Kyle Pearce: Hey, hey, hey, Math Moment Makers. It's Kyle, and you're hanging out with Jon here as well. We are super eager to dive into an episode today where we're going to chat all about trying to elevate our math resources. A little bit of background here, if you were with us last week on Wednesday night, we did a live session with over 250 participants where we were unpacking why our resources need to change. And we even did change one of our, I guess, traditional textbook problems right there, Jon.

Jon Orr: Yeah.

Kyle Pearce: And the reason why we were doing this particular episode is to bring you the ideas from that webinar, but also to remind you how you can make transformations to textbook problems, problems you've got, resources you have at your disposal. We want to make changes to those resources. So we don't have to spend so much time looking or changing or building every thing from scratch. So we want to bring you that here in this episode, and also tell you about some of the things we learned during that episode from our participants and some of the pitfalls to watch out for when transforming your textbook. So let's do this.

Jon Orr: All right, here we go.

Kyle Pearce: Welcome to the Making Math Moments that Matter podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: We are from makemathmoments.com and together with you, the community of math moment makers worldwide who want to build and deliver math lessons that spark curiosity, fuel sense making and ignite your teacher moves. Well, welcome again, my wonderful math moment maker friends. As we mentioned in the intro, we're super excited. And actually we are, I guess like ramped up to dive deeper into this idea. If you've been listening to the podcast for a while, back in episode, I think it's like 60, 62, something like that, that was like 100 episodes ago, we shared a webinar we did on transforming your math textbook. You know what? Our first session we did last week sort of built on that idea. And today, we want to dive a little bit deeper into the why, like why our resources need to change.
And then also some of the things that we want to be looking out for when we go to try to transform some of our resources. We still have some friends in the community who are telling us that this is an ongoing pebble in their shoes. So that's why we're here. And that's why we have this four part webinar series going on all throughout the month of January 2022. But Jon, tell people a little bit if they are not in that webinar series. And let's pretend like maybe they're listening to this in May 2022, or like May 2023, have they missed the boat or what can they do?

Jon Orr: Yeah, sure. So what you can do is since we're running four different webinar sessions, those sessions are going to be open indefinitely. So if you missed our first live session, because you're listening to this one week later, or when this episode goes live, then you get to join us for the second live episode. Like Kyle said, we are doing this every Wednesday in January 2022. So we could help you make those transformations this year. But if you're listening, say later after we're done and it's not January anymore, then you can still go to make mathmoments.com/transform. That's where hey, if you're ready to sign up and do episode two with us or the next session with us, that's where you're going to go to. Just register and you'll get the Zoom links. You'll get the links necessary for you to join us live. If you're following us later and you will want to say still watch these sessions, we are going to have the replays up at that link indefinitely. We want to build this as a transformational tool that we can help as many teachers as possible to make these changes in their lessons. So they don't have to say, scrounge the internet to find a brand new engaging lesson or go and pay money out of your own pocket from websites that sell you lessons or worksheets.
We want to be able to do that easily because time is a factor, but we don't want to have to use our own finances to kind of finance our math classroom. I think that's a big issue right now because Kyle, there is a big push in math education and I feel this, especially in social media to throw out your textbook. It's like I have to use these new engaging math problems to engage my students. And hey, rightfully so. We want to engage our students as much as possible. We want to get our students building and using their curiosity. We want to get our students thinking. And so it makes sense to ditch that book because most textbooks, if you're just following the textbook, like for example, when I first started teaching and this is true for I think a lot of beginning teachers, Kyle, is that when you first start, you don't have a lot of resources at your disposal.
You collect those over the years and your default, my default was to open up the textbook that say, my department head has given me and look at the examples in the textbook and use that as my lesson. I would say, "Hey, this is my lesson, example one, example two." And then I would assign questions from the book. And that made sense because I didn't have a lot of resources. I didn't know a lot engagement at that time. And so when you look at those textbook questions to use those examples, there's not a lot of engagement happening there, right Kyle?

Kyle Pearce: Mm-hmm (affirmative).

Jon Orr: When you see those problems, they're all given up front. It's kind of like these text driven questions and it's not like kids are dying to solve these problems and you are like, okay guys, I'm going to show you how to do this problem. And there's no kid going, Mr. Orr, I really wanted to solve that to begin with. Right?"

Kyle Pearce: Yeah. Kids are saying like, "You know what? You've really taken that pebble out of my shoe. I was really curious about quadratic or Pythagoran theorem or whatever it was." But the reality is just like you said, is like we're pretty limited, especially when you're fresh out of the gate or if you're teaching a new course. It doesn't matter how long you've been teaching. If you're teaching a new grade or a new course, if you're a high school teacher, you come into it and you sort of feel like you're disarmed. You're a first year teacher all over again, like you're trying to understand the curriculum, the standards and there's so much going on there. But something that I think is really important for us to understand here, when we talk about transforming our textbook problems, we're going to talk a little more about this in this episode, and we did so in this last webinar, is that not every problem is maybe ideal to be set up for a transformation.
So we're going to talk about like how you might eye that up. But then also we have to be thinking about when we're transforming these problems, we also have to think about the lesson structure we're using. So if you haven't listened to the episode where we talked about the real flipped classroom, like actually teaching through a problem based lesson, this is the type of transformation we're talking about. I don't know how you're going to create a curious, interesting, or a math moment with our class. If your intention is to pre-teach everything and sort of tell kids how to do the problem, because that sort of eliminates all that curiosity as well.
So you could work as hard as you want to try to make a problem out of your curriculum or out of your textbook. You can try to make that problem better. But if you are going to do all the thinking or you're going to do all the telling and students are going to just sit there and receive, then you're not going to be successful in that journey. So once again, pause this, if you you're like, "I'm not sure what you're talking about, Kyle. What's this real flip classroom?" Head on back a few episodes, a few weeks back, we shared the real flip classroom. We talk about a lot of, sort of our approach to teaching and this session or this podcast is really going to be about how we can start that transformation, and then also where to begin. And Jon, we talk about it a lot, but I think it's worth us diving a little bit deeper into this idea of curiosity. Our three part framework has three things. And the first thing we talk about is sparking curiosity.
Let's dive into that a little bit because curiosity's one thing. We've all been curious before, but let's talk about some of the elements that sort of why is curiosity helpful? I think we all would agree. It's like, when you are curious, you're like, "Yeah, that was great." I was curious, your attention was piqued, but what about curiosity is important and how does it help us lure students in?

Jon Orr: Yeah. And why we start with curiosity, because I think some people are like, "We got to get them engaged." And then some are like, "That's true." We want our students engaged, but the way we go about it is to capitalize on their natural curiosity. And that's why it's part one of our three part framework. And if you haven't listened to some, say the first few episodes of this podcast, way back in episodes one, two, three, four, we walk through the three part framework and specifically on sparking curiosity, but sparking curiosity, we want to build on that natural curiosity because if you can get kids to kind of go oh, or lean in and go, hmm, that's what we want.
Because if you can create that moment, then you've got the student who normally doesn't participate kind of going, I'm in, or the student who's like, oh, I already know this, wait a minute, that's something different here. We need those moments. That's what can kick off these lessons. And so this session we want to kind of bring in like, how do I pick a problem and then make that moment happen? And building on that curiosity is so important because your natural curiosity changes or lures your brain. And it's like, there's like an unconscious moment, Kyle that says like, I'm going to look at this and that your brain can't help it if it's super curious. In the past, I always used your favorite shows that have cliffhanger endings to episodes. They're creating that information gap and your brain can't help it, but go, I want to know more.
And there's that unconscious concentrating on that thing, getting you ready to go, hey, I want to know more. It's because if you have an informational gap and you need to fill it. And so when we teach with our textbook problems, there is no informational gap. Everything is there, everything is up front. You didn't even create this moment for you to go, I want to know more. That's what we want to focus here on in this particular podcast episode is how can I make that moment?

Kyle Pearce: Yeah, absolutely. And something that I think's really important to note, so again, this phenomenon, this information gap you sort of had mentioned, this creates curiosity and you and I talk about the importance of curiosity. I think everyone accepts the fact that yeah, curiosity, it would be great to get kids curious in my math class, but something that I think's really great, not only does it draw you in almost unconsciously, but also it helps you to notice things that you may not have noticed before. So if you were to think, like an example that I brought up in last week's webinar, I brought up this example of a video. I wish I knew what the name of this video was, but I feel like it's been used a lot, the gorilla video. When I say the gorilla video, I feel like a lot of teachers have seen it because it's from brain science and it really just highlights how our brains are actually so powerful that they can actually block out information that is unneeded, unwanted. And a lot of times it comes back to sort of a survival instinct that we have in our bodies. It's innate to us to save energy. We have to save energy.
And the more we think, the more energy we use or we consume. So it's like your brain is sort of making decisions all the time on what's important. Think of your drive to work. Imagine you remembered every single thing that happened on your drive to work. Now for some people, they might be maybe just around the corner. For me, it's more like a 35 minute drive. That would be exhausting if everything I saw on the way to work, my brain held onto. It's like, what do I do with all this information? I saw 500 cars. I saw these people walking. I saw all of these things, but your brain is sort of making decisions on what's important and what's not. And curiosity is this way that we can sort of get students' brains to start noticing things and almost like, dare I use the word manipulate.
It's like we're manipulating their brains to want to notice more about our math lessons. And if we go back to this gorilla video for those who are like, I've never seen this gorilla video, but there's a video of basketball players or some people in a video, they're passing a bunch of basketballs around and we're going to put the link in the show notes. I found that while you were chatting.

Jon Orr: I love it, I love it, good.

Kyle Pearce: The gorilla video, so if you check this out, definitely worth watching like this gorilla or sorry, these people are passing a basketball. And before you watch the video, they say, I want you to try to count as many passes as you can. And it's sort of hard to keep track. So your brain is like working overdrive. It's like focusing on the basketball. It's like every time it passes from one person to another person, you're counting, counting, counting, and unbeknownst to most people watching this video, a gorilla walks by and you have no idea.
It even stops and kind of looks into the camera and they go rewind the video and they play it back. So you could ask how many gorillas were in the video and people would be like, what are you talking about? You replay this video and you see it clear as day, a gorilla walks by. It's not like this wasn't-

Jon Orr: This is a different video.

Kyle Pearce: Yeah, exactly. You're like, you are pulling the wool over my eyes. It's got to be completely different. And until you actually scrub the video back, like the same video, like you use the rewind button so that they can see, it's like no, I'm not switching tabs or anything. You realize like, holy smokes, my brain completely ignored this. So why we say this is because curiosity actually sort of gets you to focus on things.
And then it also primes you for new learning. So not only do you start to notice things like patterns and it gets you thinking and drawn into this idea, but then it also gets your brain ready to actually hang on to more information. And these are all things that as math teachers, I think we can all relate to. When you teach an idea and then all of a sudden you're like, it seems like students had never even experienced it when you asked them about it a week later, two weeks later or a month later. So bringing curiosity in is so important. Not only because they are engaged, but it actually helps you with the learning process.

Jon Orr: Yeah. And so if we start with curiosity, that's going to prime that learning. And remember in this session, we want to talk about transforming in particular lessons or picking a problem from your resources and then changing that so that it can generate that curiosity if we can create that informational gap.
So when we think about picking lessons from our resources, I think you have to agree, Kyle, that some questions or some textbook resources are better than others. So for example, you're thinking about, you know what, I can't just go into my textbook and go okay, I'm doing chapter 3.2 today. I'm going to just point and I'm going to grab that question from the textbook and it's going to work. I'm going to be able to change it so that it can be engaging because I think some are good and some aren't, and Kyle, when you think about which ones are good for transforming and which ones aren't, what would you say like the golden ticket here?

Kyle Pearce: Yeah. I love it. And this is so important because I think in the past, and even if you listen to that episode way back in the 60s, like 61 or 62, whatever that was, we didn't really address this. We never really mentioned the fact that we're not making a claim that every single math problem you've ever seen is an easy one to transform. Of course, you can transform all of them, but some of them require a lot of heavy lifting, a lot of transforming, meaning you're almost maybe starting from scratch in a way. And then others are a little easier. So what we're trying to say is that you want to identify which ones are going to be more helpful for this transformation. And then also, I think we need to also be clear that we're not talking about transforming every problem students ever engage with in math class, because what we're talking about is how do we transform a problem that would be helpful for our lesson? For our problem-based lesson, that's going to deliver a new idea that it's going to spark curiosity, but then also fuel sense making to uncover some new learning or some new experience.
We're talking about that. We want to create an awesome context, an awesome problem that's going to be great to run a problem-based math lesson. There are other problems that we don't want to transform, that don't need transforming, like something, if you're just giving students an extra bit of practice so that they can develop a skill or so that they can better understand or deepen their understanding of a concept that you've already engaged a problem based lesson you're in, those problems are fine. We don't need every single problem student's encounter to pique their curiosity. We want to get them to a point where it's like, now that you're curious about this idea, here's some other problems where we want you to now kind of flex your muscle a little bit and show us that yeah, you've got a grasp on this thing, so you're getting better at this skill.
So those are two things. And then I guess one of the big pieces is like, we want you kind of looking at your resource and we want you kind of scanning, so if you're doing a section on proportional reasoning, rather than trying to transform maybe the first question in a textbook, which might just be 3/4 equals X/12, which is just a naked problem, that's not really that helpful for you, because there's no context there. What we want you to do is kind of go to the problems that might be wordy, like word problems tend to be really helpful because a word problem often has a context built around it. And I feel like that's a great place to kind of start. If you go with these knowledge base or these skill base problems, they're not necessarily ready to be transformed.
You're almost starting from ground zero other than the quantities, whereas you go to these word problems and somebody thought out a context, they sort of mapped it out a little bit. And something that came up in our discussion in last week's webinar, which I'll let you speak to a little bit here, Jon is like, most of, we sort of reflected on, most of the tasks and the lessons that you and I have created and I'm going to argue probably some of these others, like Dan Meyer or Robert Kaplinsky or Graham Fletcher, we didn't just pull them out of thin air. They were usually sort of inspired by some of the things that we've encountered through some of these resources that people are telling us to ditch.

Jon Orr: Yeah, I think we are safe to assume that almost everyone that we have create on our sites came from our experience with teaching math and seeing so many different resources. So Kyle, I guess in a nutshell, we've pretty much transformed almost all of our resources from textbook problems. And I really like that you've said if you think about some of those problems from your textbook that are contextual, those are a great starting point. We're going to give you four kind of things to look for in a moment here on once you've picked a problem, how to actually transform that problem. But another way to think about which problem to choose, you can choose problems or questions from your textbook or from your resources that are not contextual. They could be completely abstract in the thinking behind choosing a question like that or to start with for your lesson is to think about your learning goal. So it comes down to starting with your learning goal and going like, what do I want my students to know and how can I get them to kind of get there?
And that's that lesson that we talked about a couple episodes ago about flipping your classroom is putting your students in situations for them to experience or try different strategies to solve a problem before you teach it. So that's why it's so important to kind of link transforming your resource with how you're going to actually teach that lesson. So where we're talking in today about specifically how to pick a question, then modify it quickly. You still need to kind of like piece together the lesson transformation of not teaching it all up front. And so for example, you could just pick a problem that is abstract, but if you understand the learning goal, because you have to ask yourself that question, what is it about this lesson that's important for my students to know and be able to do in the big grand scheme of things of this unit?
For example, I transformed a very, very abstract lesson a few years ago. Really, it was a textbook problem, which was the learning goal was finding the distance between two points in a plane. So if you think about originally, Kyle I'm sharing my screen here. You see it?

Kyle Pearce: Ooh, I do.

Jon Orr: Okay. So that particular problem from the distance between two points on a plane or in two dimensional space or on a corner grid, in my class, normally the way I would have taught it, if I was teaching it from the textbook, the first few years of teaching, the first 10 years of my teaching, I would have said, "You know what? We're going to learn this particular skill today. Let me show you the formula. Hey, look at this ugly formula, this distance between two points formula. Hey, we're going to look at the X part of this point, the Y part of this point. Hey, there's a second point over here. Let's label them. Let's plug it into the formula. Hey, look at that. Boom. We've got the distance between two points. Isn't that nice how I transformed it?"
It was thinking about the purpose, right? What's the big idea here? So look the distance and why is the formula helpful and where does the formula actually come from? These are all questions you want to ask yourself, because if you can ask yourself those questions and answer them, you can get your students to experience this, and then it becomes a transformational problem. And so all I did was, you know what, I put two points up on the screen and I just brought up a Desmos screen and put two coordinates there. I did not label the coordinates at all. And I took away the grid. So there's no grid, it's just a white space. And I've got two points in two dimensional space.
And I said, "Hey guys, I got to do something. Can you guys find the distance between these two points? Find the length of that line segment." And students are like the heck are you talking about? Exactly, how am I going to do that? And so then they're like, well, we need some more information. And you've got some of that already anticipation happening with their brains. And so, okay oh wait, I forgot something, guys. I forgot to put up the grid. And so then it's like, now I've got these two points on the two dimensional space and there's a grid behind it, but no numbers on the grid. And so is this enough? And so kids are starting to see that the two points line up and they can see the spaces on the grid between the two points. And some students are already starting using Pythagoran theorem to find the distance between because they can see a right triangle or even one I'm sure in your class, I'm anticipating that some would even try to approximate.
If I took a box and I can see the pieces this way and I kind of measured it that way. And so some of the students are doing that and they'll say it's about this, so it's about this. And some students have used Pythagorean theorem to calculate it. And I'm like, awesome. However, is that good enough? We didn't see any numbers there. So how do we know what the scale is? So some students will say, oh right, or they might even ask for that. I don't think I have an answer that could be right. Maybe it's right. But maybe it's not. I assumed every grid was one unit long. So you have it in terms of units. But then soon as I put a scale on it, it might change some of the answers. Oh man, all the grids were two units long.
And so now we say, hey, do we have a better approximation of the distance? And so we've adjusted our answers and then is that enough from there? Or we've got kids now really leaning towards Pythagorean theorem. And then what we do is start to go, okay, well we see a strategy. Kids are using the Pythagorean theorem to solve, then what I start to do is go, hey, you know what?

Kyle Pearce: Teacher clue is coming right here, right? You're like-

Jon Orr: Yeah, do we really need the grid? So it's like, here's two other points on the screen, no grid, but now you can see them in two space with the scale still there. So students are like, oh, darn it. Now I have to make a grid or can I do this a different way? And so students are starting slowly with these thin slicing of problems, building up the idea of using Pythagorean theorem to find the distance between two points on a grid or in space and they don't need the grid.
So that's one of the big ideas of that unit or that lesson is hey, can I do this? And really it was, I took this very procedural problem to begin with. Hey, here's two abstract points, find the distance. And I said, "You know what? What's the big idea. We need to be able to use Pythagorean theorem, that's the formula really, to find the distance between these two points in two space." And we just stripped it down, which is one of the first things, Kyle, on the curiosity path on how to transform lessons. Kyle, let's talk about the curiosity path.

Kyle Pearce: Absolutely. And before we do, I want to make it super clear, just kind of reiterate because again, we are huge advocates of context when available and when appropriate. However, I want to make it clear, especially for our high school friends, especially those who are getting into more abstract concepts. I would argue the distance formula between two points is sort of like you have it for those watching on YouTube, you had the formula up on the screen. It's very intimidating for students. I remember teaching that concept to students and sort of just being like blah, there it is. And I'm like, my students have enough experience with substitution and with solving equations and all these things. So they're going to be fine. But the part that was completely missing again is first of all, they're like, why do I care about the distance between two points? And I'm not getting where that formula came from. And through that very, I guess, methodical process through what we call the curiosity path, you were able to, without a context even, of course you could have said, it's like here's Toronto and here's Windsor or wherever you are in the world, you could do that.
You can add that. But Jon just gave you a perfect example of how you created that information gap. That information gap was the key working for you in a sort of abstract sort of world and you sort of nudged them along. So here's an image that as soon as you said Pythagorean theorem, I just wanted to share this. I'm sure you folks have seen this before, but when you set students up to sort of want to find out this new information, so for example, another way we could have, let's say you back up to Pythagorean theorem. Another way we could have gone about this was sort of like just showing them before showing this image, if you had to get over to that building over there, how would you get there? Would you follow the path or would you follow this newly created path, which you see everywhere in the world about this.
It's like it's intuitive to us as humans in order to take this shorter distance. So there's so many different ways that we can inspire curiosity. But what Jon just showed was sort of an abstract way of approaching the curiosity path. So this knowledge or information gap that you created really involved the first step of the curiosity path, which is withholding information. If you had to quickly articulate Jon, what were some of the key pieces that you withheld in that particular test? You thought about, I got to figure out the distance between these two points, but what were you actually holding back and how did your thought process work when you were trying to follow the curiosity path instead of just saying here's a formula, let's just practice.

Jon Orr: So if you think about the original problem in that particular textbook in that course, and it was one of the practice problems, you think about it is a practice problem that we're doing. But most of that whole lesson would have been just practice problems like that. I would have taken the two coordinates of those points and normally you would just use the coordinates. But instead, what I did is I withheld some information. I didn't put any numbers right on the screen to start with. I put the points on the white space of the graph without any grid. And so we've withheld all the numbers, which is you can do wonders with numberless word problems or numberless, sometimes with Kyle, we call them naked problems.

Kyle Pearce: Or contextless, is that what you're saying?

Jon Orr: Kind of, yeah, contextless, but also sometimes numberless, right? So it's like, you can have context, but then no numbers or numbers and no context. And so there's going to be a lot of discussion and thinking and problem solving happening without any numbers.
And so when I put that up, we had to think about how would we calculate this without any numbers on that grid. And so then when I give them the grid, there's still no numbers. But then students were in that lesson starting to build the idea of using the Pythagorean theorem to find the distance between, even though there was no numbers on there, they could count and make up numbers to say, hey, I think this grid space is one or two or three and I can calculate what this is going to be. And you said, some kids might count. So the key idea there was withholding information and basically pulling everything away. And since there was nothing really there to begin with other than numbers, I pulled all that away and then gave them a visual. Sometimes visuals do help in a lot of cases, especially if you're pulling all the numbers away and there's no context. So that is what I did to withhold information in that problem.

Kyle Pearce: I love it. I love it. And the part that I thought was super cool too, is like and those again watching on YouTube saw the screen share and you inch from these two points that were in. The first quadrant, everything's positive. Everything's kind of easy and obvious. You're like, I can count the distance on the X and I can count the distance on the Y and then apply the Pythagorean theorem, and then slowly you worked your way towards, and then you sort of created another information gap by sliding one of the points into the fourth quadrant. And then it's like, now what? So it's like, you can't just subtract or, I mean, I guess you could subtract the X values and the Y values.
That's exactly what you're doing, but ultimately I'm going to argue that for some students who struggle with integer operations, they can still look at that grid and go, well, I can see how far it is. So they just count the squares. It doesn't matter that some are in the negatives and some are in the positives and then you can kind of go like, so now, and I liked how you said this like how could we do this without the grid? So now it's like, kids are deriving and they're generalizing this formula. And I would argue that this process, as you slowly sort of brought them along this journey, there was anticipation building, not anticipation like everybody's there so excited in your lesson that they can't hold it back anymore. We're not talking about that, but there's again, it's that information gap that sort of got you to go like I wonder is my method the easiest way or maybe some people are super confident that their method is the easiest way or is there another way? Or like, what's going to happen next? Is there a formula for this or every time do we have to actually plot these points and count them up?
And all of a sudden we're noticing and wondering. So again, go back to this curiosity idea, when you get kids curious, when you do these first two steps and there's going to be varying degrees, I would say withholding information is always super important and the anticipation's going to be a little different depending on the actual problem itself. However, those things work together in order to prime your brain, to notice more things and wonder more things. Now, some of you might be saying I try to notice and wonder, and maybe the kids didn't share as much as you wanted.
We build that in the classroom culture, but also note that just because some students aren't sharing, they are noticing more and they are likely wondering more, whether they've maybe explicitly realized this or not. Their brain is noticing more about that situation than had you just shared. Here's the lesson, here's what we're doing. They're noticing more things, whether they're verbalizing it or not. Jon, where do we go? What's this last step of our curiosity path?

Jon Orr: Just to recap and since we're completely auditory here with the podcast is we're talking about the curiosity path and how we can use that to transform lessons. And Kyle was walking through how I did that with this distance between two points lesson, and one being withholding information is key. That's the first thing you need to think about when designing word problems or any problems which builds anticipation and how can you make that anticipation happen?
And usually the withholding information leads to that. And then that will also prime kids to notice and wonder. And so sometimes you can make that explicit, like hey, what do you notice? What do you wonder about this? Kyle was talking about that, but then sometimes it's not that noticeable, like mine, I didn't say in my lesson, what did you notice? Or what did you wonder? But kids were noticing wonders because I withheld all that information. And then that leads to the step that we say, kind of like solidifies a lot of things and starting to kind of narrow down the focus and we start to estimate or predict. And so that's usually where we call the curiosity path, those four things, withholding information, anticipation, noticing and wondering, and then estimation. In my lesson, the estimation was, it's not really like we estimated a number, but we were estimating or predicting strategies can also be your kind of estimation or your prediction stage.
It's kind of like, I think this is what we're working on here. I think this is what my strategy might look like or finding the distance between this. I use the Pythagorean theorem. How does that look? We end up getting to a place where we had a particular answer, instead of saying, just like, I think it might be this. So we didn't actually have our students estimate, but there's lots of problems where you could have kids estimate before that you give them the numbers to do any calculations because that part, if you withhold the numbers enough so that they do the estimation and the prediction, that's the key idea for really problem solving and strategies to come out before those numbers come out. And if you listen to what your students are doing at that stage, you learn so much about their thinking on where they are on that particular learning goal before you even get to a lesson.

Kyle Pearce: And Jon, going back to that, I think you just nailed it. I want to be super, super clear on this because I think as well, just like we said about anticipation for estimation or that predicting piece, sometimes it's explicit. You're explicitly saying, "I want you to estimate this, or I want you to predict that.", but oftentimes it's implicit. You did have them like even early on, maybe you didn't even realize it, but when you shared those first two points, first of all, they were like, I can't even make an estimate or a prediction because there's no grid. As soon as there was a grid there, you could have some students kind of like eyeballing, and even though you didn't necessarily use the words, you were asking them to kind of, and again, it's that knowledge gap. It's that information gap, that withholding of information that's going to allow them, whether you ask for them to share it out loud or not, they're using that process.
They're activating that skill, that thinking of estimating or predicting. So that is our curiosity path. We've shared it in many of our episodes before. So for some people like oh, it's the curiosity path again. Here's the thing. We've been working with so many educators for such a long time. And we've realized most recently that we have some math moment makers in the academy that can recite the curiosity path. They know the four pieces, but they're still going like, how do I put this into action? And that's what we're really focusing on here in this episode, as well as in our four part series. So from today's podcast, let's quickly talk about a few of the big takeaways. First of all, deciding which problem you want to transform. Do I just go and kind of randomly grab one? You can do that, but that might cause you more struggle in order to make that transformation.
So kind of zoom out a little bit and kind of look at them and kind of scan them and kind of go like which one might be a good place to start? And maybe first one you pick isn't the one. Spend a little bit of time. If you're finding like I'm not really feeling it, maybe try another one that feels a little bit better. In sections like Jon mentioned where it gets pretty abstract, like distance between two points, do I need context? Do I need to go to one of the word problems? Maybe I could. That might cause more work. I might have to go find a picture of a map and I might have to put the point. If you want to do that, rock and roll, or is there a way that I can create that information gap with maybe less work?
The two points example, I think is a great one for people to kind of reflect on and go like, oh, maybe that might be a good place to go for those cases where you spend 10 minutes looking and you go, I don't know. I'm not really seeing it here with these contexts. I wonder if I could just take something that maybe doesn't have a context and strip things away. What else did we talk about here, Jon?

Jon Orr: Yeah. So another big takeaway I think you should walk away with is thinking about the intentionality of the learning goal. I think that will help you a lot with that selection process of the problem that you're going to pick. It's like what learning goal do I want to bring out in my students? How can I get them to experience that? And again, we'll just remind you to go back and look or listen to the episode on the real flipped classroom, because that kind of puts the pieces together of how that lesson can look that you is what you're going to transform once you've picked that problem.
And then finally we talked about the curiosity path here, these four things you could do, a lot of it involves covering things up or subtracting or repositioning a problem so that it gives less right away. And that can help you with building that curiosity. How can we create that informational gap? Take some stuff away, see what you can take away, take it all away and then see what you can bring in slowly with your students.
So Kyle, hey, we had a great time chatting with you here in this particular episode. Where can these folks, where can you go to learn more about our next session or hey, maybe you're listening to this later and all the sessions are done, but you can still catch all the sessions. Kyle, tell them where to go.

Kyle Pearce: Awesome stuff. Yeah, so if you head to makemathmoments.com/transform, that link is going to help you. If you're like in the moment, and you want to get in on these live sessions, like we said, last week we had over 250 educators from around the world joining us, even some friends from the other side of the world joining us very early in the morning where they were. And if you're joining us a little later here, like maybe you're new to the podcast and it's five months down the road, you can still go to makemathmoments.com/transform. When you put your information into the box, you will get a four part kind of like an email series is kind of how that will work, where you'll get a video every few days where you can actually take part in this particular process with us. Because for those who have already registered and are joining us live, we've actually asked them to take the pledge, to do this transformation with us.
And we have some friends all over the internet sharing. And like here, we have Kelly who shared on Twitter that she's taking the pledge to transform, but not ditch her math resources. And you can too. So she's got this, there's a nice little badge there. And really what we want you to do is we want you to make a commitment to yourself that you're going to try this process because it is one thing. Jon and I have been to many conferences. We've seen tons of sessions and we've learned a lot along the way, but the sessions that have the greatest impact are the ones that ask you to take action. Let's not wait on this idea. Let's think about what's a lesson that's coming up for you. And how might we be able to create that information gap? How might we be able to use the curiosity path in order to deliver a lesson that's going to create a math moment by sparking curiosity and fueling our sense making?
Now, Jon, we want people to take that pledge. We want them to head to makemathmoments.com/transform. What is happening in this coming Wednesday? This episode is going live right now, if you're listening live and two days from now, we are doing this second session. What's going on in the second session because curiosity is amazing and all, but why do we care about curiosity and why do we want students leaning in? What's the ultimate purpose here?

Jon Orr: Yeah. So second session, actually, we're going to dig deeper into practical examples. We're going to look at how to actually apply that curiosity path. We'll reiterate with more examples on which problems to choose that we talked about here in this episode, how to choose those problems. What's our thought process on choosing this problem versus that? How do I piece together that kind of idea between the lesson that unfolds and the problem that we're transforming? We're going to tie a lot of that together. We're going to give some folks an opportunity to transform one live with us. Then we're going to talk about what's happening there. That's session two we're setting, which is called setting up for success and the curiosity path. So we're going to do more on that because we do need more practice there. We can't just do this one off go, "Hey, I got these four things." No, we want to see some practical lessons that did this. We're going to do that together on session two. Session three is the idea that if we're going to do this long term, if we want to make this a regular part of our routine, that we're going to not only just take the pledge to do it once, but take the pledge to do it as many times as I can in my lessons as long as I have appropriate amount of time.
We want to focus on the fueling sense making part of the lesson. And so that's the part we're going to talk about in lesson three or session three. How can I mold the idea of the lesson progression with the problem I chose and then session four, Kyle is kind of wrapping it all up and putting things together that we talked about, but also think about how does a lesson end, because I think the endings of lessons are so important and a lot of us don't consider that and then kind of extending lessons like what's the next stage. And sometimes we call that pivoting or proceeding. So we'll be talking about that in session four. That's four sessions for you folks to join us, to transform your lessons this year. And you can again, you could head to makemathmoments.com/transform that will register there and you'll get all the information you need to take part in this transformation.
All right, Kyle, that's it for us I think in this particular episode. Tell them about where they can subscribe if they have not yet subscribed to this.

Kyle Pearce: Absolutely. If you are watching on YouTube with us, definitely hit that subscribe button and the like button. Leave us a comment, really helps us reach a new audience. And then also every week, we've got a short video, kind of like a teacher tip video that we release on YouTube as well. So we're really trying to promote that. We've had a huge, huge surge of subscribers on YouTube, which is fantastic. If you're listening audio, like Jon and I are, we listen to a lot of podcasts. We totally get it. If you haven't yet, hit that subscribe button and make sure you leave us a rating and review if possible.

Jon Orr: And also if you're looking for some more support, always reach out to us on social media. We're at makemathmoments on Twitter, Instagram. You can head on over to our free private Facebook group, where we are sharing ideas. People are asking questions, a lot of support happening over there. Also show notes and links resources from this episode, plus the full transcript is available over at makemathmoments.com/episode163. Again, that's make mathmoments.com/episode163.

Kyle Pearce: Well, my math moment maker friends, until next time. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us and a high five for you.