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. We will be discussing Christine Phelps Gregory and Sandy Spitz's article assessing perspective teachers analysis of teaching how well can they link teaching and learning published in the September 2018, 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 other work. My name is Eva Sennheiser, could you each take a minute to introduce yourselves. Hi, I'm 0:46 Sandy Spitzer. I'm an associate professor in the math department at Towson University. And I mostly teach math content versus pre service and in service teachers at all levels, elementary, middle, and secondary. And I also direct our graduate program for practicing teachers. In terms of my research interests. I'm particularly interested in how pre service teachers can learn to notice and analyze evidence of student thinking while they're in their pre service education programs. Okay, and 1:12 Hi, I'm Christine Phelps Gregory. I'm an associate professor in the math department at Central Michigan University. I teach classes for future elementary and middle school teachers as well as general math classes like discrete math. My research interests lie in two areas. First, I'm interested in college students motivation in math. And then second, I'm also interested in Sandy's research area, which is the skills related to teacher noticing for prospective teachers and ways to help prospective teachers get 1:36 better at analyzing student thinking, Christine and Sandy, thank you for joining us. 1:41 Thank you for having us. Thank you. 1:43 Could you guys give us a brief summary of the article including the results? Sure. 1:48 So this article details an assessment we created for investigating prospective teachers ability to create hypotheses that link teaching with student learning outcomes. Previous research has mostly focused on investigating prospective teachers ability to analyze student learning, but our assessment goes further and investigates their ability to connect that learning to teaching moves in the classroom. After the designing the assessment, we administered it to 16 prospective teachers enrolled in a mathematics methods quest. And we found the assessment did capture perspective teachers ability to write hypotheses In fact, all 16 perspective teachers were able to write at least one hypothesis that successfully linked teaching with learning. However, we also had four specific question prompts in our assessment to try to identify supportive contexts for prospective teachers for writing hypotheses, and we ended up finding little difference between those four prompts. So that is the assessment we found was successful at helping them write hypotheses, but not really successful, identifying supportive and more and less supportive contexts for helping them write hypotheses. 2:53 Okay, thank you. Who should read this article, 2:56 we intended the article for anyone interested in teacher reflection. So for example, that might include teacher educators who want to use our assessment task in their content or methods class, the content of the task itself is adding fractions. So it's ideal for prospective elementary and middle school teachers. And the task was designed to be used in a college classroom with some discussion, it could form a lesson by itself on writing hypotheses, but that might also include researchers who want to do work on helping prospective teachers analyze teaching, researchers interested in teacher noticing. It's basically anyone interested in teacher reflection, 3:28 what is the important problem or issue that your article addresses? So why do we care about hypotheses, we know that 3:37 four years in undergraduate teacher education program, it's just simply not enough time for pre service teachers to learn and master all the complex skills that we know go into quality math teaching. And this comes from our own experiences, teacher educators, as well as the research base. It's just pretty clear to me that the timeframe of four years in pre service teacher education is just not enough time to develop all this variety of skills, including deep understanding of math content, how students best learn that content, and particularly because how students best learn might even vary from math topic to math topic. So we know that because they don't have enough time to get all these skills as part of their pre service teacher education, that teachers have to do a ton of learning while they're in the field teaching. And we also know that teachers have differential and insufficient access to high quality professional development. So we really can't count on teachers having external assistance in their own professional learning over their entirety of their careers. So this makes me and Christine think about how pre service teacher education can prepare teachers to learn from their own teaching by themselves, but in a systematic way incrementally and over time. And our work is definitely inspired by Jim Hebrews four and what all the folks at University of Delaware are doing. And our goal is to extend that work and think about what experiences pre service teachers might need to have that would help them be prepared to learn from their own teachers. When they're in the field, 5:01 yeah, so when I was reading your paper, I was thinking that that seems to be a goal that almost all teacher education programs have is to help teachers learn as they work. And this seems to be one concrete way that would allow them to do so Exactly. The research on teacher reflection goes back like 50 years or more. But we know that sort of the more systematically teachers can reflect on their teaching and use the products as 5:31 that reflection to improve learning, that's what might really drive like long term and true improvements to teaching. Okay, this 5:38 actually nicely segues into our next question is how does this article build on the existing work in the field? And what particular theories or previous articles Did you ground your article in? 5:49 So yeah, as I mentioned, we sort of situate our work within the ideas of teacher preparation that is specifically intended to help teachers learn from their own work and be reflective. So the primary ideas that we take, like most important in our work from this article come from a 2007 article by Hubert morrisburg, and Janssen, where they sort of lay out an argument for why teachers should be prepared to learn from their own teaching and why that should be a central task of teacher preparation. We're also really indebted to the work of Roselle santagata and Beth Fiennes, and some others at UC Irvine, who've definitely contributed significantly to this research base with a lot of intervention studies. And they created an entire teacher Ed curriculum around preparing teachers to learn from teaching. So that's the primary conceptual area that we situate our work in. But our work is also pretty tightly connected to the entire knowledge base on teacher noticing, which is really developed a lot in the past five years. 6:47 And I think I remember from reading that you're also connecting to this professional knowledge base, right? We're really 6:55 interested in thinking about like how teachers could build a knowledge base of practitioner knowledge that they could both build for their own selves over time, but also share with the field. 7:05 All right, tell us a little bit more about the innovation that you created. How does innovation address the problem of practice, 7:13 as we've kind of briefly been talking about what we're really interested in is like how perspective teachers can analyze a lesson transcript so analyze teaching and make hypotheses, that is like cause effect links that link something in the transcript, something the teacher did, or something in the lesson itself, to student learning both things students actually learned and then misconceptions students appear to develop or still have. So as such, our assessment tests ask prospective teachers to read a written lesson transcript on adding fractions, and we gave prospective teachers the learning goal of the lesson we said students in this lesson needs to understand how to add fractions and the concepts underlying this operation. We chose a written transcript because previous research has shown like a written transcript is a little bit more supportive for prospective teachers because they can read it multiple times and there are fewer distractors. And we design the lesson ourselves and we so based on sort of practices that we've seen in the field, but we designed it to show both productive and unproductive teaching moves. So there was lots of hypotheses you could create both about learning and lack of learning. And so after reading this lesson transcript prospective teachers were asked to answer for question prompts, that were designed to help them write hypotheses and the prompts were designed along four dimensions. Basically, we asked them about specific students or about general students and about correct or incorrect answers. So for example, one question we asked was like, what about the lesson might have caused students in general to struggle, so it was about incorrect answers, and about general students? Or we could have asked what about the lesson might have helped Samantha do well, or answer this correctly? So we had these four prompts. And the prompts were designed to help prospective teachers sort of make detailed hypotheses about the lesson. And this addresses a problem of practice because it helps teacher educators assess prospective teachers hypothesizing ability, which really previous work has not examined 9:08 so hypothesizing with respect to the goal of the lesson. That's correct. So 9:14 around that learning goal of learning to add fractions and understanding the concepts underlying the operation. Now, prospective teachers often made hypotheses about other mathematics, but we focused on their hypotheses about that learning goal, because that was the goal of the lesson that the lesson 9:29 was designed for what research questions I was trying to think if I wanted to go a different route, but I'm gonna stick with this for now. And so what research questions did you study to document the effectiveness of the innovation? 9:41 Okay, so we had two main research questions, so I'm just going to read them and then after I read them, I'll summarize what they mean. So the first research question is what is the nature of prospective teachers initial ability to hypothesize about the links between teaching and learning as captured with one assessment task, and the second is what effects If any, do the assessment task questions have on prospective teachers enactment of their hypothesizing skills? So the first question is really a broad based question. It looks at one assessment task, how well does it capture their ability I hypothesize, keeping in mind, these are beginning prospective teachers with no previous work and hypothesizing so we're sort of looking at how well does the task help them do this skill? And then the second question is specifically about those four prompts. That is, are some prompts better than others? at helping prospective teachers do hypothesizing? Are there some tasks the way they're worded that do better at helping prospective teachers? 10:35 I think our next questions get into the evidence that you have, and the findings. So let's talk about those. So you listed the questions. So what's the evidence? And what are your findings? 10:50 As Christy mentioned, we had sort of two main questions we were wondering about when we looked at our data. So first, we were wondering what were pts initial skills and creating these reflective hypotheses that can link teaching moves and the student learning outcomes? And then secondly, we were wondering how the structure of our assessment might impact PTs and management of those skills. So I can talk a little bit about our first research question, we found a lot of pretty promising results that indicate that pts do have some ability to link teaching and learning through their productive hypotheses, even before they've had instruction about how to do this. So for example, all 16 participating prospective teachers wrote at least one hypothesis out of there four opportunities to do so that linked a teaching move and a student learning outcome. And a total about 72% of all the hypotheses contained at least an implicit link between a teaching action and student learning. So just for an example, one prospective teacher said, Sasha could have struggled because Mr. R explains that the numerator is how many pieces you take out, and the denominator is the fraction piece we should use. So it makes sense that Sasha would count up the pieces this way. So this gives a pretty like specific link between something that the teacher did, and next part of his explanation, and then what she did when she did her work. And that would make a little bit more sense if you had the transcript in front of you. But it sort of gives you the flavor of what a linking hypothesis might look like. And other about 20%, that didn't include the link, they either evaluated only the teacher action in isolation from its effect, or looking at student thinking, also sort of in isolation without thinking about what might have caused it. So for example, they might say like, this is a bad lesson because the teacher didn't use enough manipulatives. So that's evaluative but not necessarily analytical, it doesn't propose any consequences of that action of not using manipulatives, for example, 12:44 does that make sense? Yeah, as I'm listening to you, I was wondering if this is something that we didn't know, before your work, right, that teachers could do this before their content course? Correct. 12:56 So the only other research work that we know of that's looking specifically at pts ability to hypothesize is a 2000, I think nine article by Oh, no, I'm sorry, it's 2015 article by yay and santagata. And they looked at hypotheses that elementary pre service teachers wrote. And they found that their participants struggled much more to link teaching and learning. But they found something in common with the next result that I was going to tell you about, which is that one thing that both participants in our study and in that previous work struggled with, is being specific about the use of student evidence in their hypotheses. So almost about three quarters of the hypotheses that our participants wrote did contain at least an implicit link between a teaching and a learning, but they struggled much more and including the evidence of student thinking in their hypotheses. So I think only less than half I think around 45% of the hypotheses that our pre service teachers wrote included any analysis or reference to student thinking or just student work. So they mostly talked about struggle or confusion or correctness, very generally, without being specific about the student thinking inherent in that might have been the outcome of the those teaching moves. So that's in alignment with what Yan Santiago found as well that even when pre service teachers can write a hypothesis that contains a link, they're much less likely to be specific and analytical about student thinking in their hypotheses. And a final main result that we found about our first research question, basically just looking at what skills pts had in terms of writing hypotheses, is about the pedagogical principles that underlie those hypotheses. So in their work that sort of lays out their argument for why hypotheses might be important keyboard at all. This is from 2007, Hubert More's Burke and Janssen they say that the best hypotheses should take into account what we know about teaching and learning. So in fact, this One way that teachers might be able to use research or best practices to inform their teaching is to think about what do we know about how teaching in general affects student learning? And how can we apply that general principle to this specific instance in this class. And we found that almost many of the hypotheses that are pre service teachers wrote about 83% were based on such a pedagogical principles. So that's good, except a lot of the principles that underlie their hypotheses were in conflict with some of the things that we believe about best practices for math education. So for example, 33 of the hypotheses written said something along the lines of students didn't achieve the learning goal, because they weren't explicitly shown how to do the problems. So that reveals the sort of pedagogical belief, the clear procedural explanation is what's most important for student method learning. And this was concerning for us. Because these students were in a methods course, they were reading vanderwaal, every week, and every week, we were talking about problem solving, and productive struggle, and the importance of letting students construct their own mathematical knowledge through engaging with rich, authentic math tasks. But when pts looked at this lesson, they sort of blamed the presence of those very things for students conceptual difficulties. To us, that indicates the real importance of paying attention to prospective teachers beliefs, because it shows away not even just through how teachers do their instruction, but how they reflect on that instruction, that their beliefs really influence how they see even how the lesson unfolded. 16:32 So I'm gonna try to summarize some of the things I heard. And you can let me know, either, I'm right. So I think you said what you found is that your pre service teachers could link the student actions to teach her actions in the transcript. But some of the links were based on underlying beliefs that seem to not be aligned with the way that in math education, we think about learning these days. 17:03 Yeah, I would say that's a good summary. Okay. 17:06 So I'm really curious, because this article talks a lot about what pre service teachers can do. Before instruction. I'm kind of curious, is there any like work that you guys are doing on what happens after instruction, we actually 17:23 followed up this study with an intervention task. And that's some data that we're still the analysis of that data is ongoing. Oh, awesome. Yeah. But one of the things that really stood out to us is how teachers, it seemed that the prospective teachers who were participating, the thing that they really still struggled with was the analysis of student thinking as part of their hypotheses. So to us, that sort of points to the importance of that as being a prerequisite skill, and that maybe they needed additional experiences in eliciting interpreting, analyzing and reflecting on student thinking before even but possibly before hypothesizing is useful to discuss with them. So that's one of the things we're wondering about, but we definitely have some data from an intervention that we're still thinking about and analyzing 18:12 very exciting. Can't wait to read that paper. I want to close that with kind of two questions. One of the ideas with this podcast is that we want to start communication. And I'm kind of curious if you can talk a little bit about how you could see other math teacher educators using this assessment. You already talked about it a little bit, but maybe we could summarize. And then what you would like to hear back from them. And then the other question, and you guys can choose how to answer these, is how does this work in this specific work fit with your larger work 18:49 for us, one of those sort of big takeaways of the work, as I just described, is actually sort of less about the specific results of what pts can do in terms of hypothesizing as more just a sort of like a reflection on how important their beliefs are in informing all the stages of teaching both the actual instruction but also how it informs their reflection on teaching. And second, how noticing and analyzing student work appear to be a prerequisite skill for hypothesizing. So for me, one of the big takeaways that I take from this article in particular is that those two areas of the research base that we know are getting a lot of attention, it points to how important they are. And in general, if we want to build on PT skills, it's really important to know what prospective teachers can do coming into their program. So just as we if we were designing a math lesson for kids, we would want to understand their background skills and understanding, we should take the same approach towards our prospective teachers. So this fits in with all our other work and thinking about how to help prospective teachers leave their teacher education program just being more reflective and better able to learn From their own teaching over time, so if other people are doing intervention work about teacher noticing, analyzing evidence of student thinking, and then in particular using those analysis of student thinking, not just to think about sort of next steps in the lesson or sort of forward looking assessment approach, but also a backward looking reflection approach. That's where we really see our work as being useful to people. 20:26 So if I'm a math teacher educator, I might pretend to be one for a second. And I want to use this, I could just kind of either use a transcript I have or make one up that fits the content of my class. And really your intervention are those questions that you asked to go with the transcript, right, trying to link the goals to the teacher actions and the student responses with respect to the goal. So I could modify the questions you had to work for my transcript? 20:58 Yes, absolutely. And I have the feeling that you would find out interesting things, not only about your student's ability to hypothesize, but also about their beliefs about how teaching and learning work by asking them not directly about their beliefs, but asking them to write these hypotheses, 21:13 I'm assuming that you want other people to try this out. What would you like to hear back from those people? 21:21 So I can all answer that. So I think we'd be interested in two things. One, we would be interested in the way that they're what they learn aligns with ours, particularly around that beliefs piece that us that's really fascinating that like prospective teachers, beliefs that they might not share publicly, but they sort of come out when they write these types of hypotheses. And so we'd be really interested in seeing what that looked like in other contexts. I think another thing we'd be interested in is we have these four prompts. And we said, we hoped we'd discover like, which prompt worked better, and we didn't discover that we didn't really find any, like any prompt was more supportive than any other. And so we'd be interested in other people's experiences with like varying the wording slightly or varying the context slightly of the prompts in order to like figure out what does it take to support prospective teachers to do this? Well, what is like the most supportive and the least supportive context for writing hypotheses? 22:09 All right, that sounds great. Is there anything else that you guys would like to add before we close this podcast? I don't think I have anything to add. But I really enjoyed talking with you about I hope people read our article and let us know what they think I really enjoy talking to you guys to help me understand the innovation a lot better. 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.