Rounding Up The Math Learning Center

 Education

Welcome to “Rounding Up” with the Math Learning Center. These conversations focus on topics that are important to Bridges teachers, administrators and anyone interested in Bridges in Mathematics. Hosted by Mike Wallus, VP of Educator Support at MLC.

Cultivating Positive Math Identity  Guest: Nataki McClain and Annelly Rodas
Rounding Up
Season 1  Episode 6 – Cultivating a Positive Math Identity
Guests: Nataki McClain and Annelly Rodas
Mike Wallus: Today I'd like to start our episode with a bit of a thought exercise. I'd like you to close your eyes and picture your childhood self, learning math in your elementary school. What are some of the memories and feelings that come to mind? And when you reflect on those memories, what do you think the unspoken messages you may have absorbed about what it means to be good at math were? And then maybe most importantly, how did those early experiences with mathematics shape your belief about yourself as a doer of math? Today on the podcast, we're talking about identity; specifically, math identity. What is it? And how can we as teachers shape our students' math identities. Let's get started.
Mike: Well, hey, everyone. Welcome to Rounding Up. I'm excited to have our friends Nataki and Annelly joining us today. And I think I'll just start by welcoming the two of you. It's great to have you on the podcast.
Nataki McClain: Hi, Mike. Thank you for having us.
Annelly Rodas: Thank you, Mike.
Mike: Absolutely. So the two of you are currently curriculum consultants for the Math Learning Center. And I'm wondering, before we get started with the topic of the day, can you tell us just a little bit about your teaching background and your experience in education? And, Nataki, I'm wondering if you'd be willing to go first?
Nataki: Sure. Well, I have been in education in some capacity for about 25 years. I spent 16 years in the classroom. Fourth grade was my favorite year of all time. And then I've spent eight years as a math specialist. This past year, I am now a curriculum consultant for the Math Learning Center.
Mike: Annelly, how about you?
Annelly: So I started my career as a preK teacher at a head start program, and then I moved to the New York City public school system, where I taught second grade and fourth grade. Later, I had the opportunity to work as a math coach at my own school. And I supported preK to eight.
Mike: Fabulous. Thanks to both of you. So let's jump into the topic of the podcast: Cultivating a Positive Math Identity. Getting ready for this, what I found myself thinking about is that there is so much conversation in the field right now around math identity. And CTM has position statements about the importance of supporting a positive math identity. There's a ton of research that validates that need. I think I'd like to start by just asking you, from your perspective, how would you describe math identity to a listener who's new to this conversation?
Annelly: I think that it is important to understand that math identity is our own personal view on how we engage with mathematics, right? And it has to do with our disposition and our beliefs on our mathematics ability. I know for me, this topic is really close to my own personal journey in mathematics because I grew up thinking that I was not a math person and that changed with my experiences really late in life. So it has become my mission that kids get to experience math in a different way, and that they feel comfortable engaging with mathematics.
Nataki: And Nelly, um, I have to agree with you. I share a similar experience in that, I guess in my elementary school days, I didn't think of math as something that you got to either enjoy or not. It was just kind of, it's just there and you do it and you learn it. But then in high school I did not have a positive experience. I was made to feel like math was not my thing. And so, Mike, to address that question about what is math identity, it really—to Nelly's point—it really is how you view yourself as a mathematician. And again, my experience in high school was such that I did not feel like I was a mathematician. So to everyone’s surprise, when I go off to grad school I'm studying math and now I'm working at the Math Learning Center, right? It's kind of a bi 
Learning Targets  Guest: Rachel Harrington
Rounding Up
Season 1  Episode 5 – Learning Targets
Guest: Rachel Harrington
Mike Wallus: As a 17yearveteran classroom teacher, I can't even begin to count the number of learning targets that I've written over the years. Whether it's writing ‘I can’ statements or developing success criteria, there's no denying that writing learning targets is an important part of teacher practice. That said, the thinking about what makes a strong learning target continues to evolve and the language that we select for those targets has implications for instructional practice. Today on the podcast, we're talking with Dr. Rachel Harrington from Western Oregon University about creating powerful and productive learning targets. Welcome to the podcast.
Rachel Harrington: Thank you for having me. I'm excited to be here.
Mike: Sure. So I'd love to just start our conversation by having you talk a little bit about how the ideas around learning targets have evolved, even just in the course of your own teaching career.
Rachel: I started out as a preservice teacher in the late ’90s and got a lot of practice in undergrad teacher education, thinking about writing those objectives. And we were always told to start with, ‘The student will be able to … ,’ and then we needed to have some skill and then it needed to end with a percentage of performance. So we need percent of accuracy. And so I got a lot of practice writing things that way, and we always were very strategic with our percentages. We might say 80 percent because we planned to give them five questions at the end and we wanted four out of five to be correct. And then we could check the box that the students had done what we wanted. And I felt like it was really critical. We always were kind of drilled into us that it must be measurable. You have to be able to measure that objective. And so that percentage was really important.
Rachel: In my experience though, as a teacher, that, that didn't feel as helpful. And it wasn't something that I did as a classroom teacher very often. As I transitioned into working in teacher preparation, now we have shifted the way we talk about things. Instead of saying a learning objective, we talk more about learning targets. And we talk about using active verbs that, when we phrase the learning target or the learning goal, it's using a verb that is more active and not so much ‘Student will be able to … .’ And so we might use verbs like compare, explain, classify, analyze, thinking more about that. And then, rather than thinking about an assessment at the end, with five questions where they get four correct, we want to think about multiple times throughout the lesson where the teacher is assessing that learning goal and the progress towards that goal. Sometimes those assessments might be more classroombased. Other times you might be looking more at an individual student and collecting data on their progress as well. But it's more progress towards a goal rather than something that's met at the end of the lesson with a certain percentage of accuracy.
Mike: You named the thing that I think stood out for me, which is you're moving from a process where you're thinking about an outcome versus what's the action, be that cognitive or in the way that students are solving. The focus is really on what's happening and how it's happening as opposed to just an outcome.
Rachel: Uhhm. And I feel like when I started in teacher preparation, the standards were a little more siloed by grade level. It was sort of like, this is what we do in fourth grade and it starts and ends in fourth grade. Whereas with the Common Core State Standards, we see these learning progressions that stretch across the child's whole math experience. And so I think that's shifted a little bit the way we think about targets as well and learning goals and whatever title you've given them. Now, we don't think so much as, ‘What are you accomplishing at the end of today?’ but sort 
Multilingual Learners for Success  Guest: Erin Smith
Rounding Up
Season 1  Episode 4 – Multilingual Learners for Success
Guest: Erin Smith
Mike Wallus: Multilingual learners represent approximately 10 percent of the U.S. K–12 student population. And they're the fastest growing subpopulation of students in the United States. That said, multilingual learners have been and continue to be underserved in mathematics. Today, we talk with Erin Smith, a mathematics education professor at the University of Southern Mississippi, about ways to support and position multilingual learners as competent doers of mathematics. Hey, Erin, thank you for joining us today on the podcast.
Erin Smith: Thank you so much for inviting me. I'm really happy to be here.
Mike: I was really fascinated by one of the concepts that you talked about your article. You referenced the idea of positioning, and I'm just fascinated by that because I think it has so much potential for how we support students’ math identities. Can you explain positioning and how you suspect it could impact students in the classroom?
Erin: Yeah, absolutely. So positioning is a concept from positioning theory, which was developed by Rom Harré and Luk Van Langenhove. So when we talk about positioning or a position, we are really referring to a metaphorical position that you have in a conversation. So it's not necessarily like where your body is physically present, but a metaphorical position. So in the theory, they say that your position that you have impacts what is socially appropriate for you to do and say in an interaction. So in a classroom teachers and students have different positions. Teachers can do things that students can't. They can discipline students. They determine the classroom configuration. They select the tasks that students get to engage with. And in a lot of cases, teachers also get to select who gets to speak in the class, who gets floor time. So each of these decisions that teachers make can impact opportunities for students. And so when I think out positioning in particular and how useful it can be as a lens to look at how we as teachers position certain kinds of students in our classroom, and how we can use our position in the classroom to really call out the strengths of historically underserved students in mathematics, and then use that to position them as leaders in the classroom, while simultaneously also just challenging deficit narratives about who can do mathematics, who can be successful in it. And really what does it mean to do mathematics.
Mike: You know, as you were talking, what struck me as positioning in some ways related to the status that a student either has been assigned or assigned to themselves. Is that a fair comparison?
Erin: Yeah, absolutely. So in positioning we talk about both the positions that we take on ourselves and the positions that we assign others. So there is a lot of agency in that, both from a teacher perspective—like you have a lot of agencies to think about positioning—but also students can challenge the positions that you give them. And they have a lot of agency in that. So if a teacher positions a student as lacking some mathematical competency, the student can challenge that positioning by trying to demonstrate their competencies.
Mike: It's interesting because I think when we shift this to talking about multilingual learners, my suspicion is that part of the challenge that we've had is that multilingual learners have been positioned as less mathematically competent. And the strategies that you're suggesting are actually ways that we can counter that prevailing positioning or status.
Erin: Yeah. So we, in positioning theory, talk about storylines and these stories that permeate both at a larger, broader societal level, but also at a smaller individual level. So when you're talking about these stories that already exist for multilingual learners, more broadly in more social narratives, they're often really deficitoriented. And so w 
Recording Student Thinking During a Mathematics Discussion  Guest: Nicole Garcia
Rounding Up
Season 1  Episode 3 – Recording Student Thinking During a Mathematics Discussion
Guest: Nicole Garcia
Mike Wallus: If you're anything like me, learning to record students’ mathematical thinking might best be described as onthejob training, which meant trial and error, and a lot of practice. Our guest on today's podcast is Nicole Garcia, the coauthor of an article, published in Mathematics Teacher, that explores the practice of recording student thinking, and offers insights and some principles for making them as productive as possible. Welcome to the podcast, Nicole.
Nicole Garcia: Thank you for having me.
Mike: So you and your coauthors start the article by acknowledging that representing and recording student thinking—when you're in the moment, in a public space, with students—it's challenging, even for veteran teachers. And I suspect that most teachers would agree and appreciate the recognition that this is a skill that takes time and it takes practice. What makes this work challenging and why is it worth investing time to get better at it?
Nicole: Well, so I think you said a lot in your question that points to why this is really difficult work, right? First of all, it's in the moment. We can't predict what students are going to say. We can do some anticipatory work. We might have guesses. And as we move along in our careers, we might have gathered some really good guesses about what students might have to say, but you never can tell in the moment. So unexpected things come up. Students’ phrasing can be really different from time to time, even if we're familiar with an idea. And we're also standing in front of a room full of children, and we're trying to manage a lot in the moment—while we're listening, while we're interpreting those ideas. And then we're trying to figure out: What do we even write down from this mass of ideas that was shared with us? So that's a lot to coordinate, to manage, to think about in the moment. But it's really critical work because part of our goal as mathematics teachers is to build collective knowledge, to support children in being able to listen to, make sense of, interpret one another's ideas, to learn from each other, and to build on one another. And so if we want to make that happen, we need to support making students’ ideas accessible to everyone in the room.
Mike: Hmm.
Nicole: And listening is only one part of that, right? If you think about what it takes to make sense of ideas, it takes multiple representations—those are things that we're working on in math. So we need the kids in classrooms to have access to the words that children are speaking. We need them to have access to visual representations of the ideas that are being shared. We need them to have access to the ways that we typically record those things in mathematics—the symbolic notation that we typically use. And we need that to happen all at once if we want kids to be able to unpack, make sense of, and work with others’ ideas. So it's really important work. And I think it's worth investing the time in to get better at this because of the power of having children learn from one another and feel the value of their mathematical ideas.
Mike: You know, as you were speaking, part of what I was doing is making a mental checklist from principles to actions. And I felt like, check one: asking purposeful questions. Check two: connecting mathematical representations. I mean, as you describe this, so much of what we see as really productive practice is wrapped up in this event that takes place when teachers get together and listen to students and try to capture those ideas.
Nicole: And that capturing is really important if we want those ideas to stay with us, right? Like, I think about the number of times that I've been in a discussion with a group of people—it may have been in a class, it may have been in another space—and the whole thing happens. And when I leave, sometimes I wond 
Posing Purposeful Questions  Guest: DeAnn Huinker
Rounding Up
Season 1  Episode 2 – Posing Purposeful Questions
Guest: DeAnn Huinker
Mike Wallus: Educational theorist Charles De Garmo once said, ‘To question well is to teach well. In the skillful use of the question, more than anything else, lies the fine art of teaching.’ Our guest today, DeAnn Huinker, is one of the coauthors of ‘Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K–5.’ We'll talk with DeAnn about the art and the science of questioning and the ways that teachers can maximize the impact of their questions on student learning. DeAnn, welcome to the podcast. It's great to have you.
DeAnn Huinker: I'm happy to be here, Mike. I'm looking forward to our conversation today.
Mike: So, I'd like to start by noting that NCTM (National Council of Teachers of Mathematics) has identified posing purposeful questions as a highleverage practice in ‘Principles to Actions,’ and then again in 2017 with the publication of ‘Taking Action.’ And I'm wondering if you can make the case for why educators should see purposeful questions as a critical part of this practice.
DeAnn: Yeah, certainly. Let's just jump right in here. As we think about purposeful questions and why we as teachers need to be more intentional and strategic in the questions we use … I was honored to be a member of the writing team for ‘Principals to Actions.’ And in writing that document, we were really tasked with identifying a set of highleverage teaching practices for mathematics. We reviewed the research from the previous 25 years ( chuckles ), and it was really clear: There's been a lot of research on teacher questioning. And what are the characteristics of effective questioning. So, as I think about making this case for purposeful questions, a couple things come to mind. First of all, researchers have estimated that teachers ask up to 400 questions each day in the classroom. I mean, that's more than one question every minute for the entire school day.
Mike: That's incredible ( sniffs ).
DeAnn: ( chuckles ) I know. That's a lot of questions. Also, if we think about it, it's not just how many questions we ask, but what questions. Because that depth of student learning is really dependent on the questions we ask them because our questions prompt them to consider and engage with the specific mathematical ideas that we're helping them to learn. The other thing I'd like to add to this, is that our questions also set the tone for what it means to learn and do mathematics.
Mike: Hmm.
DeAnn: Are we asking questions about getting answers or are we asking questions that let students know we value and respect their inquiries into mathematical ideas into problemsolving, and that we really are about helping them make sense of mathematics? I think it's essential that we critically examine the types of questions we ask and how we can use them to best serve our students.
Mike: That's a really interesting way to think about it. That the questions we ask are really signaling to kids, ‘What is mathematics?’ In some ways we're informing their definition of mathematics via the questions that we ask.
DeAnn: Yeah, I absolutely agree with you.
Mike: Well, I think one of the most eyeopening things for me to think about lately has been just learning more about the different categories of questions and the different purposes that they can serve. So, I'm wondering if you can briefly sketch out some of the types of questions teachers could put to use in their classrooms.
DeAnn: So, in ‘Principals to Actions,’ we really looked at a lot of different frameworks that people have established over the years for questioning. And we kind of boiled it down to four specific types that are particularly important for mathematics teaching. One is to gather information. For example, can students remember the names for different types of triangles? Another is to probe student thinking. 
Culturally Relevant Practices in the Elementary Math Classroom  Guest: Corey Drake
Rounding Up
Season 1  Episode 1 – Culturally Relevant Practices in the Elementary Math Classroom
Guest: Corey Drake
Mike Wallus: There's a persistent myth in the world of education, that mathematics is abstract and its teaching is not influenced by cultural contexts. This, despite the fact that research and scholarship indicate when students see how math applies to a world that they recognize, they perform better. Today on the podcast, we'll talk with Dr. Corey Drake, senior director of academic programs at The Math Learning Center, about what it means to provide a culturally inclusive and relevant mathematics experience in the elementary classroom. This is a topic on everybody's mind, and we're excited to address it head on.
Mike: All right. Hello, everybody. Welcome to the podcast. We are excited today to have Dr. Corey Drake with us. And the topic of the day is culturally relevant practices in an elementary classroom. So, Corey, welcome. It's great to have you on the podcast.
Corey Drake: Thanks. Great to be here.
Mike: Fantastic. So I want to start this conversation and zoom way out as a beginning place. So one of the things that I'm thinking about is that lately it seems like you hear terms—like equity, culturally inclusive, culturally relevant—and those are being used across the education space almost as like kind of a catchall, to the point where it seems like in some cases they've almost lost their meaning. So I'm wondering if to begin the conversation, and really give these ideas the depth of discussion that they deserve, If you'd be willing to unpack … When you think about culturally inclusive and culturally relevant practices, help paint a picture of that for someone who's a listener.
Corey: Yeah. I think those terms do get used all the time in all kinds of different ways. And so I've been trying to think a lot about sorting them out and trying to think about a framework that makes sense for me, recognizing though that actually whatever the term is, I think the goals are the same, right? And so the goals of whether it be culturally inclusive, culturally relevant, culturally sustaining education, or to provide better experiences and more access to all students to highlevel mathematics. So that's the underlying goal. And so I don't want to get too lost in the terms.
Mike: Thank you.
Corey: Having said that though, I think there are some important differences. I think if we think about things like culturally inclusive, we think about context representations that include all students so that every student can see themselves in curriculum so that students aren't excluded by the examples and representations they see in curriculum.
Corey: So I would think about that as more along the lines of culturally inclusive. When we start to get to culturally relevant, and then culturally responsive, culturally sustaining work, now we're really starting to think about who our students are, what their experiences have been, what their interests are, the kinds of activities our families and communities participate in, and how all of that can provide access and bridges into mathematics. And then if we would get all the way, kind of on what I think of as the far end of the continuum, we really would get to terms like antiracist education. We're really there. We're talking about systemic racism, systemic oppression and privilege, and ways in which mathematics can disrupt those systemic issues of, not only who has access, but the kinds of outcomes and opportunities that students have based on various characteristics.
Mike: So let's unpack these a little bit.
Corey: Yeah.
Mike: I think one of the things that's really interesting is this idea of relevance and responsiveness …
Corey: Uhhm.
Mike: … so, particularly because it made me think about the kids in my classroom when I was a classroom teacher, so it strikes me that a part of this work is like, as you said, like really getting to know
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