In this episode of Room to Grow, Grace Kelemanik and Amy Lucenta join Curtis and Joanie to talk about how routines can provide the “opportunity and support for each and every student develop mathematical thinking and reasoning.” Although routines are used by most educators for a variety of reasons, Grace and Amy focus on “Routines for Reasoning,” which are specifically designed and structured to surface the ways that students are thinking about the mathematics and to better understanding the reasoning of their classmates to reinforce the mathematics content and thinking goals.
In this extended episode, Amy and Grace dive deeply into the “Four Rs” and “Annotation,” two of the five “Essential Strategies” that teachers employ within the routines, with an emphasis on how these strategies provide access and opportunity for all students to engage in the deep thinking of the lesson. Then, they describe the “Connecting Representations” routine in detail to help listeners understand the power of the routines in action. As Grace shares, the power of the routines and essential strategies is that they help teachers to “hand over agency to the students. Teachers are no longer are the sole authority in the classroom... it’s the students doing the heavy lifting.”
We encourage you to explore the resources below, referenced in this episode:
Be sure to join us for part 2 of this conversation next month!
Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing email@example.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.
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Every single teacher that went back and said, Well, I did this same task and I did it the same way you guys did it with me. And that's how I did it with my students. And I had students talking in class who had never talked before. I had students sharing their thinking who have never shared their thinking before, and that caused us to say, well, what the heck were we doing?
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Curtis & Joanie
Welcome to the Room to Grow. I'm Curtis Brown. And I'm Joanie Funderburk. We work together at Texas Instruments and we're glad you're here. We're looking forward to continually improving our practice and we understand that you are, too. 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 back in this episode of Room to Grow.
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Curtis and I are joined by Grace Kelly, Manik and Amy Lou Center, authors of the books Routines for Reasoning and Teaching for Thinking. Grace and Amy share some interesting and powerful ideas about instructional routines that they have developed to support students math thinking and their math learning. They share essential strategies that are woven into the routines that help teachers to surface the types of math thinking required by the standards for mathematical practice, and ensuring that each and every student has access to these types of thinking. It's a great conversation and we know you're going to love. So let's get going.
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Well, hey, Joanie, I am really excited to be recording once again The Room to Grow podcast with you today, and we've got really a pretty cool opportunity today to interview a couple of folks. I'm very excited to learn from. And before we jump in, I just would like to introduce Amy Lou Center and Grace Kellman, who are here to chat with us today.
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Curtis & Joanie
Amy and Grace, welcome. Yay. Thank you. Curtis and Joanie were psyched to be here. So excited to have you here. There are a handful of math education books that I consider my favorites, and both of yours are on that list. So thank you so much for joining us. We're really excited for the conversation. So Amy and and Grace, Amy, maybe you can go first and give us just a quick introduction of who you are and where you're from and all of those great things.
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Sure. My name's Amy Lucenta. I'm a former originally starting out middle school math teacher, turned middle school high school math teacher, turned elementary math coach, pre-service. So basically, what's the expression, master of none. I forgot the first part, but I just remember the times. Yeah, I just remember the second part is master of none. But. And now I have the privilege of working alongside Grace and working with teachers to really promote access and opportunity and support for each and every student to develop mathematical thinking and reasoning.
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So I'll turn it over to Grace. Thanks. Hi, Curtis. I’m super excited to be here. I'm Grace Kelly. Manek and I. Let's see, what do you need to know about me? You need to know maybe that I was a high school math teacher and math teacher in Boston. I worked for a bunch of years at a research and development education think tank, Education Development Center, and then worked with Amy at the Boston Teacher Residency program, where we helped grow new teachers to teach in urban settings.
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And that's awesome. Yeah, So great. Well, we've got you guys here today to chat about some of the things in a couple of your books, and we're really excited about that. And I guess maybe the place we should start is just this idea of routines as support for students and learning. So I'm thinking about this and maybe a good baseline for us to start with would be like, what are our routines when we say that word?
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It's something that, you know, it's a familiar idea, but then at the same time, what we're talking about, especially in this context, is potentially a little different than what folks might think about. So what are routines and why are they important?
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Amy & Grace
Yeah, sure. Let's I'm looking at it. It's a big one. It's a it's a big one. I mean, I think everyone listening, anyone has ever been in a classroom or taught or for that matter, had kids or really anything.
We use routines all the time in classrooms with students, in part because, you know, there are 18, 28 small bodies in a classroom and we're trying to get something done. And so routines help us do that, like walking in the door and kind of knowing what to do as you come in. The door is helpful. And so there's all sorts of classrooms and routines that happen.
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Amy & Grace
There's a lot of routines that just make every minute count in the classroom, right? So kids walk in and they get their homework in the homework bin and they take out their notebook and they write the day down and the goal for the day and start the day now. And that might be an entry in the classroom routine or during kindergarten.
It's how you line up to go to lunch and all kinds of routines, management routines for handling things that come up in the classroom. And so we know they're key to making a classroom run and they're predictable and they build habits. And so for those reasons, we like them, you know, build good schooling habits and they make the classroom kind of hum.
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I love that. The first book that the two of you wrote, or maybe it's not, but the first one that I read, certainly it was called Routines for Reasoning. So certainly there are definitely routines. I reflect back on my own time in the classroom and I had lots of different routines for different procedures, lots of them logistical, but also some that were focused on instruction.
So how do routines for reasoning differ from your standard classroom routines? And as you answer that, I'd also love to hear like what prompted the book? What prompted you all to think about and identify these routines for reasoning and call them that and put them into a book.
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Amy & Grace
Whenever someone asks that question like, How did how did these evolve?
It feels like the same question as like, how did you meet your life partner? Oh, there is a lot that went into it that made it all coalesced. But first, what makes reasoning routines different than logistical or management routines is simply the goal. The goal is mathematical thinking and reasoning versus management materials, logistics. While those might be embedded into a reasoning routine, it's not the goal of them.
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Amy & Grace
And so every piece of a reasoning routine is targeted toward mathematical thinking and reasoning for all students. And throughout it starts with a math thinking goal and then throughout all of the supports and all of the opportunities for the teacher to orient student thinking is toward that goal, that mathematical thinking goal. And then actually most of our routines end with a reflection on that thinking goal.
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Amy & Grace
So there's that is just a common thread all the way through, and that makes it very, very different and feel different. In addition, it's not just the goal and the activity and the reflection, but it's the ways in which students engage throughout the routine that make it routine. So it's not just a kind of math task. Like, I don't know, I'll pick like a card sort.
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Amy & Grace
A card sort is kind of a routine, right? Like we sort cards. We know how to sort cards. We we know we're getting a packet of cards when we were cleaning them up at the end. But what makes it for us a real reasoning routine is the way in which students, teachers and the mathematical content interact throughout that routine.
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Amy & Grace
So the way students work alone, work together, share out, discuss their ideas, are supported in the thinking throughout the routine. That, for us makes it very different from most classroom routines. Sure, I think those two components the focus on thinking and the specific designs for interaction, stay the same each time. Make it reducing routines, and this may get toward the sort of how we came to develop them or how we met them.
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Amy & Grace
And they always existed. We just are quite early years. That's when the Common Core Standards came out that had, in the beginning of them the standards for mathematical practice. And we were thrilled. We were thrilled that our profession took another pass at what it means to think in reason mathematically describe what that is like prior to that. And Tim had talked about their mathematical practices, and this was just a deeper articulation of them.
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Amy & Grace
And what we were noticing as we were working with schools is that folks were really had really grabbed on to the Common Core standards. Most of their attention was in all the content standards and mathematical practices were getting very little attention. And there was, I think, good reason for that. One was while they were interesting to read, there was a paragraph description of each of them and we were told we had to teach them K-12, right?
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Amy & Grace
And that's kind of it. And then of course, there were the 200 pages of content standards. And so that felt like emergent, right? The math practices felt like it was the important piece. And how do we develop these practices in all students so that they can use them to learn the content and work with the content and mathematize their world?
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Amy & Grace
And when folks talked about them, they were often, oh for certain kids. MM. Doing air quotes, you can't see this, but like my top kids I could do that with, but like start with the content first. And we worried that these practices were critical and they were going to be a whole bunch of students that didn't have access to them.
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And so and so we set about creating routines. And I actually don't even think it was intentional at first. Well, first we tried to figure out what do they actually mean, What do these math practices actually mean? What does it mean if you're looking for making use of structure right? Meaning your reasoning abstractly and quantitatively? How would you know what if you were doing it?
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And so we were engaging teachers in big, sexy, chunky math tasks that required that kind of thinking and reasoning. And then we were trying to highlight it when it happened right? I don't know if I should say this on the podcast, but you know that Oh, Amy, I'm looking at saying, I've already broken my ice. Now I've already started haven’t I? Well, there was a famous Senate.
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Now I'm not even going to say it. You make it about art. Can we talk about art instead? What art. We'll talk about art instead. Yeah. Early on I had a colleague that I went to art museums with. But Mark Driscoll, you all might know his name. Oh, sure. Yeah. Yeah. Thinking, fostering of geometric thinking. And I used to go to art museums with him, he was a big art buff, and I didn't know anything about art, but I go along for the ride and I never really understood it.
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And I once went to an art museum with him in California, and there were like the big display with, like chicken with Barbie doll heads on them. And I just didn't get it. And like, Mark, I just don't understand this, like, why is this art? And then there were these giant Kandinsky paintings with, like all different paint splattered all over them.
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And I'm like, Look, I could do that. Like, I could go paint and do that. I just don't get it. And I just I didn't I didn't have any habits of mind about art. I didn't know what to look for. I didn't know what it looked like when you did art. I didn't know about color and thickness of paint and shading and all of that.
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And he kind of like pulled the curtain back and talked to me about what's going on in the mind of an artist when they're creating something. And so that sort of, I guess, where we were with the standards for mathematical practice, what does mathematical thinking look like? What's going on in the mind of mathematicians when they're working? So this is a really long winded response, but we know it's awesome trying to bring that to the fore with teachers.
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And then we realized that the ways in which we were engaging in them in the mathematics was pretty consistent all the time, right? So we were trying to kind of habitués that and like routinized it into the routines. And then a mathematical thinking is a habit and routines build habits. So it just felt like a natural next step. And I'm going to hand it off to Amy.
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As Grace tells that story, I'm literally in the room in in the course we were teaching and we were having these epiphanies. And my mind is in a way I'm not. But my mind is there. And teachers, of course, didn't know how to teach these practices yet, so they would go back to their classroom and engage students in the same way as we engaged the teachers and to a tee.
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Every single teacher that went back and said, Well, I did this same task and I did it the same way you guys did it with me. And that's how I did it with my students. And I had students talking in class who had never talked before. I had students sharing their thinking, who had never shared their thinking before, and that caused us to say, well, what the heck were we doing that had this result?
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Because we didn't think it was that amazing. We just facilitated the mathematics with a focus on thinking. And and so it had us really unpacking the ways in which we engage teachers. And then as the stars aligned, we were working, as Grace mentioned, we worked at Boston Teacher Residency and Magdalen Lampert was working there as well, kind of studying the development of teachers and how teachers learn to become teachers.
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And I won't go into the long story, but she had an experience in Italy that had had her thinking about the ways in which you habitually engage students in learning. And so when our work collided with her kind of big picture thinking as a Magdalene's inimitable big picture thinking with a laser focus on details, we realized we had something special and formalized the routines we had been working with around the math practices. It's a really long winded answer for that now.
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We knew it was going to be you. You even warned us at the beginning. It's a big question, right? And I just a couple of things came up for me that I just kind of want to chime in here. And one is I was in a district math coordinator role when the Common Core Standards came out.
And yes, all of my teachers had the same response of like the standards for mathematical practice. Yeah, these are great, but how do I actually do this? What does this actually mean and what does this actually look like in the classroom? So I think just thank you so much for helping to name that and make that more clear.
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I think even now, 13 years later, I think we still struggle to understand what that kind of mathematical thinking is about. And I think it's there. Such an important part of that transition in math education across our country. Because even though the Common Core state standards are very controversial, still are in some cases, I don't know a single math teacher who reads the standards for mathematical practice and says, I don't want my kids to do that, like anybody would write those.
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So those are really obvious things. And then I was also something else that kind of came up for me. One of the math coaches that I worked with in my district used to say, and I just thought this was really profound. Like we have reading strategies for kids to have something to fall back on when they don't know what to do, when they don't understand.
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That's when you employ the reading strategies. And I think that at least in my early work with my teachers at my district, we didn't think about the standards for mathematical practice as strategies for understanding the math. Right. Like they're what we fall back on. And a student who understands math or finds mathematical thinking comes naturally to them does these things without intention in a lot of cases.
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But to be able to name them and specify how do you think this way and have the routines to provide that structure, I just think there's magic in that in supporting access for everybody. So I just wanted to chime in on those those two thoughts.
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We love the analogies to E.L.A. because hearing you say that, I'm like, yes, of course.
It's just it sounds so obvious when students are struggling with reading comprehension. We don't revert to I love the word phonics or the word or sounding the word out. That's not really helping the comprehension. And we know that right. And yet and math, right. Like was struggling students. We often when they're struggling, we revert to a procedure instead of an understanding right.
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Amy & Grace
And with good intention, of course, but less helpful in the long run. Yeah. Like for me the but often you see classroom forms where teachers have like a focused question for the year. And for me, I feel like my constant focus question is not like, what do you get or how do you do that? But how did you even know to do that?
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Yeah, you know, to do what you did. And when someone answers that question for me, most often it starts with Will I notice this? And so I thought about this, or I ask myself that. And when you're noticing and asking yourself questions, you are sitting and thinking, Yeah, yeah, that's where you learn how to going back to the art, I now know what notice and look for and what questions to ask myself when I'm looking at a painting or a sculpture.
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Yeah. So what do you do when you don't know what to do?
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We're anxious to get into hearing about some of the routines and we are going to go there for people who are listening. But as a fan of your work, you also have alongside the routine these essential strategies. So I wonder if we could just take a couple of minutes to talk about the essential strategies and how they support student learning.
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And I know this is another gigantic question. So Reader's Digest version may be enough to tease our listeners into picking up your book and refining and diving into them a little more deeply themselves.
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These essential strategies actually, we begin to articulate them as a result of teachers saying these routines are engaging kids that never engaged in these ways before.
And so we wanted to name what it was that caused students to engage in the thinking and develop the thinking. As Grace says, it's our it's the secret sauce of the routines. And there are five of them. A little side note in the first book, we only name four of them in teaching for thinking. We realized that turn in talks should be an essential strategy.
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We do talk about them a lot in routines for reasoning, but we elevated them to an essential strategy for a whole slew of reasons we won't get into. So there are five of them. Annotation Ask yourself questions. The 4 hours sentence frames and starters, and turn in talks. And I think I actually just did that in alphabetical order based on well done.
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And we lean into them for different reasons, but each of the five really shine a light on mathematical thinking. They really focus on the thinking and provide supports to a wide range of learners for totally different reasons. For instance, Oh, let's take the 4 hours for starters and Grace and I really work to say our hours when we talk about the 4 hours from Boston.
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But yes, but the 4 hours repeat, rephrase, reword and record repeat, like make sure everyone heard the idea. But what's different about the repeat is to have students do the repeating so that students are listening to students and not to us. And that's that's a hard one. Like, for me personally, I always repeated what kid said because I wanted to make sure everyone heard, Yeah, well, it's good intention, but it didn't create the culture of students listening to each other.
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It didn't help to create that. And so repeat, get the idea again. But have students repeating the idea refrain is the ideas heard? And now we want to dig into it a little bit. And so we have a student rephrased the idea and typically the words are a little different. The idea might be a little more precise, the words might be a little more precise, or it might be equally imprecise.
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And as Mandy Jensen calls it, rough draft math. So might be sitting there for a little bit because it takes a while to develop the idea in the language and then reword, add some precision to that language and the reword maybe the teacher reword it saying, Oh, we have a word for that in math and giving that just in time language name or it might be the teacher saying and what we're do we have and having students recall the word.
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So that's kind of a 5050 and then record create some residue of language that's being used so that it's not just in the air, but we have language to look back on and to use and reference as we continue the conversation. So it's kind of like the quick and dirty of each of the 4 hours. And I wanted to give you an overview of them so we could talk about how they support a wide range of learners.
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So for students who struggle with auditory processing, they're hearing it again. They may be saying it again and then they're seeing some residue of it. For students who maybe struggle with attention again, they get a second pass and not just the ideas, but also the language. And so there's like the multiple passes supports attention, it supports memory, supports a lot of processing.
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And then of course, we're making it multi-modal by having a visual support as well with the recording. So in one support that's baked into all of our routines, we can support a wide range of learners. And when we think about students for whom English is not their first language, the 4 R’s are incredibly important because they're getting rough draft language in multiple ways.
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And as I'm saying this, I'm gesturing you can't see that on the podcast, but oftentimes in the 4 R’s, you get a gesture also to support that language development. Right? So it's just so rich for so many reasons. And we could go through each of the five essential strategies in that way as well.
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I love that. I would just add one other way that that one in particular is rich.
And actually I think all of them are rich in this way in that they they slow down the thinking. And I think one of the most profound things I heard both of you say when I got to sit in one of your trainings was thinking takes time. And I think time is such an enemy of teachers. But if I'm thinking about the 4 R’s, for instance, like in order to go through all four of the R’s, I have to slow down.
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And that provides thinking space that benefits students along all areas of the learning spectrum, even the students who might be catching on quickly. That time allows for a deeper understanding. So in order to go through that, it's a way to slow things down that helps teachers feel like we're still being productive. We're not just moving slow and wandering around and aimlessly. But there's a purpose to the to the slowness.
00;23;51;25 - 00;24;15;12
Those, those essential strategies and the routines themselves create the space and time and structures to support the processing and the thinking and reasoning. Yeah, yeah. And because. Because the routines are routines and the designs for interaction stay the same all the time. There's all these things that kids don't have to think about, right?
00;24;15;12 - 00;24;42;09
Grace & Amy
They don't have to think about what's coming next, what the next set of instructions is. They know the drill, they know the routine. And so that frees up their brain space to do the heavy lifting of the thinking and reasoning. They know that when if I'm in the classroom and in Grace's just shared her thinking. They know that after Grace finishes as if she was a student, I should say that after a classmate finishes sharing their thinking, they're not likely going to be expected to rephrase that idea.
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So it's predictable enough that there's not a concern like, Oh, we have to rephrase it. I didn't hear it. They know to listen. They know what's coming at them and they know how they're going to engage. And it reduces all the time spent on directions and setting up the lesson.
00;24;58;20 - 00;25;45;10
It also just takes away anxiety, right? They realize the the predictability of it.
And that's the thing that I think I love the most about all of this is that what we're doing is setting up an expected classroom culture, right. That these routines are the way that we do things and that stuff carries on beyond my classroom. That kind of culture becomes something that students can take with them. That type of thinking and this routine of thinking and the way that they interact with other people in other classes and other learning situations, they can apply this same set of thought processes, right? I love that. I just absolutely love that. I'm so excited. It's good stuff.
00;25;45;13 - 00;26;20;23
Amy & Grace
One of the one of the strategies that's I would say very different from the 4 R’s is invitation grace. You want to talk about how that also supports students in their routines. Your annotation is done by the teacher often, sometimes by the students. But the way we think about annotation is when students are talking about a mathematical problem or a representation that sits in the routine as they are speaking.
00;26;20;26 - 00;26;58;05
So as they are sharing their ideas in the classroom, a teacher will be sort of pointing to the part of the problem that's being talked about. So it's kind of offering this little visual support and connection so that kids can it helps orient students to what part of the problem or representation is being discussed. And then as the conversation continues and the student's idea gets rephrased, then a teacher will pick out colors and start annotating the student's mathematical thinking, Hmm, getting it down on paper.
00;26;58;08 - 00;27;22;12
And it's the student's mathematical thinking in the service of the goal. And so it's really this additional processing avenue, right? This additional modality, it's offering a visual to the words students are hearing in the classroom. It's providing focus for students to kind of know where to focus in this big thing they're looking at. It stays there. So it's residue.
00;27;22;13 - 00;27;51;05
So for kids who have trouble remembering that they would a short term memory, it's there. It can be referenced as the conversation continues. That's it's very fun to do as a teacher. It's wicked fun to do as a teacher because you're listening so carefully to what students are saying and trying like in the moment to be representing it or highlighting it with color and and symbols and words and numbers and such.
00;27;51;08 - 00;28;07;00
What it isn't is describing verbatim what a student is saying. What is it? Is the teacher sort of showing the class something? It's literally happening as the student is talking. So it brings in that other modality so fun to do.
00;28;07;00 – 00;28;48;05
I can just in listening to you describe that Grace, I can see the feel of pulling the curtain back at the annotation because it's different than just scribing, right?
You're not attempting to capture every word that the student is saying. You're attempting to uncover the relevant mathematics for that lesson for all students. Because as a teacher, we know, we know the goal and where we're trying to go, but the kids don't. And so there's lots of ideas that are being thrown out that as a teacher I may recognize are relevant to the mathematics.
But pulling them together in a way that uncovers the relevant mathematics and helps students understand as well, I think is super is a it's a super powerful strategy.
00;28;54;15 – 00;29;31;05
Yeah, well, we have spent a lot of time on set up here, but I think well worth it. I wonder if in the last few minutes that we have left, if we can hear about one of the routines and through the lens of how that specific routine supports students and supports learning and especially I just value so much and I know our listeners too, we get feedback a lot on especially reaching those students who are not traditionally successful or, you know, the ones that as a teacher
are harder for us to figure out how to reach. So let's just turn it over and hear about one of the specific routines and connected to students and student learning.
00;29;31;05 - 00;29;46;27
Grace & Amy
This is this is tough. Make a choice between which child we want to talk about, but we know they're all your favorite, so we love them all. I'm thinking, Gracie, they're contemplating calculator connecting reps.
00;29;46;27 - 00;30;12;10
What we do is connecting reps. Yeah, especially after you just talked about annotation. So all of our routines start with a math thinking goal, what we're doing and why we're doing it. And that math thinking goal is very clearly connected to a standard for mathematical practice. So connecting representations is connected to math practice. Seven Look for and make use of structure and we really push on structural thinking.
00;30;12;14 - 00;30;38;16
So that's where the goal sets and then the agenda of what it's going to look like. There are five steps and we kind of do a quick overview of the steps and how students are going to make connections and share and study them in the full group. And then we'll reflect on learning. And so we do that and then we unveil two sets of representations and one set has two items in it and the other has three.
00;30;38;18 - 00;31;04;16
And so it might be let's go with stories to graphs. So there may be two stories and three graphs, or there may be three algebraic expressions and two verbal descriptions, but three of one kind and two of another. And the student's job is to ask themselves what they notice and how they might use chunks of one representation to connect to another.
00;31;04;18 - 00;31;22;10
So there are some ask yourself questions to drive their thinking when they first see these representations, and then they turn and work with the partner to make the connections. And so they're connecting either A, B and C with either one or two. So the three of one kind and two of another. It's really hard to describe this in the air.
00;31;22;10 - 00;31;44;14
I have to say. It's like robbing me of all of the visual supports and we're all visualizing alongside you. You're doing, I hope I hope students make those connections. And as students are making the connections with each other, with a partner, teachers do like the real heavy lifting, and you might not notice it unless you observe for it.
00;31;44;17 - 00;32;12;21
Teachers are going around in taking all of the student thinking, listening to the connections students are making, listening to how they're making the connections, what connection they're making, what connections they're not making, what connections they're making incorrectly. And all of that data is coming at the teacher at once, and they're quietly moving through the classroom, trying to hear from as many partnerships as possible, not interrupt their thinking, just intake it.
00;32;12;24 - 00;32;41;08
Sleuth Like going around and moving through and not interrupting. Student thinking, not conferring with them, but just in taking it and making decisions about which connections the teacher will ask students to share and in what order and makes those decisions. And if it's I'll use ourselves as an example, if we're really on our game, we can go over to a partnership and say, Can you share that connection in the full group when we pull back?
00;32;41;11 - 00;33;03;08
And that gives them a heads up to maybe practice the language they'll use and we pull that together and orient to the full group discussion and provide the roles and sentence frames that students will use when they share their specific roles. When the partnership comes up, one of the partnership is going to be the pointer and point in gesture to the connections.
00;33;03;10 - 00;33;26;23
The other of the partnership will be the speaker and do all the talking while their partner's pointing and gesturing simultaneously. And if there's a third, if perhaps there's an odd number in the classroom and there's one trio, the third will be like the manager and make sure it captures how they were talking about it. So they point and gesture and share their connection and students are observing and listening.
00;33;26;23 - 00;33;48;11
The teacher's observing and listening. Students are making sense of the connection. The teacher's thinking, How am I going to capture the annotation of this? I mean, of course the teacher plans for the annotation, but then in the moment, how am I going to capture how they've shared it? And the students often at that point return to their seat and another student in the class rephrases.
00;33;48;13 - 00;34;12;00
So like you're hearing all these essential strategies come through, right? Ask yourself question sentence frames, the rephrase as the student, rephrase as the teacher then begins to annotate the connection and enter in the annotation role. So that connection gets shared. And oftentimes there's some like meeting math idea, a structural idea that was intentional as a goal, as a lesson.
00;34;12;03 - 00;34;31;06
And the teacher has a choice to make. They could repeat it. They could say it again with more precise language, or they could throw it back to the entire class, pose a question around that thinking and have them turn and talk. And that's what we lobby for all the time. And you have that urge to be like, Yes.
00;34;31;14 - 00;34;51;11
Didn't you see how they thought about the? So to actually say so, I heard them say something. What do you think that means? Or how do you think they connected this part to this? What helped them turn and talk to your partner and then the teacher gets more intake and more data and another opportunity to annotate and the second connection gets shared in a similar way.
00;34;51;13 - 00;35;12;29
But then there's a connection that's missing. Remember we had three of one kind in two another. So two connections have been made and there's a lonely partner. So students then have the opportunity to work with their partner, to create a representation to connect to that one. And so we go from the receptive having everything in front of us to the productive.
00;35;13;05 - 00;35;35;00
And now students create their representation, and then we share and discuss that in a fairly similar way to the connections themselves. And that's really super fun. And the artwork, the annotation at the end in the representations, you can walk in and you can see how kids thought about it, which is really interesting to analyze that annotation after the fact.
00;35;35;03 - 00;36;01;27
But if we left it there, we do kids a big disservice actually, because they'd be leaving, thinking cool and math class. I learned that A went with to Yeah and we don't want them to leave right right so we end with a matter of selection and we provide three options, typically three options of sentence frames and starters for students to do a little written reflection on what they learned about thinking structurally during that class.
00;36;01;29 - 00;36;20;01
Amy & Grace
So they then have some individual writing time, share with the partner and share in the full group. And of course the teacher records a couple that are shared in the group. So it's like really the high level overview of connecting reps. I'm not sure if I did it justice. Grace What I miss that you didn't miss a thing.
00;36;20;01 - 00;36;44;13
Grace & Joanie
That's exactly right. I'm impressed with how how you captured it all succinctly. And I can picture everything you were saying. I agree. It makes it makes me want to go back to the classroom so badly, like, Oh, I like I do this with kids. It sounds like I think you set it to super fun as a teacher to be able to facilitate this and tap into student thinking and learn about how students are making sense of mathematics.
00;36;44;14 - 00;37;07;12
It makes me think like so often we walk into classrooms or lessons where the goal is not a thinking. The goal is to learn a procedure or something, and we can walk into a bunch of classrooms that are all working on that same standard. And the lessons would all look different. But the answer in the way the students got to the answers would all be the same.
00;37;07;15 - 00;37;38;09
Yeah, I'm thinking and reasoning goal using a routine. If everybody use the same routine, use those same three stories and two graphs or whatever we were doing connecting representations of. If you walked into six different classrooms all using that same task set in the connecting representations routine, the lessons would look identical. The flow of the lessons would look identical, but the annotation and the thinking would be wildly different because students Yes.
00;37;38;13 - 00;38;02;20
Grace & Amy
Now did it differently and it was captured differently. And it's almost the complete opposite. Even with the same teacher. It's the same teacher. Say is teaching middle school with three or four or five sections of the same course. The residue from each section will look vastly different. Yeah, Love it. It's very responsive and in the moment, and that's what makes it fun.
00;38;02;20 - 00;38;26;21
I can just feel the joy as you were describing this and I hadn't watching you describe this one, I can tell this is a kid that you absolutely love right out of the five and you love them all. But it's just fun to listen to you and to watch you talk us through that. But then secondly, I can imagine the joy of doing this with students.
00;38;26;23 - 00;38;56;11
Grace, You get so about this. You were I could just see you going like, I want to do this today. I think that's the coolest part because at the end, the student thinking is highlighted and then we're all connected. That emotional connection, the joy that has happened because we did it in this way, is seen and expressed and felt, and that makes the classroom culture so much more positive.
00;38;56;13 - 00;39;20;21
Curtis & Grace
And the learning of mathematics something that becomes something students look forward to, something that opens up our minds to being more receptive to those kinds of ideas. I'm just I can see the joy I can feel. It sort of changes what we think mathematics is right for sure. And who can do it. And, you know, you just hand over agency to the students, right?
00;39;20;21 - 00;39;33;23
We no longer, as teachers, are the sole authority in the classroom and students are doing the heavy lifting. They're doing the thinking and reasoning and convincing themselves and convincing each other. Yeah, Yeah.
00;39;33;23 - 00;39;49;26
Awesome. Well, there's a lot more to unpack here. And we're going to wrap up this episode for now, but we're really excited to have you back for a second episode, so we'll tease our listeners with that and thank you both so much for your time and we look forward to the next conversation.
00;39;49;26 - 00;39;52;06
Amy & Grace
Thanks, Joanie. Thanks, Kurt. It's fair to say thanks, Joni.
00;39;56;00 - 00;40;14;20
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. 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.