talking about the cycle. Could you talk us really quick through the title is a three minute cycle, right, three 7:38 minute rehearsals three minute rehearsal cycle? 7:40 Could you talk us through what the six nodes are? So we have like a mental image of what we're talking 7:46 about? Do you want specifics from this particular cycle? No, it can be general. Okay. So the first node on the cycle is doing the mathematical task. And so the pre service teachers engage in doing a mathematical task as a learner. The second note is individual analysis of a representation of practice. So in our case, this played out as the coding of a narrative case. And I do also have to say that our pedagogical focus through this cycle is on asking, assessing and advancing questions and using judicious telling. And so everything that pre service teachers analyze is through that lens. And what they're trying to get better at during the hurt rehearsal. Is those teacher What am I envisioning when you say, to coding a case to giving a story, and then we have a narrative case of a classroom where the mathematical tasks that they have just done is playing out in a classroom. And it's from some other materials that I'm an author of. And so when they code they actually go through, they print out the the case, the narrative case, looks like a transcript. And they actually go through and Mark passages that are indicated, assessing questions, and advancing questions. So 9:10 they're looking at the different questions and what the purpose of those questions was, for example, yes. Okay. 9:16 They do that individually. And then the third node is a collective analysis of that same representation of practice. So they get together in their small groups, and they talk about their coding, and they come to some agreement, and they come to some agreement. The fourth note is planning the rehearsal lesson. And I use an adapted thinking through the lesson protocol. All those details are in this article. Yes, they are. Yeah. So they plan for the rehearsal, and then individually, they rehearse for three minutes. It's a three minute rehearsal. 9:50 So now they're enacting the same task that they worked on, and they analyze 9:55 not the same task that they worked on and analyze but it's another So the tasks that they work on is proving that an odd integer plus an odd integers equals an even integer. So for the rehearsals we have given them, number theory, items like that. So similar similar, so they each get a different, well, they don't each get a different task, groups of three get the same task. But then the graduate students that were working on this, Ben Anderson and Dwayne, they developed representative student responses 10:34 and complete, so they pretended to be the students and 10:37 then they pretended to be the students. So everybody had a different student response to respond to in the rehearsal. The rehearsals are three minutes long. Because what we say that the PST is, is, this is about as much time that you're going to have with a single student in your class at a time. 10:57 So if I'm imagining this classroom, am I imagining one of the pre service teachers upfront during the rehearsal and everybody else watching? 11:05 Yes, 11:06 so if I were an instructor that doesn't have three graduate students at my disposal, I could do that by just pre preparing some responses, yes. And then I would pretend to be the child or 11:18 you could or others, you could assign those, assign that okay to the other psds in the class, and they could play the role. This is, you know, you have to present your thinking, 11:31 and then, so I'm trying to imagine what this would look like. So I have a new task in the rehearsal. What specifically am I working on? Has, does the student have just task solved already? Am I launching the task, like where 11:45 the rehearsal is couched in, you've launched this task, and you are walking around while students are working on it. And somebody raises their hand and you walk over to them. And they have an incomplete answer, but they're stuck. So what are you going to do in those three minutes using assessing and advancing questions, and you just just telling okay to get them unstuck and moving towards that mathematical goal? 12:13 Okay. So what's the next node? So 12:15 the final node is collective analysis of their rehearsals. So they actually use we use Studio code in the past. We're using keynote now. So 12:25 you videotape this whole thing? Yes. 12:28 So we videotape the whole thing. I put them in groups of two or three. They go and they analyze each person's video, 12:36 do you think this would be possible to do with just an iPad and no coding software? 12:42 I don't know the answer to that. 12:44 Yeah, I'm asking just because I'm thinking, if I want to go and take this Studio code is expensive. Yeah. Right. I don't know about what the other one was. He knows. And 12:53 it's not as expensive as Studio code for sure. 12:56 So the goal is to then analyze the questions that the pre service teachers asked in the rehearsal and kind of look at what kinds of questions did you ask? 13:07 Yeah, through that lens of those three types of teacher talk? 13:11 Okay. I do think we have a visual now. Okay, what is happening? So what research questions did you study to document the effectiveness? So you just told us what the cycle look like? And you told us a little bit at the beginning. But that's just summarize quickly, what questions did you study? And what were your findings? 13:31 Well, question was a pretty basic one, which is what do they report learning from each node? Okay. And so we present our findings through each node. So do you want me to go through each node and talk about that 13:45 you said earlier that they learned something different in each node, maybe we could just focus on a highlight or two? Sure. 13:50 I mean, one of the things that struck us about our findings was that in nodes one and two, they reported learning about a repertoire of practices and tools. So they reported learning something about how do you teach 14:05 it, that's when they were doing the math, 14:06 doing the math and analyzing individually analyzing the narrative case. 14:13 Okay. 14:13 So they also reported in the doing the math, because part of doing the math in this context is analyzing some student work around that math. And so they also reported in at least in node one, how it helped them learn about students thinking, Okay, maddix Yeah, so but they talked about those things really separately, when they talked about what they learned in node one and node two. But then when we got around to the rehearsal node, they put those two things together. Oh, that's cool. Yeah. So yes, they learned about student thinking and they learned about repertoire of pedagogy isn't tools of teaching and tools. But it was in Node five in the rehearsal where they really put that those two together, oh, can do these things as a teacher to uncover students mathematical thinking, 15:15 what would you say was the most surprising finding? 15:18 That's a really good question. I think we were most surprised about how much they could articulate what they learned. And were really thoughtful about what they learned at each node. And I think we were surprised that they felt like they really learned a lot through the planning. Okay. But they really did feel like they learned a lot about teaching by doing that node in this cycle. 15:49 And so you said at the beginning, that really one of the things you also learned is that they learn different things into different notes. And so just focusing on some might miss out on some aspects. Okay. I think that you talked a little bit about whose work you're building on in your introduction. And you did talk about the evidence you presented, which was the analysis of their self reports, right? Yes. Okay. So our closing question is usually what I'm new contributions to the field of math teacher education does this article make? Or how does it inform or influence what we do in math, Teacher Education. 16:29 So one of the things that we argue here is that most of the work around learning cycles has been done at the elementary level. So you expanded it to the secondary, so we expanded it to secondary and showed that this kind of work can happen at the secondary level. 16:46 So something I as you know, focus on Elementary, and something that I often hear is, oh, you can do that with elementary teachers. But you know, secondary teachers might not want to engage in a rehearsal. Have you found that to be true? No, 17:01 not at all. I mean, they are so excited to get up and, and, like, try out their new learnings they really talked about because this was the year that we've collected a lot of data from them. And they really talked about how going through those cycles really helped them see what teaching is all about. 17:22 And I think you mentioned earlier that it took about two class sessions to get through everybody. So if you think about a typical methods course, via either 10 weeks in my situation, or maybe 15 or 16 weeks in your situation, why should we spend that much time on that? 17:40 I think you get a lot of bang for the buck. Okay, I think it's a very tightly coordinated set of teacher activities, Teacher Education, activities and activities that teachers will actually be doing. And it's all right there together. That's one of the things I really liked about 18:00 it. Where would you place it in a methods course, like towards the beginning towards the end, 18:06 this happened? About a third of the way through? Okay, so we had built help them build a lot of knowledge about what does it mean to be mathematically proficient? What is this thing, teaching through problem solving? We had done a little bit of work about the assessing, advancing and judicious talent. Okay, one of the very first things that they do and my methods class is they analyze my teaching that night I had recorded on the first day. 18:35 So with them, 18:37 yes. That's so cool. Yeah. And so I pitched the course, as this course is about analyzing teaching. Okay, so yours and mine and other people's Yeah. So I think this cycle gives them these analysis tools that I didn't see when they were just pure teaching. 18:57 Okay, I just read your paper a few days ago, and you provide a lot of resources. So if anybody wants to implement that, we do think everything is provided in the article for people to go ahead, 19:11 either it's provided or it's referenced where you find it, like the narrative cases, part of a book that I wrote, what's the book? It was, we reasoned, and we proved for all mathematics, okay, from Corwin. And so one of the narrative case, the narrative case we read in this particular cycle is from that book, as is the opening activity that we do where we do the math. So that's not included here because it's copyrighted somewhere 19:39 else, 19:40 but it's referenced really clearly. 19:43 So I'll close with question. Do you want to add anything else? 19:47 I have to say that this work and this kind of redesigning of my methods course, really rejuvenated me. It was exciting. It was a What I thought was innovative. And so I took away a lot from this first year that we can do this. 20:07 So have you done it again? Since we have we have an echo? 20:11 Yeah, it goes, well goes, it goes, Well, yeah, we do it. Just about every year. I have another thing going on right now that is for a later podcast, okay, where we are not doing that in our secondary methods, this methods course anymore, because we've found a way to do a actual field experience. But again, that's a whole nother story. 20:32 It's been really powerful. So I've taught methods, both in a way where we could access children and in a way where we couldn't. And I think what's powerful about this is that it provides you a way of doing that when you don't have access to children. 20:47 Yeah, I agree. And it gets them up and working on very targeted practices, teaching practices. Thank 20:55 you very much, Fran, for joining us. 20:57 I'm very happy to have been here.