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 a whole group of people, Stephanie, Brett, Gladys cloudier and Jen, and we will be discussing their article design principles that support course design innovation for elementary math methods courses, published in the September 2022 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. Stephanie, Brett, Gladys, Claudia and Jen, could you each briefly introduce yourselves?

Unknown Speaker  0:55  
Sure, I'll go first. I'm EVO Kia Stephanie Sackler Rudy's.

Eva  0:58  
Do you want to say where you're at and give a little information about yourself? Oh, sure.

Speaker 2  1:03  
Okay, so yep. So I'm Stephanie, and I'm at University of Cincinnati, and I am an assistant professor of mathematics education.

Speaker 3  1:11  
I'm Brett Gardner, and I'm at the University of Denver. I study math teacher learning in the curriculum industry and instruction department.

Speaker 4  1:21  
I am guys Kraus and I am an assistant professor of mathematics education at William and Mary. And my work centers on the intersection of multilingualism and mathematics.

Speaker 5  1:35  
I'm Claudia Burley Smith, I teach in the School of Education at California State University, Chico. And I do a lot of work with pre service teachers in investigating their experiences and how it links to their teaching as a future teachers.

Speaker 6  1:54  
I'm Jen Munson. I'm an assistant professor of Learning Sciences at Northwestern University. And my work focuses on mathematics, teacher learning, and how interactions support learning.

Eva  2:04  
Well, welcome all of you. I'm so excited to have such a big group on the podcast today. So let's jump in and get started. Can you give us a brief summary of your article, including the results?

Speaker 3  2:18  
Yeah, totally. And so we came together as a group of star fellows in the summer of 2018. And we came together around this shared problem of practice of not having enough time in our elementary math methods courses, we started a collaborative self study to figure out like, what do we do when we only have one class to teach all of the content and methods for free service elementary teachers? And how do we how do we navigate these tensions, we identified three key tensions that we faced. The first is finding the time to teach both mathematic, mathematics content and mathematics pedagogy. The second was connecting theory and practice and helping pre service teachers bring what we are teaching in the classroom into their student teaching context. And then the third is promoting social context and teaching mathematics. And really finding the time to address that meaningfully amidst all the other things that we're also teaching. And as we collaborated, we shared a lot of ideas for what to do, we talked about the shared problems of practice, met regularly for over a year discussing our teaching. And we generated three design principles that we've applied to our elementary methods, courses, in different ways. So the first design principle is creating multiple goals for each course component. So we can really like leverage each thing that we do, to make sure that it's achieving multiple things. The second is developing pre service teachers dispositions over time, and really taking seriously the key dispositions that we want our pre service teachers to develop, and embedding that throughout the course rather than just trying to teach it all in one day. And then the third principle is building on pre service teachers strengths, while also addressing the need for math rehabilitation. And so really trying to elicit what they know and understand and have experienced, and then building on that to support their learning. And in the paper, we talk about a couple strategies that we've implemented in our classes for each of those design principles.

Eva  4:25  
Thank you. That was a lovely summary. I read that paper last night and paper is full of so many things. So this was really a lovely, put it pulling it together. Who do you think should read this article?

Speaker 3  4:40  
I would recommend it for any math teacher educators, especially new math teacher educators. We were all relatively new when we came together. That's where I put my bet.

Speaker 5  4:50  
That's what I was gonna add to that up Brett. I was gonna add to that it's often disorientating when you get, you know, you get hired and you're new to higher ed and you get assigned this course. And then we all Rick recognize right away, there is not enough time for us to do that which we are so passionate about. And meeting this group of people right here really got me through how was I going to design this. So I still felt effective and that I could stay true to what I truly believe my pre service teachers needed. But in community and collaboration. So you'll see in the article Well, based on what we did, and working together, I use so many of these strategies and these assignments in my class, and we're constantly tweaking. But I think anyone in that situation or even if you've been teaching for a while and you want to refresh some stuff should read this article.

Speaker 6  5:40  
Yeah, I echo that we particularly came together around not feeling like we had enough time and I came from doctoral program where I had three courses that I T aid as a sequence for pre service teachers. And even then I didn't feel like I had enough time. And then I came to Northwestern, and I only had one course, I had a third as much time and I really didn't feel like I had enough time. And I imagine that that's a common problem of practice for mathematics teacher educators. So if you experience any of the tensions that we did, we hope that we have some ideas to offer you.

Eva  6:13  
And this is really a nice segue into the next question, which is, what is the important problem of practice or issue that your article addresses, we each

Speaker 6  6:23  
only had one course at the time that we came together one required course for our pre service teachers, some of us teach at schools that are on the semester system. So that means 15 weeks, I teach at a quarter system school. So that means 10 weeks, and I only have 30 hours with my pre service teachers to prepare them to teach sixth grade levels of mathematics. So the central problem here is how do you do that? How do you do all that needs to be done and do it well, and feel like Claudia was talking about that you're being effective in your job, when you don't control how much time you have with your pre service teachers, I sort of beg them to please take the elective courses, or I can teach them more things. But I only know I know that only some of them are going to do that. So our central problem here is just sort of navigating these tensions that we all have when we have a finite amount of time. And we know that learning to teach mathematics is an infinite pursuit,

Speaker 4  7:14  
these main Ishu creates order issues that we were either seen through through the paper, these three tensions that we described in the paper.

Speaker 3  7:26  
And when we first pitched the idea for this paper, some folks like we were saying, we want to write this paper, you know, dealing with having not enough time, and some folks are like is that normal, though, like to only have one class for elementary pre service teachers, like, you know, my program has three or four classes. And we're like, wow, well, that's cool. But we don't really know how how normal that is. And so we started a parallel study that with another paper among the five of us. And we found in that study that, yeah, most programs don't have nearly enough math courses in content or pedagogy, especially for certificate programs and Master's level programs, which are often much shorter than undergrads. But even for undergrad programs, a lot of programs really don't offer or require very much in a way of math for elementary pre service teachers. And so this is a pretty widespread issue.

Eva  8:25  
And, you know, I would venture to say that your argument holds whether you have one course or three, as you are preparing people for so one course is the extreme write this, but even if you have three, there's not enough time to do what you want to do. It's also an artifact of this weird thing that the United States does, where they pull content and pedagogy apart into not just different courses, but often in different departments completely separated from each other. So I know some of you guys were sharing that there's not a content course that is a requirement. So the methods really stands on its own. Or if there is a requirement, it might not be connected to the methods. So okay, so the next question we're gonna get into is, how does this article build on existing work in the field, and you guys did a lovely job in the beginning of the article to really ground your work. So I'm wondering if you could summarize a little bit of that.

Speaker 5  9:31  
I think one thing that we really connect to is this idea of how sitting in one semester or one quarter of a course where passionate teacher educators are trying to convince you that there may be a different way to teach mathematics through inquiry through social constructivism through conversations through different interpretation of mistakes and how we deal with those in the classroom through different types of lessons. When research says that often see Students will sit through that and then go into their their classrooms where maybe they're doing student teaching and watch a teacher do more the I do we do you do traditional teaching methods, and that is what becomes adopted. And because student teachers and our our students feel like they are also rushed for time, because at the same time, they're learning math or the mean literacy methods and science methods, and you know, social science methods, what we're concerned about is that default mechanism, well, you know, I'm just going to teach the way I was taught, or I'm just going to absorb and put into my practice what I see right here in my placement classroom, and I think the time issue is about helping them develop and understand a new way or strategies to be more inclusive, when you teach math to your students, and how to build in that asset space thinking and bringing all these pieces from research that talk about are really helpful for students. But sometimes we just set those aside and go with what we know. And I think this article also addresses that and gives a call for us to, you know, wake up and be aware of these things and hopefully implement them

Speaker 3  11:07  
and even more than that, but I think the that helping pre service teachers feed themselves with asset oriented thinking, and to recognize their own mathematical strengths and abilities, is a really important piece of this as well. We know that for elementary pre service teachers, many of them have had very bad math experiences while they were in school, in K 12, and even in college. And so to really help them shift their disposition to see themselves as capable and competent mathematical thinkers. And to sort of rehabilitate that their sense of self efficacy, their sense of being a math person, and their Yeah, just relationship with mathematics.

Speaker 4  11:51  
I was going to add that when we propose the design principles, and we share the examples from what we do in the classroom. We all are using work that other colleagues or people in math education have used before, but we are also using it in our own context. As we collaborate, we also modified some of the activities and ideas that have been used before, I particularly use a lot of the work from the teach math group. And a lot of the activities that I designed for my math method scores come from the work that other scholars like Aaron Turner, and Julio Geary, all of the people around it teach math group have have done,

Eva  12:39  
this is a nice transition into the next question, which asks about innovation that you created. And since in the paper, you guys divide it like it's, you guys shared what you each are doing, and was wondering if we could do a similar thing, where maybe Gladys, you could continue and sharing one of the activities that you were just leading into, and then other people could jump in and share. Like maybe one example each, so we, and then potentially related to the design principles,

Speaker 4  13:11  
one of the theories that I use in my math method scores, and the very beginning of the semester is the math out choreography. And as I mentioned before, it comes from the teach math group or whatever, what I'm using comes from, from the teach math group. And one of the reasons why I continue to use this activity and I like it a lot is because it gives me an idea or teaches me a lot more about each one of my students, they share a lot of their experiences, learning mathematics, and I can use these experiences throughout the entire course, to talk about their learning experiences and the learning experiences of their students, and how can we use their own experiences to inform our own practices. So it's a beautiful way to get to know our students, our pre service teachers.

Speaker 6  14:09  
I've also used math autobiography that Gladys just described for the same purposes. And it is this idea of building pre service teachers dispositions over time, you have to know where you're beginning so that you can continue to draw on those dispositions and disrupt them where it's necessary. And as an extension of that one of the activities that I described in the article is one that meets the same design principle is one that I call fascinating student thinking. And my students are all in an observation placement concurrently with the course. And so their job is to be in the classroom and to watch students at work rather than to teach and so I want to send them into the classroom to expect that students mathematical thinking is fascinating, and that it is fascinating all the time happening around them and that their job is to go and find it. And I want to position them with the disposition to believe that student thinking is fascinating and that every student has fascinating thinking to marvel at. And their job is to bring at one point during the quarter, an example of fascinating student thinking back to the classroom to share. And we talk about it. And I saved the first 15 minutes of every class for people to bring in fascinating student thinking and to share what fascinates them for us to marvel at kids thinking, and then to have conversations that emerge from there, which sometimes help us to weave in content. Sometimes it helps us to talk about emergent issues that come from placements, puzzling things like how assessment works, and school policies that affect the way that students get particular kinds of grades, or why teachers responded in the way that they did to something that my pre service teachers find fascinating. And just to cultivate the disposition, that it is fascinating, and rather than to go in with an evaluative lens, and it takes a great deal of practice. So doing it, having it be a consistent expectation across the quarter. And having practice being fascinated by one another student thinking in all different grades, accomplishes quite a few goals all at once.

Eva  16:11  
Yeah, and I really enjoyed in the paper reading that piece, because you build on our extensive knowledge of noticing in mass education, and then push towards, like, I love this idea of fascinating and the acid base, like, how do we take what the child did and look at the strengths in it right, rather than saying this is wrong. So I thought that also,

Speaker 6  16:39  
how do we get comfortable with ambiguity to like, it doesn't have to be right to be fascinating. It can be fascinating in the in a mistake, or even that it's puzzling in some way. And I want them to develop a disposition to be comfortable with that ambiguity. And to still find it fascinating rather than for it to be a condition that they kind of resist or afraid of, that I don't know what to do, because I don't understand thinking, like, let's live in that ambiguity and find find it interesting. Rather than frightening.

Speaker 5  17:09  
I'll add to speed, the gift of this collaboration has been taking things and adapting them. And I do the fascinating student thinking in my class. And just last week, as a among pre service teacher English as a second language, she shared a fascinating student thinking and it was a it was in a multi language learner who is processing a problem. He did one thing, and she goes typical English learner. And I said, What do you mean, typical English learner, what? And she said, Don't you see how he I wrote the problem for him. He's rewriting it. And what he's doing when he's rewriting it is he's rewriting it in his own language, so that he can transfer it into another language. And that is the process. And we she had an opportunity to also explain that since she's an English learner, she translates everything back into Hmong. And there's a delay, you know, so anyway, this was a beautiful opportunity based on what she found fascinating in her hers in one of her students. And I felt like that was amazing that we had this opportunity to learn and listen and hear that experience and highlight her and lift her experience up as the as the, you know, the teacher in the class. And so I love the fascinating student thinking. So I want to thank Jen publicly right now for sharing that.

Eva  18:29  
Sorry, I want to thank Jen too, because I will be using this in my own teaching, and all of you like there are so many good ideas.

Speaker 6  18:38  
Okay, the thing is, it's like it's joyful like that. I think one of the things that I really love about the ideas that we've cultivated together is to is to cultivate our joy for being in the classroom with all the tensions we experience, like these are moments to be joyful, and to celebrate children to celebrate our pre service teachers. To celebrate what it means to be in the classroom, we've gained a lot from being able to navigate the tensions and not just become more efficient at our jobs, but to do so in a way that honors the Joy in Teaching so that we can make sure our pre service teachers leave us feeling that teaching is a joy and not just something that has to be managed.

Speaker 5  19:19  
And one of the tensions that we have and we write about in the article, it's it's K six, sometimes K eight span. And when we do fascinating student thinking all of my students are seeing a kindergarten example, a TK example than a sixth grade example than a seventh grade example. And you can just see, depending, you know, if they're working with kindergarteners, when they see what fifth graders do, they're like, Wow, that's a big jump. And so it just gives you an opportunity. You know, just emphasize like the learning trajectory of our students and what's going to be happening to them after they leave kindergarten or how, how grateful we are to kindergarten teachers for all the counting they do with The students, you know, and it just builds a sense of community as educators, which is awesome.

Eva  20:04  
So I'm wondering, there's a few more examples, right that we could hear,

Speaker 2  20:11  
yeah, I can, I can share mine. So I talked about the micro teaching and, and those kinds of assignments I know are like are quite common among in methods courses. But basically what students do is they, they choose a math task that they think will be challenging for their college level peers. And then they design a teaching through problem solving lesson with the before, during and after. And then they implement it during class, wearing the hat of teacher and their, their peers are truly their students. And then they have the opportunity afterwards to receive feedback from their students who are also their peers. And students just they love that experience, I think for two reasons. One is it builds their confidence as doers of math, as they have just many opportunities over the course of the semester, to engage with math tasks that are challenging than to it gets them more comfortable with reform based pedagogies teaching through problem solving, which is just so different than how many of our students including myself, learned math, that's been an overwhelmingly positive experience for my students.

Speaker 3  21:18  
And another strategy that we talked about in the paper that I've picked up from Stephanie is the of math journals, and having a weekly Problem Set basically, for pre service teachers to work on. This was like a total game changer. For my class, that's only 10 weeks, because we're on the quarter system at d u. And so to be able to have students solve some problems related to the content for that week, and then turn it in before class that allows me to sort of have a formative assessment of where they are, what they're thinking about what's been hard for them. They'll write in the journals, things like, oh, I don't really get this strategy for dividing whole numbers, or can we talk more about denominators and what that really means. And so and then that helps me shape the lesson for that afternoon, to make sure that I can really support their learning and their thinking. And so to be able to elicit that beforehand and use that in class that day, has really helped me build on on my pre service teachers thinking,

Eva  22:25  
all right, thank you so much for sharing some of what isn't a paper has a bunch more examples. Our next question jumps into, it's kind of the what research question, Did you study? Or how do you know that this, what you've been doing has been effective?

Speaker 3  22:44  
So how do we know that what we've been doing has been effective? I mean, I think for me, the biggest proof has been in my own class. And when I get feedback from pre service teachers saying that like, oh, doing the fasting student thinking every week that has really shifted how I think, or doing the math journals, that's really helped me make connections between the reading and my own mathematical sense making process. Doing the math autobiography helped me understand more about where I'm coming from as I entered the teaching profession. And really just seeing that in, yeah, and feedback from students. And in the way that the class goes,

Speaker 4  23:24  
I agree with what Brad just said, one of the things that I do, and that is described in the paper, too, is the problem solving unit. So students that pre service teachers start building, or developing a unit from the very beginning of the semester, they start connecting with a student talking to student like establishing a relationship with a student. And they start using that through the entire course to design problems and analyze the way the student is thinking or solving the problem. And seeing that shift throughout the semester is a way for me to see how students are developing their instructional practice. But the other thing that I wanted to say and I think is described through different parts of the the paper is, for me, this collaboration, talking to all of you and working with all of you like I see my own growth also, in my practice, and also, if I have a question on or I wondered about something, I also know that I reach out to them and we talk and we can improve or think in different ways. And to me that's a really important aspect of of this this work.

Eva  24:49  
Yeah, I was thinking while I was reading that paper, that there's really different levels. There's the level of all the things that you do in the classrooms that people could potentially now or also take on because you now include us into your group, right by sharing with everybody. But there's also this community that you have formed. And then you did a self study off, right? That is, like almost an example to other people to like find people, right? Whatever way not everybody can go to star star is amazing to bring people together. But even if you are not there, you know, you can find colleagues, you can read, reach out on social media, you don't even need to be in the same place. But having some people to talk to and implementing the same things, has been like really helpful for myself as well. So, so it's really like a double layered paper that you're presenting, the five of us

Speaker 6  25:51  
teach in four different time zones, in very different types of institutions. And I think that there's a temptation to believe that you need to learn from somebody who teaches the same course that you do, or that is in the precisely the same context or teaches, even teaches the same in the same type of program, like a master's program, or an undergraduate program or a certificate program. But the truth is, I think it's the diversity in this group that has taught me so much about both kind of the tensions that we share, and has opened up a lot of different ways to address those tensions. So rather than kind of closing yourself down to think I need, I need to find my perfect person who's facing exactly the same situation as I am they are collaboration, just prove to me that it's quite the opposite. You want to kind of seek a diversity of voices and people who are in lots of different situations. And that's how we can find really creative and innovative solutions that we can then adapt to meet our own content.

Speaker 5  26:46  
And I'm going to add that what Jen was saying, it's so important, because part of this self study was how can we do this, okay, we have to accept the time is the time and how can we do that and build right within that is developing a flexible mindset for us, as math teacher educators to not get stuck, it's status quo, or I'm only going to teach to the people at my talk to the people at my institution, it's about building that capacity. Yes, I'm going to have multi dimensional layers of everything we do in this class, every minute we spend together is going to be operating on all these different levels, because that's what needs to happen right now, in order for us to meet our goals of preparing future math teachers. And so this the self study, and also the collaboration is a way for us to reach out when we feel frustrated, to reach out when we've had such a great experience or something really worked. And that that has been it's been transformational, and pretty phenomenal that we can get to these places where in our own work, we're using that flexible mindset, and we're applying these things and we continue to shift and change as the needs arise.

Eva  27:57  
And if I remember correctly from reading, you guys met once a month for like 90 minutes. Is that correct? Yeah, that's, that seems a reasonable time that one could put into something like this, right? It wasn't too overwhelming.

Speaker 3  28:11  
And it's also it was also really fun. Because I mean, I think it's clear at this point, like we're we're all friends, we've developed this collaborative community. And so getting to see each other, and to talk through things has been just really generative, as like, professionals, but also as human. So to

Eva  28:29  
close out, we asked the question, and this is going to be hard. But you'll have to figure out how to answer this once the new contribution to our field that you're making. And I'm saying it's hard because I feel like there's a lot of things that you're contributing. But if you're thinking about it, from all of this experiences, what are the things that you're sharing that are new, or new ish? For math, teacher educators,

Speaker 2  28:58  
like just one thing that comes to my mind is the reflection tool at the end that feels a little bit novel? So at the very end, through the collaborative self study, we developed a reflection tool for other mathematics teacher educators to use to reflect on like, what are the tensions that I am facing? Like, are they the ones that we present in this article? Are they different time related tensions? What are the ways that I'm currently trying to address that? Do I feel they're effective? And what are other things I might do? So that's like, that's one thing that comes to my mind.

Eva  29:33  
Yeah, I'm glad you mentioned that, because that's a powerful tool that we haven't really talked about yet in our podcast that you introduce at the end, and that's available for other people to use.

Speaker 3  29:45  
Yeah, and I think another contribution is really showing how we adapt like how we've how we've shared our ideas, and how we've adapted them to each other's context. So we describe a few different points where Claudia uses instead of a math autobiography, it's a dear math letter, and where I've taken up Stephanie's math journals, but implemented them in a way that fits my context. And so really trying to be transparent and thoughtful about how we're sharing ideas and translating them into context, to help other math teacher educators think about ways that they can improve their practice and surely learn from one another.

Speaker 6  30:27  
I also just think one of the important ideas is that we can do a lot in our courses, if we're having our work serve multiple purposes at the same time. Um, rather than it just being we need to do more and cram more in it's how do we do this in a way that's multi layered, and complex, and allowing different students at different moments to be learning different kinds of things about themselves about the teaching of mathematics and about their students, kind of all at once. And I think that's how we do justice to the rich work of math teaching. And the rich work of teaching future math teachers, is by rather than decomposing it into lots of bite sized pieces that we don't have room to cram in, is to think about all the different layers at once. And to devise ways of doing that, and the ways we've put in to the article are just some of the ways that we have so far figured out how to do that. But that there are lots of ways that we believe people are already doing this. And and that's part of the reason why the reflection tool that Stephanie mentioned, starts with what are you already doing, because we believe that people are already trying to grapple with exactly that problem, and may not even completely explicitly know all the complexity that they're already doing. And that they may have things that they can share with colleagues, rather than only needing to solve problems that they may have solutions.

Speaker 5  31:50  
I think something to that unique is built within the design principles is this idea of justice, justice for our students justice for the students, they will teach one day, and it's foundational, and it's foundational for all of us. And what I really love about this work is we set those design principles. And then we also share specifically how to do this in your class. Try it, you know, and I really like this article for that reason isn't in that someone could walk away. And they're also part of our collaboration, if they take one of those pieces and tweak it and do something new, or leverage it in a way that's fascinating, and create, you know, create something that puts multiple, multiple layers in more than we had even envisioned. So I'd like that we share specific examples for people to walk away and try. And we're promoting that collaborative environment among higher education, which is often not always the case. And so I think we're pushing forwards, maybe some new ways for us to think about working together.

Speaker 4  32:51  
I love what everybody has said. So I'm not sure if I have more to say bad follow into what cloudier was saying, I hope that we have inspired all their math educators to go and try these things, and then share with the field, what they did and when they found and a new ideas or new ways to implement these or other activities.

Eva  33:14  
Well, thank you all so much for coming on the podcast. I know I'm walking away with a whole bunch of ideas I'm going to try in my own course. And it's really thrilling to see that the empty journal is living up to the idea that it was founded on white, which was to share for our field to share things we do in teacher education and allow kind of larger collaboration. So thanks again for joining me today. Thank you for inviting us. Thank you. Thank you. This has been great. For further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host, Eva Sennheiser. Thank you and goodbye.

Transcribed by https://otter.ai