Dr. Chrissy Trinter: Education, Energized.

[Opening music]

 

0:00:09.7 Audrey Scott: Welcome to this modern education podcast that explores learning from the everyday exchange of thoughts and ideas to the theories and practices behind entire systems. Think education is cool, so do we. So we pair two conversations, learn about our guests then learn from our guests, share your takeaways and come back for more. You're listening to Think-Pair-Share. With me Audrey Scott.

 

0:00:43.4 AS: Today's conversation will focus on mathematics, and to say it's not your mother's math class is a fascinating understatement since I remember quiz as being a staple in the math classes I was in. Well, a more than lighthearted get-to-know you quiz for our guest today. First, I'm excited to introduce her, Chrissy Trinter, is an associate professor of Mathematics Education of the ACE teaching fellows, and in the Notre Dame Center for STEM Education, as well as a faculty member and a fellow of the Institute for Educational Initiatives. Her work focuses on teacher development, primarily on teacher leadership and curriculum design in the mathematics classroom. She is particularly interested in the elements of curriculum and teaching that lie within the intersection of creativity and mathematics education. Prior to joining Center for STEM Education, she was a faculty member at Virginia Commonwealth University and a Research Scientist at the University of Virginia where she earned her PhD. During this time, she was the lead author on several award-winning differentiated curriculum units. Dr. Trinter works with schools nationally and internationally on ways to provide all learners access to meaningful mathematics. So without further ado, welcome Chrissy.

 

0:01:49.9 Chrissy Trinter: Thank you for having me. So fun to get to talk to you, Audrey.

 

0:01:54.1 AS: It's so nice to see you too, and even though it's over Zoom, it's nice to see your smiling face Chrissy, so thank you.

 

0:01:58.9 CT: Yours too, thank you.

 

0:02:01.0 AS: We look forward to learning all sorts of things during this podcast, but we're going to begin with a couple of kinda like fun... I don't know, you're probably like, "Those were not fun at all."

 

[laughter]

 

0:02:11.2 AS: But just sort of some things to kinda warm us up, okay. So choose your favorite: Star Wars or Star Trek.

 

0:02:17.6 CT: Oh gosh, neither. [laughter] Sorry, do I have to take one of those two? 

 

0:02:21.9 AS: No, it's great.

 

0:02:24.5 CT: I think every... You know what, yeah, If I had to pick one I would do Star Wars only because all of my colleagues like it, but... Just... But no, neither, thank you. [laughter] I've just turned off over half of the audience. They're shutting it off right now.

 

0:02:40.3 AS: There are couple of... [laughter]

 

0:02:44.1 CT: Nothing more to hear here. [laughter]

 

0:02:46.9 AS: Delete.

 

0:02:48.1 CT: Delete, probably she's not interesting.

 

0:02:52.7 AS: And yet the other half are like, "She's my kinda lady." But yeah, I have heard that there are some people that really go all out for Star Wars in the office, so I wasn't sure if you were one of them, so okay. Okay, cake or ice cream? 

 

0:03:07.9 CT: Oh, definitely ice-cream. I'm an ice-creamholic, and I don't really care for cake, honestly.

 

0:03:13.2 AS: Same thing for me.

 

0:03:14.9 CT: I love... Really? 

 

0:03:16.4 AS: Yeah, that's why people always bring me donuts in the morning at the office, and I'm like, "I'll actually forgo a donut so that I can have more ice cream later."

 

0:03:22.7 CT: Absolutely, I would forgo everything so I can have ice cream. I had worked in an Ice Cream shop as a teenager, and I ate all the profits, it was so good. Oh, so good.

 

0:03:35.3 AS: So... Alright, I love it. So, so far you're saying everything right. So I thought... [laughter]

 

0:03:39.5 CT: So you still wanna interview me? 

 

0:03:41.9 AS: Those are the right answers.

 

0:03:43.3 CT: So, you wanna continue talking to me? 

 

0:03:44.6 AS: Oh, good. Okay, yes. We've been working on...

 

0:03:45.9 CT: What happens to the people that say things wrong? [laughter]

 

0:03:51.1 AS: We have a little lab. Have you seen Charlie and the Chocolate Factory? 

 

0:03:52.9 CT: Yes.

 

0:03:55.4 AS: Willy Wonka, where they go somewhere else.

 

0:03:58.5 CT: I can shout out Mrs. Veronica one of blueberries she's...

 

0:04:03.1 AS: Yeah blueberry.

 

0:04:03.2 CT: She's choked with blueberry.

 

0:04:03.9 AS: I thought she was blue in somewhat... Okay so, checkers or chess.

 

0:04:09.4 CT: That's a great question. Checkers or chess? It just depends on the mood I'm in. I wanna think chess. If I just wanna have fun, checkers.

 

0:04:20.8 AS: I actually have to learn how to play Chess. I asked my husband to teach me how so that's on the agenda. Okay, see you passed with all those. There's a few more fun ones. As a child, crust or no crust? 

 

0:04:32.3 CT: Oh, as a child. Crust or no Crust. I don't really remember. I think no crust as a child, but honestly, my mother would have never spent the time to... She's a wonderful mother, but she just wasn't gonna spoil me with cutting the crust off, so I think I probably just ate around it and left the crust.

 

0:04:52.2 AS: I knew you'd suffer.

 

0:04:58.2 CT: A requirement.

 

0:05:00.5 AS: Do you have a favorite childhood book? 

 

0:05:03.5 CT: A favorite childhood book? Gosh. I guess the little prince maybe, because my grandmother used to read it to us. My grandparents were from France, and that was... I don't know, it's kind of a fond memory, maybe that one.

 

0:05:15.1 AS: That's a really nice one. It's a very nice one. Yeah, good. One other in the fun category, if you had to sing a song for karaoke, what would it be? 

 

0:05:21.8 CT: Oh my gosh, something very silent since my voice is so bad, but... That's a hard question. I don't know whether I can answer, I don't really know.

 

0:05:34.1 AS: I would be completely stumped too 'cause I... People pay me not sing.

 

0:05:38.6 CT: Sorry. Yeah, that's kind of... My family laughs at me when we sing Happy Birthday. It's really, going to church... Growing up where you have been in church and my family all have really great singing voices and I really don't, and I, but I love singing in church and... I'm not kidding you. My siblings would turn and look at me... They would look at me with their faces like, "Please stop." [laughter]

 

0:06:06.7 AS: I'm proud.

 

0:06:08.8 CT: So funny.

 

0:06:10.6 AS: Okay, well, we'll give you a pass on the Karaoke then.

 

0:06:14.3 CT: You should. Give yourself the pass and don't have me do it. [laughter]

 

0:06:20.3 AS: Oh my God, siblings are the best. Too funny. Okay, to lead us into the next part of the conversation, what did you wanna be when you grow up? 

 

0:06:29.6 CT: At one point when I was a child, I wanted to be a lawyer, but it was only... I really think it was only because my father used to tell me to be a lawyer since I always had an answer for everything. So I think that kinda got stuck in my head and then, yeah, I don't really know that I knew what I wanted to be. I was an artist and I thought, "Oh, maybe I'll be an artist", and then I had a great math teacher in high school and I thought, "Maybe I'll be a math teacher", but I've explored lots of different career paths.

 

0:06:58.6 AS: It's interesting to me because you have an art background and also math, those two subjects I don't normally associate with each other, are you sort of, do you feel sort of unique in that? 

 

0:07:07.3 CT: [laughter] Yes, yeah. Unique is a really nice way of saying it. Split personality.

 

0:07:12.9 AS: I mean that in the nicest way possible.

 

0:07:15.6 CT: I know. No, I know. No, yes, definitely. Yeah, I just always loved both really, equally, so I really never had more of an affinity for one or the other and I try to bring them together as much as I can in my work.

 

0:07:34.7 AS: Do you do anything artistic creative now, do you paint at all or draw, or are there elements that you still like to foster? 

 

0:07:43.3 CT: Yeah, so I honestly haven't painted in a while and I keep saying I'm gonna get back to it. My children are 10, 13, and 15, and I'm now just starting to see a potential for finding time to be able to do something like that. I had done it, really, I continued... So I loved to paint in watercolors. I like oils, but I think my heart's always been with watercolor and I really had painted my whole life, really until I started having children, and my first child was born the third day of my PhD program.

 

0:08:20.4 AS: Oh, my gosh.

 

0:08:21.3 CT: Yeah, so it was just busy. [laughter]

 

0:08:25.2 AS: [chuckle] I guess.

 

0:08:25.3 CT: So then I had two more children throughout the program and, you know, continued on. So, the past 15 years I have not done much painting but I'd love to get back into it.

 

0:08:37.3 AS: Awesome, that's great. [chuckle] You blinked and 15 years later, you're here.

 

0:08:40.5 CT: Yeah, and here I am.

 

0:08:41.5 AS: Like in the CRE. On a slightly more serious note, and if you do or don't have one that's totally fine, but do you consider yourself to have an educational philosophy, or is that not something that you formulate that way? 

 

0:08:53.9 CT: So I'll give you another immediate reaction. [chuckle] What's my educational philosophy, is love your students. So love your students, you'll figure out how to get them to learn. I mean, that's not really a formal philosophy certainly, but that's really the key to being a good teacher, in my opinion. And that's where it starts. And then more formally, certainly, I think collaborative and active learning is very powerful. Differentiating learning, so recognizing how and when students wanna learn in different ways, and really getting to know your students and knowing your discipline well, and bringing those two together.

 

0:09:37.1 AS: Do you think that's a relatively new way to look at things? Did you feel like your teachers growing up got to know you or is that sorta been a shift in? 

 

0:09:48.2 CT: I think some teachers did for sure, and then others maybe were more traditional in their approach to teaching, kinda of based on... Kinda of with the focus more on the discipline and the strategies and the structure of things. But I definitely remember many teachers really getting to know us, and I should add, and loving what you do. So if you don't love teaching, then that will come across.

 

0:10:20.4 AS: Is there a moment when you kind of felt like... That you loved teaching? 

 

0:10:25.5 CT: Yeah, definitely. So my first teaching job was in 1998. At the time, I was... You had asked earlier, what did I wanna be when I grow up? And I wasn't really sure, and I was trying to figure it out, when I graduated college and I did a year of service in the Jesuit Volunteer Corps, and I really recognized my call to service in some way. And so I was working at Memorial Sloan Kettering Cancer Center in New York City and trying to figure out where I was meant to be. And I'd always... I had a seed planted a few different times in my life for education, although nobody in my family were educators, but I was really kind of discerning trying to think about what I wanted to do, and I remembered coaching rowing when I was in college and loving being with the students and teaching them how to row, and I thought maybe I should try teaching. So I found this job on Monster Board, or I forget what platform we used then to find jobs, but it was basically like finding a...

 

0:11:28.6 AS: I think it is.

 

0:11:28.7 CT: Right? Was that what it was called? Monster Board? 

 

0:11:30.6 AS: I think it was Monster Board.

 

0:11:32.2 CT: I think so. [chuckle]

 

0:11:32.9 AS: I think it was, yeah. [chuckle]

 

0:11:34.1 CT: Yeah. And it was an all girls Catholic school in Boston. I thought, "Oh, well, why don't I just apply to that? And see what happens, teaching math." And so I applied, and I remember going up to the school, I met Sister Maureen Cane, the principal. She gave me the job right there and literally handed me the stack of books and said, "School starts in two weeks", and I said "Okay". [chuckle] So I drove back to New York City, gave them my two-week notice, rented a U-Haul, drove back up to Boston, moved in with some friends, and I taught at this school called Monsignor Ryan Memorial High School in Dorchester, Massachusetts, South Boston. And I just... Oh my gosh, I loved that job. It was the best job ever. I jumped out of bed every day to go to that job and that was really, really when education stole my heart, I just... That was it, I was done. So I'm still in touch with some of the girls who I taught at that school and they're grown women and with families, but we just had a great time.

 

0:12:41.5 AS: That's a great story. And I can tell, I know, podcast audience can't see, but the smile on your face tells the story too.

 

[laughter]

 

0:12:47.9 AS: That you really, really enjoyed that, so that's great. I love hearing that. When someone loves their job, it just makes all the difference in the world, you're right. It is. To me, I feel like that's half the battle, especially... I'm gonna be honest, full disclosure, math makes me nervous.

 

[laughter]

 

0:13:04.5 AS: Not that I didn't have probably decent teachers or whatever, but the more I hear about different ways of teaching now, I'm encouraged by all the steps forward that seems like you and others are taking to make math in general more accessible, more understandable, more relatable. I say, thank you.

 

0:13:21.6 CT: Well, thank you. Hopefully, we're trying [laughter]

 

0:13:24.8 AS: You're doing a good job. I know you are. I'd love to sort of do a big picture look at a concept that I know is near and dear to your heart, but seemed more foreign to me, which is sort of mathematics and Catholic social teaching. Am I correct in that? That that's something that you tie very closely together? And can you tell me a little bit about it? 

 

0:13:41.4 CT: Sure. So, I teach the A students, the math content A students who are middle and high school teachers. They all teach in Catholic schools across the country. And so I really try to integrate these ideas of our Catholic faith and Catholic social teaching with both how you teach and the discipline of mathematics. And so... Yeah.

 

0:14:03.8 AS: For me, I feel like that's not my...

 

0:14:04.1 CT: Because that fit...

 

0:14:05.0 AS: Yeah. It's never been something that I recall people sort of bringing those two ideas together, in my opinion. And I realize it's been a few years. But it was more like, "Here are the numbers. Here's how you solve the problem. Memorize this." Those kinds of things. And it just sort of didn't seem like a larger picture thing for me.

 

0:14:21.0 CT: Right. Well, and you're actually describing one of the reasons why I do this, is because so many people will talk about how math is intimidating or they say they're not a math person. And I don't think that everybody is going to love math. But I do think that we can help students feel like they have a place in the math classroom. I think when students are in a classroom and they feel anxious or like they don't fit in, then that speaks to our Catholic social teaching and our faith and call to community and the dignity of the individual. I feel like as teachers in Catholic schools, we really should be thinking about every student in there, and how do they feel in this space. Because if they're uncomfortable, obviously, then they're not gonna be successful. So, that's the first step. So in my class, when I teach my students, we talk about these different ways of integrating our faith life into our teaching. And so one of the ways is the way you teach, the how you teach, the choices you make when you teach. And so, for example, in education literature and education research, like we were talking earlier, more recently, we see a lot of collaborative learning. So, small group work, that social aspect of teaching and learning that we have seen can be really effective for helping students learn different concepts.

 

0:15:44.0 CT: In our... This classroom... In my class, we talk about the importance of bringing people together socially in this collaborative learning, both to learn the mathematics, but also build community and help them help one another. And we're all in it together. And we're all in it for the common good. So we talk about the choices you make aren't just about learning the discipline, but it's about who we are as humanity. And your classroom is your world for that 45 minutes or whatever. So, what do you want that to look like? And how do you want people to treat one another? And why? And then another way I think about it is students dispositions towards mathematics. And this is what you were talking about, like your identity as a math person. So, we want students to feel like they are... They can be doers of mathematics. And that gets at what I was saying earlier. It's just helping them live into their dignity while they're in your classroom. If they can't... If they don't feel a sense of solidarity with their fellow students, their peers, and then their teacher, then you're never gonna be able to get them to figure out how to divide fractions. [chuckle]

 

0:16:54.5 AS: I hear that.

 

0:16:55.8 CT: So, I kind of bring it in in that area as well. And then the third way I bring in is really through some of the content. So, I expose my students... In math education field, there's a whole body of work around social justice math. And what this is, is using math in basically authentic contexts such as what is a living wage, or say, race relations or different kind of civic situations. And then how can we use math to make sense of what's going on in the data? And there's... I will say there's a debate. There's a group of people who don't think that should be brought into the math classroom and a group of people who do think it should be brought into the math classroom. And I share that with my students and they get to read both sides of that debate. Because I really feel that as teachers, they need to decide who they are and what they want to bring into their classroom. Regardless of whether they do it or not, the students need to learn the mathematics. And that's the debate on the other side, the people who say, "No, this shouldn't be brought in," say, "You're watering down the math. You're actually not preparing them well for the real world. You think that you're empowering them, but it's getting too into the context and not enough into the discipline."

 

0:18:06.8 CT: So, there's two sides to the story. But I expose them to lesson plans and ways of thinking about using their community as a context for lessons when it's appropriate. And I tell them not every topic is going to lend itself to some sort of a community context. And you have to decide what makes sense and why you wanna do this. But I think that using math to do good in the world and to help people make sense of the situations that are going on in the world, I think is really important.

 

0:18:39.0 AS: If you feel like you're lost from the beginning, or that... As you said, the doer of mathematics, I think that's an interesting concept. Because I would have said I'm not a doer of mathematics. [chuckle] And I know I'm not alone. But at the same time, I always felt like I wish that could be different. And now that I've seen how it's useful and how it's not just a bunch of numbers on a sheet of paper, you're not just doing it for memorization sake. There's ways that can help you and your community in figuring out an application of it. Is that sort of a universal turn toward making or is there...

 

0:19:16.6 CT: Yes. That's a huge push in mathematics education today, is to try to make it authentic and meaningful. Again, when it's appropriate. Otherwise, you're just trying to fit a square peg through a circular hole. There are times when the students need to learn a skill or a procedure. And that's what they need to do. You might not have an authentic or meaningful context for every topic, but you can still do things in the classroom that make it interesting, turn it into an investigation. Using a manipulative or a technology or giving the students choice is very powerful. There's lots of ways of providing access to students so that they feel like they can be successful in the Math classroom.

 

0:20:01.1 AS: I like that. I feel like that's very encouraging. It might help people to hear examples of how you implement Catholic social teaching into your own practice.

 

0:20:09.5 CT: Sure. So yeah, so I think about my course in three movements. And the first one is that classroom culture, creating a community in the classroom, and that starts with introspection. Because I think that if you're going to be able to teach somebody something, you need to understand kind of where you are, and where... Your perspective and your lens, whether it's on the discipline or just on your classroom community. So the goal of our first class is to help the students really understand that students are coming into the class with all different backgrounds and experiences and families and insecurities and confidences, and all of those are going to play a role in the teaching and learning process. So it is so worth spending the time in the beginning of the school year to develop a really strong classroom community, because it'll pay dividends later when they're trying to get somebody to factor a polynomial. So my first... [chuckle]

 

0:21:08.9 AS: What... I'm kidding.

 

0:21:11.2 CT: My first class with them, we do a privilege activity. And it really helps them kind of examine what privilege means and what it looks like. What privileges they have, what privileges their students may or may not have. And the privileges span a range. So whether it's the color of your skin, whether it's how many parents you have at home, whether you've had a teacher who believed in you, whether you've been successful at Math before, there's a variety of privileges that students are bringing to the classroom. My students typically haven't really thought about it this way, and as a teacher, what does this mean? And then we do a collaborative learning activity where they have to engage in this activity in such a way that the only way to finish the activity is... They're all put in groups, everybody in their group has to complete the activity, and it's too long to describe right now, but basically, it's a nobody wins unless everybody wins. It's designed in that way.

 

0:22:10.4 CT: Now we've looked at privilege and all the different kind of walks of life that students are coming in with. Now imagine those students that we just examined are in this collaborative learning environment. So how do those... Their what we call classroom status, how does that impact their ability to collaborate with their peers, and how they feel in this space? And then we tie it all together with the Corinthians reading about, the eye cannot say to the hand, I do not need you, and if one part suffers, every part suffers. And so that kind of whole first piece is about setting the foundation for your course. And so we don't get into much Math the first day, because what I have found over the years is, as a new teacher, you're so focused on the Math right away, and everything that you have to cover, and how do I teach this concept, that sometimes you can miss the human part of it, and I think that's the more important part. Like I said when we started this podcast, if you love your students and really get to know them, you're gonna figure out how to teach that concept.

 

0:23:14.4 CT: So that's the first movement. And then the kinda middle part of the class, I really get into the research-based practices for teaching Math, setting goals, the balance between procedural and conceptual fluency, the types of questions you asked. So there's eight practices in the Math field that are research-based, that are called these equitable Math teaching practices. And so we focus on those and we really focus on each one and how do you enact those in the classroom and pull your students in. And I integrate, again, that all with the Catholic social teaching, and we reflect on how they are congruent and where they surface, the Catholic social teaching tenets.

 

0:23:56.0 CT: And then, once the... We're getting to the end of the course, I feel like now we are at a place where we have kind of a good handle on the discipline and how to teach and the foundational pieces, so now let's look at something that's a little bit more complex, which is really the application and the context. So that's when we get into activities where we're trying to contextualize the mathematics maybe in a social justice context, or even just an authentic context. So, for example, the students are living... My students are living in communities or houses across the country, all different cities. So one activity that I do with them is I print out the newspapers from that day, from all the different cities that they live in, and then they go through the newspaper and they create a lesson based on some... One of the newspaper stories, and it has... And I give them criteria. It has to be really rich in the mathematics, it has to be authentic. But trying to help them see how you can use an authentic situation to teach them mathematics.

 

0:25:00.9 CT: Some of the students are really interested in doing something that's very social justice-oriented, equity-focused, and they do beautiful job with that. Some students are... Do something that's just more kind of happening in their community, is something that's maybe not as much of a civic... A social justice situation, but there's a new theme park, so we're gonna create an engaging lesson around that, and that's fine too, so...

 

0:25:31.5 AS: That's really interesting. So would they make a new roller coaster? 

 

0:25:35.4 CT: Somebody actually taught... One of my students had a great unit using roller coasters for Calculus. It was really... He did such a nice job with it. Yeah. The students really enjoyed it.

 

0:25:44.5 AS: Wow. That's cool.

 

0:25:46.1 CT: Yeah. And they brought in the Avengers too.

 

0:25:49.5 AS: Woah. Alright. I can see it...

 

0:25:52.0 CT: It's an Avengers theme park.

 

0:25:54.6 AS: Oh. I like that. We'll get some funding behind it. I think it's gonna work. Do you find that your students are kinda surprised at the focus, or...

 

0:26:08.8 CT: Yes. Yeah. For sure. [chuckle] What I find is with my students, and I should also say that I... So they're surprised at a couple of different things. One is the collaborative nature of mathematics. So many of them will tell me over the years that they never saw Math as something collaborative. It was something they did by themselves, it was right or wrong. So when they come to my class and they realize that there are some ways that you can make it very effectively collaborative, and certainly there's... You don't just kinda throw a problem in the middle of a table and say, "Everybody work on it. That's ineffective." But there's structures that you can put in place and questions and designing the task in such a way. And not all tasks are group-worthy, I should mention that too. There are definitely many Math tasks that you do do on your own. And eventually, you gotta do 'em all on your own. But when you're learning them, there are some very well-designed group-worthy tasks. So that's something that's typically new to them.

 

0:27:13.1 CT: And then, I love using non-routine problems with my students as well, meaning, something that you can't just grab an algorithm and solve or find the solution in a book or on Google. So there's a lot of really kind of thought-provoking types of tasks that make you reason and critically think. And typically, Math majors aren't doing... I mean they're doing... They're certainly critically thinking and reasoning, but they're not doing these types of problems that are really non-routine, where they don't have an algorithm to use, they have to really think through. So I like doing that, because I think it gives them a good challenge. And I really like having them feel the way their students feel. Even if their students are getting a Math problem that does have an algorithm, but they don't know what it is, so they have that kind of cognitive dissonance. They're just a little like,1 I don't know. And so I think it's helpful for the teachers to feel that, and then also feel the joy when they get through it and they realize what happened. So the solution. So that's always a surprise. And then, yeah, the context, kind of authentic meaning-making math, using authentic situations or social justice issues, that's also something that's typically pretty new to them, and I think they take up really beautifully.

 

0:28:37.2 AS: I like the idea of sort of getting them out of their head a little bit and maybe making them feel a little of that trepidation that... Nobody likes to stay there for very long, but that's something that you're like, Okay, now I feel for the other person a little bit.

 

0:28:50.4 CT: Yeah. There's a body of work in Math education that we focus on called productive struggle. And the idea is that you need to struggle, but you need to struggle productively. So as a teacher, you have to find that sweet spot where students are working hard and grappling, but they're not crying and feeling dejected. [chuckle]

 

0:29:13.4 AS: This lady.

 

0:29:14.2 CT: Yeah. So you need to give them enough supports so that they can productively struggle through it and feel that sense of belonging and success. So when I'm teaching teachers, they already know how to solve the middle and high school problems, so I have to think of ways to have them productively struggle, so that they know what that feels like, and that they can then identify it and be able to use that strategy with their students as well.

 

0:29:43.1 AS: There's an equity piece that is very important to you, is there not? And can you build on that? 

 

0:29:48.5 CT: So yeah. I guess just along those lines, I just think all people should feel that they are able to thrive and flourish. And so like I was saying, that should drive all of our decision-making. So I certainly feel that that idea of human flourishing really drives a need for diversity a need for giving people opportunity for equity, for justice. That's just kind of how I think about it. So I think it's helpful, at least for me, to make that really explicit. That's the first part, and then that's why we do all of these other things.

 

0:30:28.1 AS: Yeah. And actually, maybe we can tie that into the idea of achievement gaps and opportunity gaps? 

 

0:30:35.0 CT: Oh yeah. Often, people will hear about achievement gaps, like if we have a newspaper story about Math scores, and the story will say, There's an achievement gap. And the achievement gap is between White students and students of color. And that's really important that we have that data. And we need to know this so that we can rectify it. But that's the kind of output. And so the opportunity gap is the fact that people are not getting the same opportunities, and that's why we have that output. And so as teachers, it's really important for us to be thinking about the opportunity gaps, because that's the input, and that's what we have control over.

 

0:31:14.2 CT: So sometimes if we look too far out, we just stop at the achievement gap, you may just kinda feel like, "Well, I don't know where... I don't know what to... What I can do about that." But what you can do is reduce the opportunity gap of our students. So within your classroom, within your school, how can you reduce opportunity gaps? I work with schools at the systems level, and we look at how to reduce opportunity gaps in the mathematics classroom from, say, a whole district level. So for example, are students getting tracked, are they not tracked, what makes sense for your school in terms of Math programming. From the classroom level, as a teacher, we wanna look at our students in the class, and is everybody getting an opportunity to learn? So as a teacher, this is something that we try to do all the time. And whether, again, it's at your classroom level, or your school level.

 

0:32:08.1 AS: There's two follow-ups I'd like to ask from that. 'Cause, one, I wanna introduce differentiated instruction in that conversation. And the other is, are there concrete ways that you can do that? Or can you give us an example or two of how you might work to reduce an opportunity gap? 

 

0:32:25.3 CT: Well, that... The differentiated instruction is one way. So differentiated instruction just really is a philosophy of education, it's a philosophy of teaching. So it's really what I've been talking about, but I haven't used those words, and it's just really about getting to know your students, getting to know what their preferences are, how do they... When... One of my colleagues uses this example that I like, that says like, "When you get a newspaper, when the newspaper gets delivered to your house, do you read every single word from the beginning to the end?" Do you, Audrey? 

 

0:33:03.7 AS: No.

 

0:33:06.4 CT: No. What do you typically do when you get the newspaper? 

 

0:33:10.0 AS: Read the headlines.

 

0:33:12.2 CT: Read the headlines, and then you pick...

 

0:33:12.7 AS: Go to a section...

 

0:33:15.3 CT: What's interesting, right? 

 

0:33:15.4 AS: Right. Yeah.

 

0:33:15.5 CT: So similarly, students have different interests, so they might have a preference, and that's not to say they're gonna have that preference or that interest every day, and that's who they are, it's not to pigeonhole them, but designing a lesson such that I give my students choices and maybe you get the choice of doing these math problems on the laptop, there's a station over there that has paper, there's another station that you have manipulatives... As long as it's designed that all of those areas have the same learning goal and that the teacher is able to monitor that everybody is meeting the same learning goal, but there may be approaching in different ways. So that's just one of many examples, but just one example of how you might provide students more of an opportunity, because I might be a student who really needs to... For this particular topic, being able to, like you said, visually see and hold on to this area model and piece it together might be much more powerful for me, than if I'm just working with the numbers without that.

 

0:34:23.9 CT: And again, this is not to say you just kind of throw these in front of your students and hope for the best, there's a lot of teacher input and guidance in all those ways and the teacher has to bring it all together to make sure that everybody is learning the concept and the procedure, but you're giving students opportunity to access the mathematics.

 

0:34:43.4 AS: Gotcha, that makes sense. Thanks for the clarification there, and actually a good example, and I'm wondering, do you get... What's the feedback from teachers, maybe new and seasoned? Is there some push back or they feel like, "Oh, this is gonna be... How could I possibly monitor all that?"

 

0:35:03.3 CT: Yeah, so great question. Once they really understand it and recognize that... So, one of the misconceptions about differentiating instruction is that it's a different lesson plan for every kid in the class, or you have to do it all the time for everything. It becomes kind of bigger than it needs to be. The professor, I really learned this from, about differentiated instruction at UVA, Carol Tolson will say, "It's good teaching." So, what I try to help teachers realize is you're doing a lot of this already, it's not like this is a new thing, this is not wildly different than what you're doing. It doesn't have to be that big of a deal. Take baby steps, try something small. When they do that, when they try a small thing, they make a small tweak, they just kind of enhance what they're already doing and make one small change, they are bought in right away and they realize and they really see the effect. Pre-assessment is very important in differentiating instruction, so being able to get a sense for where students are and then use that data to inform your instruction, that's another area that a lot of teachers...

 

0:36:12.4 CT: Not a lot of teachers, but some teachers don't feel they have the time for, so then when we're able to help teachers recognize low prep, easy ways of sneaking in some pre-assessment and then they use that data to then design a lesson, it's so powerful. I think I just love watching human flourishing. It's such a gift as a teacher to get to experience that with students. There's so many different ways of seeing mathematics. Many of us remember a very traditional approach, and now we have so much more information about how students access mathematics and, absolutely, algorithms are important, but there's an importance to this balance between concept and procedure and tying those two closely together. And so, when we think about our heterogeneous students in our classroom, we need to be thinking about what are they coming in with? What do they already know mathematically? What are their life experiences? How are they feeling? 

 

0:37:14.7 AS: When you give them a window to see it through and you welcome them into a math conversation, the shoulders can relax a little bit.

 

0:37:24.6 CT: Yes, yes.

 

0:37:25.7 AS: Sort of take away that fear factor.

 

0:37:28.1 CT: Yes. I often find that people in, just general, are searching for that with mathematics. "But how is this meaningful to me?" There are definitely ways of making it more meaningful to students and is absolutely something that we do, and even if as small as Starbucks coffee and the prices and... Just little things that you can do, little tweaks... The context being their school, or a movie, or just something... That definitely is worth taking the extra step to do that. Sometimes, like I said, there are just concepts and procedures that we learn out of context, but maybe they can feed back into a more meaningful context later or within a unit somewhere. When possible. And when appropriate? Absolutely. I heard somebody say once people go into teaching because they want to give, they want to do good, people wanna help each other, so it's just a matter of creating the space to make that happen.

 

0:38:29.0 CT: Everything I do, I think is... I'm trying to provide students opportunity to be invited into the community of mathematics. I really just take such joy in human flourishing, and that's what I see as a teacher's job, no matter what subject they teach.

 

0:38:46.9 AS: I think that's great, actually. I think that might be the perfect way to end. Thank you, Chrissy. Really.

 

0:38:52.9 CT: Okay, thank you.

 

0:38:54.6 AS: Yeah, I really appreciate your time. I had a great time talking to you, and honestly, I don't think I would have ever said that about a conversation that included math and...

 

0:39:02.2 CT: Thank you. No, it was so fun to talk to you.

 

0:39:05.4 AS: Alright, thanks.

 

0:39:06.7 CT: Alright, bye Audrey.

 

0:39:09.7 AS: Again, a special thank you to Chrissy Trinter for the great conversation, and thank you all for joining us for Think-Pair-Share. If you enjoyed this episode, head on over to Apple Podcasts to subscribe, rate and leave a review. It's very much appreciated. Check out our website at IEI.nd.edu/media for this and other goodies. Thanks for listening. And for now, off we go.

 

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