Impacting Teaching Practice with Routines for Reasoning

00;00;00;00 - 00;00;25;11

Amy

Teaching inherently is an art of continuous improvement. We're never there. It's a little mathematical to think about. We always have distance to go to get there wherever there is. And the routine allows you to like, do just the what of the routine the first time out and the second time pick an essential strategy or pick a shift and work on that shift through the routine, pick an essential strategy and work on that.

00;00;25;14 - 00;00;50;11

Amy

And you know what? Maybe this time I forgot to mention the sentence frames in starters throughout the entire routine. And they were on the slide, but I never mentioned them. Next time I do that routine that's going to be in the forefront of my mind. Right. So there's always like there's just a little something you can work on each time, which also makes it more rewarding.

To your point, Johnny, about change, to like, feel the success, feel the impact and keep the momentum going. 

00;00;53;00 - 00;01;12;01

Curtis and Joanie

Welcome to 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 better.

00;01;14;17 - 00;02;03;00

Joanie

In this episode of Room to Grow, Curtis and I continue our conversation with Amy Le Center and Grace Kelemenic, Authors of Teaching for Thinking and Routines for Reasoning. Our previous conversation centered around how the routines and essential strategies that Grace and Amy outlined in their books support all students abilities to engage in deep mathematical thinking. Today, we shift the focus to teachers and the ways in which the routines and essential strategies help teachers to be better at their craft. We acknowledge that teaching is a complex and difficult endeavor and showcase how teachers can focus on student thinking. Get out of the way of student learning and support productive struggle for all students. We know you'll get some great ideas that you can implement in your setting right away. So let's get growing. 

00;02;04;17 - 00;02;40;07

Curtis

Well, Joanie, I am so excited to be back here with you again today.

And we are continuing our conversation with Amy Le Center and Grace Kalemenic. And really today, we're going to be focusing now on the idea of routines as support for teachers and talking about and having the focus on teachers. So for our listeners who maybe listened to the last episode, we really tried to look at those routines as support for students and how we support student thinking and engage with and focus on and highlight student thinking through those routines.

00;02;40;07 - 00;03;02;25

Curtis

And this time around, we're going to be really talking more about from the teacher standpoint and thinking about how those routines support teaching of the mathematics. And so really excited for this episode. And so I'm just going to jump right in, Grace and Amy, and ask you a pretty direct question, but it's huge. And that is what makes teaching hard.

00;03;02;27 - 00;03;15;00

Curtis, Grace and Amy

I think what makes teaching. How much time do you have that we could do like a whole year of podcasts on that? We could. We could. Let's do the Reader's Digest version of that, though.

00;03;15;00 - 00;03;31;27

Grace

 I think what makes teaching hard is two things. It's a human endeavor. And because it is, you have to make a hundred million decisions in the moment throughout a lesson based on kind of what's with the interactions with students and what's coming at you.

00;03;31;18 - 00;03;56;13

Grace

Like, as much as we plan our lessons, we are about what we want students to learn, the way in which they go about learning it and the way in which they interact around the contents. Always different and unexpected. And even if we have a plan B and a C and, you know, A now and thought about what they know coming in the door, we still are constantly making decisions in the moment and that's what makes teaching so challenging.

00;03;56;13 - 00;04;43;04

Grace

And we haven't even talked about classroom management and all the interruptions and parents and administration and all of the other things, right? And testing like, we haven't even gone there. But just the business of today is the day to day. And so, yeah, so routines are super helpful supports for teachers in that way. And in fact, in the in the previous podcast, Amy had mentioned Magdalen Lampert as someone who was thinking about using routines, although she called them because she's much smarter than we are, instructional activities, structures, structures in which you put instructional activities and she lives in the pre-service world.

00;04;43;06 - 00;05;43;25

Grace

So these instructional activity structures, a.k.a. routines, were developed first as supports for new teachers. Because teaching is such a complex endeavor and a new teacher is just barely keeping their head above water, There's just so much to learn and so much to do. So if you can hold that design or the structure of a lesson study, it frees up the teacher to be able to be responsive.

Yeah, in the moment and student thinking and do that hard work of like student centered teaching. So I routines for reasoning really have their origins in Magdalene's work, like coming out of the pre-service world. In fact, when Amy and I were at the Boston Teacher Residency program working with the Mass residents, that's how we worked with them to learn how to teach through the routines.

We taught content, really routines, and we taught them how to teach them the routines.

00;05;43;25 - 00;06;32;07

Curtis

 Yeah, I love that. The pattern, the consistency is great for students, right? Because we see that students can get comfortable, but it's also so supportive for the teacher, both early and pre-service teachers, but also just experienced teachers in continuing to be free to be able to respond and to think about what students are doing, what they are thinking, to recognize their thought processes and be able to think about how they develop and draw out and help students make connections.

So I love that. I love that very much. Just thinking about that. And the essential strategies that you talk about, how do those come alongside of those routines? How do we build those in support of teaching? 

00;06;32;07 - 00;07;21;27

Amy

When we think about the essential strategies with the lens of pre-service teachers and teachers just learning to teach, they're giving them concrete strategies to engage all learners in mathematical thinking.

And oftentimes in the pre-service world, supporting special populations comes last. And while true, it's the higher thought of it. And and maybe they're not ready to learn why and how. And the critical nature of these central strategies in supporting special populations. But they're starting out supporting them without even knowing it. Right. So if a new teacher or an experienced teacher is implementing annotation, ask yourself questions for hours, sentence frames and starters and turn in talks.

00;07;21;29 - 00;07;49;26

Curtis, Amy and Grace

Yes. Who alphabetical again? I love it. Well done. I should buy a lottery ticket two times. Right? If. If they're implementing those, they're inherently supporting each and every learner. And through time they'll realize how and why and how critical those essential strategies are. So they're not making decisions like, I just read this student's IEP and they need a visual for everything that's being said.

00;07;49;28 - 00;08;11;11

Amy

And I just read this students IEP and they need multimodal learning and this student needs things repeated to them and this student needs support and language production. And now they're like overwhelmed with all the supports they need to provide. Right? And all of the ones I just mentioned are supported through the essential strategies. So in many ways those are essential strategies.

00;08;11;14 - 00;08;35;27

Amy and Grace

Do a whole lot of heavy lifting. Whether teachers are aware of it yet or not. I'm not sure that answered the question. I think I went on a little bit of a tangent, but I think it was great to yeah, great start there with supporting all students and, and I think just to kind of maybe fill it out a little bit more, it's supporting all students to develop the capacity to think and to reason mathematically.

00;08;35;29 - 00;09;04;08l

Grace

Right. And so teaching thinking is, we think, different than teaching students to learn a particular procedure or for sure it's a different it requires a different kinds of interaction. And we always talk about it as it requires sort of three big shifts for teachers. One is to focus on the thinking, make sure that's where the conversation, the intention and the focus is.

00;09;04;11 - 00;09;29;16

Grace

The second is to step out of the middle of classroom interactions and have students working and talking with each other. And then the third is where Amy started, which is supporting productive struggle, making sure every student has access to the thinking. We can see that there's their thinking and they keep thinking and they're reflecting on it and building their capacity to think mathematically.

00;09;29;19 - 00;09;56;22

Amy

Yeah. The tricky thing for us as educators is it's not always the way we've been teaching. And so to make these shifts, we need supports to do it. And what whether you're brand new teacher and maybe your experience as a student didn't look like that. So now you have to recreate this image of a classroom or your veteran teacher of 30 years and you have you have some habits you'd like to shift and maybe even create new habits or break old habits, both cases.

00;09;56;22 - 00;10;32;02

Amy

That's really hard work. And so routines support that work through and through because routines are, well, routine. We get to do them a bunch of times, right? So we're not just saying, I'm going to work on stepping out of middle tomorrow and I'm going to do that by facilitating turn in talks tomorrow. It's every time I do this routine, I can work on stepping out of the middle and focusing on facilitating productive turn and talks.

And I can do that regularly and routinely every time I implement the routine. So the routines really help teachers toward that endeavor. 

00;10;32;02 - 00;11;09;02

Joanie

I really appreciate that you brought that up, Amy, And I'm thinking too, about, you know, change is hard. Change is hard for any of us, and change is really hard for teachers. But some of the things that motivate and support change are like there has to be a desire, right?

Even as a 30 year veteran, I think there are ways for me to say, there are some kids, I'm still not reaching, so I am motivated to do something different, to reach more kids or to take more kids to deeper learning. And then the other thing that helps sustain change is success, right? Like we have to be able to take little steps towards change and feel good about them.

00;11;09;02 - 00;11;29;13

Joanie

Like, that actually made a difference. That motivates me to continue to work on doing something differently. And I think the routines and the essential strategies provide those structures for teachers, too. First of all, we're going to see more kids. I mean, you guys talked about that in the first episode, right? Like teachers who go back and do these with their students are going to see change.

00;11;29;13 - 00;11;49;13

Joanie

They're going to see students participate who didn't participate before. They're going to you know, I think about a comment that I've heard often. Like I had no idea that kid could think that deeply about the mathematics. So that's going to be exciting to feel like they're reaching students they didn't reach without these routines. And then also they're going to feel that success. So I think that's awesome. 

00;11;49;13 - 00;11;57;02

MUSIC 

00;11;57;02 - 00;12;15;02

Joanie

Could we talk a little bit? I don't want to just reproduce the conversation that we had on the previous podcast episode, but I want to hear a little bit more about how and maybe we start with those central strategies that we talked about on the last one and through the lens of how do those directly support teachers.

00;12;15;10 - 00;12;48;11

Grace and Amy

I'm tempted, Amy, to tell a story that's sort of a knucklehead story. When we were working with the math residents at the Boston Teacher Residency program and touching your face and our proudest moment and our proudest moment, and we we had been helping them learn to teach through the routines and we would go into classrooms with them and they would facilitate a routine and the lesson would look just like amazing and all students would be talking and working and thinking.

00;12;48;11 - 00;13;17;23

Amy and Grace

And in residence, man, we had this really rigorous rubric that they from time to time would get evaluated based on that rubric and they would nail it. Yeah, they would be so good. And then we'd go in to watch another lesson that didn't have routine. It would be completely different. They would be like, Get out of the room explaining things and showing things, and kids would have worksheets on their desk working independently and they'd be walking around conferring with kids and we were like, Well, how is this happening?

00;13;17;24 - 00;14;14;24

Grace and Amy

How can they be so different? And so we had the opportunity to go to a, I don't know, conference, a place with pre-service teachers, and we bring a problem of practice and have people help us with it. So we brought this problem of practice to this meeting and said just what we said to you, like we don't understand and we put this whole big presentation together.

Here's our problem of practice. You have 45 minutes to work this out. And was it l'Homme? I don't think it was him, but the very first question, the very first question was, would have you told the residents that the things they're doing in the routine, they should also do in their other lessons? And we were like, yeah, you know, we just assumed it would kind of permeate the routine.

00;14;14;24 - 00;14;39;12

Grace and Amy

And then there are other lessons, like you have to be explicit about it. And so that put Amy and I on a trajectory to like explicitly name things like the essential strategies and pull them out and work on them at the brain size. So while you can use a routine to practice and work on developing a particular essential strategy, you ultimately we want we want to be using them in all of your lessons, routine or not.

00;14;39;14 - 00;15;43;04

Amy

Like, for example, you asked how they support teacher development and to get really specific, how the essential strategies support we can take the 4 hours and actually even just one of the hours. Rephrase and rephrase. We know that's a discourse move. It's a talk move, whatever you call it, we call it one of our 4 hours. But to rephrase specifically in the classroom allows teachers to step out of the middle and allows teachers to support productive struggle and to focus on thinking and how.

Because when an idea is shared and it involves or supports the development of mathematical thinking, the teacher can make a choice to have students hear that idea again and to step out of the middle by having students share the idea again. Rather than the teacher. So students are the ones doing the rephrasing, and that's creating a culture of student agency because they're listening to each other, they're looking to each other for ideas, they're co constructing ideas in the classroom.

00;15;43;06 - 00;16;32;25

Amy

So that rephrase move takes the teacher out of the middle. It supports productive struggle because students are now getting an opportunity to hear the ideas and the language again, right? Or maybe be the one doing the rephrasing and produce that language and idea again. And of course, the rephrase is all about, I mean, the teachers making a choice to have the idea rephrased is because it's about mathematical thinking. So a small teaching move can really support all three shifts. And it also allows the teacher to work on breaking that habit, that knee jerk reaction that many of us have to repeat what students say or or say it more clearly, or more precisely or more accurately, and without giving students that opportunity. So that's one example of an essential strategy.

00;16;32;25 - 00;17;01;23

Amy and Grace

I think the other essential strategy we talked about was annotation. You want to talk about that Grace and you want to talk about annotation in terms of how it helps support teachers. Yeah, Yeah. Again, it's supporting teachers is step out of the middle. So we talked about annotation as happening during a full group discussion. When a student is sharing an idea to their classmates in the whole class and often that's a back and forth between the student and teacher.

00;17;01;26 - 00;17;29;00

Grace

And we want the teacher to be out of the middle of the conversation and we want the conversation to be between students. And so annotation helps the teacher step out of the middle. So their role is as a student is talking and sharing an idea to be annotating it visually while the student is talking. And so the teacher is not writing on the board what they want the class to know.

00;17;29;02 - 00;18;14;17

Grace

The teacher is annotating and highlighting students thinking, and so the focus is on the thinking. That's what's getting annotated. The teacher is stepping out of the middle and not being the authority and the producer of the thinking. They are holding up the students, thinking and it's bringing in that second modality, that visual and residue to support students who might struggle to process auditory or might struggle to understand something being said in a language that they are not yet familiar and comfortable with, or a student who has working memory issues and can't remember things, or a student who is not quite sure where to focus in a conversation.

00;18;14;17 - 00;18;36;05

Grace and Joanie

All for all of those and myriad reasons, it's supporting that productive struggle and student's thinking and reasoning mathematically. Yeah, I appreciate that you came back to annotation as well because I was thinking even in the previous episode when we were talking about that, I just want to pause for a minute and talk about the fact that that is not a simple thing to do.

00;18;36;05 - 00;19;38;24

Joanie

It's a simple thing to talk about. But in the moment, annotating a student's thinking and knowing how to, you know, should I use a different color now or should I highlight that thing or not highlight that thing? Curtis knows one of my soapbox issues is how much more information teachers have to have in their minds around what they're teaching.

Like, it's not enough just to know the mathematics. That's the end goal of my lesson. I have to know so much more mathematics that surrounds that, especially when I'm centering student thinking and trying to step out of the middle. I have to be able to navigate and grace to your earlier point to like kids go every which different direction.

And even if I'm teaching the same class that I taught last year or last period to a new group of kids, things are going to go a different way. So there's an incredible amount of information the teacher needs to know and those in the moment decisions that you talked about that make teaching so hard. So I already know the answer to this, but I want to set you both up like, how can teachers think about getting better at that?

00;19;38;24 - 00;20;04;09

Amy

Well, you you hit the nail on the head, Joanie, when you said it's a complex endeavor, it's imitation is not simple. However, when you see a teacher in a state like I would say fluently, they make it look, as we say in Boston, wicked easy, wicked easy, because they've got color, they've got just enough imitation. It's not messy, it's not cluttered, but it's got enough.

00;20;04;16 - 00;20;34;03

Amy

And that you could look at it afterward and understand some of the conversation that went on and glean some mathematical ideas from it. So it can look simple for sure, but as Grace was saying, it's really responsive to what kids are saying. Right? And so as much as you've planned for it and you've really thought about how kids will think about the task at hand and how they'll go about sharing their thinking in the moment, you still are making a lot of decisions and a few tips.

00;20;34;05 - 00;22;03;23

Amy

One point in gesture while the first student is sharing and as you point in gesture, even though you're doing it silently, the students will give you feedback. No, no, no, not that. No. Over here, I was talking about that eight knots at eight. You know, like stuff that in a vacuum doesn't make any sense. But when it's responsive to your pointing and gesturing, you get a little more clear on the student thinking.

And we also stick to we like two colors and we introduce a third if necessary, but that helps keep it organized and clear. Once we introduce a third color, we run the risk of creating too much going on, right? So keep it simple. And annotation is a process. So get get some annotation down and then take a step back.

You don't have a ton of time. That's the other thing to share is you know as on the rephrase the student shares the rephrase and your annotating while the rephrasing you can't stand there annotating for five more minutes or you're going to have paper airplanes going across them. Right, right. So, so the third tip is remember that it's a process because you can get a little bit down and all you think, I wish I got more think about the more you would have liked and facilitate a turn and talk around that And when you come back from the turn and talk, you get to annotate a little more and layer some more in.

00;22;03;25 - 00;22;27;02

Amy and Grace

And finally, if you're really stuck annotating and you're at a loss, ask kids to turn and talk. How do you think I can capture this thinking for you? Then that's when you get a little more time to think about it. That's brilliant. And I would say that one of the things about annotation is it really lends itself to working collaboratively with colleagues.

00;22;27;08 - 00;23;01;16

Grace

So when you're planning a lesson and you're in a routine and we talk about the connecting representations routine earlier, but it doesn't matter what routine, one of the things you want to do is practice how you might annotate something. What are all the ways students might talk about this particular thinking and how might I annotated and you can kind of practice that offline, you know back at your Yeah but we really advocate for during department meetings or during lunch with your colleagues like okay let's let's think about this how would you annotated if a student said I did blah blah blah, how would you annotate it?

00;23;01;19 - 00;23;30;24

Grace

And practice annotation in that way and then step it up a bit and have a colleague say to you, like, pretend they're the student and say how they might have went about connecting these representations or quickly calculating or whatever the prompt is, and practice annotating in the moment while they're saying it to you so you can practice it offline where you have all the time in the world to think about it, bring in other colleagues to help you.

00;23;30;24 - 00;24;13;14

Grace

So you see other perspectives and other ideas for annotating, and then have a colleague help you by pretending they're the student and have you practice annotating moment. And and then here's the thing. It's what you're not doing is practicing so that you have the perfect annotation and then going into the classroom and reproducing it. Right. More like an actor who's practicing their lines with another actor, you know, working out a scene like you're going to move this way and I'm going to step over here and then you're going to say this, and I'm going to say that, and you work out the scene and you run it two or three or four different ways.

00;24;13;17 - 00;24;36;21

Grace

And then the director says, action, and the camera starts rolling and you let all that practice go away. And in the moment you're focused on that other actor and you're just reacting to them and you're trusting that what you did before is going to come to the fore in your acting. It's the same with annotation. You've done all this practicing, you've played around with colors, you've looked at options and different ways to do things.

00;24;36;24 - 00;24;48;04

Grace

And then when the students start sharing their thinking and it's getting rephrased, you throw all that out the window and you focus on what the student is saying and the annotation will just come out. 

00;24;48;04 - 00;24;56;04

Curtis and Joanie

That was so beautifully said. my goodness. I love I love so much about that. I can't even I to tell you, I can't either.

00;24;56;24 - 00;25;23;16

Curtis

It makes me really excited, especially if I had an opportunity to go and do this. It makes me think about the tutoring sessions that I'm going to be having with my with my middle schooler when he comes home this evening. Right. And we're going to be talking about dividing fractions or whatever it is. We're going to be doing the things that I can take and apply that I'm learning right now as I'm thinking about this, I'm thinking about being someone.

00;25;23;16 - 00;25;52;03

Curtis

So I've picked up your book and I've read this, and now I'm excited to go and try to put this into practice. What are some things and you said just now, practice, practice, practice in three different ways and I love that. What are some strategies use or are those the key strategies and how do I keep my head up when it doesn't go the way that I thought it should at the end of class?

00;25;52;05 - 00;26;17;10

Amy

Well, Curtis, unfortunately, we've been in that situation many a time. We all but ultimately the routine supports us. So these essential strategies are living inside of a larger instructional routine. And so when things start to go haywire, Grace was talking about all the decisions we make in the moment. It's almost like the routine pulls you back into place.

00;26;17;12 - 00;26;47;04

Amy

And so if I'm say, in a routine like Contemplate, then calculate in a student sharing strategy. And we just did this deep dive into the strategy that was unexpected because it needed to be discussed and processed and re discuss and reprocess in order to create some collective understanding of the thinking behind the strategy. I've now taken a bit of a detour from the routine, and it's the routine that pulls me back into place.

00;26;47;06 - 00;27;11;14

Amy

I'm not saying what's next. I'm saying, well, that was the second strategy shared. Usually we share two or three. I think we have enough structural thinking to move to the reflection. It's like that. It's your beacon, the routine and the thinking goal. And do we have enough thinking that came out throughout this for students to reflect on? So that has helped us a lot.

00;27;11;16 - 00;27;31;04

Amy

The other thing, which is a little bit a flip side of this, is to stick to the routine. If we make changes to it, we need to understand why, because every time we make a change, we we get something by making a change, but we also give something up. So understand the design of it before you start making changes.

00;27;31;04 - 00;27;58;11

Amy and Grace

It's a little tip I'd give around that. And I and I think be gentle on yourself. Most importantly, trying to develop a new habit. And you know, you don't go from not doing something to the very first time you do it being perfection, and now you're perfection. Like this is how you're built, right? And so the routines again, help you with that because they're meant to be repeated.

00;27;58;11 - 00;28;22;28

Grace and Amy

So you're going to have another opportunity tomorrow or two days from now when you use routine again to work on this essential strategy or this move that you're trying to build into your practice and teaching teaching inherently is an art of continuous improvement. We're never there. We always have. It's it's a little mathematical to think about. We always have distance to go to get there wherever there is.

00;28;23;01 - 00;28;44;24

Amy

And the routine allows you to do just the what of the routine the first time out and the second time pick an essential strategy or pick a shift and work on that shift through the routine. Pick an essential strategy and work on that. And you know what? Maybe this time I forgot to mention the sentence frames and starters throughout the entire routine and they were on the slide.

00;28;44;24 - 00;29;05;06

Unknown

But I never mention them. Next time I do that routine that's going to be in the forefront of my mind, right? So there's always like, there's just a little something you can work on each time, which which also makes it more rewarding. To your point, Joanie, about change. So like, feel the success, feel the impact and keep the momentum going. 

00;29;05;08 - 00;29;27;28

Joanie and Curtis

And there's always room to grow. That is, I see what you are all about. I've been told not to that one for a while. This is, this is great. And I really appreciate how you've shifted the focus on to the routines, on the essential strategies supporting teaching and the things that make teaching hard. And one of them is the lack of experience.

00;29;27;28 - 00;29;59;22

Joanie

And I appreciate it. Like Amy, when you were describing the opportunity to use the term to talk, to give yourself a moment to pause as a teacher. Like these are great things for early career teachers to be able to do and then grace your idea around doing prep with your colleagues. Like that's a great opportunity for even an experienced teacher who might be teaching content new for the first time.

And like, I don't know what kids stumble over. I haven't taught this content before, so I might not have my own thinking about the mathematics might not be enough to have me well prepared for the lessons.

00;29;59;22 - 00;30;05;24

MUSIC

00;30;05;24 - 00;30;19;24

Joanie

Yeah, I would love if we can shift in the last part of this conversation again to talking about one of the routine specifically and through the lens of how that supports teachers and teaching.

So I'll let you guys pick. What do you want to talk about now? 

00;30;19;24 - 00;30;55;02

Amy

You know, contemplate then calculate. Although it does not appear in print until teaching for thinking, which is our second book, Contemplating Calculate was one of our first babies and we leaned on it heavily when we were in Boston working with pre-service teachers and we used it as Grace was talking about develop all of these teaching habits and and built our syllabus around it, actually to use it to teach content to the residents to develop their mathematical thinking and all the moves embedded in it to develop students mathematical thinking.

00;30;55;02 - 00;31;19;28

Amy

And it's kind of bite size, it's pick up the ball, it's maybe 15 to 20 minutes long and it has a lot in it to work on over time. It's also a refreshing experience for students. So in that regard, it's inviting to start out with so contemplates and calculates starts like all of our routines with a thinking goal, in this case a structural thinking goal.

00;31;20;00 - 00;31;51;27

Amy

We start with what we're doing and why we're doing it and contemplate, then calculate the what is finding a shortcut. And shortcuts sometimes has a negative connotation of mathematics, right? But this one does not. Yeah, it's not a shortcut without reason. It's a shortcut based in mathematical structure. And why we're doing it is because mathematicians often look for elegant, efficient ways to think and work based on mathematical structure, not based on tricks.

00;31;52;00 - 00;32;15;15

Amy

Yeah, we'll go down the tricks road and then the overview of the steps of the routine. There's going to be a part where students notice. Then they're going to develop a shortcut with their partner. We'll share and study them in the full group and then finally reflect on learning. What's unique about contemplate. Then calculate is that students don't pick up a pen or pencil until that reflection part.

00;32;15;17 - 00;32;47;12

Amy

And so that's incredibly refreshing in that for some students, they don't realize they're doing math and they're not writing until the very end. And it starts with the noticing process and the noticing process and contemplate. Then calculate is a flash of a task, a flash of a visual, a numeric expression, an equation, a graph, a mathematical object or task and flashes for about, I don't know, like 1.2 seconds, like really, really fast.

00;32;47;14 - 00;33;20;09

Amy

And students, their task is not to do anything with the task except notice and ask themselves, what do I notice that might be mathematically important? And then they quickly share that noticing with a partner and listen to their partners noticing those notice things, and then the teacher in takes them and has students share out a few and the teacher records a few of those notice things just enough for the class to then use some of those noticing to work with their partner and develop a shortcut.

00;33;20;12 - 00;33;43;29

Amy

And the test comes back up in front of students and they work together to develop a shortcut collaboratively rather than find a shortcut and tell your partner, but together use a noticing and develop a shortcut based on mathematical structure. And while students may be developing a shortcut based on mathematical structure, they may not understand that it's based in structure.

00;33;44;01 - 00;34;11;16

Amy

They might be focusing on the what. And so in the full group discussion, we then share the shortcut, but students share it with their initial noticing. We notice blah, blah, blah. So we blah, blah, blah and we get a rephrase out and we get some annotation out and maybe a turn and talk on about the structural thinking or the noticing or why it was helpful or if it's allowed.

00;34;11;16 - 00;34;47;07

Amy 

Is this shortcut really valid? So a turn and talk about the thinking behind the shortcut and maybe share a second one, maybe even a third one. And so it's engaging because students are hearing how each other are thinking. They're hearing multiple ways to think about one task. The,  the process is inviting. Students are hearing it multiple times. They're seeing it through annotation and a lot of times and contemplate, then calculate you get the big aha in the room and you don't just kids don't just have it.

You hear it, it's audible.

00;34;47;07 - 00;34;58;28

Joanie, Curtis and Amy

That's so fun. I love it so great. and as soon as you hear that, that's a great.

00;34;58;28 - 00;35;28;17 

Amy

You thought that was cool, Wouldn't you like to think that way in the future? And you can go back to that structural thinking. What do you think caused this partnership to develop that shortcut?

What did they notice that helped them develop it? And it really allows students to buy in. Like, Yeah, I would like to use that kind of thinking again and maybe next time I have to look for negative space. So I have to connect to what I know about area or exponents or, you know, whatever that whatever the noticing might be.

00;35;28;19 - 00;35;56;23

Amy

And then of course, we end with a reflection. And again, there are a few options for sentence frames, and students now pick up their pen or pencil and do a little individual writing, reflect on their structural thinking throughout, contemplate, then calculate share with the partner we share in the full group and record. So in that little nugget, teachers have the opportunity to work on Ask yourself questions.

00;35;56;23 - 00;36;26;24

Amy

That very first one. What do I notice that might be mathematically important? They have the opportunity to work on annotation during the full group discussion. They have the opportunity to work on the 4 hours when a shortcut shared it then gets, if necessary, rephrased reworded and some recording some sentence frames and starters. Every time students share out in the full group or in writing their sentence frames and starters to support them.

00;36;26;24 - 00;36;55;12

Amy

So teachers get the opportunity to work on how they're framing sentence frames and starters for all students, not just providing them on the slide, but modeling them, ensuring that kids use them. When kids share out, reminding them to use them. So that focus on thinking stays throughout and turn in talks and turn and talks happen again in that social group discussion based on responsive to the shortcut being shared.

00;36;55;14 - 00;37;27;04

Amy and Grace

So all five essential strategies are in there for teachers to work on in this like really short class time, relatively short, all the while building class culture and student agency and all the good stuff we talked about for students as well. There's a lot, I think like the standards for mathematical practice, the math teaching practices are really important and we are all as educators trying to live into them, right?

00;37;27;06 - 00;37;59;24

Grace

Just like the S&P is. The math practices, those math teaching practices are big and they sound really good. And I want to do them like facilitate meaningful math discourse. Yes, sign me up. I want to get good at it. And using a routine and focusing on the 4 hours or turn in talks and annotation during class discussions helps you facilitate meaningful math discourse that the brain size is, as Amy says, pick up.

00;37;59;24 - 00;38;10;02

Grace

All right. It's something it's sort of the right brain size to work on to get toward that big teaching practice. You're trying to get better at.

00;38;10;02 - 00;38;24;18

I love that. I love that. I'm just in awe. Yeah. I'm sitting here in just are today listening to this and just one wishing I had heard this and had this with me when I was in the classroom.

00;38;24;27 - 00;38;47;03

Curtis and Amy

I just think about the things that I did just naturally that were pieces and parts, but the fact that you've got it so well structured and so followable, it's it's tangible. I don't know if that's a good way to say that you are on our team. It's implementable, it's pick up a ball and now it's follow up and now that's valuable.

00;38;47;03 - 00;39;12;15

Curtis

I just feel like these are things that I could go out tomorrow, put into practice and yeah, it would take me practice in doing it, you know, routinely over and over again. But I'm just so excited about this content and these practices and routines and the strategies that support them and that are built in as a part of each one of them that's why I was speechless, which doesn't happen very often.

00;39;12;15 - 00;39;42;19

Curtis 

Johnny can tell you, Curtis being speechless just isn't something that happens. But I just was very I was taken aback and so excited and then seeing this as the support for teacher, right. So really thinking about how do we help teachers in the teaching of mathematics and really developing that mathematical thinking in their students. We see the benefits for students, but then just seeing this, it gives me hope for the help and the benefit for teachers, I'm just so excited.

00;39;42;26 - 00;40;01;26

Grace

When we wrote Teaching for thinking we really hoped the teachers would pick it up and use it with themselves and with their colleagues to develop their practice. And we assumed we're going to say this out loud because we've learned that if we don't say it explicitly, it might not happen. When we had to go across the country to that meeting.

00;40;02;02 - 00;40;41;15

Grace, Curtis and Joanie

Right. Right. You learned your lesson there. Learned our lesson. We also kind of had in the back of our mind coaches, right. Routines are just lovely vehicles around which to coach to help support teachers work on practices in a school. And so, yeah, they're just a nice tool. I think that's so powerful. And even thinking about administrators and classroom observations and helping administrators understand what to be looking for in a math classroom can be really valuable, especially for our secondary teachers, where we don't always have administrators that have the content, knowledge, background and they can get a little hung up on that from time to time.

00;40;41;18 - 00;41;10;02

Joanie

Also, just share Curtis's excitement. I just think the two you are amazing and your work is so powerful and incredible and just so grateful that you took the time for not just one but two episodes with us. I want to acknowledge that you have a ton of really amazing resources available, not just your toolbox, but on your website.

We'll link to that in the show notes. But I wonder if you could maybe just pick one or two things to direct people to, you know, as they dive in? 

00;41;10;02 - 00;41;10;02

Amy

Yeah, our virtual home is that fostering math practices dot com and we try to keep it as updated as possible. When you go there, you'll find resources on avenues of thinking and special populations, but The most heavily trafficked area is around the routines and there's a drop down on reasoning routines and we have a page for each routine.

00;41;34;01 - 00;42;00;29

Amy

And when you get there, you can access classroom resources like a planner and a student reflection sheet. And the slides, the Google slides you can make a copy of and use in your classroom freely or in PDF or however you'd like. There's also a place where you can view tasks to see the kinds of tasks that work and routine, and really to develop your own eye, to grab your own tasks, to insert into schools.

00;42;01;01 - 00;42;19;08

Amy

Some of the routines have videos as well so you can check those out and some PD materials around them or articles or blogs relevant to each routine. If we have them, they're up there and you'll also find where to find us. So hopefully we'll see all in person. 

00;42;19;08 - 00;42;52;29

Curtis

Well, Amy and Grace, I just say again, it's hard for me to even have anything to add to any of this.

I'm so excited. And thank you guys so very, very much for taking the time to do these two episodes with us. I know our listeners certainly have an opportunity and can get really excited behind this. I know I am excited to go and to share this content with folks that I run into and so I know I, I learned a ton and so I'm really, really pumped about this.

00;42;53;01 - 00;43;05;25

Amy

Well, thank you for having us here today. And on the last episode, it's it's really helpful to get this information in the hands of teachers. And thank you for doing that work then. Really, really great. Appreciate it very much.

00;43;05;25 - 00;43;46;06

Joanie

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.