Episode #27: Building Number Sense With Estimation 180 – An interview with Andrew Stadel
- How to build number sense into your daily routines;
- What the difference is between a guess and an estimate;
- Where can you get resources for estimation prompts:
- How to maximize your time to build number sense;
- How to focus on what students KNOW.
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Andrew Stadel: So I would first encourage anybody, novice, expert to estimating really fine tune your definition of guess and estimate. Because we’ve all been there where kids are just like, 3,000. They just blurt out numbers and that’s literally what it is. It’s a guess and if you accept that, accept their guesses, then they’re going to continue to give them to you and it’s their easy way out of not thinking. If you find a strategic and welcoming way and inviting way to get them thinking by saying, “Hey, you know an estimate is more like a strategic choice of a number.”
Kyle Pearce: [crosstalk 00:00:35] You’re hearing great words and great wisdom from estimatation180.com creator, math change agent in training and all around great guy, Andrew Stadel. In this episode we’ll dive into a great conversation about Andrew’s math teaching journey. Where he came up with the idea to create the math class favorite resource, estimation180.com, and how we can maximize the use of his resource to build number sense in our students and promote mathematical discourse in our classrooms, each and every day. Hit it. Welcome to the Making Math Moments that Matter podcast. I’m Kyle Pearce.
Jon Orr: And I’m Jon Orr. We are two math teachers who together-
Kyle Pearce: With you, the community of educators worldwide who want to build and deliver math lessons that spark engagement-
Jon Orr: Fuel learning-
Kyle Pearce: And ignite teacher action. Jon, are you ready for an awesome episode with Andrew?
Jon Orr: Of course Kyle. Of course. What you’ll notice in this episode is how passionate and thoughtful Andrew is when speaking about building number sense with his students, and also teacher pedagogy with the teachers he works with. We know that you’ll have lots of good takeaways from this episode. For example, listen carefully to how he explains the difference between a guess and an estimate.
Kyle Pearce: Before we get to the interview, it has come to our attention that some of our listeners are unaware of some of the many math resources we have available on the web. If you teach Kindergarten through grade six, or you have young children at home and haven’t been to Jon’s site, Math Before Bed at mathbeforebed.com, you are missing out. Be sure to check out the over 200 visual math prompts to engage in amazing math discussions with your children before bed or at the start of your class. Who said bedtime was resolved for reading only? Check out mathbeforebed.com. Without further ado, here’s our chat with Andrew.
Kyle Pearce: Hey there Andrew, welcome to the Making Math Moments that Matter podcast. We are so excited to have you on the show today. How are things over on the West Coast?
Andrew Stadel: Awe man, things are beautiful here. It’s Springtime. I’m exited to be here with you guys hanging out, talking math.
Kyle Pearce: What is the weather right now over there? I know it’s Springtime for us, but Springtime for you has got to be something different.
Andrew Stadel: Yeah, so the sun’s up a little bit earlier now these days, around 6:00 in the morning. The weather is probably here in California, where I am, throughout the day, it’s probably between 70 and 80. We’re starting to approach mid ’80s here in the next couple of weeks.
Jon Orr: Nice.
Kyle Pearce: How far from San Diego are you? We were just in San Diego recently for NCTM. How far is that from you?
Andrew Stadel: That’s about a 50 mile drive, which is about an hour with no traffic. A good way to describe my location is pretty much the mid point of San Diego and Los Angeles.
Kyle Pearce: Andrew, we know who you are, we’ve chatted, we’ve talked to each other at conferences before, but maybe our listeners don’t know exactly who you are. Maybe they’ve used some of your resources before, but maybe they’re not knowing your name. Could you just fill us all in a little bit about yourself and your teaching journey. How you got in to teaching and where you are now, what is your role?
Andrew Stadel: I would say, I’m going to steal this phrase from Steve Linewan. I’m a change agent in training more or less. My day job is an instructional coach in my district, Tustin Unified. And I’ve had the pleasure for the past five years working with secondary math teachers as an instructional coach just trying to do our best, thinking about pedagogy, instructional moves, stuff like that. And prior to that, I was a middle school teacher for over 10 years, something like that.
Andrew Stadel: I really fell into teaching. I’ve noticed that some that you’ve had on before, in terms of your interviews, I’m one of those people that literally feel into teaching and started off with I needed something to pay the bills, because music wasn’t working for me. So, played a lot-
Kyle Pearce: Whoa, whoa, whoa. Hang on. Music. Tell us more about that.
Jon Orr: Kyle’s a musician too, maybe you guys can jam.
Andrew Stadel: What do you play, Kyle?
Kyle Pearce: I used to play, I always say used to. I haven’t picked up the bass in a while, but I used to play the bass and sing lead vocals for a band for a while in university to pay the bills.
Andrew Stadel: Nice. How many piece band were you?
Kyle Pearce: We were a three piece when we did covers like casinos and things like that, but when we did original stuff, we used to bring a fourth member, another guitar player. So, it was kind of a dynamic trio slash quadro.
Andrew Stadel: Right on. Yeah, the couple main bands on, we were three pieces as well. Our bass player sang as well. I played guitar and yeah, I played in a couple bands in and out of college and once I got my degree, which was not in math, I started substitute teaching just to have some money, but then also have some flexibility with this, hey, we’re playing music, we’re jamming, we got rehearsal space, we got shows, stuff like that.
Jon Orr: Wait, did they base School of Rock off of you?
Andrew Stadel: Kyle, Kyle. Off of Kyle [crosstalk 00:05:52]. So then once the music thing just started dying down, it was just this weird perfect timing where I was subbing at this private school and public schools, but the private school, I subbed one Friday in a middle school math class, and the principal invites me in to their office that afternoon after school, goes out and puts a stack of books on the desk and is like, “All right. So, how would you like to be our full time math teacher?” Because this was about February of the school year and their middle school math teacher mind of went m.i.a., and so they had this revolving door of substitutes and finally they’re like, look, we got to bring somebody in and they probably noticed I was green behind the ears and were like, let’s get this guy in and it just worked out well.
Andrew Stadel: And what I loved about it was I had been working with kids ever since I graduated high school. I went back to my former high school and coached. So I was always around kids, did summer camps, so that was nothing new to me and I enjoyed rolling up my sleeves as that new math teacher. Like relearning math with the kids. That was what was cool about it. I didn’t come in with this like, “Hey kids, I know everything.”
Andrew Stadel: But eventually, I got to some point after a few years of experience, I felt pretty confident about the stuff I knew and then I noticed there was some … That confidence worked against me actually. It was almost sometimes feeling like a showoff, like “Hey, check out all these cool math skills that I know. You should learn them, and I’m going to show you how to do this.” But somewhere along the lines, some other things came into my life that changed my thinking. I’m like, wait a minute, the kids, go back to the kids. It was fun rolling up our sleeves, let’s do that again.
Kyle Pearce: You know, it’s so interesting, we’ve had variations of this conversation in some previous episodes and we often sort of think that often the people who come out of school thinking, I’m good at math and I’m going to go and I’m going to teach that to kids and what we forget is how much that intuition is built just through experience right? Hey, I’ve taught this course six times now, so there’s a lot of the details there that I’m not explicit about anymore because I just sort of assume everybody knows it now. Whereas, in those first couple of years, like you were saying, you’re making sure, I’m covering everything, I’m trying to make sure it’s super crystal clear as possible and despite the fact that you may not have had, let’s say, the content knowledge that you had after the first couple of years of experience, you probably spent more time being explicit and that probably paid off much more so than us kind of zooming through things and doing like you said, that “showing off.”
Andrew Stadel: Totally. It’s a good summary, man. I feel like we probably lived parallel lives there.
Kyle Pearce: Right. For sure.
Jon Orr: I was on the other side, I was the teacher that went into math … As a student, was good at math, went in to teach math because I was good at math. Went through university, all of that, going in being like you know what? I’m going to show kids how to do math in a great way, but for years, for 10 years I taught it a very traditional way. Like Christina Tondevold calls herself the recovering traditionalist, that was exactly me. I am now switching or it has been a good number of years now that I’ve switched over to trying to almost forget the math I already knew so that I could be more beneficial to the students.
Andrew Stadel: Oh sure. Yeah. And the older you get, the harder we have to work at playing dumb. And not in a pandering way to kids, more of a, hey, I have an idea of how I might want to solve this, but it’s more important that I listen to you first and you’re thinking about this or where you’re stuck, because you and I know.
Jon Orr: I could just easily come over to your desk and bail you out of this math problem.
Andrew Stadel: For the most part of what we can teach. If you put me in a calculus, or the past couple years, the teachers I’ve supported, you put me in their calculus classes and it’s like, then I’m legitimately, I haven’t done this for a long time, so I’m relying heavily on the kids to be like, I’m not playing dumb here. I’m not gaming you. I literally don’t know what to do here. So, you need to teach me that.
Jon Orr: We’ve got to ask you this, and I think you know this is kind of coming if you’ve been listening to some of the episodes is that we want you to think back into your education and what would be your most memorable moment from math class?
Andrew Stadel: I got a lot of directions I could go. I was the kid that gamed. I used math to game the syllabus of the teachers when they passed it out. All right, so how much homework do I need to do and how many tests do I need to get A’s on, when can I get a C? I used the syllabus in my favor to do the least amount of work possible and God forbid my kids hear this episode in years. But anyway, I was able to use my math skills to a weird advantage at the time, but that’s definitely not one of my favorite math moments. Sorry.
Andrew Stadel: I had a lot of upperclassman in my math classes in high school and so I would benefit from having sometimes better math skills than them. So I had one buddy that had culinary before our math period, so our exchange for me helping him in math class, he would frequently bring me food. So that was always cool.
Andrew Stadel: As for teachers creating those magical math moments, I didn’t have a lot of those and so I was thinking about that. I had a pre calculus teacher who played football in college and what else did he do? It took seven attempts to pass the bar exam. The guy was not happy about teaching. The moments I remember where he would get through explaining something on the chalkboard, and a lot of us would raise our hand and be like, can you explain that one step again? We didn’t get that. And he’d be like well, I already explained it, you should get it. You should already know how to do it. He was sending a message to us that, yeah, well we don’t get it, kind of thing.
Andrew Stadel: But I would say my favorite math moments outside of being a student in high school, would be this recent year as an instructional coach. We did instructional rounds with our math teachers where they got to go see other math teachers teaching their own classroom. So part of my job as the coach is leading up to those instructional rounds.
Andrew Stadel: So all right, let’s say Kyle is going to teach something. I’ll work with Kyle. Kyle, what do got planned? What do you want to do when other teachers are coming in? It’s not a dog and pony show, but what’s something that we’ve been working on, you and I together, collaborating on? Okay, so let’s put that into action. So then on the day of the instructional rounds, Jon and I and a couple other teachers would come into your classroom and we’d pretty much take notes. Kyle would give us evidence, or areas of focus that we want to pay attention to for you and gather some evidence since there’s additional sets of eyes and ears in the classroom.
Andrew Stadel: But Jon and I would essentially be there to steal ideas from Kyle, the classroom teacher, and then the same thing, in the same day, we would switch. So then Jon would go to his classroom and Kyle and I we would go in your classroom and do the same thing and steal ideas. There’s a pre-brief in the morning and a de-brief at the end of the day and those were my favorite moments from this school year, because the teachers were giddy.
Andrew Stadel: It’s like wow, we’re finally getting into other teachers classrooms. We’re seeing each other teach and you know that had such high impact on them because they took those ideas and implemented them almost immediately, I’m going to take that thing I learned in Jon’s class and I’m going to use it in my class. I’m going to take that thing from Kyle’s class, and I’m going to use it. So, recently, those have been my favorite math moments. When teachers see each other teach, and side note on that is, you see teachers practice those skills with students who aren’t theirs.
Andrew Stadel: So when the teachers would be in the other teachers classrooms, helping other students, just seeing them working on questioning strategies and stuff like that, because there’s not necessarily this personal responsibility that this is my student. No, this is somebody else’s student, so there’s lower risk there, but for the most part, the point is just teachers seeing each other teach is so valuable. And it was amazing this year and the highlight of my school year this year.
Kyle Pearce: Right.
Andrew Stadel: Those have been my favorite moments.
Jon Orr: In my district, my school, we’ve been involved in lesson study for the last four years, which is our math department has been getting together quite periodically, given release times, so substitute teachers go into our classrooms while we go meet in a room and we co-plan lessons together. And the great part about that is we’re all bringing different things to that lesson and we’ve picked a focus to say, we’re going to try to get better at this. We’re going to try to address this learning need for the students that we’ve kind of identified in advance.
Jon Orr: And what I love is that my math department has variations of different teachers, and they all bring different things to that table and we co-plan a lesson that is … Since we’re co-planning it, we’re all putting something on the table for that lesson and then one of us will go and deliver it, and we all go watch. And like you said, it’s awesome not only to see other classrooms and other teachers in their classrooms, but it’s really awesome to see how the kids react to something you’ve planned. Because as a teacher, you’re watching students when you’re delivering lessons, but you don’t get to see everything. And when you’re in the back, or on the side, and you’re not on the main stage, you can watch different things. And you get a sense of how the students are reacting in different ways and it’s so valuable to see some of that.
Jon Orr: I totally agree those are the most beneficial ways that we’ve done PED in our school and in our district is adopted that in the last couple of years. So it’s kind of district wide now, but it’s been a great night. I totally agree with what you just said too. So I relate for sure.
Andrew Stadel: I’m so glad that we were able to do it too, because my first few years as an instructional coach, I found myself almost like, wait, I’m getting paid to do this? I’m in so many other teachers classrooms where I was able to steal ideas. So take an idea from one other teacher and say, hey, so and so, Jon’s using this in his classroom and you might be across the district, across the city, and I’m working with Kyle, well, hey, Jon tried this in his class, so check this out. That was cool that I was able to see it in other teacher’s classrooms, but it was like, there’s still a missing piece here. It would be awesome if they saw each other teach.
Andrew Stadel: Because I found myself making a Google form when I’m in teacher’s classrooms. If I ever return to the classroom, I’m going to take all these ideas and take pictures and make this spreadsheet of things that I want to do, because I was growing so much more as an educator because I was outside the classroom in other classrooms. How do we get other teachers to do this and there’s something to it. Once you get past, or I shouldn’t say get past, but probably the trickiest part to those is navigating the human, emotional, adult side of things in terms of our passion, vulnerability, there’s a lot to learn with that. And that’s tricky.
Kyle Pearce: We do a lot of going into classrooms in my district. We call it a consulting role, but we do a lot of in class work with teachers as well, not just workshops and it’s really finding ways to help, and I want to say it’s like convincing teachers that we are going in and we are going to make it asset based. We’re not looking for deficit, we’re not evaluative, we’re not trying to judge. We’re trying to go in and like you said, I like how you framed it, we want to go in and kind of selfishly steal from you. Is that okay with you? And people feel a little better about that, but I find it’s like initially, there’s still that hesitation, but once people do it, it’s like the Band-Aid’s ripped off and then people are like, “Oh, yeah. Let’s do this.”
Kyle Pearce: The part I love, selfishly for myself, often times I’ll be going in and I’ll be doing some co-teaching with teachers as we go. Sometimes they want to feel comfortable with somebody else there to kind of help out, but I love sitting on the side like you both were discussing, and really, just watching kids but then also, I’ll pull up a chair next to some random kids and I’ll just want to ask them some focusing questions. I’m just really curious about what they’re thinking about the work that they’re doing and it’s so interesting from those experiences, it makes me completely re-evaluate how I used to assess students in my own classroom, because when you look on the page, it’s like I approach a kid and I’m watching them work, and I’m making an assumption about what they’re thinking and then I have the conversation and this student knows so much more than what was put on that page. And often times, what I’m looking at, the assumption that I’ve made is completely off base.
Kyle Pearce: So it just really for me, again, selfishly, I’m there learning about how important listening to what students are thinking and asking them to share what they’re thinking instead of just taking that stack home and trying to mark it at night and interpret what they tried to put down on paper.
Andrew Stadel: Totally. You mentioned focus questions. That in itself is, in order to do focusing questions, you also have to listen, like you said and if you’re not listening, if you’re doing the following questions, where you’re just like, you want kids to get to one thing and you’re kind of like, “Hey, just fill in this blank for me of this word, this one word or this one concept, or this one number,” with following questions, then it’s crazy. And what I noticed was, we did some work on that with the teachers, and it was so fun to listen to them work on their questioning strategies, specifically focus questions. Of questions that they were asking kids that required them to listen and then adjust how they proceeded in that conversation, based off of what that student was saying, and that was so cool. Another cool moment to see educators do that.
Kyle Pearce: Right. Almost like automatically, we want to, essentially, we know where we want to send the kids, so I’m going to essentially tell you what to do, and I’ll put in the form of a question. Oh, are you sure you want to try it that way? Have you ever thought about using this? And then it’s like, okay, I guess I’ll use that. Those two types of questions have been on my mind. A colleague of mine and good friend, Yvette Lehman, from my district, talks about this type of questioning quite a bit. So it’s been on my mind and I think every time I’m asking kids a question, I’m thinking to myself, all right, was that a good … I’m constantly evaluating myself thinking did I just send them down this funneled path, or am I actually leaving it open enough where they can actually see their strategy through based on what they were thinking and not what I was thinking. So, super cool.
Andrew Stadel: And sometimes you got to ask a closed question to get you to a better open question, I’ve learned. In the sense that, so do you agree that five x equals 20 x is four? I don’t even know, but okay, so you’re good with x equals four. Now, what do we do with that in this next part? If it’s a linear system or something. I don’t know. But sometimes, I’ve realized that asking focusing questions, or too many open questions is frustrating for kids as well as time sucker upper, or whatever you want to call it. It sucks up time sometimes and you’re like, oh man, why didn’t I just get to the point? So there’s no one way to do it I’m learning, however, it’s almost like reading your audience. Is this kid kind of a good closed question kid? Or an open question kid? What can I give? Give and take with this kid.
Kyle Pearce: What do they need in this moment?
Andrew Stadel: Yeah. [crosstalk 00:20:58]
Kyle Pearce: Those moments and figuring out, I always say nowadays, my answer to everything is, it depends. Because I used to give hard, fast, kind of rules about things. You never do this, or your always do that, and now it’s sort of like, it just depends. I’m glad you mentioned that because we don’t want people driving certain kids nuts, because that’s not the time for that type of questioning.
Andrew Stadel: Yeah. Totally.
Jon Orr: I want to chat about a resource that you have built and if I think back to my first experience with your resource, you were being a little bit modest in your introduction to yourself about what you do, and I think there’s a lot of people out here who know about Estimation 180 and that you are the creator of it. I think back, I think one of my very first presentations at any sort of conference, or workshop was sharing your website, estimation180.com. I would love-
Andrew Stadel: Still waiting for the check on that, by the way Jon.
Jon Orr: Yeah, I will send it your way. But I’ve been loving this site, I know every time I go somewhere and talk about great resources teachers are using in their classrooms, I ask about this, and so many teachers know about this. So I think people listening would like to know a little bit of background on it. Want to fill us in on maybe if they don’t know what it is, what is it? But also where did you come up with this idea?
Andrew Stadel: Awesome. I’m super happy to share with you about it, and I really appreciate that I was part of your first presentation man, that means a lot.
Jon Orr: It means a lot that you were right here talking to us.
Andrew Stadel: If you had asked me this question a few years ago, I’d probably have a different answer, but now I think of it as a website for teachers and students to enjoy together as they build number sense and to make math connections. So, if you haven’t visited this site, there’s over 180, there’s over 200, I think actually now, visual estimation challenges that serves as a conversation piece in classrooms for teachers and students and it allows them to engage in many aspects of the mathematical process.
Andrew Stadel: I’m going to list a few, it’s not an exhaustive list of the mathematical process, but simply asking questions, thinking critically, creating a reasonable range, formulating plans, executing that plan and revising things once you get more information. So when you’re attending to precision, you’re kind of going throughout that process, it’s kind of like a loop and you can do all of those again, you can do some of those again. I feel like it’s a low risk environment because the visuals provide a conversation piece, the product isn’t so much what’s of value, it’s more the process that I learned in my experience and I feel, I’ve talked to teachers and when they email or Tweet me, or talk to me at conferences, that’s kind of how they feel. “My kids love it.” “Okay, why do your kids love it?” “Well it gets them thinking and they get really upset if they’re off by a little bit.”
Andrew Stadel: And right there, that’s where I could probably have a 30 minute conversation with that teacher. Okay, they’re passionate about something if they cared that much. Does that mean that they invested a lot of time? Yeah. So, if they’ve invested a lot of time in coming up with that estimate, I think at first glance you’re thinking, oh yeah, they value the product, their estimate. No, it’s like they value the process. The time they spent asking questions, thinking critically, formulating a plan about it.
Andrew Stadel: So it came out of an area in my teaching career, the idea of Estimation 180, where I found myself saying year after year, oh man, the kids kind of lack number sense and more specifically, they’re unable to connect numbers with things in our world. It’s just kind of crazy that I could say to a kid, “Walk five feet over there,” and they have no idea what five feet is or something like that. It’s a small example.
Andrew Stadel: So it was inspired by a few sources. One would be, like I just mentioned, I was frustrated with my students lacking number sense, what can I do to help them, help themselves kind of thing. The other was, once I found out about Dan Meyer and starting exploring a lot of his work, it was this idea of making a guess or an estimate with creating a two lower, two high, guess. That work was embedded in a lot of his 3 Acts.
Andrew Stadel: Also, included some kind of questions in his warm ups. I noticed questions like, how many black keys are on a piano? Or how many white keys are on a piano? And I tried those questions out with kids, just I typed up the text, and it was like the kids have no idea. And I was like, I have no idea either. This is kind of a fun fact thing to Google, or we would talk about it at a party, but how do you guys access this? And even if we had piano players in the room, would they even know? I don’t know. So once I started experimenting with the 3 Acts format and the videos and the visuals, they weren’t all videos, it was like, wait, there’s something here. The kids are like … It’s a conversation piece and they have access to that conversation through the visuals. So that was big part of it.
Andrew Stadel: And so the third point of inspiration was, how do I do this? Where am I experiencing these moments where kids are actually intuitively making estimates? And as a teacher who is tall, as a person who is tall, and a teacher of middle school students, where I naturally tower over a lot of them, I’d walk into classrooms of other teachers or kids on the first day, first week, would be like, “Dude. Mr. Stadel, how tall are you?” And I didn’t pick up on this for the first few years that kids were doing this, because I just quickly told them my height. And I was like, oh, okay.
Andrew Stadel: And then I stared thinking about it. Wait a minute, there’s something to that question. So when I flipped the question back on them, I said, “All right, now tall do you think I am?” And all of a sudden, it was amazing. They started thinking, well, I think you’re about this height. And then I’d be like, “Okay. Why?” And then they would do different things, which was amazing also. So kids would stand next to me. “Can I stand next to you?” “Sure. Why are you standing next to me?” Or “Can you stand over there? I’m picturing my dad standing next to you and my dad is 6’2,” or something like that.
Andrew Stadel: So the kids were intuitively putting a plan together. They asked the question, and then they started putting a plan together and then they executed that plan because I allowed them to do so. They came up with a estimate and then I learned that if I prolonged that answer to them, with my actual height, then they were more invested. Once I told them my height, 6’4, the reaction was no longer like, “Oh, okay.” It was like, “Oh man. I was so close. I was 6’3,”
Kyle Pearce: Told you.
Andrew Stadel: Yeah.
Kyle Pearce: Right.
Andrew Stadel: And some kids were super bummed because they were off by two inches and that took me a while to realize, wait a minute, why are you bummed? Yeah, you want to be accurate and you want to be close, but two inches is phenomenal. If you’re two inches away from somebody’s height, especially with women. If you overestimate their height, they’re like, “Oh yeah, I’m not arguing with you.” [crosstalk 00:28:02]
Kyle Pearce: We can go [crosstalk 00:28:04].
Andrew Stadel: So when I started picking up on that stuff and then it’s like, there’s more to this, I got to keep doing this and then something intuitively was driving … It was more of an intuition, but also how much can I milk this? Because I came into one school year going, I’m going to try and do this every day of the year, which was a lofty goal. And for me to make that happen was I had to milk situations as best as possible, and it actually paid off in the end because it was like, well, let’s do my height, now let’s do my wife’s height. Now let’s do my son’s height, now let’s do my daughter’s height. Let’s do this height of this random parking structure. I was milking it, but at the same time, I was building these connections because kids had reference points.
Andrew Stadel: I’m a late learner in the sense that how often did I not provide opportunities for my kids to make connections in math class? Not just estimation alone, but just in math class by comparing things and referencing things and so that process of Estimation 180, there’s so many transferrable skills that can be implemented into the regular math curriculum, any math course, any math grade level, I believe in and am confident that kids enjoy that process when they have access to it through visuals. That’s been my journey. There’s other things I could share with you, but I could probably talk for hours.
Kyle Pearce: Yeah, we’ll dig into them. I’m super excited, there’s so much to even unpack and what you said there [crosstalk 00:29:30]. We’re in our Google Doc here, and I’m like [inaudible 00:29:35] all over the place here, and I’m sure I’m going to miss one, but I’m going to work backwards and start with this idea, like you were saying, it’s like you were milking these scenarios and I’m in my head picturing, you’re helping kids anathematize the world around them.
Kyle Pearce: You’re looking to scenarios and you’re helping kids to see that there’s so much math thinking around us that we just ignore every single day. And you’ve found a way to bring this into their lives and to help them notice some of this stuff. And going way back to the beginning of the conversation, where kids, you were saying, they’re off by two inches and they’re getting mad about it.
Kyle Pearce: And on some level, some people are like, “Well, we don’t want kids to be mad.” But no, they’re frustrated because they want to be more precise. When has that ever happened in a math classroom? Where kids are upset. They were just trying to get the work done in the past, because that’s what you’re supposed to do. I just got to get this done. I don’t care how close I am or not. Will the teacher accept it as is? That’s sort of the goals for many kids in their math class.
Kyle Pearce: So for them to look at that and for you to obviously, luckily for all of us in the math community, luckily you clued in to this idea that wait a second, we need kids to be estimating and as you were talking, Jon’s saying, i’m typing like a madman. I pulled up the Ontario curriculum from grade one to grade eight. I wanted to get the numbers right, but if I search for the words like estimate or estimation, in the Ontario curriculum from grades one to eight, it comes 92 times. How often [crosstalk 00:31:14]. Give me a reasonable range. What’s your low, what’s your high?
Andrew Stadel: An average of 10 per grade level. 10 times you should be, I don’t know how to explain that.
Kyle Pearce: But at least 10 standards right? Average it out. Most of the, in Ontario, most of the, we call them expectations, have estimate and then investigate and then blah, blah, blah and then determine or calculate or whatever the wording is. But even the word calculate or calculation, that comes up only 86 times. So estimate actually comes up more than word and just to kind of drive home this point, I taught for almost, before I really started focusing in on getting kids estimating and through the use of the 3 Act math, through the use of Estimation 180, I was not having my kids estimate. I was the kid in school that would look at part A question was estimate, part B was calculate, I would calculate and then I’d take two off and call that my estimation. [crosstalk 00:32:20] I was that kid just looking to get it done.
Kyle Pearce: So you’ve created this tool that allows us to pay more attention, and for me, I’d look at this and I think about the spatial reasoning that we’re allowing. You said like making it visual, so each kid can access the task. Well think about the implications of where we go from spatial reasoning through counting and additive thinking and multiplicative thinking. And I look at the different visuals on your site, and I look at them and it’s like, as a teacher, you could milk these, you’re talking about milking the scenarios from your daily life, but you could literally go into Estimation 180 and milk some of these ideas to draw out some pretty complex thinking around fractions, around that multiplicative relationship. I don’t know, just through what you said there, it was like all these crazy fireworks were going off in my mind. So I’m sure I’ve got a ton in there.
Kyle Pearce: But I was excited to hear you sharing that and I hope people at home are looking and thinking about this as like wait a second, am I maximizing the use of this tool? So I’m going to put it to you and say, how do you believe teachers can best maximize the resources on Estimation 180. What might that look like? Feel free if you want to share, what if you’re just getting started, or maybe you’ve been using them for a while, how might you maybe up the ante a little bit to draw out as much number sense out of it as possible?
Andrew Stadel: Yeah. I’d love to talk about that. I would first encourage any teacher familiar with it, or new to it, to just first think through the idea of the difference between a guess and an estimate. This is pretty big, you might think they’re pretty similar. And so I have some stuff online, resources where I can lead some people if they’re interested. And I think this is a valuable part of the process, because here’s how I typically explain it.
Andrew Stadel: If the three of us sat down at a restaurant that has those red painted catsup bottles, you know there’s catsup inside, but you have no idea how much catsup is inside. And I said to one of you, I said, “Hey, Jon. How much catsup do you think is in that bottle?” Now Jon might start reaching with his hand to pick it up and I just say, “No, no, no. Just guess.” Because that’s what it is. Jon has no idea how much is in there unless Jon was watching the restaurant patrons beforehand squeeze a bunch of catsup onto their french fries or something. I don’t know. But you didn’t have that chance. So you have zero information and the bottle is painted red, so you have no idea. That’s a guess.
Andrew Stadel: And so the second Jon picks up that bottle, he now has more information and we’ve now transitioned from a guess to an estimate. Because he can use the weight of it, he can shake it, he can do something with it that’s going to provide him with more information to say something like, it’s about half full, or there’s about a quarter left or something. He’s narrowing it down to about, a range.
Andrew Stadel: So I would first encourage anybody, novice, expert to estimating, really fine tune your definition of guess and estimate, because we’ve all been there. Where kids are just like, “3,000,” they just blurt out numbers and that’s literally what it is, it’s a guess. And if you accept their guesses, then they’re going to continue to give them to you and it’s their easy way out of not thinking. If you find a strategic and welcoming way and inviting way to get them thinking by saying, “Hey, you know an estimate is actually more like a strategic choice of a number.” Graham Fletcher and I have had multiple conversations around this, and I love Graham’s definition that an estimate is a strategic choice of a number. So you’re choosing a number based off some strategy, some plan that you executed. I love that thinking. So that’s one step in maximizing the resources at Estimation 180.
Andrew Stadel: The second is, I’m going to take Graham’s definition and extend it to an estimate is a strategic choice of a number within a reasonable range. So spend some time on a range, the range is important. And the website is dated. I have plans this summer to update it and one of the big updates it’s going to get is changing the terminology between too low and too high as your range. I’m going to change that to lower limit and upper limit. Because what happens is, if how tall is Mr. Stadel? And a kid says too low is one inch; they’re correct. They’re absolutely correct. If I say, “What’s too high?” And they said, “100 feet,” they’re absolutely correct. That’s too low and that’s too high.
Andrew Stadel: I like the phrase of upper limit, lower limit probably because I’ve been hanging around a bunch of high school math teachers a lot and that idea of limits is very popular vocabulary. But more importantly, limits make us I think, get us to the point of, well, you know what? Yeah, but what’s a height that you know I can’t be below? You can’t be less than six feet. All right. So then put that as your lower limit. And hey, I’ve never seen somebody past seven feet tall, so okay then, put that as your upper limit.
Andrew Stadel: So that would be the second point to maximize Estimation 180 is to spend some time on that range. And the range is a beautiful place to be, because it allows some flexibility in your thinking. It’s more inviting for to kids to say, look, I can fall within these two numbers and it’s a good challenge. And you can get meta with that. What’s the range of the ranges in the classroom? So that’s another way to do it.
Jon Orr: I just want to jump in here. I love that idea of the range and I’ve been using Estimation 180 stuff for a while now and it happens in all the classrooms that kids say a billion. Or like one. It’s more than one. And so one way, I don’t know where I heard this, I didn’t make it up, I heard it somewhere, someone using it and then I adapted it to, what’s riskier than that? You said a billion, but can you make a riskier too high or a riskier too low, and so then they automatically, that risky word comes out and they’re like, “Oh, okay. I’ve got to get closer.” I got to risk it.
Jon Orr: And then when somebody else says, I don’t know what we’re estimating, it doesn’t matter, but then somebody will also bring it down. And then it’s like okay, anybody riskier than that? And then it’s like, who’s the riskiest in the classroom? And then we can say, I’m riskier than that, because I’m going to say this and then I just throw your hands up guy’s like who’s that too risky for? And then a whole bunch of kids will throw their hands back up and then the class riskiness factor can go back up a little bit. Okay, or as a class we’re about here, otherwise we’re too risky for most of us and then we start bringing it up from the floor. I’ve been using risky, but I like the upper limit, lower limit too.
Andrew Stadel: You can still incorporate risky. I’ve heard Dan Meyer say “Be braver.” So that’s the equivalent of your risky and it’s the same idea, just like [crosstalk 00:38:46]. Sometimes a lot of this stuff is like, wait, it’s like telephone. You heard it from somebody who heard it from somebody that heard it from somebody.
Kyle Pearce: Sometimes molding it to your own personality and those types of things, I think those are key too. Sometimes I think it’s easy for us as educators to we’ll go to a workshop or we read a book or we read a blog or whatever, and then it’s sometimes we try to force things to look and sound the same exact way that somebody else does it, I think that’s kind of some of the fun too. How do you make it a little bit your own there? And i think kids appreciate that too. That they don’t see you trying to fit a mold that isn’t actually you.
Andrew Stadel: Or even the terminology that kids might use. You just latch onto that and say, “Hey I really like the way Kyle described his range and I asked him about it and he says, ‘Well, I wanted to be a little risky today.'” It can even come from what kids say. I would say another way for teachers to maximize Estimation 180 would be there are opportunities for you to use the tasks with the content that you’re required to teach. Admittedly, there’s not process for you to just say, yeah, I’m teaching this standard and click on that standard and Estimation 180 challenges populate in your life. That’s definitely on my list of things to do at some point. But don’t let that hold you back.
Andrew Stadel: You can pick any day, and for example, I’ve got a series of cheese balls on large plates, small plates, baking trays, stuff like that and you could do it in a high school class. I’ve done it in a Kindergarten class, I’ve done it in a third grade class, I’ve done it in middle school classrooms, it doesn’t matter. The kids think about it in very similar and different ways. It’s the skills that the students bring into the task that you can now transfer to the things you need to teach.
Andrew Stadel: So in those specific examples with the cheese ball, you’re talking about area. You’re talking about how much area is being covered by a cheese ball. And then you’re talking about the defined region, so like a circle, a rectangle, you’re talking about possibly negative space and the strategies that kids come up with. If you’re listening, to maximize the resource is listen to what your students are coming up with, tap into those and those now become the skills that you can transfer to the stuff that you are doing in your class.
Andrew Stadel: I know a lot of teachers think of it as a warm up, and that’s awesome. I agree. When there’s opportunities to use it with your curriculum, fantastic. If you can get a full on blanket of using the skills and transfer those skills by comparing the previous day to today’s, that’s huge within math. So that would be one of the other ways for teachers to maximize the resources is by looking for skills to transfer.
Jon Orr: Yeah, those are really great and I had a note here to ask what happens is when we share resources at workshops or in those lesson study meetings or when you run into teachers, I’m sure this happened to you before where you share a 3 Act math kind of thing or Estimation 180, teachers will say, that’s great, but I don’t have time to spend on that. I have to teach the curriculum. I have to teach the standards. So, I think you’ve just touched on a lot of answers to that main question of help those teachers see that you’re teaching more than just the curriculum and also, if you want to address the curriculum, hey, these do that too. So, would you say anything else to those teachers that they always have that, oh, I can’t do that, because I don’t have time. My class is only 60 minutes and I got to get right to the punch here. What would you say to those kind of teachers? More than you’ve already answered that.
Andrew Stadel: Have a beer. I would love to ask why. I don’t know what I would say to them, I’d want to listen to them, probably ask them a question and just say, “So what’s holding you back?” And I probably know most of those answers. Time like you said is one of them. So then it would probably fall back on, well, what skills do you want your kids to have? And when you’re doing the math that you need to spend the time doing. And if they start listing things like, I want my kids to think critically, I want my kids to stick with a problem, I want them to make sense of it, I want them to use appropriate numbers.
Andrew Stadel: Oh, okay, everything you listed there, it doesn’t have to necessarily be everything that they listed, but I noticed you kept going back to thinking critically and executing a plan or something. So, then I would segue into, so you can do that with the estimation tasks and you’ll see your kids doing those skills that you want them, and it’s your opportunity to name it and call it out and say, “I loved when Kyle used this strategy of stacking.” And guys, he’s adding these stacks together and we call that math the additive property.
Andrew Stadel: Or Jon, over here saw one thing, but then he noticed that he could get 10 of those in that defined space that we did in this estimation task. So he multiplied and said, that’s called a multiplicative property. There are opportunities for etchers to name the skills that they see their students doing and say, “I want you guys to do in this stuff we’re supposed to teach too.” So I think I’d probably start with questions and then listen to what the skills that they want their students to have and say “Yeah, you’ll see those come out when you do these estimation tasks.”
Kyle Pearce: I would already, just like you said, learning more about what the challenges are, what are the at least perceived hurdles that teachers are having and a question I might want to ask a teacher is, so where is estimation coming out in my classroom? So if not through this resource, where am I purposely drawing on students to make meaningful estimates? If think the struggle is if I’m resorting to let’s say, my text book or my worksheets or whatever it is, it’s very difficult for students to make meaningful estimates because all the information’s on the page, right?
Kyle Pearce: You can’t ignore the measures that are on the diagram or those types of things, so that withholding of information I think is so important and I like how you mentioned, take these and try to like them to the concepts that you’re going to be working on that day. You don’t have to start with day one, just because that’s what the website is, day one. I could go to the cheesy poofs section, because that’s related to area and I’m going to be working on area. So I really like how you help sort of paint a bit of a picture of how that might actually be used most effectively in the classroom.
Kyle Pearce: The next thing we wanted to ask you and we’re looking at the time here, we don’t want to run out of time, but word on the street is that you might be planning on bringing us another math podcast to all of our wonderful, wonderful listeners of Making Math Moments that Matter podcast. Do you mind telling us a little bit about that? What are your plans? And what’s it going to look like? Sound like?
Andrew Stadel: Yeah. Thanks man. The word on the street, it’s a small street right now. For sure. The podcast [crosstalk 00:45:37]. Like shouting across the street from each other. So, here’s the deal, the podcast I’m entertaining and getting ready to launch this year at some point this year is Math Confessions. And what that means is, I want to use the podcast as an opportunity to interview math educators and I want to hear their stories about times when they regret using certain methods, practices, things they did at one point where they were like, they thought that was the best that they could do at the time. And at some point, they realized, oh, there’s a better way to do it. So they learned a lesson. They learned something about themselves. So I want to hear the story about something they regret, a confession and what they learned and what they did with what they learned.
Andrew Stadel: So for me, an example, I remember teaching integers in middle school and I came up with two acronyms and it’s not my proudest moments teaching. I came up with this whole football scheme for slope intercept with y equals mx plus b. Not my proudest moments. But there’s a story there. At the time, I thought I was doing the best I could for my kids and then I realized later on, at some point, I learned some lessons that I was doing them a disservice and I changed my ways and I’ve been growing ever since.
Andrew Stadel: So I think there’s a lot of power in us hearing from each other that this is a journey for all of us, we had to start somewhere. What are some lessons we’ve learned along the way? And I think for an audience that would say, okay, I’m not the only one with these challenges and then at the same time, offering some resolution for those. And reassurances too that it’s like, all right, cool, so I can still take something that I learned and move forward in my teaching career or as a math educator. So I’m looking forward to interviewing a lot of people, yourselves included. I would love for both of you to share your stories and what lessons you’ve learned.
Kyle Pearce: We would love to [crosstalk 00:47:28].
Andrew Stadel: That’s Math Confessions and if you head to mathconfessions.com, you can sign up and I’ll holler at you when we got some episodes in the bank and are ready to launch. Probably in the Fall sometime.
Kyle Pearce: The Fall of this year?
Andrew Stadel: 2020 is the goal, yeah. Or no, 2019. Geez. That’s this year. Fall 2019.
Kyle Pearce: Cool. That’s exciting. I’m pretty pumped to listen to that, and also to chat, for sure. That’s awesome of you to, and exciting of you and lots of work coming your way. But I think the math community needs it.
Andrew Stadel: I appreciate that. That’s cool. I’m looking forward to it.
Kyle Pearce: Well, listen Andrew, we’ve had a pleasure and a blast just chatting away with you. You just shared out mathconfessions.com, so make sure that you head to mathconfessions.com. My guess is there’s going to be some sort of opt in box there for you to hop on his list. Andrew, where can people find more from you? We heard Estimation 180, is there anything else out there that people should be aware of? Maybe where they can follow you on social media? Just to make sure they’ve got a complete view and then we’ll make sure to also include all of these links in the show notes.
Andrew Stadel: Cool, thanks. Yeah, the best place to find me is probably at estimation180.com. You can find me on Twitter, it’s Mr_Stadel and if you head over to Estimation 180, I’ve got place for you where you can subscribe to a newsletter that I’m going to rejuvenate here and start sending out some ideas and some good stuff your way in preparation for my hopes is to also have an online workshop available to teachers in Spring of 2020.
Andrew Stadel: So the intent behind that is to share a lot of the things and resources and lessons I’ve learned, not only from my own classroom, but from other teacher’s classrooms and their experiences and dive into a lot of the things that I just discussed here in terms of how to maximize the resources at Estimation 180. And then I just had a side note, a quick thought, I was thinking, oh gosh, if you guys are on the Math Confessions podcast, we could title that one, Tap Into Geek Minds or something like that. I don’t know.
Kyle Pearce: [crosstalk 00:49:37]. Rebrand, right now.
Andrew Stadel: But, yeah, that’s how people can get a hold of me. My phone number is [inaudible 00:49:48], so they can also call me there too.
Jon Orr: One, 900, what?
Kyle Pearce: Awesome stuff. Awesome stuff. Andrew, we want to thank you for spending the last hour with us. It’s been a pleasure and we’d love to connect with you in the future, so we definitely want to thank you and hope you have a great rest of your week and back in the coaching role, but we’re pretty pumped to talk with you further.
Andrew Stadel: Yeah, I want to thank you guys too before … You guys can definitely say the final cutoff, but I can’t thank you guys enough for this. This has been a lot of fun talking math and Estimation 180 and everything else. So I’ve learned a lot from you guys and I’m excited to hear more podcasts from you guys.
Kyle Pearce: Thanks so much Andrew. We will catch you soon. We are super excited to see the launch of that podcast and we’ll see more stuff coming on Estimation 180 as well. So we’ll talk to you soon and have a great, great evening.
Andrew Stadel: Thanks guys. See you.
Kyle Pearce: We want to thank Andrew again for spending some time with us to share his insights with us and you, the Math Moment Maker community.
Jon Orr: If you haven’t checked out estimation180.com yet, what are you waiting for? Kyle, what was your biggest takeaway from our chat from Andrew?
Kyle Pearce: My biggest takeaway is how we can take any math resource and in particular, his Estimation 180 resource and find ways to make it more rich by applying it to the learning goals for that particular lesson, that particular day. Let’s not think about trying to use a great resource like this, and then worrying about trying to fit it all in. How could I take that resource and how can I actually use it to help complement the lesson that I’m going to be teaching that day anyway? I think Andrew did a great job of really heeling us see how we can actually incorporate this particular resource without having that worry of jamming it all in. How about you Jon? What resonated with you?
Jon Orr: What I took away from that conversation was when he was explaining his role as a change agent, but also helping teachers change some of their classrooms, I really enjoyed his big moment that he said this year about having teachers watch other teachers and bring them together and learn from each other. I resonated with that. You could hear that in the episode, because we do that in our class, but what I really took away from that was how he was bringing teachers from across the district together to learn from each other. Like only take good things from this lesson. Don’t watch for judgment, watch for assets only and then take that away and take that back to your school. I really enjoyed that and I think I could take that away for my school and my district too. So that was my big takeaway.
Kyle Pearce: Awesome. Awesome. Yeah it can be really difficult to get that culture started, so I think that’s the thing we got to do. We just got to do it. Rip that Band-Aid off, get in there, get uncomfortable for a little while and you know what? Try to look at every single lesson and try to take at least one thing away that you can implement in your own classroom.
Kyle Pearce: So awesome stuff. So how about you at home? What’s your big takeaway from this episode? We want you to share it with a friend, a colleague or send us a message at social media at makemathmoments on Twitter, Instagram and Facebook, because remember, if you’re not sharing your reflection, you’re not going to actually bring that new learning with you.
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Kyle Pearce: Also, if you’re liking what you’re hearing, please share the podcast with a colleague and help us reach a wider audience by leaving us a quick review on iTunes and tweeting us at makemathmoments on Twitter. Show notes and links to resources from this episode can be found at makemathmoments.com/episode27. Again, that’s makemathmoments.com/episode27.
Jon Orr: You can also find Make Math Moments on all social media platforms and seek out our free private Facebook group, Math Moment Makers, K through 12. Don’t miss our next episode.
Kyle Pearce: well, until next time, I’m Kyle Pearce.
Jon Orr: And I’m Jon Orr.
Kyle Pearce: High fives for us, and high fives for you.
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