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 Sennheiser. And today I'm talking with crystal Emily and Tracy, who will later introduce themselves be discussing the article, support and enrichment experiences in mathematics, CT math using case studies to improve mathematics teacher education, which was published in September 2021 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. Krystal, Emily and Tracy, welcome to the podcast and can you please briefly introduce yourselves?
Crystal Kalinec-Craig 0:57
Sure. Hi, I am crystal Kellen and Craig. I'm an associate professor of Curriculum and Instruction at the University of Texas at San Antonio.
Emily P. Bonner, 1:04
Hi, I'm Emily Bonner. I'm a professor of curriculum instruction and math education at same place University of Texas at San Antonio.
Traci Kelley 1:11
And I am Tracy Kelly Elmore. I am a graduate candidate, and they're working with crystal and Emily for several years now,
Eva 1:22
a candidate who just learned is almost done right, revising the dissertation. So congratulations on that. And thank you. Welcome you all. Let's jump in and just start with a brief summary of the article including the results.
Crystal Kalinec-Craig 1:40
Sure. So the article that was published in math teacher educator was based on a number of years of work that we had conducted at our home institution, UTSA. And essentially, it was modeled after the program called Roadrunner readers, which was crystallized at the University of Texas at Austin. And essentially, what it is, is it's helping teacher candidates, specifically elementary teacher candidates learn how to work with a single child over multiple sessions about their mathematical thinking. So what we did is we took the teach math module, the case study module, in which they learn about children's ffensive knowledge, they get to know the child, and then they conduct a series of tasks throughout the semester with the child to get to know how to elicit children's thinking, how to encourage them to exercise their rights as learners to help them to strengthen their problem solving skills. And then at the very end of the semester, the teacher candidates conduct a mock parent teacher conference with the instructors of their math methods courses. And that's where they get to shine and show what they've learned after all of that the work that they've done with the child over the past semester. So our article details, kind of the philosophical and theoretical framework of that program. And then kind of gives a couple of examples as to how our teacher candidates have represented each one of those pillars of the program itself. And I forgot to mention C math stands for support and enrichment experiences in mathematics. So it's not tutoring, it's intended to be something that begins with where the children are, and also considers that to be the same way with our teacher candidates to begin with, where they are in their journey to learn to become math teachers.
Eva 3:22
So who is the audience for this article who should be reading it?
Emily P. Bonner, 3:27
This article is actually relevant to several different audiences, especially our colleagues and math, teacher education. So much of what we write in this article, as Crystal said, details the program. So it talks through why we're providing this type of formative field experience for teachers, prospective teachers, and how it helps them to approximate practice and a bunch of different ways. So not only are they working with one student to understand their mathematical thinking, understand the context in which they live so that they can formulate relevant tasks. And then, of course, at the end doing a parent teacher conference, which is something of course they're going to have to do in practice. So that would probably be our primary audience for this article.
Eva 4:11
So anybody who does like teacher education, math, teacher education, who wants to connect it to working with children,
Traci Kelley 4:21
I would just add to that, also, that we also over the years have seen with our integration of the case study with the other methods classes, such as reading, assessment and science that, that teacher educators and educator preparation programs would be a larger, maybe a larger audience that could really benefit from this idea of a case study for their teacher preparation. Yeah, well,
Emily P. Bonner, 4:48
let me add to that. That kind of got me thinking more. So the education educator preparation programs, for sure, could take several things away from this, but especially like I mentioned, We really want teacher candidates to build skills that they will use in the classroom. And this is a really specific and focused field experience that, again, approximates practice from the classroom. So I think it could be used in several different areas for education, educator preparation programs, but just having that experience of working closely with the child, in any subject area could be relevant, but it's a structural change to the program. It's an additional field experience. That's formative. And I think that's important, too.
Eva 5:31
So what is the important problem of practice or the issue that you address with this paper?
Crystal Kalinec-Craig 5:40
So I would say that in thinking about the teach math modules, for those who aren't familiar with teach math teachers empowered for advancing change in mathematics by a number of colleagues all across the country, they tackled the idea of the ways in which Math Methods math teacher, educators, can consider how they can make very purposeful moves in their practice through these modules to help teacher candidates to make connections between children's funds of knowledge, and cognitively got the research base of cognitive cognitively guided instruction. And so by bridging those two things together, they theorized about this idea of children's multiple mathematical knowledge bases. And so what this program does is it helps to also unpack that notion across multiple experiences. And so when we think about how does a teacher candidate learn to elicit children's Funds of Knowledge, I mean, we could just give them, you know, a list of questions to ask, and then just ask it of themselves. But that's just asking an adult, which they're probably going to get maybe similar responses. It's very different if you were to ask a kid where they like to go, what they like to eat, what they do on the weekends. And probably one of the most interesting responses, or one of the most interesting questions I think we ask is, where do you see math outside of school? And a lot of times kids say they don't. And so that just becomes an amazing opportunity for our teacher candidates to ground themselves on the ideas that yeah, maybe we as adults, we can see math everywhere. But maybe that might not necessarily be the case just yet for kiddos. And so it's taking the things that they're learning in their math methods class, and no kidding, translating that and applying that through the scaffold of experiences, so where we're not just throwing them into a classroom and say, Okay, go learn how to pose some really challenging, purposeful questions, go ahead and learn how to elicit children's funds of knowledge are, you know, help kids to encourage their rights as learners without giving them some scaffolds along the way. And so that's why the program builds over time. And it provides them with those purposeful opportunity so that by the time that they finish their semester, and they sit for their mock conference, they are cross our fingers, hopefully more prepared to be able to gather evidence to be able to analyze evidence across multiple experiences, and then be able to put their own finishing touches on whatever that mock conference product comes to be, in terms of how they're going to communicate to a parent, which is something that is real life, purposeful, something that they're gonna see once they go out into the practice. And so all of these are authentic experiences, besides just saying, Good luck, go off into the field experience. And there's not any type of structure that comes with it from their methods, instructors.
Eva 8:34
So let me try to summarize some of the things I heard and then see what I didn't hear. It seems like there's two big themes. One is to really connect the learning in the methods worse to some real experience, in this case with a child that's either is pushing beyond the exclusive focus on context free mathematics, to bring in other knowledge bases, as they're working with the children.
Crystal Kalinec-Craig 9:10
Correct, which is the nice, I think, opportunity that we have that we have reading, science, and an assessment class, all taken right now within the same block of courses. And so to be able to make connections between math and science, we have that in our community Math, Science session and C math, to ask kids or to ask Teacher candidates to go out and select a children's book that's appropriate for their child and then use that as a launch to do a math task. There's tons of research that's, that's out there that talks about ways in which teacher candidates or teachers can do this. And so then at the very end, we also have them do an engineering projects where they kind of completely strip away all of the traditional notions of mathematics. And we just hand them a set of materials and say, try to make a tower as tall as you can or try to make a catapult and launch this piece of candy across the room. And so I think we start to get even closer to helping them to see mathematics in more concrete ways that they can translate in between the school and the home a lot more fluidly.
Emily P. Bonner, 10:14
I hope, I think, another thread running through this that I think is crystals touching on but it's not as explicit, but it's definitely a focus of ours. And another problem of practice, it's kind of embedded in the major themes that you're discussing, is trying to also view students in a very asset oriented way. So thinking about what student what funds of knowledge they're bringing to the classroom, of course, we talked about contexts and making tasks relevant, even building on like a more culturally responsive type of practice where they're putting the relationship with that student at the forefront. So through this experience, that not only benefits the teacher candidate who's learning how to teach through problem solving, and this really meaningful, but somewhat structured experience that's supposed to be an impactful, you know, field placement type thing, but also the student they're working with, we hope isn't in our data show is experiencing some kind of identity bolstering in math through this whole process. And they're building a relationship with their see math tutor. And that seems like a really powerful thing too. So then students move our students moving forward, that prospective teachers see the value of building relationships with students and communicating with them and effective and culturally responsive ways. And then using what they know about students in their instruction. So all of those things kind of underlie what we're doing, and have been a huge outcome from this program.
Eva 11:31
So this leads me into the next question, which I think we already talked a little bit about, What work does your work build on? And what particular theories are you drawing on? Is there anything that you want to add to what you already said,
Traci Kelley 11:48
I might just add that my area of passion is really in teaching mathematics, with and family engagement. And so not always and in every context in which we've been able to do see math, have we had direct content with caregivers of the of the C math children, that we have been able to do that? At our downtown campus, we were actually able to talk to the parents as they came with their children. And they brought them to the C math environment. So our students had an opportunity that is very seldom found in teacher preparation, where they were actually able to do weekly communication with a parent of a child, and learn that these are resources and assets for them as teachers to build these relationships with families. And I love that spin. And especially for our Latin X teacher, student teachers. I don't believe that it's often that they that they're told or that they're reinforced that their families and their culture, have assets and resources that should be brought into the instructional environment.
Eva 13:05
So let's keep in mind that our listeners have not read your paper. Can you describe the innovation in a way that we could imagine what exactly it looks like? Then once you did that, how it addresses the problem of practice.
Crystal Kalinec-Craig 13:23
So if you hadn't read the paper, something that we might consider is maybe what traditional mathematics methods courses look like, it would be you probably come to class, you might read out of whatever popular Math Methods textbook, you might do a couple of problem solving tasks, you might, you know, watch some videos, you might think about, you know, the different theories of funds of knowledge. But then there may or may not necessarily be connections to kids in the community, maybe not even until you get to student teaching. And so, if we think about trying to pull together even closer, on almost a week by week basis, in terms of what you're learning in class, with the ways in which then you can go out and practice this and test this and hone your skills and hone your noticing skills with a child in the community. So where you build those relationships as you're taking your course, because your instructors are very much invested in not only your education, but then reinforcing what Bonner had said or building on what Bernard said, but then also playing a role in supporting a child's education and a child self concept as to how they see themselves smart in math, then what C math does is it just provides kind of like a framework or an idea as to how we can make those connections even stronger. So we've already published a set of curriculum materials that the AMT supplementary materials group went ahead and requested from and so that's publicly accessible if you happen to use those materials. Just Make sure that you cite us, which then means also, you should be citing tons of things by teach math by Louise mole and Martha Seville and the rest of them. There was amazing scholars. And so if I may
Eva 15:11
interrupt you for a second, as I'm trying to envision this, like you're teaching a methods class, how and where are they meeting these children?
Crystal Kalinec-Craig 15:22
That's a really good question. So it depends for us. Whenever we would teach our classes out at the elementary schools, we would stop our classes early, and then walk from whatever class we were in, whether it was a portable ad on the baseball field, or whatever, and then walk into the main building of the school, to then go and collect the children to bring them back to our methods class, work with them, and then re deliver them, bring them back into their classroom, then we would do that on the elementary school campus. But then we also had opportunities where we would bring families on to the UTSA, downtown campus where they would pay a very small fee for a parking pass for about an hour and a half, two hours. And they would get the experience of being at the downtown campus amongst all of the college students there where they would have
Eva 16:10
their clients know, I'm imagining being a method instructor and wanting to set something like this, how do I find these people who are willing to bring their children? I'm imagining those are even in classes, right? Because you can pull them out of schools. So how do I go about doing that?
Traci Kelley 16:30
Well, I did a lot of the recruiting for the C math program at the downtown campus. And it was just amazing to me working through our community school partners at the, at the elementary schools where we had filled experiences already and we establish relationships, I was just able to tell a little bit about the program. And parents were so incredibly excited about the fact that they could provide this extra opportunity for their students, they went to a lot of trouble to get to a busy downtown location at 530. In the evening, once a week with our kids, they really, really want their children to have these opportunities.
Eva 17:13
So going to schools and talking to schools is a good way of working with that. Often there's a struggle on how do I do this. And if you're lucky enough to have your own children, like I've always just brought in, like, my kids, friends, or like my friends, kids and our friends. But I think like if you don't have that access, then just going to a school and talking to them, I have found usually leads to an interest. But sorry, Emily, what we
Emily P. Bonner, 17:45
that's okay, I was just gonna say, well, first of all, I think that's funny, you said that because I've tested a lot of our curriculum materials on my children have lots of videos and stuff of them doing CGI tests. But we're fortunate because our university is pretty embedded in the community. And so there was definitely a building period, it didn't just happen overnight that we and it's still you know, that right before the semester starts, there's always like a kerfuffle around who's going to be working with who and where are they going to be. So it's not seamless, but it definitely helps that we have a leadership program here. That's really strong. And so we know bunch of principals and administrators around the city, especially in these kind of higher need areas, which is where we want to be. And we also have a lot of former prospective teachers who are now practicing teachers who are willing to have us not only in their classroom for field experience, but also to help us recruit for C math. And so that's another great resource for people to use is, because a lot of I don't know if it's like this everywhere, but in San Antonio, a lot of our teachers just kind of go back to the communities where they live or grew up. And so that's a good resource. And it just benefits everyone. And it's such a nice full circle moment when that happens. But build keeping those relations, maintaining those relationships. So treating them well. Really trying to adjust and adapt based on what the students need and making sure that these experiences within our curriculum, stay scaffolded so that our prospective teachers know what they're doing. They are very directed in terms of what they're doing based on what the student needs. So they're doing like a, you know, these pre interviews, the cognitively guided interviews, to determine what kind of tasks they're going to then implement, and we do those in class and then they do them in C math, and then eventually doing bigger project based tasks, and then at the end, doing this mock conference, so just trying to respond to the needs of the community and then maintain those relationships does help but there's definitely a building period. That's
Eva 19:38
again, Oh, it sounds like you're starting with some assessment that you provide to the previous service teachers that then they assess the child that they're working with. And then the following meetings, are you providing the tasks or how does that work? So
Emily P. Bonner, 19:55
we do have a whole curriculum for each week laid out but we have found not the best approach is to be a little bit flexible based on what the students need. So there's a general curriculum for the week for that hour for that week. But the tutors definitely have the option to adjust and adapt it to what the students need. Or if they need to like if the student is absent one week, then we have to figure out, you know, do we just jump to the next week? Or do we go back to the task, they missed? Things like that? I think our main goal is to provide resources and structure that builds the curriculum over time. But within that there's a lot of flexibility.
Eva 20:33
And that is all accessible either through the article, or through the links to the resources, correct. Okay, correct. So let's move to the research question. What was your research question that you wrote about,
Crystal Kalinec-Craig 20:47
we wanted to see the ways in which teacher candidates can learn through the CMF program to elicit and incorporate children's sense of knowledge into mathematical problem solving tasks, to strengthen children's problem solving skills, and to encourage children's rights as learners. So they have the right to be confused, they have the right to claim a mistake that the right to speak, listen and be heard. And they had the right to do right and represent what made sense to them. And so through those research questions, we took a look at our curricular program. And I went through a lot of materials from all of the mock conferences, and pulled representative example pieces of those materials that really showcased and highlighted the ways in which teacher candidates do this. An example of one of those was, I think her pseudonym was Miss Alicia. And she was working with Valentina, a young child who was a recent immigrant from Mexico. And she had heard that Valentina had just moved from Mexico and was really missing her home. And so Miss Valentino also who had fam or sorry, Miss Alicia, the teacher candidate also had family from Mexico and so knew how to make these connections to Valentina. And so in addition to some preassessment, problem solving in are some pre assessment questions that were in Spanish in terms of like skip counting, can you shade half a triangle, can you do some introductory type CGI problems, then she moved on to doing something like a scavenger hunt with Valentina and looking for certain shapes around the room that they were at. And then as CMF progressed, they came up to the community math exploration task. And then that task, the rest of Miss Alicia has peers and the math methods class really wanted to focus on a bingo hall that was just down the street from the elementary school. And Miss Alicia was super excited about that. But she's like Valentina doesn't necessarily know what a bingo hall is, or what the game of bingo is, but she knows what loathe that is, which is a similar game in Mexico. And at the very end of that game, when you when you say why maths, and so she made her a lottery, a game that had different coins on it. So where she would have to match up the numbers with the coins, she would have different fingers up like a photograph of a hand to show how many fingers there were, and then maybe a numeral of three to show three fingers. And so Miss Alicia saw that by asking Valentina about the experiences that she that she had, that she really missed and being in Mexico and kind of how lonely she was, and also in seeing Valentino's amazing mathematical strengths. But that weren't always necessarily brought to the forefront, because she was still trying to learn English at the time. And so she was still learning to make that bridge between her mathematical knowledge in English and Spanish, Miss Alicia was able to make this really strong, amazing connection to Valentina. And so I was there in the room, and just watching her play, the game just like brought tears to my eyes. And so that was a moment in which I could see our teacher candidates could make these really strong connections between just uttering the word funds of not or the phrase funds of knowledge in some type of a term paper that they might right, but actually literally manifesting that in a task that can make a child's face light up, I think that there is something so purely amazing about having that opportunity to witness something like that. And so that was one of the things that we had written about in the paper was the way in which we unpacked how Miss Alicia really elicited that knowledge from Valentina, and then translated that into all of the tasks that she did with the child over the course of that semester. And it was great. They had an amazing time together. And we went back to that school for a few years after that, and Valentina would not stop talking about the look that he had gained because it made such a powerful impact. And so when teachers can when teacher candidates can see the powerful impact they make on kids, whether it's one session or eight sessions that I think is going to be an emotional experience and an emotional response that will hopefully translate with them once they graduate and have their own classrooms.
Eva 25:11
So another thing you wrote about were these Venn diagrams. Do you want to share a little bit about those? Yeah, sure.
Emily P. Bonner, 25:19
So the Venn diagrams are the very first thing that our C math tutors do with their students the first week, and it's really a getting to know you tool. So the idea here was that a Venn diagram provides a place where they can list and talk about things that they have in common, and things that they're interested in that they might not have in common, of course, just as a, you know, double Venn diagram. And then also, of course, then the student is learning something about a mathematical tool. So it's kind of you know, accomplishes both goals. But what we found with the Venn diagrams is that the teacher candidates use them throughout the semester, and they continue as a pair to come back to them and revise them based on student interest. And if the students like, Oh, I thought about this other thing that I wanted to talk to you about. So again, it really gets it that those notions of learning about what students know and like and value and using that in your math instruction, and then also finding those commonalities to build relationships. And we have some that are, there's a couple of examples in the paper, where you can see kind of like the illustrations that they do, we've had some just really incredible outcomes from that. And like I said, I think the teacher candidates really learn a lot about the students from doing that. And the students find it a very accessible math idea. And we've actually had some semesters where we have one, tutor well, both ways like either one tutor working with two students, if we got too many see math students, or we've had like, if a student is absent, then we'll have two tutors working with one student. And so they might do like a three way Venn diagram. And that opens up a whole nother conversation, and they can show it to the people around them. So it's just a really nice, it's really simple. It just takes like a piece of paper or but we use butcher paper and markers. And that's it. So it's a really effective and powerful way to just start that conversation about, about student interests.
Eva 27:12
Yeah, I really enjoyed that. And also, in the paper, you trace kind of the evolution of those. So we don't have to touch everything in here. But that's really worthwhile looking in there. Let's kind of summarize up what, what would you say is the new contribution that your article makes to the field,
Crystal Kalinec-Craig 27:35
I would just say that teacher candidates can learn and do great things. And when they're given multiple opportunities, to test and revise, and to make new connections to knowledge that they're learning in their class that they're learning in their broader field work. And when they're given opportunities to work and build a relationship with a single child, then I think that that really does start to lay the foundation for the ways in which teacher candidates can extend this across their practice more broadly for whenever they think about whole group settings. And we know that multiple scholars have talked about, you know, kind of the ground up work about doing this, this just happens to be our take on the ways in which we can help our teacher candidates to have it firmly embedded in our course. And it also extends the research base of the teach math group, so where it's beyond a module, and so where if we like pull the accordion of that module out into thinking about it as a curricular package from start to finish, both for the child and for the teacher candidates, and for them and the math teacher educators as maybe a tool for assessing teacher candidate knowledge. I think that that just kind of helps to hopefully push our field in a way so where we can consider these ideas as coherent across a semester, and also within each single week that they're there in that math methods class and engaging the child in these ideas. I'm sure my colleagues have some other things to add to.
Emily P. Bonner, 29:11
I do, I was thinking, to me this the whole just the whole SEMA program is a very specific practice based example of how a purposeful field experience can lead to really effective teaching practice. So again, I mean, just echoing what crystal said about what they're learning to do, and how to like how they're learning to teach through problem solving in this context, that's a really purposeful field experience. And then also though, being able to develop those skills that we don't usually touch on in teacher education, so we don't touch on them in a field experience kind of way. So Asset Based Thinking is at the forefront the relationship building we talk about a lot, but this is a way where they have to really do the work to build that relationship and see how often activities. And then lastly, the mock conference, I think is a really effective approximation of practice. Because I mean, as a parent myself, I really value that 10 minutes that we get right with our, with our child's teacher where they're trying to cram everything in. And so giving them practice, just honing that skill of not only explaining to a parent, what their student understands and what they might, what their next steps might be things like that. But keeping it positive, like that's what I always emphasizes, how can you I mean, this is my child, you're talking about, like, keep it positive, how we use these asset based sentence frames just to give them structure around this, but really developing those practice base skills. I think this really adds to that literature in terms of having a real example of that.
Eva 30:43
Well, this kind of brings us to the end. I did want to open up and ask if you want to add anything before we close out? I don't think so. That just means I'm a brilliant interviewer and everything I read, thank you so much for coming on today.
Emily P. Bonner, 31:04
Thank you for having me. Thank
Unknown Speaker 31:05
you, so it's fun. Thank you so much. It was really fun.
Eva 31:10
For further information on this topic. You can find the article on the mathematics teacher educator website. This has been your host, Ava Sennheiser. Thank you for listening and goodbye.
Transcribed by https://otter.ai