SPEAKER_01 0:00

There's certain sort of fundamental things and um that I think we we still have to grapple with that that is sort of impeding progress. Um and until we grapple with those things, it's gonna be really hard to get what what I think people jointly want.

SPEAKER_02 0:20

Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Fenderberg. We work together at Texas Instruments, and we're glad you're here.

SPEAKER_00 0:27

We're looking forward to continually improving our practice, and we understand that you are too.

SPEAKER_02 0:31

We hope that you'll find this podcast as a room for you to grow along with us as we wrestle with and explore ideas about teaching math even better. In this episode, Curtis and I share a powerful conversation with Dr. Julia Aguirre. Julia co-authored the book The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices. Julia's work examines the roles that race, ethnicity, culture, class, and language play in students learning mathematics. Based on her own experiences learning math and other STEM disciplines, she works to build and cultivate positive learning spaces for students who are historically marginalized from these experiences. We certainly grew from this conversation and hope you will too. So let's get growing.

SPEAKER_00 1:18

Well, Johnny, it's super exciting to be recording another podcast episode again with you today. We have a really great opportunity in front of us today. We get to chat with Dr. Julia Aguirre then uh today and talking about uh mathematics and our students' identities as mathematical learners um and some of the great work that she has been doing. So um really excited to have you join us on the podcast today, Julia.

SPEAKER_01 1:47

Well, thank you for inviting me.

SPEAKER_00 1:48

Yes, yes, we're really excited. So um go ahead, Joni.

SPEAKER_03 1:53

Oh, I was just gonna say I'm very excited too. And um the two of you are together in person, and I'm I'm distant from you, but um, it's good to have some video, and I'm really excited for our conversation today. I've known Julia and her work for quite a few years, um, and I'm excited for her to have an opportunity to share that with our listeners. So um, Julia, we thought a fun way to have you introduce yourself to us in our audience would be to have you share experiences from your own school and work and life that have contributed to your current passions in math education. So just tell us a little bit about yourself and why you care about the things you care about.

SPEAKER_01 2:31

Sure. Um, well, let's see. I can start, you know, it's usually traditional where you sort of introduce yourself through your family. Um, so um I actually um am the named after the Mexican cousin who raised my father while my grandfather was fighting in World War II. Um, I grew up here in the Pacific Northwest. Um my parents met at the university where my father was one of the first Latinos to play football. And my mom um had a passionate heart for education. And um and they were they got together in a time where um mixed marriages weren't um didn't happen and certainly weren't approved uh by many places in the in the United States. So I identify myself as a mixed-race chicana. Um I have um Mexican descent uh on my father's side and um English and French and Irish descent on my mother's um and I uh grew up here um in the Seattle area and I went to a a high school. Um and you asked me um how did I get started in this work? And so the experience was that in my high school, I was an athlete and an honors student. Um and my two sports were basketball and soccer, and I was one of five students of color in the honors program at that time uh in a school that was half black. And um, all of my basketball teammates who were mostly black were not in my honors courses, and all my soccer teammates who were almost all white were all in my honors courses. And so my school was two schools under one roof. And that stuck with me um because I could see inequities there.

SPEAKER_00 4:38

For sure.

SPEAKER_01 4:39

Um and then and yet at that particular school I got introduced to a program called Mesa, Math, Engineering, Science Achievement. And Mesa was a program that was designed to support more um diversity in the STEM uh pathway, right? And um in Mesa, I could uh explore STEM careers, STEM ideas without having to leave myself and my my identities at the door. And that was a very powerful experience for me because there were many messages of saying no, you no, you can't. And um Mesa was a place, a space, where there was messages of yes, you can. And um, so that took me to um the University of California, Berkeley. And at Berkeley, I was participated in different kinds of programs like that. Um one was called uh the professional development program or emerging, you might know it as emerging scholars program. And um that was a very special time in my life, again, because I was surrounded by people of color, all who were really smart people, interested in STEM. Um and um we didn't have to leave who we were at the door. And so that those experiences um I knew it could be done. I knew that that there were these experiences in learning mathematics, science engineering, um, where you could bring your whole self to the learning. And um that was one of the reasons why I decided to go into math education because I wanted to uh build and cultivate those spaces for students who are historically marginalized from um STEM education. And so um uh that is those are some of the um sort of foundational moments for me about why I do the work that I do in math ed.

SPEAKER_00 6:44

That's really good. That's really good. And I I love that um so much of what you uh are passionate about comes from your background, comes from um your experiences in those things. And I know that um a lot of the work that you are are doing kind of brings that out and draws that out a little bit. So talk to us a little bit um about your uh research experience, how you see teachers um their own identities playing out in uh their classroom practices and beliefs. I know that when I was in the classroom, there was so much of my experiences, my own curiosities and things that just drove a lot of the kinds of questions that I asked my students. And I'm just freely admitting that I spent a lot of the time thinking about things that I was curious about or things that I was interested in, and then trying to spend my time getting my students interested or excited about those things um because it was just natural for me to do that. So is is that kind of a normal thing? Um, do you see that that is the way that that people do this? And is that effective?

SPEAKER_01 7:58

Well, I mean, I I think for the first part of your question is about uh math teacher identity. So all of you know, we all have different identities. Um, we move in different spaces, and so do students. Um so our math teacher identity has everything to do with how we grew up um and how we experienced math, and then all the new and different ways um we learn as we teach mathematics to young people. Um so I mean, I think it's natural for people to who are teachers, you know, they're curious about the world, they want to, you know, share their experiences with young people. Um I think that's part of like half half of the work, right? But the other half is that the students are also coming in with curiosities and interests and aspirations and questions. And so ways in which you are tapping into their experiences, their family activities, their community things that they um get involved with and then connect mathematics, mathematical ideas to those experiences. I think if we did more of that, I think students would A, stop asking us why do we need to use this. And then also um we're sort of stoking or cultivating that idea that everybody is mathematical. Um we all are uh uh ask mathematical questions in our daily lives, um and that um we need uh more opportunities to develop that sides of ourselves. Um and I think the the concerns that I have is oftentimes for certain groups of students, um, that opportunity to cultivate curiosity or have them utilize mathematics in a way that might transform their community is set aside because they are being asked to um perform on a standardized test. Right. And that that is what is used as a way to evaluate their um mathematical um performance and therefore how they see themselves as math learners.

SPEAKER_00 10:17

For sure.

SPEAKER_01 10:17

And they they think of themselves, I think young people know that they are more than just a test score.

SPEAKER_00 10:22

Right.

SPEAKER_01 10:22

But that's not necessarily the message that they receive in school.

SPEAKER_00 10:32

Do you have some examples of those things? Because I'm sitting here trying to think of like all the ways that that we um typically try to teach mathematics and we contextualize it, right? We we give the students some kind of a story problem, or we give them some kind of a um a piece that has whatever the standard is is buried down in there among all the words. Yeah, it's buried down in there in the in the way that the question is asked or whatever. So we're targeting some standard and we're we're really just getting at the math, and we've we've kind of put this window dressing around the outside edge. Talk to me. Do you have some examples of things that are that are maybe more than that, or is that what you're talking about?

SPEAKER_01 11:12

I actually talked about that today. Awesome. So uh so there are um I'm I have uh projects that I've worked with. I have some wonderful colleagues. Um, we have a project that was called um mathematical modeling in cultural community contexts. And now we have a project called Equistem, um advancing equity and strengthening teaching with elementary mathematical modeling.

SPEAKER_04 11:40

Okay.

SPEAKER_01 11:40

Um so in both of those cases, we're looking at essentially cultural responsive mathematics or mathematical modeling. And the activities that we're developing um in concert with what we're learning by working with teachers and what they're learning about their kids are uh types of modeling tasks. You know what modeling is, right? Like the high school content standard, right? But the K-12 math practice standard, right?

SPEAKER_00 12:06

The two high school math standards and high school math teachers here and modeling. It's a content standard, right?

SPEAKER_01 12:12

It's a content standard for for um high schoolers. It's a K-12 mathematical practice, right? It is so if we want our kids to do well at the content level at high school, then we should start actually giving them opportunities to do that as they're growing up, right? Don't you think?

SPEAKER_03 12:30

Our very first podcast episode was on mathematical modeling. So we have to. You didn't have me.

SPEAKER_00 12:35

We didn't we it would be because it was just the two of us and having a conversation, but I love that that that is your passion. This is so oh, I'm so excited.

SPEAKER_03 12:44

We already have our topic for bringing you back for a second time.

SPEAKER_01 12:48

I will bring people to come with me. I love it. So a first example is something that we call mathematizing the world. So I'm gonna show uh you can't see this. I love it, uh, but I'm gonna show this picture. This this picture is uh um in a place uh regionally here. Um and why don't you describe that picture to the audience?

SPEAKER_00 13:11

Okay, so we have a picture. Um it's uh taken from a building uh or and a surface that's high above a street. Um there's a couple, there's another building across. I see uh a uh in the distance there, there's a field on the on kind of on the left-hand upper part of the picture. I see a field, uh maybe it's a soccer field or a park or of some kind, um, and a few families or people out um in get in small groups and gathered. Uh, but maybe the chief focus of the image uh is sort of down uh and to the left of the image. There's a large gathering of a large crowd of people, um, some with what appear to be signs, um, and then uh uh maybe a section of people where they don't have a whole lot of signs. They're all kind of gathered and turning and talking, it looks like, to each other. And then uh there's a row of folks on I guess the right hand side that all have umbrellas and uh things, and then right uh maybe and there's an open gap. And as I'm describing this, uh I'm getting more and more uh a feel of what the image is actually a picture of. Uh on the on the true center of the image, um, there's uh rows of people that look like they're in um gear, combat gear, or something uh like that. Um, and then they're backed up by folks that I can I can't see real well, but it looks like they may have some uh guns or uh other things. So they're army, navy, you know, police, somebody uh is in the image. Um so this is probably some uh a protest uh of some kind um that has been organized or um whatever. So anyway, I just trying to give a a little bit of a picture in the background so that people can see.

SPEAKER_01 15:07

So so this image, right, is actually a picture of a Black Lives Matter protest in the summer of 2020. Okay. And um we would might use this picture as a way to um have uh kids um uh make connections to the world. Right. So you might ask these questions like, what do you notice? And then they would tell you, there's the people, there's people with umbrellas, there looks like uh police officers there. What what do you wonder? Right. And so kids are now starting to question, well, I wonder why there's so many people there, I wonder why they have umbrellas there. Um how and then there may be questions of of how do you connect with this? What what's your feelings about this right now when you look at this image? And then the the next question is what questions can be answered with math about this image?

SPEAKER_00 16:03

That's so interesting. Um, because I I I recognized this image as soon as you as you brought it up. And um the previous time, I may have even seen your slides, I may have even been in one of your sessions now that I'm thinking about this. Um and this is so funny. This is very familiar to me. And here's the reason why this is so interesting, because um, the context within which I have seen this image before, we saw it in a math context. And immediately the questions were asked, what do you notice? Well, I'm already in I'm in math class or I'm in a math session at a conference or something. And so the questions that I'm already noticing, the things that I'm noticing and wondering about as a math teacher and a math nerd, uh I'm I'm wondering, okay, how can I best approximate the number of people that are in that crowd? Or it the context of what the image was about was not something that I immediately thought of. When you asked me to do this just now a minute ago, and this I was we're in a totally different context. I'm not in my math class, I'm not in a math session at a conference, and you asked me to describe this image. None of those math questions were the first things that I that I thought of. I think that's an important distinction for us all this time.

SPEAKER_01 17:29

So so part of this is to then invite with through images. This is a image, you can use other images for students to start to uh practice their observation skills, practice their problem-posing skills, practice uh uh creating and cultivating empathy and uh practice uh posing problems with mathematics.

SPEAKER_04 17:52

Sure.

SPEAKER_01 17:52

And um, and then after that, when you, for example, you said, Oh, I I wonder how many people are in the crowd, how could I approximate that, right? Well, then my next question is well, who might care about that number? Why would that number be important?

SPEAKER_00 18:06

Yeah.

SPEAKER_01 18:07

And so doing something like that with kids as a routine, like a mathematizing a world routine, like you do a number talk was a is a routine.

SPEAKER_00 18:15

Sure.

SPEAKER_01 18:15

Different kinds of images can provoke kids thinking about the world, right? And then asking questions that um uh can be answered with this uh I these ideas that they're learning in math class, right? And these are the kinds of things that people do care actually, how many people are in the crowd, and they care about how many people are in the crowd in comparison to the two rows of uh officers that are facing off with them, right? And um we have uh um a t a teacher, a third grade teacher, who brought this um image to uh a back to school night. And she brought the image to explain to the to to share with the families that this mathematizing the world routine is part of what she does. Right. And she shared with us that the families um she uh that what she had when they looked at that photo, they're like, Oh, I was there in that crowd. I was there wow and so it meant something, and she she knew that, she knew there was a good possibility about that. But what was powerful is that the families are seeing how mathemat how mathematics and mathematizing is is uh being shared with their with their children, and that there is truly an authentic connection that this uh that this particular teacher was making. I mean, she also showed other photos like like the Ferris wheel and other kinds of things that um but that kids need to have those opportunities often to make the connection. Right. And um and I think that uh you know you asked me, I think earlier about well, how do teachers do this? Well, part of it is again trying to listen to your listen to your students what gives them joy, what do you notice that they seem to play with? What are their strengths? Um and I get like do you know where your kids might like to travel in their world? Sometimes um with young people, middle school and high school students um from particular um areas, there's a sort of a belief that you know they're never gonna go outside their neighborhood, but that doesn't mean they don't have aspirations to, right? Or that they might want to travel the world. Um that's a big assumption sometimes that I think is wrong about young people, that they actually do have dreams and aspirations and their families have dreams and aspirations too. But there's a whole system that's set up to um see them as a problem or something to be fixed. And uh we need to move away from that model. Um kids are not to be fixed, uh, they have strengths and growth areas like everybody else. Yeah. And um we need to create experiences for them to be able to build on their strengths and stretch and grow um uh to to learn more things.

SPEAKER_04 21:16

Yeah, for sure.

SPEAKER_03 21:18

I I want to chime in because I I just so appreciate that example that you just gave. And um, you know, when Curtis gave his um talked about his experience as an educator and bringing his own passion and his own mathematical identity as a way to try to motivate and you know, encourage the learning in the classroom. And I think um, you know, your response of like that's only having to engage in the kids and these open ideas I love the idea of using a visual image and just getting kids to talk about it and getting kids to share, you know, what do they see and what connections are they making? Because you're right, Julia, like we don't know what we don't know about our students. create structures and opportunities to learn about them and then we have to authentically listen and and find you know those things that we can connect to so that we are ensuring our instruction is relevant for them. It's not a question of, you know, I've got to go out and get a degree in you know multicultural studies to know how to teach my kids. I just have to ask them questions and then listen and then do something with what they tell me so that I can foster those experiences. Circling back a little bit to your introduction because there were several phrases that you used in describing your life experience and what's brought you to your current work that that really um that really hit me and I want to hear you talk some more about those. So the one phrase that I want to ask you to elaborate on is leaving your identity at the door. It just hurt my heart to hear you say that. And I feel that you know in my experience I think there are educators in systems that do that to certain populations of students. They ask essentially ask them to leave their identity at the door. And I also want to say I don't think I don't think most of that is intentional. So I'm wondering if you can shine a light on this you know I'm I'm a white woman current a white man I don't have that experience of being asked to leave my identity at the door so I don't know what that feels like or what happens that would cause me to feel that way. And I'm wondering if you can help us understand that better.

SPEAKER_01 23:46

So well I think um so what I was trying to say earlier was that Mesa, the Math Engineering Science Achievement Program was a space in which I did not have to leave my identity at the door right um and so uh I could bring my whole self into those experiences. There are ways in which we subtly do that and there are ways in which we are you know uh uh giving messages uh to girls to to boys about um um uh how they should look how they should act um and so uh so I'm not sure if I'm answering your question uh correct or you know answering your your um answer question fully but I was in a space in which I could be my whole self and that gave me strength to face times when people would question my um reason for being in a particular room or being at a particular university or you know um wondering how I got in there. Um and these programs were available to me to to to help me meet other other individuals um who shared similar things that I similar things that we we we liked. But maybe you're not asked I mean uh you're you're not asked to leave your identity at the door because in many cases your identity is affirmed going in and all these spaces um and um what we need to recognize is that there is a new norm in our schools the norm is that we have a much more diverse uh culturally rich groups of kids who are um learning in our schools and that we should honor that um and that's gonna have to um make us reconcile the systems that we have put in place to rank and sort kids so that they remain segregated.

SPEAKER_00 25:59

What were some of the things I'm just curious you brought up the um that Mesa was the place where you didn't have to leave your identity at the door and one of the things Johnny's taught me a lot about is like what are the things that we can talk about that um were the positive side of things that we can learn from what are the things that allowed you to bring your whole self to feel like you could bring your whole self to the space because I'm not familiar with the Mesa program.

SPEAKER_01 26:32

Right. So I mean part of it is just um assuming that we were all smart like everyone had something to contribute and then we all had strengths. And that wasn't something that we had to earn or something that we had to uh um like prove it was just who we were and so I I would like people to think about how they um how they see young people when they come into the door. What are the words uh what are the things that are floating around that child's head that you that um may be informed by stereotype may be informed by by bias um and uh if if they're especially if they're negative how are you sort of taking that deficit language and reframing it to be more asset focused right and so um so you're creating a space like Bettina Love calls um some of the ways in which young people are um who identities are affected is as spirit murdering when you are calling them low slow bubble kids other ways in which you objectify their their personhood when you use those terms you are in effect dehumanizing them. And uh I I I just um when she came up with that description it was exactly what it is. When you refer to children in those terms you are engaged in spirit murdering and that is about identity right and so we need to make sure that we are not engaged in that kind of um those kinds of actions that have detrimental impacts on um students and their way they perceive themselves as in this case math learners. Right um children should be able to uh learn in a way that gives them joy and um and and uh challenges them and um stokes their their curiosity and um and have it be about curiosity and um creativity and not about control. But if we really want to you know get down to the some of the things that we were talking about in the book or when I talk about culture responsive math teaching it is about um uh centering your instruction on the children that you have and knowing that those children have gifts in their humanity and their full humanity is coming to you and you should be able to leverage that as a way to to um strengthen their what strengthen their understanding and also stretch them to learn more.

SPEAKER_00 29:34

So wow this is an opportunity to transition I think um to some some things that you talked about in uh in the book which were the five practices you had some five equity based practices um that are listed in your book and we'll have some of these resources available for um for our uh readers which one or maybe let's focus on one or maybe two let's not let's focus on five yes you know why I say that yeah I'd like to yeah because I love the fact that you just say that I want to hear it I want to I want to hear why I don't know why.

SPEAKER_01 30:11

So we have five practices and some of the feedback that we've gotten is that people just focus on the first one. Ah tell us what the first one is going deep with math here going deep with math yes so uh we need to in this next second edition we need to help people understand that this is not uh one two three four five in order of importance you need to think about these either as strands or you need to think about them as a circle right yeah so they're all important yeah right and they all need detention and um it's it's um it's a safe way to go if you only focus on the first one because then you don't have them stretch much.

SPEAKER_00 30:55

Right.

SPEAKER_01 30:56

Because it's always been about going deep with the math and math reform. And um these other things like leveraging multiple mathematical competencies so seeing the strengths and the different strengths kids might be bringing to the to the mathematical space, affirming mathematical learner identities. So what are way are we keeping what you know how do you want kids to leave your classroom um feeling about math right so I will say that I am a math teacher educator. I work with um every year I work with teacher candidates in the in the K8 elementary um getting their K8 elementary endorsement and every year I have over 50 60 70% of my my my teacher candidates are having to reconcile and heal from their own experiences with mathematics that they do not want to pass on to the students that they're teaching. So as a you know as a community effort in math as math teacher educators we have to take responsibility for our teacher candidate experienced violence experienced humility or um humiliation perhaps um while they were learning math and they can pinpoint it right they can pinpoint it it was having to do uh be fast with my times tables right just memory third grade everyone fractions is another mad minute yeah mad minute fractions fractions is another around the world uh uh you know um algebra is another sort of piece but at the same time I have students do their origin stories right their math origin stories and there is a teacher that um turned it around for them usually right um or there was a teacher that that derailed them right and so but teachers really matter in this yes in this um uh in this journey and so these five right so affirming mathematical learners' identities is important challenging spaces of marginality so where how are we pushing kids out rather than bringing them and calling them back in and having everybody feel like they're um can can make meaningful mathematical contributions in the class how are we affirming multilingualism in the class because that's a way in which kids might be communicating their ideas in multiple languages um and then finally uh drawing on multiple resources of knowledge again how are we getting to know the students that we're working with the strengths that they're bringing their interests that we can connect to you know when you're invited to go to um a uh like an important event from a family go right do a community walk go around and see where people you know visit uh family owned businesses go to the kids' basketball games at the rec center right be seen and and then utilize those opportunities to then um not only build relationships with students but utilize those with an opportunity to meet families to um communicate with families because they are also you know you are another adult in their child's life that makes an impact and so um I think all five are important um I worry when people just pick the one that's most comfortable for sure and never move beyond to the others and so we have to uh make an effort to see these things as um as a circle um or uh as strands that all must be attended to I love it I love it I may or may not have set you up for that um I love that I'm just gonna leave that as a mystery up to our listeners to to find out whether that was a teacher trick to get you to to draw all those together or not so Julia I I we've certainly spent the conversation today talking about a lot of work that's yet to be done that I would love for you to reflect with us as we wrap up you know what are you feeling most helpful about what what have you seen um that you could mark down as progress or what conversations or work have you been a part of that uh makes you feel like we can get closer to where we need to be uh so I would say everybody should read um the Todos anti-racist mathematics education position statement Todos Mathematics for all um I think that uh particular document it won the NCTM publication award um helps spell out what what is needed um uh and so I think that those kinds of materials and it's it's not that we don't know what to do. We do know what to do actually. It's do we have the will to do it. And we have to really push ourselves to understand why we're hesitant. And um and I think that that is uh the you as we move closer um as we uh you know I have like my colleagues um you know Karen Mayfield Ingram Danny Martin um Nicole Joseph um you know uh Macy Golson Maria Zavala you know uh we we we're moving toward trying to uh help shine a light on the brilliance of children um that they don't have to earn that that's that that it is there and um and no one should have to experience humiliation and violence in a classroom in a math classroom.

SPEAKER_00 37:05

And when we use even you know I I'm sure you have experienced uh kids or teach uh colleagues saying my low students or my high students or my advanced students or you know those those language that language seeps into how we see children seeps into how we see the kids but it's used so commonly and so um what I'd like to see is uh that that deficit discourse out of our registry out of our lexicon out of out of we don't we don't describe children in that way anymore we don't engage in spirit murdering anymore we we're not doing that um and uh I would like to see and hope to see that um there's a new set of books um let's see and she reaches for the books there's uh um uh put out by Corwin that are mathematics lessons to explore understand and respond to social justice social injustice and they have an element early elementary they have an upper elementary they have a middle school and they have a high school versions and these are lessons that have been done in classrooms that um engage kids in um in thinking about their world our world and mathematizing our world and engaged in mathematics so what's special about these is that all lessons connected to the standards the math standards and they connected to the social justice standards there are social justice standards by the way and so when you're having to do both you're engaging young people in thinking about a more fuller aspect of of real life actions that are happening um than just thinking about only math um these things are intertwined and they need to be held um together um and honored in both in both ways wow you've given us a whole lot of things to talk about to think about to go away and I know I'm going to have to go away and really think uh deeply about a lot of the things that you've you've brought up um really appreciate sure your passion uh for this um yes thank you all of the the resources that you listed here we'll make sure that we make sure that those are uh available sure I can see yeah for sure that would be wonderful to have those for the for the show notes and and anything uh everything for our um our participants to to uh look forward and look into um and investigate so and Julia just thank you thank you for joining us for the conversation today and thank you for all the work that you're doing to help all of us get better at at having all of our kids be successful in mathematics I really appreciate all the specifics and tangible and challenging ideas you gave us today.

SPEAKER_02 40:16

Oh you're welcome thank you for having me well that's it for this time be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us consider leaving a review to help others find us and share the podcast with a fellow math educator. See you next time