SPEAKER_00 0:00

So, I mean, that's that that gets us to the to the idea, right? That what we're trying to do is us let go as teacher, right? And let students control the direction and all of those things in order to let them have the ownership. Like that's what this whole thing is is all about. Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Funderberg. We work together at Texas Instruments, and we're glad you're here. We're looking forward to continually improving our practice, and we understand that you are too.

SPEAKER_02 0:31

We hope that you'll find this podcast as a room for you to grow along with us as we wrestle with and explore ideas about teaching math even better. So let's get growing.

SPEAKER_00 0:42

Well, Joni, it is super exciting to be recording our first episode in season two of the podcast. And today we get to record in person at the TI offices.

SPEAKER_02 0:54

It's like you're three-dimensional.

SPEAKER_01 0:56

You're not just this image on my screen, and there's no lag between hearing your voice and watching your mouth move. It's really, it's really awesome. It is amazing.

SPEAKER_00 1:05

It is so exciting to be doing this uh in person. So I'm really excited. Um, and today we're going to be talking about something that I am really passionate about. Um, this idea of curiosity in the classroom. And I think that's a really good place for us to start. Is it really what do we mean by putting students in a position to have curiosity and how do we maybe engage with them in that?

SPEAKER_02 1:27

Yeah, I and I think this is such an interesting question because of course any math teacher would be like, Do you want your students to be curious? Well, of course I want my students to be curious. Like that's a dumb moment. But really, too, I think we all, especially, you know, you and I have our background teaching high school, and we've all taught those students who it feels like their curiosity has been killed by the time they get to us in school, right? So, how do we think about getting back in touch with what is really a natural state of humans, right? To have that curiosity and how do we get back in touch with that and leverage that for actual learning in the math classroom? And I love how when we were planning for this episode, Curtis, you talked about this sort of familiar phrase in math teaching and how to flip it on its head frame.

SPEAKER_00 2:06

So yeah, the idea, yeah, this this idea, and and it it came to me as always putting in a uh conference session for I don't know which conference, probably an upcoming NCTM. And uh I was thinking through, okay, I was gonna put in the typical exploring the world through mathematics as kind of a preparation for a modeling session, right? And that makes some sense. Um, and certainly it's a good, it's a great way to do things. But then it struck me that, you know, what I'm really trying to do is I want the students to look at the world and have questions that can then be answered through the concept of mathematics. And so the idea then was exploring mathematics through the world, which kind of reverses the phrase maybe a little bit or flips it over. But the idea was, hey, how do I get um situations or ideas in front of students that cause them to have questions that can be and should be explored through mathematics that maybe I'm trying to teach that week or or or trying to explore uh in that time. And so that was really the idea of this flipping the phrase on its head was thinking about it in reverse.

SPEAKER_02 3:16

And I like that because I when we think about that phrase, it reminds me of, you know, the the math teacher's lament of the constant student question we get is when am I ever gonna use this? Right. So instead of saying, here's the math, and now let's struggle to maybe find some sort of fake, you know, honestly, some fake real world application, two trains or you know, leave the station at the same time. Like that is not authentic real world connection. It's a it's a imposed context to make the point of the mathematics that we're trying to do. And what you're talking about is like the solution to that. It's it's the opposite question that we want students to ask, which is hey, what's the math that answers my question instead of what's the when am I ever going to use this in the real world? It's like, what math do I need to answer this thing that really matters to me in the world?

SPEAKER_00 4:08

For sure. And that that actually kind of lent, I was while you were talking about that, it lends me to think about um, for example, the kid who's driving along the highway um and they're driving over a bridge. I grew up in Oregon. Yeah. And um there's a there are many bridges in Oregon, some that go over relatively large canyons that have fairly deep uh, you know, rivers down below. And the question was, how high are we as we're going over this? And so actually, when I was a kid, I asked that question, and my dad and I happened to be stopped at the edge of a bridge. And so we did answer the question using some mathematics. We were throwing rocks off uh of the bridge and and timing uh the length of the time to get to the bottom. And my dad talked to me a little bit about this idea of motion and how much time it should take and how we can figure out based upon the amount of time the height of the bridge, and we could approximate it. And of course, I was, you know, I might have been 10. So I wasn't really thinking in terms of quadratics and this whole idea of we weren't really doing, I mean, we weren't doing it perfectly, but we were doing some approximations and using this acceleration due to gravity concept. And and so it was really kind of cool to be able to have that conversation, but that's the the experience that we're trying to generate. Um, is we're trying to uh allow students a place where the curiosity question comes up and the answer happens to be, hey, we're gonna do this mathematics to be able to come up with that solution to answer your question.

SPEAKER_02 5:45

Yeah, I like that. And I think we're in agreement that the heart of curiosity is that that the question is generated by the student rather than the question being generated by the teacher. And I think for for both of us, there's a whole, and maybe for our listeners too, there's like a whole lot of spinning questions, like the list of yeah, buts that come in, like, oh, that's all well and good, except I have curriculum to cover. And, you know, what if they come up with a question that isn't related to the math of my course or or grade level? Um, so you know, we're foreshadowing a little bit that we're gonna try and address some of those things today.

SPEAKER_00 6:18

But yeah, I yeah, I think that's I think that's important. But I think that, you know, what we're really trying to do here is establishing this idea of uh curiosity and exploration in the classroom and how it's crucial that we provide those experiences uh where mathematics is meaningful to answering a question that the students care about.

SPEAKER_02 6:39

Right.

SPEAKER_00 6:40

Right. I mean, that's really what it what it is that we're talking about here. One of the ways that maybe we can propose doing that is the more and more opportunities uh for students to be in the driver's seat, if you will, uh of the learning, right? I mean, it we talk about that uh a bunch at conferences, and and you hear about this is that students should be owning their own learning and they should be in the driver's seat. Um, and this is one way that we can really put students in the driver's seat, right? Is proposing and coming up with a scenario or a situation hypothetically, or maybe in reality, you know, we set it up so that they are doing something that is actually uh uh corresponds to a question then that they're gonna come up with. Oh man, well, how does that work? Why does this do, why does this act that way? Right. Um, and then they can talk about the mathematics that that is kind of inherent in that.

SPEAKER_02 7:40

Right. And that idea of like actually giving them, like I even take that a step further and saying actually letting them ask the questions rather than the I mean, there'll be times where the teacher's gonna come up with the question or the the s situation, the, you know, the guidance, the, you know, defining the road and which lane we're gonna drive in, so to speak, uh, if we're gonna use this driving analogy. But really, I love that. I love this analogy of putting students in the driver's seat because it makes me think back to, you know, myself as a teenager learning to drive or my two children when they were going through this process of learning to drive. And there's there's real excitement and energy that comes from that. And that's exactly what I know, Kurt. This is why you're so passionate about this idea of curiosity and exploration, because you're so fueled by that sort of passion and excitement that that's that's inherent in who you are around mathematics. And I've watched you bring that to other people, and that's just sort of what, like, you know, makes you stand a little bit taller, right? To get that excitement going. So, thinking about how can we create the situation for our students where they feel that excitement that they might feel getting behind the wheel for the first time and the learning to drive versus like becoming proficient at driving. And if we can take that analogy and try to translate that feeling into our mathematics classroom. So, how do we give um you know, students the opportunity to feel that like mix of nervousness and fear? Like we know that that's a normal part of the first learning how to drive. So I think this, you know, I've worked with teachers and they've tried to move to a more student-centered kind of approach in the classroom. And yeah, to your point, we talk about this all the time. It's built into our teacher evaluation rubrics, right? Like to have students taking ownership for the learning. And but teachers get nervous because that's hard to do, especially when kids aren't familiar with it. So maybe recognizing that like when they learn to drive, it's perfectly normal for them to feel nervous and fearful and you know, jerky kind of reactions at the controls. And so maybe anticipating that as we in the very early stages of implementing this in our classroom can help make that feel more comfortable for us as educators and not shy away from it before we even get it off.

SPEAKER_00 9:58

Absolutely. But I think that comes down to us the the that comes down to our planning, right? I mean, that's that's really what it what it is, right? Because uh a kid who's going to learn to drive. I mean, I don't know about you guys in Colorado, but when I was growing up in Oregon, I had to sit next to a person uh in a car that was built for learning to drive in, right? Um, in order to go and get my learner's permit. I had to do some of this driver's ed and all of those kinds of things. And I sat down next to a person who knew how to drive. And on their side of the car, there actually happened to be a brake pedal and like there were some say there was a little bit of safety uh on their side to be able to control the car and keep us in the lane, if you will. Right. Right. Um, and and so the same thing comes whenever I'm planning for an activity or an experience for my students. I kind of have to come in with uh I I know the end goal, right? Like I know why I'm doing this now and not three weeks from now. Right. Right. Because it corresponds to what I'm doing uh at this particular time. And and that also just uh I know we're gonna get there in terms of of how much we include this in the classroom, but it I don't think it needs to be every day. Um, you know, as much as we can, as much as it makes sense, but you know, especially when we're we're trying something new once a semester, even if I mean, if we can come up with one time during the semester that I'm doing this, then then maybe this makes sense. But it really goes to me planning and planning ahead and me thinking about what are all the different directions that I can come in, and knowing that my students are gonna come from somewhere else. Yeah, right. I have to think of all the possible things that I can think of, but then my kids are gonna have other perspectives and knowing that that's gonna happen and being comfortable that they're gonna ask questions that maybe I might not know the answer to. All of that goes into sort of how we do this, right?

SPEAKER_02 11:57

Yeah. I so appreciate you said that because I think there's there, it's not exactly two ends of the spectrum, but it's thinking about a balance between this giving the students freedom means I've got to let go of some of the control. And I've got to accept that I'm not gonna have every answer to every question that may come up and to be comfortable with that and to and to show my students that I can be comfortable with that. And I think that actually is a model of curiosity and exploration in and of itself. For sure. Model for kids like, hey, it's okay to ask a question that I might not have an answer to and be okay to just let the answer come. Like I think that's totally fine. But at the same time, it's also not all bets are off and you know, there's no rules of the road and it's loosey goosey and do whatever the heck you want. There still has to be some level of intention and planning and structure that as an educator, as a teacher, that I'm gonna put in ahead of time to, you know, create the best outcome. And I'm I back to our little car analogy, it's it's the balance between, like you said, the the driver's education school knows like, okay, hey, the uh the instructor that's sitting over on the passenger side needs this, this, and this control. And at the same time, I'm thinking about like sitting in the car with my student, my own kids, teaching them to drive. In particular, I wanted my kids both to learn how to drive a manual transmission. I just like that was really important to me that they know how to do that.

SPEAKER_03 13:26

Yeah.

SPEAKER_02 13:26

And being ready for the level of frustration that they would experience.

SPEAKER_00 13:32

And was that productive struggle? Were we on that?

SPEAKER_02 13:38

The wanting to scream and get out of the car that on their part, like I knew this was gonna be a frustration. So I knew like not getting frustrated because I needed the frustration to be with them, but like letting go of that a little bit and and saying, okay, we're just gonna be able to muddle through this. And I know that the end result is gonna be worth it.

SPEAKER_00 13:57

But you went into this knowing that that there was a certain set of boundaries, right? And and it would be really easy for us when we we're using this lane mark, lane uh idea and this driving uh piece. It could be really easy for for us to say, well, I've got to, I've gotta create a curiosity experience for my students. And I so I just throw them into this this place and and there's all kinds of room for them to roam. I I don't want us to to communicate that it's just, hey, there's a free-for-all and we're just doing these things. No, it's a well-planned thing. There are lane markers, there are uh things that we have set up as teacher to try to make sure that my students are um staying in the in the sandbox or in the lanes, right? Right. So as a teacher, I've also given them tools, right? I I've taught them some things, we've done some stuff. So we're not going into this completely blind, I guess is what I'm really trying to kind of get at is that we're doing we're not doing this just totally uh blank.

SPEAKER_02 14:58

Um And at the same time, we're not trying to control like everything, the actual steps of how they they think and what are the things that they think about and what are the conclusions that they reach and what are the questions that they ask. We're we're providing flexibility in that area, but knowing where those lane markers are so that we keep the conversation and the exploration productive and that it actually leads to a learning outcome.

SPEAKER_00 15:33

Let's talk now uh a little bit more practical.

SPEAKER_02 15:37

Yeah. I in fact, I have a good transitional story. Yes, practically. Let's do that. Yeah, because I'm thinking about, you know, your your comment around providing the structure and providing kids the tools, but then providing them this kind of open freedom to explore. And it reminds me of, you know, we both taught AP statistics, Kurt. And any AP teacher knows there's sort of the dead zone that happens after the AP exam and before the end of the school year. And any of us who have taught AP statistics have probably done the, you know, design your own study and, you know, ask a statistical question and gather your data and then run your statistical analysis and then interpret your results. And when one of the years that I taught A P statistics, I had a student who really had a passion. And I think this is a really uncommon passion for a high school student, but he was so interested in genealogy and studying his family tree and studying um, you know, the the characteristics that get passed from one generation to another and that sort of thing. And he designed this just amazing research study that brought that passion to life. And it was something I always knew about him. Um, I had taught him as a freshman. I had taught him again uh junior year and then senior year in AP statistics. And, you know, I always knew this was kind of a passion of his, but to watch him actually, it's exactly what you said. It was like, what's the question out there in the world that matters to him? And then how can he ask the question and find the mathematics that answers the question? And just like don't you just get chills here? I do.

SPEAKER_00 17:09

Well, because of the way that project was set up, right? That that he had an opportunity to tackle something that was truly his. And he got to think about. I mean, he did the teacher part of this thing, really, which is really cool because he thought about I I've got this project in statistics that I've got to be able to do some statistics and demonstrate that I know some stuff, that I've learned things this year. Um, and and I've he had to think through uh what's a question or a scenario that's gonna give me an opportunity to demonstrate all of this statistical knowledge. So he, I mean, he took it another step farther even than that, um, which is so cool that he got to do that and that you provided them that opportunity in their classroom. That's just uh that's such a cool project.

SPEAKER_02 18:00

Yeah, and I think it's I think it really nails what you were talking about in terms of having the guidelines, right? Like, yeah, no, you had to be able to use the statistics we learned this year, and you had to be able to generate data with your question, right? And then be able to report out the data after having applied the math to it. And I think that is a it was is a great example of the play between structure and freedom.

SPEAKER_00 18:25

Right. So, I mean, that's that that gets us to the to the idea, right? That what we're trying to do is us let go as teacher, right? And let students control the direction and all of those things in order to let them have the ownership. Like that's what this whole thing is is all about, right? That's awesome. All right. So, so to kind of play off of then your uh project and AP statistics, not all of us are teaching AP statistics, right?

SPEAKER_01 18:57

Or have this like extra two weeks of like something, I need to, I think something fill the time that doesn't matter.

SPEAKER_00 19:04

I don't think I've ever asked that question as a classroom teacher, like, hey, do you have something for me to do in the next two weeks? I think I've got these two weeks, I just don't know what to do with. I don't think that's ever happened uh in the classroom. And so the I guess that gives us so how do we do this? Like, what are the steps? What are the things that we can do? Um, because we all know it's important. Everybody's talking about it. NCTM, uh I mean, everybody is talking about you can't pick up a teacher uh magazine or article that doesn't have some uh ties to this conversation. So but what are the practical things? What are the first steps? What can we do?

SPEAKER_02 19:46

Well, honestly, I think the answer to that is is the same answer to a lot of other questions that we're answering, right? Like, how do I get through a packed curriculum in general? I think my short answer to that is really figure out what are the big ideas that actually matter. Right. So instead of, you know, this is a common pushback I heard in all in when I was working with classroom teachers. And I'm not saying this to dismiss this as a concern because it's a very, very real concern. But it's, you know, I don't have time to do those fun projects with my kids. They take time or letting kids guide the learning and ask the questions, like that takes away from my precious time for instruction. And I think that what's at the heart of that concern is and I don't know that people would actually say this as a belief, you know, back to our beliefs episode. But it the heart of that concern is a belief that I have to give students exposure, and I'm making air quotes when I say that, exposure to every topic in my curriculum. Because if I don't at least expose them to it, they're not gonna learn it. Well, that's actually not true. Like if we can build up students' robust understanding of big ideas, then they can make sense of individual topics that fall under the umbrella of that big idea without direct instruction. Right. So I think the first step when you say what's the first thing to do, I think it's identifying like what are those really big concepts that are like, man, I really wish students understood the idea of rate of change. Like that's a huge concept that spans multiple grade levels and really has application to a lot of mathematics. So identifying what are those, like, oh, this is a power, a power topic. And then those are the topics that I actually give myself the space and time to explore. And that might mean I don't teach, you know, five ways of finding the slope of a linear equation. Maybe that means I I just really provide this opportunity to explore and let students make sense of it and let some of the individual pieces go.

SPEAKER_00 21:57

Yes, I think that's I think that's a huge. uh huge step right in in identifying the big topics that we um that we are teaching right i mean that's that's probably the biggest step in doing this is because generally these kinds of explorations don't c turn up uh factoring a by uh a polynomial right right or not procedural i'm not i'm not getting into a procedure and maybe that's maybe that's another place to to say okay we've identified maybe the big topics um i don't think i think we can eliminate or or at least put to the side um this idea that we're gonna be able to do this with a particular procedure right right the the the whole in the whole idea is in fact to try to teach students the concepts or to allow them curiosity about a concept not necessarily about how a procedure particular procedure might work right um and so i you know dealing with the idea that i teach a lot of procedures and that's a good thing we should be doing that right students should get exposure to those kinds of things um but there's gonna be times when what I'm intending to teach is a concept what I'm intending my students to to get is uh an an observation about how two things work together um or or how this mathematical concept is related to another mathematical concept um those are the times right when I can set up this kind of exploration when I can set up a curiosity statement um I think that's it I think it I think it ties back to to so many other things that we've talked about through season one of the podcast Curtis like it's it's not just about the mathematics learning that happens as a result of this.

SPEAKER_02 23:47

I mean I know we're talking about fostering curiosity uh and and passing that along that excitement and energy for being curious about mathematics onto our students and I think we need to remember that you know this kind of uh of a lesson and the time that we're taking to doing this is going a long ways towards establishing culture in our classroom and establishing a relationship between ourselves and our students that that we care about them and we care about their interests and we value what they're bringing to their learning. And it's creating a really an intrinsic motivation factor, right? So moving away from I mean it's it's sort of the old platitude of I I teach I don't teach math, I teach students. But there is something really true there. And it goes along yes and and I think moving away from the like checklist off my curriculum to wait, I'm I'm in this and I know I'm making an assumption but I believe all of our listeners really care about their students as people too and this is an opportunity to say that's what this is about. And we can let go of the like math for the statewide assessment that happens at the end of the year lens for these kinds of explorations. So back to your point about like this is not an everyday thing. It couldn't be an everyday thing if we're letting kind of the math get on it.

SPEAKER_00 25:15

You gotta you gotta do that other stuff. Right.

SPEAKER_02 25:17

You have to exactly so how so how might a teacher think about how often should I be doing this and how do I know if I'm doing it right or or you know what what are your thoughts about kind of advice if a teacher wants to try this?

SPEAKER_00 25:31

I mean so perhaps uh thinking from a cyclical approach something that is um a a part of the learning cycle a part of what we're doing um and so you know you mentioned all of the the standards things that we have to get done because we know we're gonna have this assessment and those kinds of things that that direct instruction type of thing is a part of the is a part of the of the plan right I mean that's that's a place um I think this is a this student guided piece um is an is another place right this this idea of exploration um and and we can kind of work through sort of a a cycle that is you know a a part of that and and I know we've had this discussion before of uh in fact I think we just had this discussion in our last episode about procedural uh fluency versus conceptual understanding and where do we start when we're topic by doing new topics. And I ended that last episode with a probably a controversial thing saying that I think we should be starting with conceptual understanding all the time. So so if I was doing it, uh me as the teacher, I might intentionally start with one of these kind of curiosity explorations that gets at the main idea or the main the main topic uh that we're going to be studying in the next several weeks, right? And so this might be an opening thing for me in an introduction. I a lot of things are coming to mind. I'm gonna try to not refer to every single one and have them all be AP statistics examples because that's you know that's just where my mind goes. But the idea of setting up uh my students for one of these explorations is really important, I think, in terms of setting the mood for the next couple of weeks as we go through the explorations and the and the and the uh procedural fluency kinds of things that I need to do to make sure that we're actually getting it done. But if I start off with this, then it sets the tone. You you mentioned that a moment ago that this sets the tone and I want to add to that that this also sets the tone for students seeing themselves as doers of mathematics. I really think that as they get their curiosity kind of peaked and and they start seeing that they are uh driving some of the questions um they see that mathematics is something that they do. Yes. Right? Yes. And and then that kind of creates this idea that hey it's not just this abstract thing that somebody's forcing at me that I have to do because they've told me I'm 11th grader and I have to be able to factor this is what you do as an 11th grader. But instead I'm answering questions that kind of matter to me and it's and it's through this lens of mathematics and it does answer the question like when am I ever going to use this? Like it we do get to that. So making it a part of a of a cycle not doing it every day but making it sort of a a a part of the cycle and some people may say no I need to end my I need to end with those curiosity questions.

SPEAKER_02 28:42

And that's certainly possible.

SPEAKER_00 28:43

Maybe it's equipping the kids with those lane markers for equipping them with the with the tools right I mean if we if we change the analogy and make it a sandbox right like if you give them the tools to play with in the sandbox they got to have a bucket and a shovel and whatever like then then that is what you're doing and you're doing it at the end of a sequence. But I think it's part of a sequence of things. That's that's maybe my big advice.

SPEAKER_02 29:08

Yeah I I totally agree I really like that approach and I like that cyclical idea of like because there is sort of you know we you and I both lived through the math teaching wars so to speak of you know is direct instruction the way that students learn or is a discovery based approach the way that students learn and I think you know we're in agreement that it has to be a balance of both. It's not you know one extreme or the other is not going to be what has the greatest outcome in student learning. And then I think the other thing that you know I would throw out there and I would encourage you to comment on this too is is our own expectation of ourselves as teachers. Like you might people might be listening to this and be inspired by our enthusiasm for this topic and say, oh I I want my students to like get totally engrossed in the question and be excited and you know they might not. It's true. And that's okay. And it could be that you know maybe the genealogy question was super exciting to one of my students and might have made the other students roll their eyes, right? Yeah. But it was okay because it sparked the passion in that one student.

SPEAKER_00 30:13

Absolutely.

SPEAKER_02 30:14

But I also think like trusting that okay I'm gonna try this and I might not see the enthusiasm and excitement from students that I heard Joni and Curtis talk about, but that doesn't mean it wasn't worth the time to do.

SPEAKER_00 30:26

Well exactly at the risk of making a corny pun out of our room to grow podcast name we're planting seeds here. Exactly and and we may be the person planting the seed we may be the person watering a seed we may be providing the sunlight to help grow the seed whatever it is like it's part of a process and and you know to your to your statement earlier we teach students not mathematics like these are people who are going to leave our classroom and they're gonna go on and go into another classroom and eventually they're gonna graduate and they're gonna have a life and they're gonna do things and that life may or may not be uh hugely impacted by the the mathematics that we taught in that particular grade at that particular time. And that's okay. Like we we need to remember that what we're really trying to spark is curiosity and joy of learning, right? I mean that's the big thing. Right. That's what these experiences really are about.

SPEAKER_02 31:34

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