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Desiree Harrison 0:00
Strategies for getting kids to talk about math, don’t always come naturally to us and that’s why I’m so excited for this week’s episode where we talk to two of the authors of the new text, Activating Math Talk: 11 Purposeful Techniques for Your Elementary Students.
Desiree Harrison 0:48
Today’s special guests on the Kids Math Talk Podcast are Paola Sztajn and Kristen Malzahn and so I want to welcome you to the podcast. I’m so thankful for the NCTM community that has brought us together and for the 100 days of Professional Learning that they’re providing because otherwise I don’t know that we would have been connected. So thank you for being on the podcast today!
Paola Sztajn 1:12
Thank you Desiree for inviting us, ah, we are excited.
Kristen Malzahn 1:16
Yeah, thank you.
Desiree Harrison 1:17
So here on the Kids Math Talk podcast we’re all about practical tips to engage students, to increase discourse, and to create positive mathematical identities and you all had an extremely powerful webinar all about practical techniques that seem to evolve from the work that you all are doing with this Project AIM. So I’m wondering if you can tell us a little bit about this work and the guiding principles.
Paola Sztajn 1:45
Yeah, sure. So again thank you for having us. We started thinking about this work based on the amount of work that there has been in math about math tasks. And we know that tasks are so important and key for engaging students in discourse and meaningful math conversations. At one point it felt like tasks suffice, you know, you give kids a good task and everybody will talk and I think we were a little frustrated with that image because if you give a good task, yeah, you may get five kids to want to talk but how are you gonna to make sure every kid can talk and will talk and will engage. So, that’s where the principles come from.
Ah, first we have this idea that students need to learn to talk. And so you have as a teacher, you have to do um, some practices and for that we provide some techniques that help kids learn to talk in the ways that we consider productive. Yeah, kids talk, but do they talk in the ways that we want them to talk in math that’s really not the natural way where you say, “oh yeah I hear your argument and now let me, you know, this is my idea” that’s not how kids talk, uh, definitely not in the early grades and I don’t think even in 5th grade it would come in that way if we didn’t teach them - this is what we want a math conversation to look like. So we wanted to have techniques that teachers could use that would teach kids to talk in the ways that we think are productive in mathematics. So, guiding principles, ah, techniques need to be readily available for teachers, you know, teachers should have a toolkit of such techniques that they can use in the classroom. They need to be easy, they need to be ready, you can use - that’s our principle number one.
Number two is that techniques really help students learn to talk in very specific ways and they need to learn to talk. And our principle number three is that actually all students can learn to participate productively if they’re given the opportunities to learn to participate. So those are the three guiding principles when we started this work, now over ten years ago.
Desiree Harrison 4:11
Wow so I hear that them of equity being pulled out in those guiding principles and just ensuring that all voices are heard and valued which you know equity is such a large buzz word but those guiding principles, that’s the how, instead of just having this face value concept, you’re really, like, digging into how to make it happen.
Paola Sztajn 4:34
Exactly. And I would say, um, really thinking about each and every kid, right, I think that’s how NCTM is trying to reinforce that all means each and every kid. That’s what we were thinking about. How are you gonna to provide them the opportunity so they can learn.
So in the book we also talk a lot about emergent multilingual learners and we talk about, we actually say that all kids are emergent math communicators, in the early grades every single kid is learning to talk and is learning math vocabulary, so we should really think about every kid in the early grades as an emergent math communicator. But we also have in the classroom, emergent multilingual learners who are, ah, perhaps learning English. And so, we also provide, ah, several principles on how to work with emergent multilinguals. Kristen do you want to say a little bit more about that, this is an area where you have done so other work. But we tried to think in the book, in our work, along the equity component also bringing in emergent multilinguals.
Kristen Malzahn 5:55
Yeah, so, um, as Paola said, um, we do provide particular scaffolds and supports with each of our techniques to help, in particular, emergent multilingual learners, and these are really based on three, um, three other guiding principles of effective instruction for emergent multilingual learners, um, and one of those is to challenge students, making sure as Paola started, you know, talking about early is making sure that everybody has challenging high cognitive demand tasks, right, so you don’t want to um, lower that cognitive demand so everybody needs these challenging tasks. The second idea is using, um, multiple modes of communication. So you know having students communicate their ideas does not necessarily just have to be verbal, um, or written that students can also use, um, pictures and diagrams and, um, gesturing and what not and that really provides more access in particular for students that don’t have the English language or maybe are still developing their mathematical language-that they can use those different modes. And then the third one is promoting academic language. So allowing students to use some of their everyday language. but also then helping to develop their, um, academic language as they’re making sense of mathematical ideas. Um, so those are the three that we really try to, um, incorporate into our techniques and into the work that we do with our teachers.
Desiree Harrison 7:29
So, the piece about your saying developing as students are making sense that’s oftentimes not what we see happening in classrooms especially if we have pre-made math vocabulary walls or we say like this is gonna be the vocabulary of the week then it might be totally abstract for students-they don’t have any context to connect it with so that is important to remember and also that those multiple modes of communication especially since so many of us are in the remote learning situation right now and we’re thinking about different ways to engage and to have the discourse we often have such a narrow definition of discourse where we always think it has to be verbal but thank you for reminding us that there are so many different ways to communicate and pictures is gonna be, I mean pictures is huge, if you’re online you can draw you can use, you can use like, a Google Drawing, or you can have some clipart even or take a picture with your phone and upload it and take a picture
Kristen Malzahn 8:33
Right.
Desiree Harrison 8:34
I was on a walk earlier during my lunch break and I took some pictures of some flowers for a possible what do you notice? What do you wonder? Like, you know, how many, some subitizing activity, and a kid could do that and communicate their understanding. So thank you.
Paola Sztajn 8:54
Um, Desiree, I also want to add, you know, kids can use their own, ah, own ways of saying informal language, their first language, all of that is very important in this making sense part. And at the same time as they’re making sense, we do want to connect it to academic vocabulary so that they learn to develop that vocabulary. That is a purposeful teaching action, right, so, I think sometimes when we say, “oh the kids should, we need to let the kids use different modes of communication, different language, some people hear, oh then we don’t teach academic language. That’s also not what we are saying, because we also have to help them connect and develop that language. So it is this back and forth as you are making meaning we provide you more vocabulary to help you express that meaning, ah, is really important.
Desiree Harrison 10:00
And you’re getting to the math practices, it’s not a linear progression is what I kind of hear you saying. It’s messy, but that’s the only- learning is messy, that’s the only way to really be effective.
So when we’re thinking about discourse and the math classroom, during your webinar you all asked the audience what features , ah, they consider most important, and then after some conversation, you talked about four different types of discourse, so not what we- not necessarily what we talked about earlier with having pictures versus verbal but you talked about four different types: correcting discourse, eliciting discourse, probing discourse, and responsive discourse. And, can you just talk a little bit about those four types.
Paola Sztajn 10:58
Yeah, so, in this particular case, when we are saying discourse, we are looking at the overall of the classroom interactions and how the teacher and the students are interacting with each other throughout the lesson. So this is discourse with a bigger idea of, you know, what’s happening in the lesson, what are the patterns, um, and in which ways are kids interacting.
Alright so we use a definition of discourse in the book that is patterned ways of using questioning, explaining, listening, and different modes of communication in the classroom to promote conceptual understanding in math for all learners. But I wanted to emphasis the pattern part, you know, are these ways in which we engage kids and, uh, have them talk that become what we do and how we interact and the norms and kids quickly learn, you know, should I raise my hand not raise my hand, do I need to worry about this or can I just sit here and not pay attention, or, you know, am I gonna to be expected to explain something or not, so they learn these patterns. Kids are very good at noticing these patterns.
When we say discourse in this case of the four types or four different patterns in which kids and teachers engage that are repeated over time. So correcting discourse has long been known by the academic community, it’s called I-R-E sometimes, Initiatie, Respond, Evaluate and the teacher basically is correcting what the student saying. So correcting discourse is when the teacher is basically listening for right or wrong answers and the goal is mainly to fix it. So everybody has access to the right answer so the teacher ask a question, the students answer, teacher says “yes/right”, “no/wrong”, “next one,” and it goes like that. So that’s one pattern. That pattern actually is good if you are trying to work on- if kids have definitions or facts. But if you’re really focusing on understanding, that pattern of discourse is not promoting understanding, um, in the way we would like kids to make sense of mathematics. So that’s Correcting. Then Eliciting, I think it’s something we have seen a lot in the classroom, particularly when we started saying, you know, you’ve got to engage conversation, you have to bring them in and encourage them to talk, and many times that goes without pushing for mathematical accuracy. So now everybody’s talking but I’m not really quite pushing them. Many times I think teachers do that
‘Cuz you want your kids to feel welcome, you know, to participate and so we call that Eliciting discourse. You elicit a lot of ideas into their conversation but as a teacher, you may not act on these ideas. And again, it’s really powerful if you have somebody who’s not participating, who’s shy, who would completely draw in with you were to say something or correct, or feel insecure, so Eliciting discourse opens up the conversation, but it doesn’t push for mathematical learning or accuracy because you can stay at a very superficial level.
So then comes probing discourse, which is when the teacher starts probing. So asking questions from students, making sure we are discussing mathematical connections, or mathematical understandings, asking why, asking how, you know, really pushing for understand the mathematics, so the kids are not only sharing but they are being pushed for more mathematical depth.
And then the last one which is responsive discourse, has everything that I’ve said so far, so it has all the features of eliciting and probing, and on top of that the kids know they are also responsible for the discourse. So now it’s not just the teacher probing, the teacher asking questions, the teacher telling students, the teacher, you know, every time a student says something the teacher responds - but kids are talking to each other.
So when one student proposes a particular solution, the teacher doesn’t need to go, “great who wants to ask a question?” because now kids know they are asking questions so another student may ask questions and they respond.
And so, it moves away a little from that pattern- that is student/teacher/student, another student/teacher, another student/teacher, another student teacher, which is typical of all three prior types of discourse, but now you have the teacher says something, students are talking to each other. Somebody answers, somebody asks, another question comes and go back to that ask, and then the teacher asks something else. So that’s the responsive discourse, is when kids understand that they are responsible for the conversation as much as the teacher is.
Desiree Harrison 16:43
And that sounds like, ah, when you have the responsive discourse, you’ve build a really rich and inviting classroom community and it’s not going to happen overnight, by any means, and I guess just overall what you were talking about reminded me of Principles to Actions and some of those, like, probing questions, so thinking about your goals ahead of time as the teacher before you go into a lesson so you can see which level of discourse you’re really gonna get into--
Paola Sztajn 17:23
And the teacher may, may want to have different ones for different purposes at different times, right, so, there is a time for practicing something that you’ve been working on and maybe you are interested in accuracy at that point it makes sense and you may want to engage in correcting discourse. You probably wouldn’t start something with that kind of discourse, um, so, the teacher may use different types of different moments for different purposes. What we tried to say in the book, ah, is that if your goal is for kids to develop conceptual understanding and procedural fluency, then you want to be on the probing responsive side. The other side serves other purposes, but it’s not really gonna foster conceptual understanding and the kind of procedural fluency with flexibility that we wanna see continue to develop. And sorry Kristen I interrupted you.
Kristen Malzahn 18:25
No, not at all, I think we were just chiming in. Um, one thing, Desiree, when you mentioned thinking about goals, I’m glad you brought that up because one thing that we talk about in the professional development that we’ve, um, developed over these years with our teachers is that it’s important of course to think about your content goal but we also talk about thinking about your discourse goal. Which is exactly, I think what Paola is talking about when we think about these different types of discourse. Um, you know, and that as you are planning your lesson, you really have to focus on, yes, what do we want the students to come away with understanding about the mathematics, but also what kinds of skills do we want to teach them as far as how they are participating in discussions, um, the active listening, and being able to ask those probing questions of each other and explaining and providing justifications and stuff and those I think are really important to think about as well.
Desiree Harrison 19:26
Yeah, there’s been intense learning and planning happening every day and thinking about how to do some of those pieces in the virtual environment like with the discussion board or just having different icons to say okay now this is - like a little ear to say this where you’re going to listen and like a pencil, like this is where I’d like you to respond or a like a microphone to say let’s try out using this sentence stem so that everything is a step-by-step process, like, piece by piece you’re adding on to your goals towards that responsive discourse.
So we’re thinking about, like, all these practical and purposeful ways of doing things, and, ah, as a parent, you watch your your child develop and grow and you know if your child is speaking to you, then you might be under the assumption that they can just automatically talk about math but you spoke earlier about how all children are emergent math communicators. So what’s one piece of advice that you have for parents as they’re working with their child with mathematics.
Paola Sztajn 20:46
Be curious. [laughing] When a child says something to you about mathematics, be curious! “How did you think about that?” “What was in your mind as you were answering this question, or when you saw something?” And so really try to get to where your child is coming from and don’t necessarily assume that the child is thinking like you are or that the child did something because they understood it and know exactly how to do it, or the other way - they have a mistake because they have no idea. So, really be curious. Sometimes, children say fascinating things! So, listen! Try to see where they’re coming from. Don’t take it for granted that you know what they were thinking when it comes to a math problem. Whether they are right or they are wrong, ask them, “How did you think about that?” and have them talk to you. I think where I was going earlier is - and even when there are mistakes - try to understand why would they be doing that mistake; what might they be thinking? Because sometimes it just makes sense to them; it’s not that they were benign careless or, you know, not interested. Sometimes the mistake just makes sense to them. So, you’ve got to be curious.
Desiree Harrison 22:21
That simple question of oh “How did you get that?” like, that could open up a whole new world.
I’m reading a few different books about online teaching right ow, or listening to them on audiobooks, or on Audible, and one of the books was talking about how discussion boards and chats allow you as the teacher, so it could be you as the parent, um, in this case like just it allows you to enter the mind of the child and to see the beauty - because us who are really passionate about mathematics talk about how mathematics is beautiful and the patterns are everywhere in nature, and just there’s inherent beauty but there’s also that beauty inside your mind and pulling that out- the only way to see that is for us to start to talk about it and write down and seeing that you just get a whole new perspective of how somebody thinks and views the world.
Paola Sztajn 23:23
Mmhmm. You know I just thought another thing for parents, too. If there is something that you don’t quite get, ask the teacher. You know, teachers are doing things slightly different so give them credit for what they’re doing and if it’s different from what you used to do, go ask them why because there might be a really good reason why we’re doing it differently now, and so-or if you get to something you can’t help your kid cuz you don’t know how to do it - ask the teacher, “how can I best help my kid here, cuz I don’t know how to do this” and establish that relationship I think it’s also really important, I think now more than even because kids are spending a lot more time with their parents, and,uh, you know, that relationship with the teacher, especially in the early gr-I’m talking K-5 right, especially in the early grades, we are gonna to have to partner. We really are, or it’s gonna be a clash, of, “oh,well, the teacher says this, the parents say that,” and it happens already in the classroom, but I think we have ways to deal with it when we are in the classroom and we are seeing each other and parents and teachers are interacting, but now without that interaction, you’ve got to make it happen purposefully so you can partner with your kid’s teachers. And I think teachers are amazing, they are trying to do the best they can and they want to partner, they know parents are important, so.
Desiree Harrison 25:08
Teachers are doing the impossible right now, and, yeah, the more we work together, the better it is for everybody, and for children, which is ultimately why we’re here.
Paola Sztajn 25:23
That is why we are here! [laughing]
Kristen Malzahn 25:25
Yep!
Paola Sztajn 25:26
Yeah, the title of the book is Activating Math Talk: 11 Purposeful Techniques for your Elementary Students. And in the book, we have the first few chapters are really about conversations about discourse in general, some general ideas about language learners, it’s really all these frameworks for you to think about the classroom. Cuz we think you need that for the techniques to make sense, because techniques for techniques sake really doesn’t achieve any of your goals. And so we lay out the framework and then we provide eleven techniques that are ready to be used, and we also share vignettes of teachers who use those techniques in their classrooms, so these are teachers who have worked with us for many years and so, th- we write with them the vignettes about their experiences both about what worked and sometimes what they would do differently in the classroom. Mostly to remind everybody these are not meant to be the perfect classes, you know, ah, instruction happens everyday with the good, the bad, and, you know, the unexpected, so, uh, the vignettes are really true stories, and uh, teacher’s reflections.
Desiree Harrison 26:52
And those will be so appreciated because that is real life and acknowledging that things don’t always go perfectly is so important.
Paola Sztajn 27:04
Yep.
Desiree Harrison 27:05
We’re taking a quick pause here to say that you can find the book, Activating Math Talk, on corwin.com and if you are enjoying this episode, please leave a review, so others can find this podcast. Now, let’s get back to the interview.
Kristen Malzahn 27:22
And one more thing I want to say about the book is that we also wanted this book to be useful for schools or districts that may want to do professional learning communities or some professional development, um, on their own, and so there are tools within the book that are very practical, so moments where we ask the readers to pause and think about certain situations and how, um, they can connect some of the techniques that we talk about to their own practice and we have them, you know, give them some ideas, of, you know, things they could to go back in their classroom and try it, and some discussion questions at the end of each chapter that are called, Discuss with Colleagues, and so it really is meant to promote more at the school level some, you know, professional learning opportunities for teachers to come together and really think more critically about the ideas in the book and how they can implement them with their students in their classrooms.
Desiree Harrison 28:20
I could even see that being a part of a, like, a virtual coaching community too.
Paola Sztajn 28:28
Yeah.
Or a PLC or- a any kind of community, yes. We wanted it to have opportunities for that.
So, we are also in the process of finishing a PD that districts could participate in eventually. And so the idea that we have is that the book is kind of the textbook for the PD and a district that is interested, we will be able to prepare a coach or facilitator or somebody from the district, to use the professional development and the district will get all of the learning management system from us and be able to use it in the district and just offer the professional development themselves. We have the professional development and the learning management system already and now we are finalizing the facilitator preparation part so all of this can happen fully online or hopefully if we are together it can happen through some face and face and some online asynchronous materials, but again it will be ready for use next summer where a district can say, “I’d like to do this professional development.” We’ll train somebody in the district and that person will get all the materials and be able to do it.
Desiree Harrison 29:58
That’s going to be a really fabulous resource.
Paola Sztajn 30:00
Yeah. Thank you.
Kristen Malzahn 30:03
We hope so.
Paola Sztajn 30:04
We hope so.
Desiree Harrison 30:08
So, in this, in this book , and in your work you have all these different techniques. And, tell us about one of those.
Paola Sztajn 30:16
So, I’ve been thinking about...from the strategies that we have right now, what would it take for a teacher who is engaged and online, learning at this moment. So, and I’ve been trying to think about about what would each of these strategies look if now I’m teaching online. I believe bet lines can continue to happen. In fact, bet lines can be a lot of fun.
So, let me tell you what bet line is first and I believe teachers can take most of our techniques and begin to adapt them. The book was not written with COVID in mind, so you know we are all adapting.
Desiree Harrison 30:59
Yeah.
Paola Sztajn 30:59
But bet lines is a technique that is used a lot in literacy for kids to make sense of text. And what happens is as you are reading, you stop and ask, “wow, what do I think is gonna happen next?” And, at that practice of thinking what happens next, you know, really helps you make sense of what’s happened up to now and what are the possibilities. So we adapted that techniques to use in math, for problem, for story problem and problem solving. And so, as the teacher is presenting a story problem, the teacher stops, you know, reads perhaps a sentence or two sentences, at a point where it makes sense, and you say, “what do you think is gonna happen next?”
And then the students start providing their bets. That’s why it’s called mathematical bet lines. And from there, you keep reading and the kids can reevaluate their bets, they can change it. And so the kids get very excited because it’s kind of fun. Um, they are also making sense of the story to be able to provide a bet of what may come next. And it really opens a window for the teacher to be seeing what the kids are paying attention to- which kids might be connecting to the math parts of the story; which kids might be focusing on contextual features that perhaps are not as relevant for the math discussion. And so it opens a lot of opportunities for teachers to make sense of what their kids are thinking as they’re making sense.
So, where I was gonna go earlier, and this could work in second grade, ah, late first grade, but second grade kids could actually put bets in the chat. You know, and now you would have a lot of kids betting, instead of in the classroom, where you may get one or two bets, ah, it could actually be fun to see a collection of bets in the chat or a discussion space. Um, and then the teacher can also-the teacher has a better opportunity of choosing which bet before discussing it, because when you pick somebody who raise their hand you don’t what their bet is going to be and where it will take you. But, if kids wrote their bets, now you’re like, “Oh, two interesting bets, I’m going to pick on their two.” Fascinating.
Desiree Harrison 33:25
I remember reading the article in the, um, Teaching Children Mathematics, about the mathematical bet lines, and I never got a chance to actually use that with my students while I was in the classroom. But it’s such an exciting idea and a few episodes ago on the podcast, we were talking about the different types of engagement and I view this as connecting to cognitive engagement and emotional engagement. And like you were saying, it just gets kids so excited. And I wonder if for Kindergarten, you know, they wouldn’t be able to type in the chat necessarily - what would you all say about forced choice in that situation?
Paola Sztajn 34:11
Um, so for me there is a move that people use a lot called, agree or disagree? And that seems a little bit on agree or disagree with the teacher’s bet. Which I think is very valuable as well. Um, it’s probably different than you listening to the kid’s bet. And oftentimes the bets are even before, you know, you get to the part of the mathematical questions. So, you may stop way before where the numbers are still not there and the kids have to start saying, “oh I think more,” and that would be the increase, right. But in context right.
Desiree Harrison 34:53
Right.
Paola Sztajn 34:53
There are - we used this problem for some other stuff - there are seven bees in the hive. What may happen? You know, and then you can talk about - bees can leave, more bees can come in. And that is part of the bet. That’s a little before the bet of, “well is it increasing or decreasing” that helps them also understand the context from a mathematical perspective.
Desiree Harrison 35:19
Yeah, that makes sense. This technique sounds like an excellent point for formative assessment. And just to, just to have some observation points that could eventually lead to an interview if you have some breakout groups.
Paola Sztajn 35:34
Umhmm. I think you can still do it, um, if the kids are using the microphone. You can still pick a child to provide the bet and then allow that child to offer the bet. The reason why I was thinking about the chat is that the chat would allow everybody to bet. Right, and when we are talking, we really pick one or two. But you can still use it with a mic.
Desiree Harrison 35:19
And hopefully, if a kid is camera shy, or whatever, and they have their camera off, but then they have all these engaging tasks, and, you know, hopefully that will prompt them to say, “oh, you know, I do want to be seen,” so, uh, the turn around will happen. But-
Paola Sztajn 36:23
Yeah, that would be awesome.
Uh, yeah, so we have created this video cast, um, and it’s a set of colleagues here, who we all work in elementary math education. We were all thinking about caregivers and having to think about math with kids. So, it’s called, Unpacking K-5 Math for Caregivers, and it’s here on the NC State website. And we just pose a question to ourselves and we start talking about it. And it’s a discussion among us. They last about 10-15 minutes each. So, we are trying to support caregivers, thinking about what they can with their kids. And that idea about being curious with the kids comes from those conversations.
Desiree Harrison 37:09
Okay. Cuz, yes we’re always looking for more resources for parents so, I will link that in the show notes. And I just want to say thank you both for such an enriching and valuable conversation. And K-5 kids, K-2 kids especially, so often get left out when we’re thinking about this discourse piece, we tend to go toward bigger kids, and it’s just as important for all learners. So thank you for your work and for your dedication and for your time on the Kids Math Talk podcast.
Kristen Malzahn 37:45
Thank you, Desiree.
Paola Sztajn 37:48
Yeah, thank you for the invitation. And I look forward to other opportunities. Maybe we can partner together in the future.
Desiree Harrison 37:53
I would love that.
Paola Sztajn 37:55
Yeah, we would too.
Desiree Harrison 37:57
If you are a member of NCTM, be sure to check out the webinar that’s mentioned in this episode that was a part of the one hundred days of professional learning. It’s definitely worth your time.