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Episode 19: 5 Practices to Improve Your Practice - An Interview with Peg Smith

Updated: Jul 30, 2021

Desiree Harrison 0:00

Before we get started with today’s learning, let me ask you - Did you know that there is a FREE National Math Festival happening online? I was first introduced to this festival two years ago and let me tell you it was one of the most fun weekends! And did I mention that it’s free? The 2021 National Math Festival is for people of all ages and brings together fascinating mathematicians to explore the playful side of math, as well as games, puzzles, film events, book readings, and live performances for all ages. The NMF showcases the beauty, power, fun, and importance of math for everyone. They have an amazing lineup of activities happening now through the middle of April! This is a great opportunity for families and classrooms. Find out more at

If you're listening to this episode while you're working out, or doing chores, or driving, you might want to listen to this a second time when you have the chance to sit down with a pencil and a notepad because Dr. Peg Smith is a master and you're going to learn so much from her. I'm so excited for you to listen in.

A headshot of Dr. Peg Smith
Dr. Peg Smith

Desiree Harrison 1:50

Today’s guest, Dr. Peg Smith, has written almost one hundred books and articles (that's so impressive) and she has devoted over two decades to creating research-based materials for teachers and teacher educators. In addition to receiving numerous awards for her accomplishments, she was an NCTM Lifetime Award recipient in 2019. She is an amazing gift to the mathematics education community and I am so honored to have the opportunity to interview her.

We have our special guest, Peg Smith, welcome to the

Kids Math Talk Podcast!

Peg Smith 2:33

Thank you for having me! I'm excited about talking with you about the 5 Practices.

Desiree Harrison 2:40

Yes. If this is your first time listening to the podcast, or if you've been here before - The 5 Practices is something that I reference a lot. So Peg, you have this new book, The 5 Practices In Practice, and it's actually a series. So, we're gonna be focusing on the elementary version, but if you are a middle school or high school, you have access to that too. So you have this nice collection.

Kids Math Talk, we're all about getting kids to engage in deeper discourse, so if you wouldn't mind just giving us an overview of what the 5 Practices are for those who might not be familiar with it.

Peg Smith 3:16

Sure. So the 5 Practices was intended as a model to help teachers engage students in authentic discussions, and the real emphasis in the 5 Practices is on advanced planning prior to a lesson so there was less improvisation needed during the lesson. So rather than having every decision you make to be thinking on your feet, it's trying to front load a lot of the decision-making to happening before you ever set foot in the classroom.

Practice #1: Anticipating

So the original 5 Practices begin with, Anticipating all the ways students might solve a task, the questions you might ask students who produce different, who engage with different solution strategies, the solution strategies that you think are gonna be most useful to helping highlight the key mathematical ideas from the lesson.

Practice #2: Monitoring

And then the next practice is monitoring, which is about paying careful attention to what students are doing or saying as they work individually and with their peers in solving a particular task. So the key to monitoring is really trying to get a sense of who is doing what. So of all those strategies that you anticipated students might do, which groups of students are actually using which strategies. And keeping track of that in a very purposeful way, so that when you're ready to enter into a whole class discussion, you have a really good written record of what's available in terms of the ideas that you can pull into a discussion with the whole class.

Practices #3 and #4: Selecting & Sequencing

The next two practices are Selecting and Sequencing and it's kinda hard to separate those from each other. But Selecting is about deciding which solution strategies you're going to highlight because of the mathematics available in the solution and which student or students you're gonna ask to present that strategy. And Sequencing is about- once you've decided which solution strategies are gonna be the focus of discussion, what order are you gonna have those in. And ordering them in a way that tells a story. We think about it like a story line - How are you going to start and how are you going to build up, sort of crescendo, to get to the big idea.

Practice #5: Connecting

And then the final Practice is Connecting. And Connecting is about two different kinds of connection - it's about making connections between different solution strategies that have been presented and then connecting each strategy to the key ideas that you're highlighting in the lesson. And this is really among the most challenging of practices-a lot rests on the teacher in terms of asking the questions that are gonna help students make the connections so that the teacher isn't telling the students what the connections are, but she's asking the questions that will cause them to reflect and explore the solutions they've just been looking at.

Now, I said the original 5 Practices because every on in talking about the 5 Practices, I was working with a group of coaches in Los Angeles Unified School District, and after I presented these, one of the coaches said, "Peg, I think you're missing something." And I said, "Oh?" And he said, "What about setting a goal and selecting a task?" And in our minds, and when I say "our", my colleague in writing the original book was Mary Kay Stein, we had thought- of course you have a goal and a task before you started engaging in the Practices, but it became very clear that it was really important to specify the importance of setting a clear goal about what students are intended to learn as a result of engaging in the activity, and selecting a high level cognitively demanding task that aligns with the goal for the lesson. So, we had already written so much about the 5 Practices that I decided to call it Practice Zero, and then Zero sub-A and Zero sub-b. Yes, I know that's actually seven, but there was already a big fat five on the book that was coming out and, so, we left it as five plus.

Desiree Harrison 7:54

You know, I like that five because that's less than ten...cuz when you get to seven, then it starts to feel overwhelming to some people. But if you have this five, you're right in the middle and you can think that, this is doable. And then I also like what my mind does when I think about zero because I think about that foundation and this is my true starting place before I move on to Practice One. So, I actually like that the, sub floor and foundation analogy and it helps me talk about these practices with other teachers and how, it's really strong foundation - that you have to have that goal, setting a goal, but then also you're talking about setting a mathematics learning goal versus just a performance goal. And there's so much rich conversation that can be laid in that foundation.

So then, if we're thinking about the Anticipating Student Responses, you were saying how, if you're actually doing that and you're having that advanced planning, then every decision you're making in the classroom isn't so haphazard, I view it, and I find that when I was in the classroom, I didn't think about Anticipating Student Responses, so then it was kind of - a student's response often caught me off guard! And then, you become a little flustered, and then you have some decisions to make - do you truly honor this thinking that you never would have thought of in ten years, or do you stick to some type of original plan that might be in the curriculum guide that you have next to you. And that decision is oftentimes a split second decision if you haven't done this practice of Anticipating Student Responses, which can lead to equity issues, it can lead to disengagement issues, and it's just - so much is in this. It's so important and why is it still so challenging for teachers to take this step of advanced planning?

Peg Smith 10:05

Anticipating I think is really hard because most of us learned one way to do something, so that's our expectation, is, there's one way to do this, and that's the way I learned it, and so my job is to help you learn this way to do it. So, or, the challenge is trying to break out of that, and thinking about, okay, this, let me get this one out of the way. This is the way I learned it. I know that I solve a proportion problem by setting up and using cross multiplication. And I know how to do that. And, that's what I want you to learn. But what that does, as you say, it's an equity issue because it sort of ignores all these other approaches that might be equally valid and that may give you all kinds of insights about what students are thinking. Now maybe they're not initially the most efficient, but when you're first starting to work on something, it really isn't about efficiency, it's about trying to get at understanding how this thing works. You can build up to efficiency later on if that's necessary.

So, Anticipating is really important to do because it positions you not to have to respond to every student and every group in the moment. It sort of gives you the luxury of time by thinking about what they might do and how you might respond to that before you ever set foot in the classroom.

So what you want to think about is - What are all the ways that students might solve this task? Could they use a picture? Could they build something with the right manipulative? Could they use symbols, or numbers, or anything that would give them more access to the task. And whatever you identify, then make sure you've got those resources available so that students can actually build it if they need to. Draw it on a nice size piece of paper with different colors if that's important. And then think also about the things that might go wrong. What are they likely to confuse? What strategies might be dead end? Because you'll be better positioned to help them move past some of those incorrect or incomplete strategies, if you've thought through them in advance of the lesson.

And then for every strategies, correct or incorrect you came up with, think about - What would you want to ask the student who produced this? Or the group that produced this? What questions are going to illuminate how they are thinking about the task? What questions are going to help them move beyond what they've done-whether it's correct or incorrect? Even if they've got a correct answer, there's always a question that's gonna help push them.

So, in my work with teachers over the years, I mean a lot them will just throw up their hands and say I can only do it one way. And then it's like, ok, well, suppose you try to draw a picture of what was happening here? Suppose you made a table? Suppose you had this manipulative and you could build something? So, actually for every problem trying to run through - What are my representational options here that might trigger me thinking about some other way to get into this. I mean, when I started doing work with teachers, you know some decades ago, I didn't have a huge repertoire of ways I solved problems. I sort of got better at it - I challenged myself to, for any given problem could I draw a diagram? The answer is, you can for lots of problems. And sometimes the diagram itself at least gives you - lets you enter the problem even if it doesn't get you to the solution path. I was even working on a problem today, where making a table, for example, to look at an exponential function. It isn't the most efficient way to do it, but what it allowed me to do, is to see the pattern, and then the pattern allows you then to go to something else.

So, what I've encouraged folks to do is, you know, run through the representations. If that doesn't help, give the problem to somebody else to do. And ask them how they would do it. I've even suggested, post the problem on MyNCTM. People are on that thing 24 hours a day, I swear, and they're always asking people questions. My guess is if you came home from school, and you posted a problem, by the time you were finished with dinner, you'd have people who'd given you solutions to it. I used to make my husband solve problems, you know, when you were in a restaurant that had crayons and paper on the table, and I got a lot of intuitions (laughing) a lot of ideas from just those sort of settings. So I think it's really about trying to move beyond your original thinking about something and trying to just dig a little bit deeper.

Desiree Harrison 15:23

What you were saying about, the, just having things on MyNCTM, I've also seen that on Twitter. Where somebody will just throw up and say, "Hey, how would you solve this?" And, I think that making the mathematics more public is a wonderful thing because then you're no longer in isolation.


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Desiree Harrison 16:01

Overheard shot of woman preparing meals in containers.

Thinking about the pieces of the 5 Practices that are done ahead of time, and if we encounter teachers who are hesitant to that, to think about other aspects of our life and how a little front end preparation can make the actual day of the end so much more pleasant and run so much more smoothly. And that reminds me of meal prep actually. And how much I hate meal prep on Sundays! And if I chop up food, ah, chop up vegetables, and get everything packaged, how that - you know it might take me a half hour to prepare that, but then when Wednesday comes, and I can just go in the refrigerator and pull that out, and then I have my mise en place, I think it's called in the cooking world, where I have everything ready to start. So then I'm not thinking, like, "Oh, it's Wednesday at 6 o'clock, I don't have - I need to like go back to the store cuz I didn't something." Like, you already have those things in place, so you can just put it in the skillet, and start cooking. And then you monitor while you're cooking, so it doesn't burn, but it just reminded me of that and how it definitely help- it's a pain, but it definitely helps.

Peg Smith 17:19

And then the one added advantage over the cooking metaphor - that lesson planning has is that you don't have to do it alone. I mean, a lot of times we end up in our kitchen doing all this prep by ourselves, and you can't just phone a friend and say, "Can you chop these onions for me?" But you can say -"Here, tell me how you would solve this task?" or "What questions would you ask this student?" Or two people who are teaching the same grade level, deciding to work together on a task and shifting the burden from time to time on who's going to take the lead so that you don't have to take it on all yourself. So it's even less of a hassle.

Desiree Harrison 18:01

Yeah. Just thinking about it, in a different way. So, that it sounds like more, but in the end, it's actually less. And it's gonna be better for everybody.

Peg Smith 18:11

I had a teacher, this was a practicing secondary teacher, and she was involved in a course that I was taking, so she didn't really have much choice but to do what I had asked her to do, which was to carefully plan a lesson in advance using the 5 Practices. So, she did and she, you know, she came back the next week and she said it took a really long time to plan the lesson the way you wanted me to do it. And I said, okay. She said - but it probably went better than any lesson I had ever taught! And I'm like, okay, well that's something to keep in mind.

But lesson planning gets easier as you engage in this thoughtful kind of planning over time because you just get better at Anticipating. You get better at knowing what are good questions to ask. And then it doesn't take quite as long as it might have when you first started doing it. I mean, next week I'm doing a professional development virtually with a group of high school - middle and high school teachers and I'm using a task that I have used before. And I spent the morning just going through the task and all the nuances of it again because I haven't done it in a little while and I want to make sure that it's all still right there so that no matter what comes up I can respond to it.

Peg Smith 18:11

You were talking about efficiency versus understanding and having these scenarios to paint the picture. So, if we as educators are thinking about a certain picture ahead of time, then when we get to that Practice 5 and we're trying to - well really Selecting and Sequences and then Connecting the Representations - then we have an idea of the picture in our mind that will help us paint that picture for our students. We learn the most when we're telling a story. And mathematics has a story to tell and oftentimes we see that's it's chopped off at the end of a lesson, there's no summary point and there's no collective storytelling. We have to stay connected through stories and how important these Practices are have everyone tell their story.

Peg Smith 20:39

And if you don't Anticipate, you mentioned this earlier, but if you don't Anticipate, every time you encounter another group of students, you have got to think about - "Okay, is this a valid strategy? Is it always gonna work? Does it make sense? Have I seen it before? Can I connect it something else?" That is a ton to think about in the moment, for every group that you encounter. And you tendency as a teacher is to go with what you know because you don't want to call somebody up to present something that you're not comfortable with.

In my experience, you can't Anticipate everything that kids do, but if you have a little bit of collaboration on putting together your list of possible solutions, you can probably do 75% of what kids are gonna do. And over time, if you use the same tasks, it's only gonna get better. And then at least you're cognitively freed up to really engage with the one or two that you hadn't anticipated.

Desiree Harrison 21:41

In your books, you're saying that some things definitely do happen during, and I mention that word during intentionally because, in the chapter, chapter 4, for Monitoring Student Work, when I was reading back over that - and by the way, the way that you're latest book say been organized, I really appreciate the charts that talk about the challenges and then also what it takes and then it gives you questions to help you reflect - and so as I was reading that Monitoring, I noticed that the word during appeared more than ten times throughout the chapter. I think that especially since educators have become so much busier - there's so much more demands that are upon us, that the Monitoring aspect often times gets shifted to when the students are no longer with us. It's turning in just an exit slip. You're looking at a student artifact, which I'm not saying that isn't important, but it has to go along with this piece that you're Monitoring while they're actually doing it. You're interacting with them. So that's why I was underlining and really noticing that during because that's a key piece that I think that we need to talk more about as educators to get into formative assessment. Can you just speak more to the Monitoring student work during instruction.

Peg Smith 23:09

Yes. But let me say - before I talk about during, let me back up a bit. The interesting thing about Monitoring, which you've really honed in on, is that you do Monitoring during the lesson. And as a result, a lot of people make the assumption that there's nothing you can do to get ready to monitor cuz it all happens in the moment. And creating a monitoring chart - there are some illustrations of that in all of the books - where you've listed the strategies, correct or incorrect that you think are likely to surface and for each of those, you've listed questions you can ask to determine how students are thinking and then questions that will move them forward from where they currently are. So you go in to the monitoring process during the lesson with this tool that allow- will allow you to keep track of the thinking as if unfolds. So, I think that by doing that front-end work, you've freed yourself to listen more and to jot down some notes about what kids are doing.

And one of the things that I did not initially think when we started this, and we started working on this in like 2006, although the first book came out in 2011. There was an earlier article in 2008 I think. But what I came to realize is that once you complete a monitoring chart that say, you know, this group did this, and this is who I'm gonna call on, and so on; that really becomes formative assessment data. I mean, it allows you to have a snapshot of where students are on this day on this task. And I can use that data to make decisions immediately about who I want to ask questions of during the whole class discussion, but also, it might allow me to make decisions about- who seems to be struggling with this idea right now? Should I regroup- reformulate my groups so that might help the students see things differently?

Or, I might look at the monitoring chart, saying, nobody's exactly where I thought they would be, so what tasks can I come in with tomorrow? So, thinking about this in a very formative way, as data from a lesson at a point in time, rather than - I mean you collect the written work, and that'll tell you one thing, but it's not gonna give you the same insight into students thinking as when you ask some of those questions about their solution. I think part of the thing is we look at a solution sometimes on the student's paper and we think we know what it means to the student, because we know what it means to us. When, in fact, you ask the question about, you know, "So, tell me about this?" or "How did you get that?" or "What does that mean?" and then they don't see it the same way at all. And you've now have learned something about that child that you did not know before. And you've also learned that you've gotta be careful not to make assumptions about how kids think and what they know, only looking at the work that they produce in writing.

Desiree Harrison 26:43

We got into another piece of their identity that we can then later bring into a new task when we're back to level zero. By not making assumptions, it just helps us get to know our students more and helps keep them engaged and to these mathematics learning goals and just so powerful when we actually sit down and deconstruct everything that we're doing in the classroom, and take it one bit by bit.


I’m taking a quick break to remind Kids Math Talk listeners about all of the math professional development books that are available through Corwin Mathematics at Many of the authors of some of the latest titles have been guests on the podcast, search for Teaching Math at a Distance, Activating Math Talk, Building Thinking Classrooms, and also the book referenced in today’s podcast, The 5 Practices in Practice, to get you started. Want free shipping? Of course you do! Then use our special code K-M-T-S-H-I-P, that’s KMTSHIP, all caps, at checkout. And stayed tuned until the end of this episode for a very special announcement! Now let’s get back to the interview.

Desiree Harrison 28:16

I just want to circle back quickly about the mention of tracking and just to clarify to listeners that there are different types of tracking. And that this sense of tracking with monitoring is tracking student progress.

Peg Smith 28:37

It's keeping track of...

Desiree Harrison 28:38

Yes. Yes. Keeping track of and not to track students into ability groups which is, unfortunately, still something that people engage in and it's something that the mathematics community is actively working towards shifting mindsets away from tracking and ability grouping because it hinders students. And this is meant to be a selfless act to get to know the children. So the piece that you were talking about- Appendix B is the Monitoring Chart - and I love charts so thank you for providing this- and you give Appendix C. You give an example of a worked out Monitoring Chart to help us get that visual in our mind. So I'm thinking that if we're using this in the classroom, that is absolutely wonderful and we have that we have that record, but then some push back that I have received before is - How do you monitory all the students? That's a new point of overwhelm for teachers. So, what's your suggestion on making that more manageable?

Peg Smith 29:51

The chapter on Monitoring, one of the challenges that we identified is involving all members of the group. And, I think that this really goes to the issue that you're raising about how do you keep track of what everybody's doing - is that when you go to a group, you've gotta make sure that your conversation isn't just with one member of the group. It's with the whole group. And someone's gonna start doing the talking, certainly, but how do you then check for understanding by using some of those talk moves - Can somebody say back what Jennifer just said? Can somebody say that in their own words? Do you agree with that? Could you say it another way?

So trying to do some check for understanding among the group members so that you have some sense that this wasn't the work of an individual. And in this chapter there are some really, I think, nice examples of the 1st grade teacher actually doing exactly that. And there are a couple of times when she talks to a group and their work would suggest something different than what they're saying. Like, they've done something that actually appears to be wrong, but when she inquires about it, she learns that they really understood it. It was more about the recording of it than it was about the fundamental idea behind it. So, this notion of really talking to - but not just talking to one person.

What you notice in the example in the Appendix - and again all three grade bands have an example at that grade level - but the teacher actually tried to keep track of the names of the students in each group. So, you might even write that down ahead of time. So that, when you're talking to the group, and, okay, they're using this particular - okay they've built this using Base 10 blocks, okay, did anybody seem to be struggling with the model, or did you check for understanding across the members of the group? So that, trying not to think about it as an individual endeavor, but thinking about how can I think about the group as the unit of analysis? But not lose the individual in that?

Desiree Harrison 32:17

Thank you, that helps because that's often a discussion point and a frustration point. So thinking - I wrote down a group as a unit of analysis and remembering that and also that it's okay to not get to every single student every single day as long as you're still having conversations with all of your students throughout the week. And you're still getting to know all of your students, you know, as the weeks, and months go on.

Peg Smith 32:46

And you're actually looking - I mean you're paying attention to the non-verbal cues that you get from a group. I mean if someone is just, you know, sitting there and appears totally disengaged, then you certainly want to say, "So tell me what you think about this answer and how we got it?" Or if somebody sort of suggests that they don't understand what's going on and they look puzzled, I mean trying to read those cues and when you're seeing those, making sure that you're investigating. Cuz if you just say, "Does everybody have this?" and everyone says, "Yes, Mrs. Tirus, we've got it," don't believe it. (Laughing)

Desiree Harrison 33:24

Mmhmm. Well that reminds me of another part of that chapter and the monitoring piece is that you've broken down the types of questioning. To have the assessing versus advancing questions and to really think - Are they understanding the mathematics behind this? with the assessing questions. And then if they are, let's giving an advancing to continue that learning. And then not staying with that group to always wait for the full answer, but then to leave them with that to marinate and then move on to another group. And that's sometimes very hard to do because you want to listen to everything. But leaving them with that and then making sure that you don't cut the lesson off short.

As elementary teachers, when we're engaged in reading and writing workshop, the summary is a crucial point of the lesson and that doesn't always transfer over into the mathematics lesson, but that summary is just as crucial, so coming back together, and then at that point that's another moment when not just you as the teacher but the other peers can get a listen into what the conversation of the group was with those questions.

And another piece that I really love about this book is all of the videos that you all have and they have the QR codes so I can just pick up my phone and watch them really easily. And they're not too long - they're so helpful. And then you all have the questions to help you reflect on the video clips all throughout every chapter. You have the written examples of the student work, and you have scenarios here and then that along with the video clips - it really helps me remember everything that's being said. Because there's a lot being said.

Peg Smith 35:24

In fact, I mean one of the- the big motivation for writing this series is that ever since the publication of the original 5 Practices book in 2011, teachers and teacher educators came up to me at meetings and would say, "We need video! We need to be able to show what this looks like." And it's like, yeah, I know, but video is really hard to come by (laughing). Good video that's really gonna help make the point that you're trying to make is a challenging thing to try to capture.

And then people would tell me about all the things that were challenging about the practices, like some of the things we've talked about already - Why anticipating is challenging, why trying to keep a group together, why trying to keep a group accountable. I mean, this as things that lots of teachers experienced. So, over time, I tried to think about how could we try to come up with a resource that might actually provide some visual images of what this looks like. so, The 5 Practices in Practice was born, along with a new set of co-authors working on this phase of the work. We thought it was really important to shoot the video in urban classrooms and so we were able to do that. And I think the teachers, I wouldn't call any of them, and they wouldn't want to be called experts, but these are teachers who were working really hard to try to provide their students with the math experience that was going to enhance their understanding and build their identities.

Desiree Harrison 37:06

Well, you all have succeeded. Because we talk so much about how children need meaningful, relevant context to help them engage with and connect with mathematics, and teachers and teacher educators need context as well and this book helps. Even though we're still reading this, it pushes the theory into practice - the 5 Practices in Practice. And all the video clips and scenarios, it helps.

Alright, I want to thank you Peg so much for this engaging and enlightening conversation about the The 5 Practices plus the Practice Zero.

Peg Smith 37:45

It's really been a pleasure talking with you.

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