Ep 46. Strategic Questioning in Math to Further Student Thinking

Johanna Kuiper 0:00
All right, hello, hello. So today we are doing a co hosted episode our first one ever, so bear with us as we try out something new. To introduce myself. I’m Johanna Kuiper. I’m a eighth grade math teacher. And I’m excited to be sharing with you about math questioning strategies.

Mona Iehl 0:20
And I am Mona eel. And I am a teacher and math coach and former math avoider. And I’m really excited to be here and talk about one of my favorite things, which is talking.

Johanna Kuiper 0:36
Exactly. I think sometimes in the math classroom, people always see you as like black or white. And I feel like there’s been a movement recently, maybe the past couple of years of going from direct teaching into being, I think you even call it this, the the guide on the side. And these math questioning strategies that we’re going to be talking about today lead with that. And one of my favorite articles that I’ve read recently is called Never say what a kid can say. It’s by Steven Reinhardt. And he has some really amazing things to say in this article. But overall, it just comes down to making sure that when we are questioning students, that students are actively engaged in learning math. Love it. Yeah, I, it’s really good article, he has so many good things to say. So I’m going to give you a scenario that I feel like most teachers will encounter at least once in their in their life is, when a student raises their hand about a question, they’re always asking, Is this right? Or is this correct? And when we answer it as yes or no, it stops students thinking, and it’s not allowing them to truly feel confident and whether or not they’re doing it. So we have to use process questions, not product questions. Is this something you’ve seen in your classroom?

Mona Iehl 1:57
Oh, my gosh, I love this so much. Because I feel like as teachers we want to help kids get to the answer is like quick as possible, because we feel like that’s our job. But really, our job is to help them think right, help them learn how to think. But it’s just, it’s feels better on both this for the student and for us, when we just help them get to the answer. Right. But it’s way harder to ask them a question that focuses them back on trying or working through the process.

Johanna Kuiper 2:29
Yeah. And to you, I feel like because most teachers have a ginormous class, like I have a class of like, 30. I know other teachers have even more, it takes time. It’s not something that can be done in a quick moment. And it’s a process it has to be done in order to help students understand deeper and retain that for more math things.

Mona Iehl 2:57
And, I mean, I think like, when you answer someone’s question, like you had already said, like, the thinking stops, but like, then we’re also sending them the message of like, you can’t do this. I mean, I know that sounds extreme, but like, if you tell them if they’re right or wrong, then they don’t have to develop that skill of deciding whether they’re right or wrong.

Johanna Kuiper 3:19
Yeah, it kind of cripples their confidence, because they can’t go into another problem and feel confident that they know how to do it, they’re going to be reliant on someone else for that validation.

Mona Iehl 3:31
Yep, totally.

Johanna Kuiper 3:32
One thing that I like to do is when a student asks me, is this right, or is this correct, is to tell me what you’re thinking or walk me through your process. And that kind of helps me understand what the student is thinking and kind of formatively assess what they understand about whatever topic we’re doing. Plus, a lot of times as students kind of walk me through the process, or tell me about the problem. They’re noticing errors that they made, or things that they need to go back and fix because it didn’t make sense. And so they’re self reflecting as they’re going. And it’s helping continuing that thought process.

Mona Iehl 4:10
Yes, yep. 100%. I like to always say, like, when I’m asking students, what they’re up to, I always say I’m mining their brain. Because when students are talking in our math class, they are showing us they’re telling us they’re thinking, and so often, it’s like, we’re just missing that piece in our classrooms, and we’re all doing the best we can. We’re all working on staying on pace and getting all the problems and pages done and, you know, getting through the things so we can get to the end of the year, right. But we forget that if we just go through the motions, and we don’t slow down to figure out what our students know. Then we’re just perpetuating the problem of answer seeking, which is what happens when we tell them if they’re right or wrong, then our classrooms become about answers instead of about thinking. And so I love that. As soon as the kids like, I don’t get this, you’re like, Okay, walk me through it. Tell me what you’re thinking. Because Don’t you think when they say I don’t get this, it’s like, that’s their flag of like, help me. And they just really just like, want you to do it for them. Right?

Johanna Kuiper 5:24
Yeah, I totally agree. And have you read the book building thinking classrooms by Peter Liljedahl?

Mona Iehl 5:30
Yes, yes. I love that you said his last name. Because I’ve always wondered.

Johanna Kuiper 5:35
I know, it’s, it was definitely a weird one. But I heard him say it on another podcast. And I was like, Alright, I’ve got it. We’re good to go.

Mona Iehl 5:44
That book just affirms so much that I know it’s true, and really pushes our thinking in a lot of ways. And I know that it’s been a big work of yours in transforming your classroom in the recent years.

Johanna Kuiper 5:59
Yes, definitely has. And one thing that I’m trying to implement this year, because you can only implement or change so much in a school year. So the one thing I’m trying to work on this year is he calls it checks for understanding. And the way it works is you give students problems, but you also give them the bare bones answer. So it helps them really focus on finding the process and understanding the process because they already know what they’re trying to get to. What do you think about that?

Mona Iehl 6:28
I absolutely love giving kids the answer first, like, the thing is, is like we should be giving our students problems that are complex, right? That are going to make them think, so that they can be in that productive struggle, I always call it grappling. That feeling of it’s not just coming quick, like a snap in easy to you. But that it’s a problem that you actually have to slow down and think about and problem solve through. Because if we don’t give students those opportunities in math class to practice problem solving, and problem solving is just an add on at the end, once we get the concept, then we’re missing the whole point of math. And I think like you said, at the beginning, there is this shift that we’re seeing in a lot of math classrooms right now, where we’re focusing more on problem solving, we’re focusing more on the process. So when we give students these more complex math tasks, one great way to boost engagement and get students to take risks in their thinking and actually try is to say, okay, the answer is three fourths, let’s go figure it out, you know, like, that takes the pressure off, and it really shows them what we value. I’ve been talking a lot on my podcast about having a math vision, and how that math vision can really help you make decisions with your resources and with your instructional moves, and all of that. And one of the things that’s in my math vision is that thinking matters more than answers. We talk about it as a math norm, even in our classroom. And when you give kids the answer to a problem at the beginning, that totally like, shows them you mean, what you say? Like, I really don’t? I’m not here for the answers. I’m here for the thinking.

Johanna Kuiper 8:21
That’s awesome. I really liked that as that you put it as a norm within your classroom, because it shows how much you value that and help instill in the students of like, this is one of our goals is the process over the answers. And I think more if we, as all math teachers put that as an emphasis, I think we’d see a great shift in the mass culture.

Mona Iehl 8:45
And it’s so hard because, again, we have all these things pulling for our time and our attention and our effort and our capacity, right? And so, yes, the pacing guide, yes, the next lesson. But if you pause and you say, I’m really going to spend time doing three problems today, not 30. And the notebooks are going to be past blank at the end of the year. Right. But you’re like, but you can confidently say, but I know they’re going to understand it because I’m going to do checks for understanding, because I’m going to give them time to talk. And I’m going to listen deeply to what they’re saying. So that I really understand where they’re at, which kind of leads me into my strategy that I was thinking about sharing here today about just engaging students. We talked, we talked about questioning strategies, but I really want to say I think there is no perfect question. Like I love the question that you said, of like, What don’t you get or walk me through what you’re thinking? There is no one question that’s going to help everyone understand. When I talk to teachers, often they’re like you have but what questions do you ask in the math discussion right? It like, it hits that low, or I just like, I don’t ever know what to ask. And it’s like, well, there isn’t one, there isn’t a sheet of questions. I mean, I do have a sheet of questions that I can give you. But like, not any one of those is better than the other. What really matters most when questioning students is listening. And because of what we’ve already said, if like, it’s a formative assessment, right, I have to know what you’re thinking so that I can help you move on to the next level of understanding. And I like to talk about that as like a progression or a trajectory of understanding our standards point us in that direction, right. And so when we understand like, where our student is coming in in that progression, then we can better ask a question to help them move forward. I think a good example of this is like if a student is making an error with regrouping. Okay. And we ask them to walk us through what they’re thinking, we can see, you know, on their paper or with their manipulatives. And through their words, what they don’t understand. And then we can say, okay, oh, but we need to talk about making groups of 10, from ones to 10s. They don’t quite get that. But I’m really seeing the big misconception here from 10s to hundreds, or whatever it is, right? So when we give students time to talk, without judgment, we can see where their errors are. So we know what question is the right question for them.

Johanna Kuiper 11:43
And to build off that one of my favorite things is when I see like there’s a misconception, one of the things I’ll tell students is like, Oh, I see how your brain is thinking, let’s talk more about this. Because it validates what they were thinking already. And it doesn’t tell them that they were wrong. Because any My thinking is good thinking. But like helps me put them in the right direction of like, I see how you were thinking, with this part of the regrouping. Let’s talk about this, or let’s dive into this. And it gives me an opportunity with a one on one to help them re clarify whatever they were missing it to begin with.

Mona Iehl 12:18
Yes, I love that. Because we have to be constantly thinking about math, confidence in math mindset as like that glass ball around everybody. And we just have to make sure that we keep it protected, right? Because one little thing, everything could come crashing down kind of thing.

Johanna Kuiper 12:37
Yeah. And we want to make sure because I feel like society itself does not necessarily have a very positive view of math. I always think it’s either a, you’re like a super nerd to the extreme, or it’s just the normal to be bad at math. And you say this, too. But there’s no such thing as like a math person, because we’re all math people. It has to do with how we were taught, and it wasn’t necessarily maybe taught in a way that we understood it. So it makes you think you’re bad at math, when actuality that’s not the case.

Mona Iehl 13:12
Yep. And sometimes your strengths just lie in other areas. And so society or your culture tells you just go with that. Right, like, and it’s just, it’s really wild, how strong those voices are. But that’s actually part of making math culturally relevant is understanding the, you know, messages that students get from their home culture, about math, right, like, in sharing that with each other and talking about that, and not labeling that as right or wrong. But really just understanding what’s going on in our home cultures and in our media that we consume. And just being cognizant of it really,

Johanna Kuiper 14:00
yeah. What are your thoughts on? I guess it’s a whole other episode, but what are your thoughts on helping make it culturally relevant in the way maybe we ask questions or questioning strategies?

Mona Iehl 14:11
One of the things that, I guess I kind of just said, but also is something I’m constantly working on. And part of listening is being like thinking about your stance. Right? We all have it, we walk up to our partner at home, and they’re still working at 530. And your stance is automatically like, annoyed because why aren’t you making dinner yet? Right? Like, that comes across into your stance when you’re like, when are you going to be done working? That’s saying a lot. And so we do the same thing in our classroom. I think when we’re like, Well, why are you doing it that way? Wait, you know, and it’s not necessarily ill intentioned, right. But being conscious of your stance and how you’re coming in to a situation and really being mindful of staying neutral. And so I talk a lot with teachers I work with about a neutral stance, when they ask those questions like, how’s it going? And I like to ask these really super open ended questions with kids when I, when I go into conference with them, which is like, just what you’re up to, how’s it going? And it kind of lets them talk about whatever it is they want to talk about. Instead of, you know, kind of when you see a kid that’s off task that’s literally doing no math, and you’re like, why haven’t you started yet? Like that already has a has a skew, right? So be conscious of your stance in staying neutral. And you spoke about this earlier of not confirming or denying whether their answer is correct or not. Same thing with their strategy, or their model, or the accuracy of their model, or, like really anything and just kind of always putting that back on them of like, what what do you think, or, you know, and obviously, in conferencing, you will take opportunities to directly teach and give that like direct nudge. But for the most part, I think, not coming in with your own bias and really trying to stay neutral is something that is culturally relevant.

Johanna Kuiper 16:27
Yes. And to a lot of times, I have when I come in hot with that, well, why aren’t you working yet? It’s as simple as like, Oh, I didn’t get a paper or I don’t have a pencil. And I’ve come in with this like, attitude of like, why aren’t you working. And it’s something as simple as they don’t have their materials yet. And then it’s a matter of just getting them a pencil and making sure they get the materials to help them get started. Yep,

Mona Iehl 16:53
a coach told me in my like, first or second year of teaching, Seek first to understand because every behavior has a reason behind it. And so we’re so quick sometimes to just like, kind of jump on and stop those behaviors. But if you just watch for a second, you can kind of see what’s happening before you respond. And, you know, a lot of that can kind of settle out. And what a great opportunity to kind of just teach a kid like, Oh, if you don’t have a pencil, let’s remember those procedures we have for getting the things you need, right? Or how to advocate for yourself, like, really great ways of teaching kids, those self advocacy skills in a conference, which are conferencing doesn’t always have to be math.

Johanna Kuiper 17:38
Yeah. And to sometimes when kids don’t have are when they’re sitting there and seemingly doing nothing, and you walk up to them. And you’re like, Well, what’s going on? Or as you say it, how’s it going? And sometimes their response is, I don’t get this. And I know sometimes as teachers, people can take it personally of like, well, we just did this whole thing together, and you’re sitting here and you haven’t done anything or you don’t get it. And sometimes kids don’t know how to try. And we have to find ways to get into their space and get into their world to help them figure out how to try and how to then replicate that for another problem. So what kind of things? Would you ask for a student or ask a student when they say I don’t get this?

Mona Iehl 18:23
I think that’s like one of the hardest things because yeah, I instantly go to like, What do you mean, you don’t get this? Like, I totally get that. Like, but I, you know, being open to that feedback, because that’s really, the kids are giving you a feedback in that moment of like, Yep, I don’t get this. And so saying, like taking a step back and not taking it personally, and really thinking about like, okay, they don’t get this. Where’s my teaching moment here, right. And to be honest with you, a lot of times in that moment, I give them the first step, I will point them back to the problem and say something like, let’s reread it together. And I’ll read it. And then I will say, maybe we could draw this out. Let’s draw this out. 32 chairs in seven rows. Let’s see if we can get them into seven rows. You know, let’s write out seven rows. Like I will just give them the first step of like, telling them what to do. And then I love I love this strategy of like, giving a nugget and then going I’ll check right back on you and walking away. Because I think kids have a really hard time. Maybe humans have a really hard time of following a redirection in front of the person who’s redirecting them. Yep. So what do you think about that? What do you do when kids don’t try?

Johanna Kuiper 19:50
Yes, I always ask them well, what part don’t you get or which are asking you a question about the problem? Because saying like I don’t get it or I don’t know, does it inform me of how to best help you? Maybe it’s a person who is struggling with reading the problem, maybe there’s bigger words than there used to. Or it’s like a math piece of like, if there were 32 chairs in seven rows, what does that mean? And so it’s more of a mathematical side. So instead of me just like going on what I think they mean by I don’t get this or I don’t know, putting it back on them to figure out which part where are you stuck. So that way, I can better help them get started from there. And I liked your thing of giving them like a nugget and walking away. Because I know for me, if I’m given a redirection, it feels like such like a spotlight moment. And I don’t like that. And so it’s going to be harder for me to get started, or I’m afraid to make a mistake. And so having them like walk away, gives me the freedom to like, think about it, ponder it, and then take action on whatever the nugget was.

Mona Iehl 20:57
Totally. And I really was thinking about while you were talking, like the courage it takes for a student to even say, I don’t get this, and then be able to put to words, what they don’t get. So like you were saying like that precious math competence like that congratulations of like, Thank you for saying that good job, like letting me know that you don’t get it. Because I know there’s tons of teachers out there that are like, I just wish a kid would say I don’t get it, instead of just sitting there and doing nothing, right. I mean, that honestly, that might be a moment where I stop everybody. And I’m like any jail. Obviously, I check with the kid, first of all, like, Hey, can I share this, but just I need y’all to look over here. So and so is having some major math, like math courage right now. And just letting the class know like, this is a shout out in such a good way of like, I need you all to replicate this kind of thing. But that recognition of that courage is just such a great way to build your classroom community.

Johanna Kuiper 22:03
Yeah, I really liked that of like spotlighting their confidence in their courage, because going back to like what you said earlier, the norm of process over answers, it helps build the culture in your classroom of we are here to learn together. And answers aren’t necessarily the end all be all, it’s the process we’re all taking to get to where we are to succeed and to deeper, deeper, more deeply understand the math itself. And one thing I was thinking about too, is I had a scenario with a student the week before winter break of, they didn’t know where to start. And so we had a conversation about it. And estimation and guessing is such a huge part of math. And I think people forget that of it doesn’t always have to be this perfect, pretty algorithm to get to an answer. It can be messy, and it can be estimation, and it can be guessing, because that’s going to teach us something over just plugging numbers in. And the scenario was in four minutes, they read 1000 words, how many men? How many words can they read in 10 minutes, and sitting down with the student and thinking, Well, what does it mean to read 1000 words in four minutes, and talking about what it then means to read in one, and just drawing a diagram of like four minutes? And I was like, Well, how many thing? How many words do you think they read in a minute? And then guessing, and they guessed 700? I was like, Alright, let’s try it out. So it wasn’t in that moment. Like I knew 700 was a guest, that was not necessarily the best guess. But it was something. And so having them walk through the process of like, Alright, 700 700 700 700, what does that make? What do you think of that number? It’s like, it’s too big. All right, we know, 700 is not the right one. So let’s move it down. And just having them guessing check until they actually got the answer. And then the confidence that they had after that of like, oh, I can actually do this. And it was really cool to see that progression of confidence throughout the process, because I chose to work through with them rather than be like, Oh, or just give them a thought of like 1000 divided by four, and then you multiply it by 10.

Mona Iehl 24:19
I love that. Because the thing is, is that like, if they can’t guess them, they can’t and they can’t, they don’t know what to do like, then they can’t try right and so not allowing a student to make that kind of like inaccurate estimate really just takes the opportunity for them to try a way. And what’s going on in our classrooms all the time is that we’re trying to teach kids to problem solve, to take risks, to know what to do when they come up against a roadblock. And like, all of that has to happen within the context of problems. And so they have to have that like in Prague graphs thinking visible. And that has to be normalized, because otherwise they can’t learn all these skills of risk taking, and, you know, pushing ahead when they’re at a roadblock, because they have to be comfortable having messy work having inaccurate work, man, that’s, I love that example so much. But this is also getting me thinking about when you just do not have the time to have these kinds of conversations with 30 students, and what you can do to kind of like have the similar kind of conversations with students, but on a bigger level. So one of the routines I use in my classroom, as lunch, I launched the problem students productively struggle, and then we have a share in a discourse. And then we reflect on that and kind of think about the application for the next problem. And during the share in the discourse, I use the concepts from the five practices for orchestrating productive No, is that right? For No, let me start over five practices for orchestrating math discussions. That’s an NCTM book, if you don’t have it, it’s a quick read. And it’s so good. But I use the concepts from that to choose who in my class is work, I want to highlight that day. And so it’ll just be two or three kids and I make their work visual. So everybody can see it, that might be on the document camera or on the whiteboard, or in a chart paper, but making kind of like blowing up their work to make it big. And having them describe like we’re talking about we would do in a conference, but I have them do it for the whole class, while we’re circled up, it gives us an opportunity to talk about somebody else’s work, and really kind of put the spotlight on that, which builds the confidence of other kids, those one, those kids that aren’t ready to share their thinking, who aren’t even sure how to solve the problem, or maybe weren’t even successful at getting started that day. But being able to participate in analyzing someone else’s work, and turning and talking about their strategy, their model, builds their confidence, and builds their understanding, so that on the next problem, they have something to try, or they have the chart paper that they can go back to refer to, and try that the next day.

Johanna Kuiper 27:28
That’s really cool of how you highlight other kids work because it puts the spotlight on, there’s more than one way to solve a problem. And one of your peers in your classrooms thought of this way to solve it. It wasn’t the teacher telling them this is how you solve it. It was a kid coming up with that on their own. And then being able to share with the class, this is how I solved it. And maybe you were one of the kids who wasn’t confident enough yet to go up there and share a problem or how you solved it. But that’s how you did it. And so it’s validating in and of itself of I did it. I did it that way too.

Mona Iehl 28:07
Yes. And I think like, you know, in building thinking classrooms, when we have the students working together in those in like triads at whiteboards, something similar could happen and does happen in those groups of three. So that’s also something that people could do. If you’re like, you know, I just don’t have the time to conference with every single kid, even every week, then just popping into those small groups at whiteboards to conference with that small group is effective as well.

Johanna Kuiper 28:39
Yes. And one of the scenarios I talked about in a previous episode of my podcast was, when students were working at the whiteboard, they were talking about the volume of a pool. So the pool was filling up, and how long did it take to fill it up? And the group said, seven minutes. And so we we did discuss it and talked about it. What do you think does it in real life? Would it take seven minutes to fill up a pool? No. And so just having that small discussion of that doesn’t seem right allowed them to be like, oh, we need to reconsider either what that seven represents, or we made an error somewhere in our math. And so it helps them recalculate and recalibrate themselves within the problem.

Mona Iehl 29:25
Love that in that simple nudge, right of like, think rethink, this helps them kind of circle back. I mentioned one more book, which is called in the moment. It’s a book all about conferencing, and the different kinds of conferencing conferences that you might have with students. And she gives just really simple, easy to use both frameworks and questions based on different kinds of ways that you might want to prompt kids.

Johanna Kuiper 29:55
That’s really cool. I like that we have a lot of books that we can Go back to. So when it can you say that one more time? It was in the moment?

Mona Iehl 30:05
It’s called in the moment. Yep. And I don’t know who it’s by, so I will put it in the show.

Johanna Kuiper 30:10
Okay, sounds good. Awesome. Well, is there anything else you would like to say in terms of math questioning strategies?

Mona Iehl 30:19
Um, I don’t think so. I think that like, I love this episode, because what’s inspiring is that it’s happening in your classroom. It’s happening in my classroom. And hopefully, it’s happening in lots of the people who are listening classrooms, too. So I’d love to hear from folks, if you have other ideas that you are using to, you know, get your students talking, and what questions you ask or even just something you heard today that resonated with you. I know, we would both love to hear what you enjoyed about our episode today, but also like, what do you want to hear more about?

Johanna Kuiper 30:54
I love that. Yes, please either send us a message on Instagram or email us whatever way you have of contacting us do it. We want to hear more about what you think and how you use math questioning strategies in your classroom.

Mona Iehl 31:09
Yes, and I have a new question that I’m asking everybody at the end. And I know you have one too, right, John? Yes, I do. Okay, so my new question is, and I, we didn’t preview this. So we’ll see what happens. What is one thing that you wish all teachers did in their math classrooms, like everywhere in the world, every

Johanna Kuiper 31:31
so many things, but I think one of them is give space for students to think how they think there’s always one more than one way to do math. And I wish more teachers allowed that creative creativity for students, because that’s where math confidence comes from is being creative. And finding the way that you can do math.

Mona Iehl 31:54
Yes, I love that. My husband always says that, that like he’s a computer programmer, I think, yeah, I always get a job wrong. And a physicist, and he’s always like, math is not about an answer. Math is about being creative. So I love that you said that. And I totally, totally agree.

Johanna Kuiper 32:11
Yes. All right. My question is not as deep as that. But my question is, what is your favorite math joke or pun?

Mona Iehl 32:20
And I did not think of this. And then when I thought about, I know you asked this question, and then when I was asking my nose like I don’t have one, but I I feel like I do. It’s a cute baby. Because I have a cute baby. Are they an angle? I love it. I love it. Oh, right. All right. Exactly. Oh my gosh. Yes. So again, oh my gosh, this was so fun to do. Thank you so much for chatting with me.

Johanna Kuiper 32:55
Thank you. It was a new adventure doing a co host and episode and I hope we were able to do more in the future.

Mona Iehl 33:00
Yes, for sure. All right. Bye.

Johanna Kuiper 33:03
Bye.

Transcribed by https://otter.ai