Season 5 Episode 6:

Pose Purposeful Questions

00:00:00:00 - 00:00:02:00

Opening music

 00;00;02;01 - 00;00;34;18

Joanie intro

In today's podcast, Curtis and I continue our exploration of the mathematics teaching practices, from NCT m's principles to actions with a conversation on questioning. Specifically, we talk about the types of questions teachers ask and how they can assess student thinking or advanced student thinking while staying anchored in the mathematics learning goal of the lesson. Although questioning is common and frequent in nearly all math classrooms, there really is a lot of nuance in using questioning purposefully and intentionally. So let's get growing.

00;00;37;13 - 00;02;38;18

Curtis 

Well, hey, Joanie, I am super excited to be recording again with you. I believe this is our 49th or 50th now episode of the Room to Grow podcast. Super excited. Yeah, this is a big milestone. If it if this isn't the big milestone, then our next episode will be. And I'm sorry I didn't do my homework ahead of time to know the answer to that question. But today we're going to be talking. We're continuing our, conversation around the principles to actions, and CTM’s publication and principles to actions, its 10th anniversary. And we are moving into a new math practice, math teaching practice, which says effective teaching of mathematics uses purposeful questions to assess and advance students reasoning and sense making about important mathematical ideas and relationships. And I love this one. This is this is a favorite topic of mine, this idea of questioning. And in in that interaction in our classroom, you know, we've had a lot of conversations about culture and students feeling safe in our environments.

And all of those things set us up to be able to do this, to be able to ask those questions.

And to be able to to make it in an effective environment for our students to kind of experience.

So really, I want to kind of maybe start this question, this conversation off with, a little bit about assessing questions or thinking about what, what role assessing questions maybe play in this, in this back and forth with students versus, thinking about and advancing questions. And I like that language, but I'd like to know maybe or think a little bit more and expand on, those two different questioning types.

00;02;38;18 - 00;04;41;20

Joanie

Yeah. I think that's a great place to start. And, you know, I love each of these, mathematics teaching practices that we've talked about in the last five podcast episodes. I, you know, there's so much meat in these sort of simple one sentence statements about what this, how this contributes to effective teaching of mathematics. And in some ways, questioning is kind of like the roll your eyes.

Well, duh. Because you know any for for. We always think of questioning as one of the primary roles of an educator. Of course, as a teacher, you're going to ask questions of your students, like everybody that that comes to mind is obvious, but the some of the specific language around effective, purposeful questions like, oh, that takes it up a level, right? It's not just about asking questions, but it's about asking purposeful questions that actually serve, an important part in students developing and understanding mathematics. So I, I love that and diving into that. So yeah, I really like in both in principles to Actions and in the follow up, texts, the Taking Action series, there's a lot of time spent differentiating between questions that assess student thinking and questions that advance student thinking.

And as I reflect back, you know, as as we are, as we often do on our podcast conversations, Curtis, like, I think back on my classroom teaching days and the time I spent in the classroom and this is for sure something that I got better at over time. But I would love to go back with the knowledge that I have now. Because I think I could be a much more effective questioner. And I, I want to start by saying, like, questions that assess student thinking are probably already happening in every classroom. I mean, I even think about representations of horrible teaching like, you know, the Ben Stein character from Ferris Bueller's Day Off, attempting maybe to ask us asking questions and that this is, you know, the guy who says, Bueller?

00;04;41;20 - 00;04;42;25

Curtis

Bueller

00;04;42;25 - 00;04;44;08

Joanie

Yeah. You can do him better than I. But the way he asks questions, you know, or basically he starts statements and then waits for kids to finish them and they don't. But assessing questions are just like, as a teacher trying to figure out what is it that kids know. So I think these are an obvious place to start.

And, and something that every teacher is already doing. And I would guess most teachers are already doing well. So when we're asking students to recall facts or, elaborate on a definition of something, or tell us how to solve a certain kind of problem or what to do with a certain kind of mathematics or, or to elaborate on an approach that they took, how they're thinking about something or how they're working through a task like gathering information and probing students, thinking those are going to be the kinds of questions that assess student thinking. So knowing that, like, I would love to hear you sort of develop your thinking on what role do those play in student learning? I mean, how, how is asking a student and assessing type question? How does that contribute to the ending part of this statement? I'm going back up advanced students reasoning and sense making about important mathematical ideas on relationships.

00;06;04;12 - 00;08;31;12

Curtis

Well, I it seems to me. And I think we've even had this conversation before on the podcast. Although I can't remember when thinking about this idea of assessing questions. I have to have those questions, and I have to ask them. And I have to listen carefully to the student response in order to be able to ask advancing questions. It's a little difficult for me to ask any kind of an advancing question that deals with either a miss or preconception and redirects, or maybe provides direction towards the mathematical goals that we set last, last month. And in our podcast. It's difficult for me to ask probing questions to be able to you to, to guide and, and in, you know, redirect student thinking or things of that nature in order to get to that mathematical goals if I don't know where the kids are. And so I have to I have to ask these assessing questions. I have to kind of get at, do I know and understand what my students have grasped hold of? What have they mastered? What are they still developing in terms of their understanding of this topic?

And, and where are the things that I need to to kind of work on. So these are information gathering questions for me. As I'm getting to know what my students know about this topic. And as we're working through, problems together, these can be as simple as procedural kinds of things or as deep as what you suggested. And, and having a student really walk me through what their thinking was in, in a reflective sort of manner, walking through their, their thinking. Here's what I thought when I did this. Here's why I did this, sort of thinking to be able to then ask a follow up question about their thinking about their conception to do one thing or another. Why did you take this step or what was the thinking there to be able to kind of guide that and then to be able to connect that back to and I use that word purposefully connecting it back to you the mathematical goal or the concept or the thing that we're trying to approach. You know, I can't do that without the assessing question to begin with.

00;08;31;12 - 00;10;01;03

Joanie

right. Yeah. I really like that. And I'm thinking about, you know, in, in kind of doing my research for this conversation today, I read through both in, in Taking Action. There's a lot of these little vignettes, and in NTM articles, you'll see this a lot to where they'll be a description of this being implemented in a classroom. And they'll give you a little scenario like, here's the task and here's what the teacher said. And then here's what these three students, you know, talked about. And they'll, you know, kind of put you in the moment of a classroom. And one of the things that I noticed in all of the vignettes that I encountered in in preparing for this episode is and going back to like, what I could have done better when I was a classroom teacher. Like in every case, when the teacher is asking in assessing question and a student gives a correct answer, the student the teacher will ask, well, why? Or how do you know that? Or they'll ask a follow up question to a correct answer. And I'm like, oh man, I didn't do that enough. I didn't I didn't get to what students and how students were thinking. If I thought they had the right answer. I made the assumption that their thinking and their reasoning behind that right answer were also correct, or were also in line with my mathematical goals. And I think seeing that and, you know, picking that out of several examples in a row and going, oh, like, it is so important to ask that follow up

00;10;01;07 - 00;10;04;27

Curtis

Yes. Oh, wow. That's.

00;10;04;27 - 00;10;56;27

Joanie

Even though they have the right answer because thei,r their reasoning could be completely flawed.

And then, you know, two, two problems later or in the very next phase of the task they're working on that could fall apart. So again, I love how you described it. As for the purpose of knowing what to do next, what direction to take the student, what question to ask next, what new problem to put in front of them. That feels a little more obvious when we're uncovering misconceptions or common errors, right?

Because we're kind of on the lookout for those things. But when we get an accurate answer to a procedural or, you know, just a, a mathematical question that has a right or wrong answer, it's easy to make a whole bunch of assumptions around that that aren't true.

00;10;56;29 - 00;13;35;00

Curtis

It is. And I find myself surprised. You know, the follow up question to a correct answer is such an important piece of the puzzle because, often, even if the question that I ask, the assessing question that I asked has something to do with, and understanding. Right. So you told me this was the answer.

And I ask you now to explain you know, so what was your thinking? What made you think that, you know, to, to do this this way or how did you come up with that response? What was your procedure for getting to here? Often that exposes to me to the students thinking in a, in a, you know, their misconception or their, their correct conceptions, like their, their depth of understanding of a topic gives me opportunity to probe further and to ask an advancing type question.

Well, what do you think if, you know, what would happen if or can you. Okay, so let's take that and let's apply it in this situation. Suppose blah and and all of those things can be done. If I've asked a, a, an appropriately probing assessing question such that now I can take the, take the opportunity to take that advancing question and, and, you know, push the students reasoning and sense making, maybe outside of their the box that they that they were in and I see it happen all the time with my son Teagan.

I was just when you were saying that, I was like, oh, man, you know, there's a lot of the time when he'll give me a correct answer and, then I follow up with, so help me understand how you got there. And then I get this. What? Well, I, I mean, this is what I did, and I'm like, well, okay, but that's not that's not really it. And so then we have a little bit more probing conversation to have, rather than just me saying, oh yeah, that's awesome. Which, you know, side rant. This is one of the problems I have with all the digital, assessment that happens on students. You know, if we're just typing in answers that are balled and we don't have any understanding of how the students are getting there, we're not seeing any of the thinking. We're not seeing any of the explanations. It's very, very difficult for me as a teacher to know what's going on in your little brain.

00;13;35;02 - 00;13;36;00

Joanie

Totally agree.

00;13;36;02 - 00;13;46;10

Music break

End of Segment 1

Start of Segment 2

00;13;46;10 - 00;16;18;02

Joanie

The other thing that I was thinking about as you were talking about how it is when you work with Teagan, like that we our questions uncover what's important to students. Right. Like, again, here's something I would like to go back and alert my students to like, it's not just me. Like, you don't need to just pay attention to your teacher to get information right. Like the teacher telling you what to do or how things work in on the questions and if, if a teacher is asking effective questions and a student cues in on them, it uncovers what's important about the mathematics.

I think that I don't know, maybe this is me having a silly moment that everybody else had ten minutes ago, but that cuing into asking a follow up even to a correct answer, cuz that just the answer isn't enough to say you really understand mathematics, right? So just being able to, you know, correctly, find all the factors of 56 doesn't mean you really understand the relationship between a number and its factors. I don't know, I probably could have come up with a better example of that, right. But it there's so much more to what we value in mathematics than just getting correct answers. So just with that, like asking the follow up question to a correct answer, we're signaling to every student in the room that, okay, yes, accuracy is important. The correct answer is important. I'm not saying it's not, but if that's all we cared about, we wouldn't need to ask a follow up question. We wouldn't need to probe how do you think about that and how did you get there? And even, you know, thinking about our routines for reasoning. When we had Grace and Amy on the podcast, like getting kids to react to one another,

how do how does your way of thinking about that relate to Curtis's way of thinking about that, like those kinds of questions? Although those would fall under advancing questions, which we can kind of maybe define a little more clear specifically here in a second. But they also signal like what's important and how the deeper understanding of mathematics is malleable.

00;16;18;02 - 00;18;04;08

Curtis

Right. Well, you had, you actually had a quote in the notes that you shared with me here, a little bit ago that I want to just kind of, maybe use as a as maybe the beginning of a second portion of our conversation here. That is effective questioning supports students to use their own thinking to make sense of the mathematics. And so your statement about, hey, asking a follow up question around correct mathematics sets the tone that there's more to this than just getting correct answers. And I think that quote kind of directs us, directs us to think about that a little bit, that it's really when we do that, when we ask those kinds of questions to support students using their own thinking, about, the mathematics in order to make sense of it, even following up a correct answer does that.

Right.

It drives me to think, oh, well, shoot, I thought all I had to do was get get you the answer to this. I wasn't really thinking about how I got here, and now I need to know if. Could I do this again if. If you asked me with different context or different content, would I be able to, to perform this procedure or maybe even more so? Could I apply this procedure or thought process to a different area of mathematics or a different type of of question where maybe the response isn't, you know, as in the same form as the one that I'm currently responding to. And I think, you know, just getting the students to go, whoa. Okay. Now, now I've got to make sense using my own thinking,

Yep.

here, that's you know, that's a that's a big a big part of it.

00;18;04;08 - 00;20;06;20

Joanie

Yeah. For sure. And kind of aligned with that to one of the other things that I noticed in a lot of the little vignettes and descriptions are the ways that teachers, the teachers in these little stories helped to uncover those misconceptions or help to uncover more like what was what was the important mathematics,  was never about like signaling to the student that they were incorrect, but instead asking a question that shown the spotlight on something that maybe a misunderstanding, a common error, or that was relevant right to to the bigger mathematical goal. So,  I just think there's not enough emphasis to put on the importance that of tying into how students are thinking and and not just towards like that's important to do, obviously towards their learning. And, you know, shining the spotlight, as we said on what's the important mathematics and connecting back to our mathematics learning goal that we talked about on our last episode, but also the ways that asking the question to tie into how they're thinking and reasoning and making that visible to themselves so that they can truly understand or identify misconceptions or errors. Also, I'm just thinking of kind of coming back to the very first place you started with the culture and safety. It's all about building their own sense of identity and agency. As mathematicians like, you have everything you need to understand this mathematics. And I'm going to ask you a question that will cause you to elaborate on your thinking, or describe your thinking, or analyze your thinking, or adjust your thinking, to get you to mathematical understanding and how, man, that has payoff beyond, you know, this lesson, this task, this math cool.

00;20;06;20 - 00;21;35;04

Curtis

Yeah. For sure. I mean, I, I think, you know, one of the one of the points that I think we wanted to make here was you know, asking these questions also now requires me as a teacher to listen, and to not just listen for correct or incorrect answers. But, you know, we are listening to the students and, and making sure that we have the opportunity to, to follow that up with, you know, ways to encourage, you know, and promote student thinking. And I, I was just I was also just thinking about what the questions, what the follow up questions often give us the opportunity to do is to, to highlight the fact that their student that they're thinking is valuable and to make this a place where, you know, to go to the culture conversation, to make this a place where…and it it's a safe space, but where they're thinking is valuable and where they can, can answer without fear, where they can answer with confidence. And and even if that confidence is, is, know, they're confident that they have it. But maybe they've got a misconception realizing that they can still be confident in their adjustments to those misconceptions. 

Right.

And, and, walking, walking along, in that.

00;21;35;04 - 00;21;35;29

Joanie

Yeah. For sure.

00;21;35;29 - 00;21;46;20

Music break

End of Segment 2

Start of Segment 3

00;21;46;20 - 00;23;14;02

Joanie

This math teacher article. Mathematics teacher learning and teaching article that I reviewed. And I'll put a link to it in our show notes. It's called Planning and Implementing Effective Questioning. That's the title of the article. And it was in the February 2025 issue of MTLT. But I, I really loved the way the author shared that, you know, as a teacher and I want to shift to this thinking too, like, how do we think about effective questions and how do we prepare ourselves to have effective questioning?

Because you're going to ask questions right? But the question you're making, like, if you don't plan ahead of time, you're not going to ask as good of questions. And, you know, planning

For sure.

But I just thought the author did a really nice job of describing that. Yeah, you have to plan some questions ahead of time.  And I want us to unpack a little bit about what that might look like. But they also brought to point that in the moment, you're going to need to adjust because the questions that we ask in the next question that we ask is going to be dependent on student responses, right?

For sure.

So you can't plan every question. You can't pull up a script and say, okay, after this question, I'm supposed to ask that one. You have to be responsive to students in the moment. But let's talk about a little bit about preparing for assessing and advancing questions. So how do you think about that? What does it look like to prepare your questions ahead of time?

00;23;14;02 - 00;26;10;26

Curtis

Well, I think there's a couple of things that go go into that. And I know that, you know, preparation is one of your key stone things to, to highlight, right?

It’s my soapbox topic

But I think, for me, anyway, good questioning starts with good understanding of the mathematics myself and the things that we're going to be looking at. And so I, I have to be prepared by, first and foremost, knowing the work that we're actually going to be doing. And I know this sounds crazy, and I know that probably a lot of people are saying, well, of course, Curtis. But reality is, if I have not gone in and thought deeply about each one of the 2 or 3 tasks that we're going to look at, or maybe I've got, you know, 3 or 4 examples that we're going to be talking about at each each of them highlight something different that I want to make sure that's true about a particular concept or whatever the, the, whatever the planning is that I've done ahead of time. I have to be really thinking deeply about both the procedures, the conceptual understandings, the things that go deeply into those and then all of the little possible rabbit trails that those things could, could lead to. Right in the questions, in the, in the steps, along the way and the places where I'm, I'm going to need to stop and make sure that I clarify or we have a conversation, or if we're leading a guided task or some kind of, hey, this is an activity that my students are going to be working on as, as groups, and I'm going to be listening for conversations that happen there. I have to be thinking and putting myself into that moment of, okay, while they're working, what are the things that I anticipate hearing right. Along along the way? What what what am I going to want to you, you know, organize, those responses into is there some sort of an order of responses that's going to make more sense in developing this idea? And I know you're smiling because you can hear in my like, as I'm saying these things, right? Like, so I and I don't want to keep I don't want to be I don't want to be so obvious there. But it's so important that I've taken some time to really be ready for those things. And one of the first things I can do is actually go into and work the mathematics and think about what it is I'm thinking, in order to you and what are the connections that I'm making and what are the things that I'm drawing upon, not just working the problem. I'm not just working the problem, I'm working the problem. And I'm looking at the structure, and I'm thinking about what are the tools I'm drawing upon. And I'll wait a minute. Should I be thinking about it this way or or have I have we developed that, that bit of knowledge yet? Is that a place for us to go off and develop a little bit of knowledge before we manipulate a little bit further?

00;26;10;28 - 00;26;33;12

Joanie

Right. Exactly. And I'm just going to build on that because that is my. That is my soapbox moment for planning and what I want to say is all the things that you're describing, like thinking about the different ways students might approach the mathematics and thinking about the different backgrounds that students bring and how that may alter how they think about it.

Right.

And, and for this reason, I just this is why, for me, planning collaboratively is so important because I might not be able to think of all those things myself. I might not have deep knowledge. You know, if I'm teaching 10th graders, I might not have deep knowledge of sixth and seventh grade content that may come up and be relevant. But one of my teaching colleagues might or maybe an opportunities for a vertical articulation with those sixth and seventh grade teachers, those things can be brought to my attention. So yeah, I really think, I'm 100% with you, like working through the tasks deeply, understand the mathematics and the different approaches that students might take so that we can anticipate and then think carefully about how will respond and what are the questions we may ask, and how might we, uncover the relevant mathematics or redirect the rabbit holes that aren't relevant to what we want students to engage with on that day? It's so important. And then again, coming back to that, also being able to be flexible in the moment, if I've really thought of lots of different ways students might approach, then as I'm observing different approaches, I can redirect students like, you know, Curtis, I see that you you've determined that this is true about this task, but I notice that Teagan is thinking about that differently. Go chat with him about what he thinks like

Yes. Yes.

to not always be the owner of the information as the teacher, but to create that collaboration among my students and again, to value the different levels of thinking, which are all components to deep understanding of mathematics.

00;28;14;21 - 00;30;00;02

Curtis

For sure. Well, I have one last little, statement for us to to maybe wrap up on. And, one of the things that you put in to your notes is we were kind of preparing for this was, you know, thinking. And I think it relates quite a bit to the, to the planning idea, which is, is really about the timing and frequency of the questions that you ask. There's a strategy, to doing this, which could be a podcast in and of itself. I think,

you know, thinking about the way that we ask those questions. But really bringing that to keeping that in mind. And, and there's plenty of research out there. There's plenty of conversations out there about the kinds of questions and who we ask the questions of and this, podcast that we, are planning to have.

And as a matter of fact, very soon, in a in a few months, we're going to be chatting, with Pam Harris and, and talking a little bit about developing, mathematical reasoning. And through some of these questioning things. 

Right. Since they can’t see us, I’ll just hold up the book…

Joanie and I are. You're right. Joni and I are on video call here at being able to, record this podcast, and she pointed out that, yeah, we're in just a couple of months we're going to have Pam Harris join us in talking about this idea of developing, understanding. And one of the key things is about the way that we ask questions and the timing of those questions and the frequency of the questions and the where we ask those in the lesson, all of those things. And so just a pre, preamble to that conversation a little bit.

00;30;00;05 - 00;30;38;10

Joanie

For sure. Well, I love that we've come back full circle, because, again, I think the whole reason we've taken. And we'll continue to take a couple more months out of our podcast topics to talk about the mathematics teaching practices, from principles to actions, is that these things are really effective in developing the kind of thinking and engaging with mathematics that we want students to do.

So, questioning like kind of started out saying, this is a dumb moment, but hopefully where we've uncovered that there's actually a lot of nuance and a lot of skill, and this is such a powerful tool for student learning.

00;30;38;10 - 00;30;39;14

Curtis

It really is.

00;30;42;08 - 00;31;00;11

Joanie Outro

Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us, consider leaving a review to help others find us and share the podcast with a fellow math educator.

See you next time!

00;31;03;21 - 00;31;06;07

Music out