Episode #64 – Are You Missing The Mark With 3-Act Math Tasks? An Interview with Graham Fletcher

Feb 17, 2020 | Podcast | 0 comments


Today we have GFletchy himself! Yes, today on the podcast we have 3-Act Math Task Builder, National Speaker, and Math Specialist Graham Fletcher.

Stick around while we chat with our good ol Canadian friend who’s transplanted in America on what it really means to assess, how to leverage engagement in your math class, where some teachers miss the mark when teaching through tasks, why tasks are great for formative assessment rather than summative assessment, and how to view your lesson from 60000 ft instead 6 inches.

You’ll Learn

  • How coaching sports is like teaching math & how it’s not. 
  • What it really means to assess. 
  • Where student intuition lives
  • How to leverage engagement in your math class
  • Where teachers miss the mark when teaching through tasks
  • Why tasks are great for formative assessment rather than summative assessment
  • How to view your lesson from 60000 ft instead 6 inches. 


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Graham Fletcher: I’d love to create something to where, maybe, I could put a little note on you, or something like that, and it would be a like a heat filter, and I could see where you are, and spend most of your time in a classroom.

Graham Fletcher: Because, if we could actually monitor where we spend most of our time in a classroom… Is it at the front of the board? Or, do we always go and talk to that gifted student, because those conversations are a little bit easier?

Graham Fletcher: Really interesting. If we could just find a way that we could just heat map the space, and where we spend time in a classroom. [crosstalk 00:00:28].

Kyle Pearce: That there, is the one and only Gfletchy himself.

Kyle Pearce: Yes, today on the podcast, we have 3-act math task builder, national speaker, and math specialist, Graham Fletcher.

Jon Orr: Stick around while we chat with our good old Canadian friend, who’s transplanted himself in America, on what it really means to assess, how to leverage engagement in your math class, where do some teachers miss the mark when teaching through tasks, why tasks are great, formative assessments, rather than summative assessments, and, how to view your lesson from 60,000 feet, instead of six inches.

Jon Orr: Here we go, let’s do it.

Kyle Pearce: Hit it.

Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast. I’m Kyle Pearce, from TapIntoTeenMinds.com.

Jon Orr: And I’m John Orr from MrOrr-IsAGeek.com.

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.

Kyle Pearce: John, are you ready to talk with our dear friend, Mr Graham Fletcher?

Jon Orr: Of course, Kyle, of course.

Jon Orr: We’re pretty pumped to have one of our good buddies on the show today, and chat about 3-act tasks, assessment, and even coaching.

Jon Orr: We met Graham, kind of like, Kyle, how you and I met, online through Twitter. And while meeting up in conferences across North America, we became pretty good buddies.

Jon Orr: We’ll even chat a little about that in the episode.

Kyle Pearce: Yeah, you’re right, John, it was great to, finally getting a chance to meet another person that we’ve been collaborating with and connecting with on Twitter for such a long time. So, it’s great that we can now call Graham, a good friend, and someone that we can turn to for advice.

Kyle Pearce: Before we get into this, though, have you shared some of your feedback on iTunes yet? Take a moment, tap that subscribe button, and spend a minute letting us know how you’re enjoying the show.

Kyle Pearce: Just like shershey0303, who must be our dear Math Moment Maker from the Academy, Mr Shaun Hershey, I can’t imagine it being anyone else.

Kyle Pearce: Here’s what his review says.

Jon Orr: Down to earth and practical strategies to implement right away. Kyle and John are two passionate educators who could relate to our struggles, and are willing to tackle tough issues, head on, with practical advice.

Jon Orr: They offer actionable steps to help with topics such as, but not limited to, classroom management, concept based lessons, mathematical practices, managing your time, engagement, selecting technology, et cetera.

Jon Orr: This is a very worthwhile and beneficial podcast for any educator looking to enhance their pedagogy, and deepen their understanding of mathematics.

Kyle Pearce: Wow, thanks so much to Shaun for posting this review, and subscribing.

Kyle Pearce: And did you know that we actually have more reviews on the US iTunes store, than on the Canadian iTunes store?

Kyle Pearce: Come on, Canada, we live in Canada. Send us some love by giving us a review, and subscribe now.

Jon Orr: In this episode, we’ll talk with Graham about 3-act math tasks. You can find many of those tasks on our site, MakeMathMoments.com.

Jon Orr: We actually have a task search engine. Head over to MakeMathMoments.com/Find, and type in any topic you’re currently working on with your kiddos. What will pop up is tasks from websites that we’ve curated, so that you can spark curiosity and fuel sense making with your students.

Jon Orr: Head over to MakeMathMoments.com/Find.

Kyle Pearce: Well, let’s get onto the conversation with Gfletchy.

Jon Orr: Hey there, Graham, welcome to the Making Math Moments That Matter Podcast. We are super excited to get you on the show today. We’ve been trying for a bit now, and pumped to talk to you, finally, here.

Jon Orr: How are you doing this evening?

Graham Fletcher: I’m doing great.

Graham Fletcher: Yeah, I know we tried and it failed the first time, but glad to have finally circled back around. It’s always fun getting to hang out with you and Kyle, and just chat about math and just other things on the way, so looking forward to it.

Kyle Pearce: Awesome, yeah, that’s fantastic Graham.

Kyle Pearce: We are super excited every time we bump into you at conferences. The last time, I believe, for us, was what, NCTM, just a month or two ago? And we had an opportunity to dive into some really cool conversations, so, hopefully we’ll be able to bring some of those to the table, here today.

Kyle Pearce: But before we do, can you fill in the Math Moment Maker audience on your role, where you’re located, and maybe, a little bit about what got you into this teaching gig?

Graham Fletcher: Yeah.

Graham Fletcher: So, right now, my current role is, I’m not with a district. I’ve taken choice to do some work on the side, I guess, which has really allowed me an opportunity.

Graham Fletcher: It’s strictly selfish, to be honest. My wife and I, we both have daughters, we have a daughter going into grade seven, and a daughter going into fourth grade. And so, what I’ve done is, I’ve stepped away from a district year for the past… I’ve just finished my second year, and it’s really allowed me to just spend a little more time at home with my daughters. But then also, go out and support certain districts all over the place, as well.

Graham Fletcher: And so, that’s where I am right now, but, very much like you, and with John as well, I’m sure, the journey is a long one, it’s a fun one, and I’m just thinking about that growth over the years that’s bought me to this place now, where family comes first.

Graham Fletcher: So, that’s where my brain is. And then math, obviously, comes second, for sure.

Jon Orr: You know, I would love that opportunity to spend more time with my kids, that sounds quite amazing.

Jon Orr: Graham, do you mind filling us in a little bit of a backstory? I know there are a lot of fans of yours listening, right now, and I think they would love to hear about how you got into teaching from the start. You’ve told us where you ended up right now, but where did you begin this journey?

Graham Fletcher: The journey began back home in Canada, and then I ended up in the States, on a soccer scholarship, and I ended up getting a business management degree. And I went back home, worked in Milton, Ontario, for a little while. And it just wasn’t working out for me.

Graham Fletcher: But in the meantime, I stuck together with my, then at the time, girlfriend, who is now my wife. She was going through school at the same time, and she became a teacher. And I was doing a lot of coaching, soccer, back home in Canada, but then also in the United States as well. And just that love of being around kids and showing them something new, or showing them a new move, and allowing them to take that, and then practice it, and then come back, and be able to perfect it, and then put it in a game situation, is something that I really truly loved.

Graham Fletcher: And the best way to make a career out of that, if you’re not coaching, is teaching. Because I think that’s what we do, we can’t jump on the soccer field and go play the game, or kick the ball for these kids. And so, for me, it was setting those kids up in a classroom. So, I actually chose teaching as a second career, after sales, for about two or three years.

Graham Fletcher: And then I traveled down to Daemen. I actually was still just living outside Toronto, traveled to Daemen College, in Amherst, got my teaching certificate. And then moved to the United States, and the rest is history.

Graham Fletcher: And now, I’m married to my wife, who is a kindergarten and first grade teacher, and so, that’s the journey where I am right now. That pretty much sums that part of it up.

Kyle Pearce: I love the connection going back that you started as a coach, and I find we can learn a lot from coaching in sports.

Kyle Pearce: And in the math classroom especially, even though I did some coaching, I never made the connection that when I coach students, you always gave much more specific and differentiated advice to your players, because you’re watching the game, you’re analyzing them playing, you make your practices and you adjust your practices based on how your team is performing. And it seems so obvious now, that I should have been doing those things in my classroom as well, however, in my classroom, I was doing something completely different.

Kyle Pearce: I wasn’t really watching them play the game, because I didn’t really give them much time, early in my career, to actually play in front of me. I was like, go play the game, and I’m going to skip it, and what I mean by that, is I’m going to send you home, and you’re going to do homework. I’m not going to be there to actually observe the game, and then you’re going to come back tomorrow and I’m going to run another practice without actually knowing how well you perform.

Kyle Pearce: So, I don’t know if you can see that piece, where if coaching had some sort of influence on your teaching? At least, maybe, early on? Or was it later for me, I totally missed the mark until later on.

Kyle Pearce: What was that like for you?

Graham Fletcher: So, at first it was a struggle. Because you’re trying to, basically as a teacher, force kids to do things that they might not be able to, but that’s also part of the learning curve. So, to go back to that coaching analogy on, say, a soccer, field, coaches, athletic coaches always try to put their players the best position they can be to succeed.

Graham Fletcher: So, for instance, if you’re not a very fast player, a coach wouldn’t put you out on the wing. And so, it was after quite a few years in the classroom, to where I realized, I kept putting those students out on a wing, and that might not be where they will thrive. Maybe they thrive in a different position, which is a differentiation connection.

Graham Fletcher: So, the only thing that I can really say is that, I really missed the boat my first couple years of teaching. But then, what’s happened is, is over time, I’ve really realized to see, hey, what connects with kids? What doesn’t connect with kids? How can I, as more as my capacity builds as a teacher, it’s like, the more that I’m able to connect and ask that purposeful question to move student thinking forward.

Jon Orr: I can extend this a little bit further.

Jon Orr: Because I resonated with this metaphor that when you said, you would help a kid, you would show a kid a skill, and then you would have them practice that skill, and then they go and perform that skill.

Jon Orr: And I remember, distinctly, that’s the way I viewed math class too. I even said that this is what we do to students. I would go tell students that exact formula. Kids would say, why are we learning math? And I would say, well, you’re learning math, mostly because you’re training your brain to think a certain way, in which is what I think we all try to say that to our students, but I would say, specifically, that, math is the only subject where we’re training you to think about a skill, or learn a new skill, and then apply your learning to that skill, and solve a problem with that skill.

Jon Orr: You’re going to do that for the rest of your life in any job you get. You’re going to have to learn new things and apply those things. But I was very literal in that with the students, I would say, I’m going to show you how to do these skills, exactly, and then you’re going to apply those skills onward.

Jon Orr: So, I’ve changed my tune a little bit in the sense that, I’m not showing my player exactly how do exactly every skill. We’re exploring the skills a little bit more, before showing them exactly how to do it. So, I definitely agreed with you, how you approached teaching, or approach coaching into teaching, I’d set it up, very similarly. But I think I’m taking a little different path, since then.

Graham Fletcher: Yeah, totally.

Graham Fletcher: And a lot of the times, just because you’re a really good teacher in a classroom, might not necessarily make you a really good coach. There’s a whole lot of different things that play into that. Maybe you’re a really good coach for teachers, or maybe you’re a really good coach of students.

Graham Fletcher: Like, I look at Michael Jordan as a prime example. Best player of all time, but when he tried to become a coach of the Washington Wizards, it didn’t go out so well.

Graham Fletcher: So, even though you know the math or you do the math, there’s a whole much more of nurturing, and really just listening to students and doing what’s in their best interest to move their thinking forward. So, I couldn’t agree more.

Kyle Pearce: We’ve mentioned this many times, just this idea of, if you felt that math felt natural, I never want to say it is natural, like you’re just born with it, or anything like that, but it’s like, the experiences you had in your life led you to feel as confident in math, and you didn’t really feel that struggle.

Kyle Pearce: The same as in coaching, where, as a hockey fan, I remember when Wayne Gretzky was coaching then, I think it was the Phoenix Coyotes, and really struggled. And I really think it has a lot to do with this idea of not actually understanding how everybody else plays the game. It just feels so natural, because he was so young when he started to play.

Kyle Pearce: That sort of resonates with me when I think about, especially secondary math teachers, John and I being high school, or former high school teachers, I come out of the classroom thinking, I didn’t really experience the same struggle that a lot of other students did, so, it’s really hard for us to try to figure out how we’re going to help them get through.

Graham Fletcher: And I think that’s a really, super important part. I think it’s something that I know I’ve worked really hard to do, and you have, and many teachers have. It’s not something that can ever be complacent in, because kids are always changing. So, what are we doing to continue to evolve as teachers that we continue to meet the needs of those kids, as they continue to change and evolve.

Graham Fletcher: So, yeah I think that’s a great point, Kyle, for sure.

Jon Orr: Yeah, and we can dive into that a little bit later. But before we get into all that, we have to ask you the question we ask every guest, and that is about your memorable math moment from math class.

Jon Orr: So, when you think of math class, back as a student, it also could be as a teacher, many people do give teacher or student memories. If I say the word, math class, what has just popped into your mind, Graham, to remember about math class?

Graham Fletcher: For me, it’s working with kindergarten students. There’s one particular story, that really resonates with me, and I’ve actually shared it in quite a few conferences.

Graham Fletcher: And one of the things that I love about kindergarten class is that student intuition lives. They’re so vibrant in that classroom, and they’re not tainted with rules that many parents teach, teachers teach, lots of rules, rules, rules.

Graham Fletcher: So, I was playing around in a kindergarten classroom, and I ran into this little guy, Mac, and he was actually trying to add up all of these different colors of candies. And so, as he was adding up all the candies, he drew the pictures out, and there was actually two white candies, but he didn’t draw the boxes. So, he as able to actually image those candies. So, if you were to count what’s on the paper, you would count eight pieces of candy. But because I was listening to Mac, I was able to see that there was ten pieces of candy. Because he actually imaged the last two.

Graham Fletcher: And so, that really took note with me. And it’s funny that you asked that question, because that story happened, I don’t know, maybe, three, four years ago. But it was maybe about two months ago now, that I heard on Twitter, that the Latin root word for ‘assess’, it means to sit beside.

Graham Fletcher: So, I wondered, how many times do we truly think that we’re assessing what a kid knows, if we’re not sitting beside him? And so, when it comes back to that Mac story, I wouldn’t have been able to truly assess what was happening on his paper. I would have seen eight, and just said, yep, it’s done. But because I sat next to him, it was affirmation that I have to do everything I can to continue to sit down next to students so I can hear their thinking.

Graham Fletcher: Because it’s beautiful, and who are we to guess what’s coming out of the mind of a five, six, or seven year old?

Jon Orr: I was going to add, that’s been a realization for me, for the last few years, also, in the sense that, how many times in my past teaching life, did I sit down next to students just to listen to how they approach problems, or how they shared their thinking.

Jon Orr: And even when I started to change my teaching style, to be a little bit more like that, and a little bit more open in how I presented or assessed my students, I still probably didn’t make a point to sit down with everybody at some point.

Jon Orr: And I think there was a semester that went by, that at the end of the semester, I realized, you know what, I don’t think I ever sat next to that student, or listened to that student. I only marked their papers, or I only marked their quizzes. I never got over to their desk to hear them or, to the wall space. And I thought, you know what, I’m never going to do that again.

Jon Orr: And at that point, one of my tools was to create a chart, to make sure that I hit everybody in a certain timeframe. So, that’s huge for us to think, and I’m really glad you brought up how the Latin root for ‘assess’ is to sit beside, I think that’s huge.

Graham Fletcher: Yeah, and as we’re talking about that, John, and it’s something that’s been in my brain for quite some time, and I’ll kind of to share this, and then maybe, the people that are listening to the podcast, they can maybe chime in here. But I’d love to create something to where, maybe I can put a little note on you, or something like that, and it would be like a heat filter, and I could see where you walk, and spend most of your time in a classroom.

Graham Fletcher: Because, if we could actually monitor where we spend most of our time in a classroom… Is it at the front of the board? Or, do we always go and talk to that gifted student, because those conversations are a little bit easier?

Graham Fletcher: Really interesting. If we could just find a way that we could just heat map the space, and where we spend time in a classroom, would tell us a lot about our effectiveness as a teacher, I think.

Jon Orr: Yeah, this brings up an interesting study I heard a while back, and I don’t know, this was, I think this was when I was in university, or teachers college, and it goes to the idea about that we flock, I think, as teachers, to good feedback. Like, when you are teaching a lesson, you’re naturally drawn to the kids that are nodding their heads, or asking questions, like you want to go that route. It’s harder to go to the other kids that are not engaging in that way.

Jon Orr: And it brings up this study that I heard they did a test on a professor at a university, and when the professor went to the left side of the room, he would pace and forth around the front of the room, and when he would go to the left side of the room, all the students in the room were directed to not look at him. And so then, when he went to the right side of the room, they would look at him, and nod their heads, and look like they were paying attention.

Jon Orr: And so then, over the course of the hour lesson, and what happened was, progressively, they would make sure that the farther he went right, the more he’d look at them, and eventually, this guy ended up in the side aisle, because he was realizing everyone was watching him only when he was on the right side, so he just spent all his side over there. And never went back to even the middle of the room.

Jon Orr: He was directed to go over there just from the feedback he was receiving from the audience.

Kyle Pearce: It’s funny because, as Graham, you were mentioning, this idea of the heat sensor, and I’ve seen some people do this on Twitter quite a bit, where, let’s say, they’ve made a change in their classroom, and I’m thinking of Chris Lee in particular, I wish I knew his Twitter handle off the top of my head, but we’ll include it the show notes. But he had shared a time lapse video of how his class looks now, versus what it used to look like.

Kyle Pearce: And it was really cool to see it, because you see the 60 minute, or 75 minute, or whatever the timeframe of the class, and you see the kids are up, and they’re at the whiteboards, and he’s moving around the class, and he’s all over the place in comparison to these… I don’t know whether it was an actual video from a couple years ago, or whether they were just imitating the way he used to teach, where he would just stand and deliver at the front.

Kyle Pearce: And it think it’s something for us all to be thinking about, because something I’m noticing now, now that I’m actually aware of how important it is to sit and listen to students, I still struggle, even though I am next to them and listening. Sometimes, it’s like I’m in my own brain thinking of the question I want to ask the student next, that I haven’t even heard what they were saying.

Kyle Pearce: So, even just to sit beside them is obviously a step in the right direction, but then it’s like a whole new skill to develop, especially if you’ve been teaching your whole career, not doing that, to actually go and actually become an active listener, and actually listen to what the student’s saying, and then, essentially, on the fly, try to connect what they’re saying to whatever solutions, strategies, that you have anticipated ahead of time.

Kyle Pearce: And then it’s obviously extra work if it’s a solution strategy that you’ve never seen before, like, the example of Mac, in the kindergarten class, where you probably would have assumed he was just wrong, because there was only eight candies on the page, but whether it was with his finger that he had motioned the other two white candies, or whatever it was, you were there to actually pick up on that. And, obviously, to really show him that you were listening to him, and that he was being heard.

Kyle Pearce: So, that’s such a cool point.

Graham Fletcher: Yeah, it’s those moments that make it all worthwhile for us.

Graham Fletcher: When we see kids that flourish, and that light bulb moment, I think that’s what… Everyone of us wake up so early and we put in the extra hours to do the things that we do. I think that’s it, we just want to see kids succeed.

Jon Orr: I want to ask some questions about some of your teaching experience.

Jon Orr: I’ve always been curious, what’s an example of a classroom experience you had, where you had some success, and what did that look like?

Graham Fletcher: In a classroom? I think it’s when, I don’t know if there’s one pinpoint story that I could actually nail down, and I think it would be more of an evolution, in terms of my teaching, to where I’ve seen success. There might be little snapshots, and little moments that happen over time, but it’s hard to pinpoint any one of those. I think the biggest thing for me, is what I’ve realized is, I was surrounded by some really great people.

Graham Fletcher: So, I was a third grade teacher for eight years, and then I had a math coach, and his name was Mike Wiernicki. He now works at our State Department, but then there was our math coordinator, Turtle Toms. And so, one of the things that they did was, they brought me in as a coach, to that community, and then as I was working in classrooms, and things like that, being able to empower teachers, or being able to work with kids and push their thinking forward.

Graham Fletcher: But the biggest struggle was, is just letting go, and trusting the process. And so, once I’ve actually been able to put a good task, and realize that, hey, it’s okay, that if this kid doesn’t get the right answer today, well, if I’m using it as formative, and summative… If I’m using it as formative and diagnostic assessment, then it doesn’t really matter.

Graham Fletcher: Right answers only really matter when it’s summative. So, I think me relinquishing some of that control, to know that, hey, it’s okay if kids struggle, and they don’t get the right answer, because we’re building up to something better.

Graham Fletcher: So, for me, it’s not one single moment, but I’d say in terms of my journey, that’s probably the thing that I’m most proud of, is that ability to relinquish that control.

Kyle Pearce: I’m so happy that you shared that, because when we were chatting a few months back, I remember asking you that question of, what got you on the path to thinking differently about math class?

Kyle Pearce: And I remember you mentioning both Mike and Turtle, and I think, how awesome, for those coaches, to be able to look back and, obviously, they must realize that they’ve impacted, not only you, but, probably countless other educators. And then, just thinking about how many students that that’s actually impacted. It’s so huge.

Kyle Pearce: And clearly, I love the idea that you’re sharing with us about trusting the system, and I came out of my classroom after so long, thinking, today I was supposed to get through this. And if students didn’t get that, it was like, I don’t know what else to do.

Kyle Pearce: But, when you think about math differently, and you think about every single day as this opportunity to hear about what kids are thinking, and then, to essentially, respond to it, just like a coach would, at practice. Where, just because we did one timers in hockey, in the first couple practices in the season, doesn’t mean we’re not going to come back to one timers if the team’s not able to use them in a game situation, you’ve got to come back to these things.

Kyle Pearce: So, what I’m hearing is that the math class is like a dynamic space. It’s not supposed to be static, it’s not supposed to be 100% scripted. Even though, planning is so important, but just knowing that the plan is there, to guide you, and then it’s making those pivots, and being okay and comfortable with pivoting, I think, is so important.

Kyle Pearce: So, I really think that’s awesome, how you have articulated that in that last comment.

Graham Fletcher: One of the struggles that we go through… We have so many resources that are pushed on us, so I think it comes back to us to how do we be wise consumers? We have to vet the things that we are putting in front of our students.

Graham Fletcher: And then what’s a struggle is, whether you’re a coach or whether you’re a teacher, maybe you’re the only person in your building, and you need someone to bounce ideas off of. I love the fact that the three of us met through twitter. So now, we’ve stayed in touch, and stayed connected over the years, but maybe Twitter’s not your jam. But how is it that you can find somebody as your math soul buddy. To where you can meet with them, not only as…

Graham Fletcher: Because when you do that, then that’s only going to make you better. And so, if you have an idea, I think the whole story of having Mike and Turtle for me, there was also a whole group of coaches. There was maybe about five or six of us, many teachers who are still active in the math Twitter blogosphere as well.

Graham Fletcher: So, it’s surrounding yourself around people who are go getters, and people that want to aspire to do the best for kids, even when it’s sometimes the most difficult decision at the end of the day to make.

Jon Orr: Right, and so important, definitely, to have someone to share that with, and being so awesome, in today’s age, that you can do that through Twitter, but it could be on Facebook. But it could be through email, it could be lots of different ways, it doesn’t just have to be in your own department. And I think that’s why our support groups are so big, and so useful, and we’ve probably grown so fast as educators in the last few years, just because we’ve shared through Twitter and met up online.

Jon Orr: Like you said, we met through Twitter, originally, and we’ve met through conferences, same with Kyle and I. Even though we live down the road from each other, we didn’t meet until online space, and then, supported each other for a number of years after that.

Graham Fletcher: I also think that I can attest to the kind of work that you and Kyle are doing as well. Just setting up communities where teachers are like, you know when they need somebody.

Graham Fletcher: There’s a lot of rural places across the United States and Canada, and the world, and what you guys are doing is you’re providing that platform to where, hey, maybe you don’t have somebody in your building that’s your math soulmate, well, maybe you can find somebody through you all.

Graham Fletcher: So I appreciate the work that… I’ve always appreciated the work that the two of you are doing to bring that in, and to help that, and foster just that community aspect of our mathematics community.

Jon Orr: Definitely, I think that’s one of our main goals, especially with this podcast, is providing professional development, and support for teachers, wherever you are. And also, whenever you want.

Jon Orr: I think that’s key too, and it’s definitely a different time. Like, I never would have imagined, when I first became a teacher, that I would be doing this right here, but also listening to podcasts, on my drives, during my time off. It’s definitely a different world because of the opportunities we have.

Jon Orr: Let’s start moving into, talking about some 3-act math stuff. Because I think that’s something that all three of us have been really advocates of, from Dan Meyer’s work, with the math task structure.

Jon Orr: One of the things I’ve always been curious about, and stuff that Kyle and I have been working on, and thinking about, and sharing, is about the lasting power of 3-act math tasks.

Jon Orr: Like, for example, I think most people are drawn to 3-act math tasks themselves, because of the visual elements to engage students. But I think you know, and we know, that there’s so much more to that structure, and then how you handle that, just engaging kids in math.

Jon Orr: In your opinion, what is it about the structure itself that’s much more than just engagement?

Graham Fletcher: I think it’s the whole open middle aspect of the task.

Graham Fletcher: So, I’ll be honest, just my own little journey here, with 3-act tasks. When I first started doing them, I was really just super engaged, super pumped up, right alongside the kids. Like, we’re both high-fiving, we’re clapping, and then it’s like, 45 minutes, an hour passes by, I’m jacked up, the kids are jacked up, everybody’s had a great time in math class, and then, after doing that three or four more times, something clicked.

Graham Fletcher: And I said, you know what? Kids are never engaged in school. And here they are, they are engaged, for whether it be 50 minutes. What am I doing about engagement?

Graham Fletcher: And what I realized is, as much as I was super pumped up that kids were engaged, I wasn’t leveraging that time to really learn what the kids were doing. Because, they were so willing to talk, they were so willing to share, because just the structure of a 3-act task, what it does it, and both of you know, it really makes it really accessible to every kid in your class, every single kid in your class can make an estimate. No matter what labels the school system has put on you, every single kid can make an estimate, and that’s that [inaudible 00:28:15].

Graham Fletcher: So, my big journey was doing the task, but also now understanding what are we doing to use this, not as an engagement tool, necessarily, but more as that formative and diagnostic assessment.

Kyle Pearce: That sounds exactly like our journey, and I know so many other people who experience the same… You’re hooked. How could you not be? The kids are hooked, you’re hooked, everybody’s having a blast.

Kyle Pearce: But, at the end of the day, I realized afterwards, the way you start to frame the questions, and the way you start to really… John and I like to coin it, a spark in curiosity. You start to realize that while the visual element is so important and so helpful for so many students to make sure that we’re making sure that floor is low enough, you start to realize that every single day doesn’t necessarily have to be a video in order to accomplish some of those things.

Kyle Pearce: But it’s those elements, like you were saying, like, getting them curious, and it can happen in so many different ways. Now I realize, it’s like, if I can focus in on the pieces, the parts that really help kids want to just jump in and dive in, and take a chance, if we really focus on those things, those kids will have some success.

Kyle Pearce: Now, our next question we have is, in your opinion, and I feel like you were hinting at it, just a little bit, you would say, what was I doing with all of that engagement?

Kyle Pearce: And we’re wondering, where do you think teachers can easily miss the mark when we use 3-act math tasks, or anything along those lines, where we’re really trying to get kids to lean in. Where do you feel like sometimes we can come short, if we just get wrapped up in the engagement, and really don’t think much further beyond that.

Graham Fletcher: I think it’s where we purposefully and intentionally use the task.

Graham Fletcher: For instance, I think, many of us, I’m guilty of this, we might use something like problem solving Friday, where we’ll use a 3-act task on a Friday, and what that does is it sends message that, hey, we only do problem solving on a Friday.

Graham Fletcher: Or, you save your 3-act task for the end of the unit. Well, by then, what’s ended up happening, is all the students have tiered and ranked themselves, whether we agree with it or not, and then it’s summative. And summative assessments, we save it for the end of the unit. Summative assessment is the autopsy. The learning’s done, the learning’s dead, it’s over, there’s no more learning that’s going to be taking place, if we save it for the end of the unit.

Graham Fletcher: So, what would happen if we take that really good task, when the kids are going to be engaged, when they’re going to be enthusiastic about coming into class, and putting it at the beginning part of the unit, or maybe, two to three weeks into a unit, to where, now, the playing field is still level, and everybody now has a common voice, because it’s new learning for everybody in the classroom. To where, now students, it’s that equity piece, where certain students have access to certain content, but a good problem like this, a good problem like a 3-act task, nobody has the answer.

Graham Fletcher: And so, there are students that always want to jump in and just get the numbers and steamroll forward, while the task will slow them down. And then the other students, some of our most thoughtful students, who are some of our more meticulous students, who think a little bit slower. We’ve actually allowed them to engage in the conversation now.

Graham Fletcher: So, I think where we use these tasks is where we [inaudible 00:31:40] the mark a lot. We use them formative… Most of the time is summative, but I think it’s diagnostic and formative is where we need to be spending most of our time with these.

Kyle Pearce: We couldn’t agree more.

Kyle Pearce: Oftentimes, that’s the number one email we get, and I’m sure you get many of these emails, too, where if someone replies through your blog, or through a task, and says, I tried this task, and it just didn’t go well, it flopped, or the kids didn’t want to notice or wonder. And some of that is building the culture, of course, you have to really build the culture with your students so that they feel comfortable to share what they’re thinking, and to not feel like there’s just one right answer right from the get go.

Kyle Pearce: But then, oftentimes, what we get down to, we ask them, where are they using the task, to paint us a picture of the current unit of study, and oftentimes, they do say, we did it at the end of the unit. And, John and I often reference that, and we call that the rush to the algorithm. So, it’s like, I’m going to feed you stuff for four days, and then, all of a sudden, I’m going to give you this task.

Kyle Pearce: Kids know, obviously, all this stuff you just pretaught me is probably what I need to do for this task, so, not only does it kill the curiosity, but it also pigeon holes me into a spot where I’m not actually being asked to problem solve, I’m being asked to regurgitate steps and procedures.

Kyle Pearce: So, I love that idea of flipping it and using it to introduce ideas, and early in that response you had mentioned, purposefully and intentionally. And that’s a part where we admit, wholeheartedly, for the very long time, we were doing this, and we were just happy that it looked like our kids were alive in our class. Coming from the secondary side, we were like, man, they are alive, they’re not dead on their desk, that’s amazing. And we went with that because that was so much better than what was going on previously, but then after a while, we realized that we did not have that intentionality at the forefront of why we picked that task, and when we used that task.

Kyle Pearce: And then, we always say, we left a lot of learning on the table, because it was like the task was a means to an end. It was like, okay, we found an answer, and then we moved on. We didn’t actually use the task and the student thinking to take their student strategies and then try to make connections, and then, essentially, try to lead us to the next piece of the learning, to really elevate, to really push that learning up.

Kyle Pearce: That, for us, is huge, and we coined that as, fueling sense making. And that, to us, is such a big part of what we’re trying to do with all the folks that we end up working with, either in live workshops, or in our online academy, we really focus in on that fueling sense making.

Kyle Pearce: So, let’s get them in there, let’s get them engaged, with an amazing 3-act task, by you, Graham, or by Dan, or by anybody else out there. And then, once we’ve got them, then it’s like, they’re just waiting, and there’s so much that we can do.

Kyle Pearce: So, I love that you focused in on that purposeful and intentional use of task. I think that’s so key.

Kyle Pearce: So, I’m wondering, if you’re thinking about this, or someone at home’s thinking, they’re going, yeah, I really think I should do this. But, I’m not sure, I haven’t used a 3-act task before, what would you say to teachers who say that, ah, I’m just really struggling, where am I going to fit it into my teaching day? What do you say to someone who, you’re just trying to help them get started, and they’re really struggling to figure out where it all fits.

Graham Fletcher: So, it’s easy to say, look back in retrospect, and I would say, now, that I don’t have time to not have the time. To actually do one of these tasks.

Graham Fletcher: Because just seeing, so many times, we look at our learning objectives, or we look at our content standards, and we break it down into such a granular level, that it seems like such a daunting task, to where we can go ahead and tackle all of these things over the course of the year.

Graham Fletcher: So, if you’re not sure where you can fit one of these tasks in, maybe you’re looking at the task from a granular level. So, if we come back to that formative and diagnostic assessment that we were just talking about there, Kyle, is what happens if you take this task and then you build the understanding from there, not at a granular level, but at a 60,000 foot level?

Graham Fletcher: So, you’re looking at multiple standards, because you’re looking at estimation. You know, if your kids can place the number on the number line in their range, you’re looking at computation, you’re looking at justification, you’re looking at reasoning. You’re not looking at a granular thing that’s just a checklist, like I’m doing this learning objective on day two of week three of month four.

Graham Fletcher: And so, you’re looking at it at more of a comprehensive, because you’re going to get far more from one task than what you’ll ever get from one granular lesson on a day.

Jon Orr: Right, and if you think the other way, you’re going to get frustrated, probably, that you will never have enough time to teach all the standards, and how am I going to cover everything, if I’m spending all this time in this one task, on this one day. I think that’s huge, is to, how do we ensure people open up and look at it from that 60,000 foot view.

Jon Orr: Graham, you work with teachers all the time now. How are you helping them see that 60,000 foot view?

Graham Fletcher: For me, it’s getting into classrooms, really. A lot of the times, when we talk about PD, I think it’s the working side by side with them, as much as possible.

Graham Fletcher: So, if you’re not comfortable about using one of these tasks, I think what makes it really powerful, is when you go and see somebody teach one of these tasks first thing, and you’re like, well, I can do it. Because both of you have been working alongside teachers, I’ve been working alongside teachers, or even if, you don’t have a coach in your building, ask your principal to come watch your class, so you can go co-teach one of these lessons.

Graham Fletcher: You don’t have to do it alone. I think a lot of the times, whether it’s a workshop, it’s coming back and it’s that community piece. So, how is it that when, you do see a good idea, like a 3-act task, and you want to try one, how is it that you can pair up with somebody, and find that accountability partner? That, for me is always going to be a, I’m not doing this alone. So, when you see a good idea, when you go back to your district, how do you plan to put this into practice?

Graham Fletcher: And so, just asking teachers to think thoughtfully about that, before they walk out the door, has really helped.

Kyle Pearce: Yeah, that’s excellent advice.

Kyle Pearce: I really like this 60,000 foot idea, because when you really think about it, and you said it already, where, we can look back, it’s so easy when you think in hindsight, that, really, at the end of the day, what is it that we want students to walk out of our classroom with?

Kyle Pearce: And when I asked teachers that, usually they come up with these other elements that we aren’t focusing on. We tend to hyper focus on these little tiny pieces, these granular pieces and concepts, like you’ve mentioned, or skills, and yet, when we ask then what we really want for students, it’s usually not those things.

Kyle Pearce: We’re usually talking about things like being able to problem solve, being able to be resilient and persevere. All of these pieces that you want students that think positively about math class, and yet, we spend all of our time trying to make sure that every tiny little piece that we’ve, quote, unquote, taught it, and at the end of the day when we actually think to, how things are going now, like when you say so like, how’s that going for you? I know for me, it was like, they’re not really learning that stuff anyway. Like, as much as I’m trying my best to do those things, a lot of students are walking away with none of those things, or just little tiny pieces here and there.

Kyle Pearce: So, I really like this idea of focusing in on really, what are those big ideas that we want to take away, and we want students to walk away from, and then, how am I going to do this? Well, don’t do it alone. Find somebody, whether it’s online, or whether it’s someone in your building. Just get vulnerable, I think, without being vulnerable, you’re not going to be able to do anything.

Kyle Pearce: Like, you just have to be okay with saying, you know, I just don’t know. I’ve been doing this for years, and this is the result I’m getting. And some kids are getting it, but some kids aren’t. Can we work on this together, and let’s see if, maybe we can put our heads together. And typically, two heads are going to be way better than one.

Kyle Pearce: So, it’s a great message that you shared, so, that’s huge.

Kyle Pearce: I’m wondering, for those who are thinking, and there might be some at home going, yeah, I’m definitely going to do this, this is something I want to look into, do you have any favorite tasks that are really fresh in your mind right now, that you’re really liking?

Kyle Pearce: I know for me, I get really excited about a certain task for a little while, and I try to use it in different ways and different classrooms, and then you find another, and you sort of move on.

Kyle Pearce: Is there anything that’s like that for you right now, one that you’re really excited when you have an opportunity to do it in a class, or share it in a workshop?

Graham Fletcher: The one that is a very good tell tale task for me, is, there’s two tasks.

Graham Fletcher: There’s one with the light bulb, and skittles inside there, and then the other one that involves skittles as well. Those are two really telling tasks, because it asks students and teachers to get engaged in quantity estimation, and it’s amazing to see. It never really fails, really, how much we don’t use estimation in our classroom.

Graham Fletcher: So, it’s a little bit of a sucker punch task for teachers, but it’s also a very good way to formatively assess how well students are estimating.

Graham Fletcher: Because, for the listeners, could you count on one hand, how many times you had your kids engage in an estimation activity, last year? So, it’s like, if we’re not estimating, estimation is not something you could be doing once every two, three months, otherwise, you suck at it.

Graham Fletcher: And so, what ends up happening is that something that you need that repetitive practice, and I think that’s where Andrew Stadel’s estimation 180 comes in really, really handy.

Graham Fletcher: So, yeah, that estimation needs to be happening a lot, for sure.

Jon Orr: You got me a little bit of curious, here, Graham. Could you fill us in a little bit about this light bulb, skittles, task?

Jon Orr: Walk us through… We’ve talked about being intentional with the task. What are you aiming at for, as a content standard, and then how does that task unfold?

Graham Fletcher: I would use the task primarily with grade one, grade two kids.

Graham Fletcher: And literally what I end up doing, is my wife actually was creating a teacher appreciation gift for our daughters a couple years ago, and inside it was a… I guess, Amazon has this craft light bulb. And so what she did was, she was stuffing the skittles, and she did five different layers of skittles inside the light bulb. And so, when we flipped the light bulb over, you want to know how many skittles are inside the light bulb.

Graham Fletcher: So, kids are adding a set of numbers, most of the time teachers will estimate, roughly, about 45 to 50, and there’s actually 91, inside. And so it’s almost, half the quantity. And so, it’s just really, really telling.

Graham Fletcher: But then again, the numbers that it comes back to that intentional and purposefulness, where the numbers, there’s a lot of friendly numbers, there’s double numbers. I think the numbers are 19, 19, 17, 15, and 21. So, there’s a lot of opportunity for compatible numbers, doubles numbers, and then just seeing the strategies that students can come up with as they begin to combine those numbers.

Kyle Pearce: Awesome, awesome. I’ve done that task with you, actually, at workshop you did recently here in Windsor. And I feel like a long while ago, what I started noticing, was, I would do tasks ahead of time, five practices, the anticipation, and I would do a legit estimates with the 3-act math tasks that I was trying. And what I always found with quantity estimates, your typical guessing jar type estimates, was that I was always ridiculously low. So, I’m now in this habit of taking whatever my estimate is, and I double it.

Kyle Pearce: And I did that with you. My table, I don’t know, Graham, if you’ve noticed, but at my table, they were like, you know this problem. I was like, I actually don’t know this problem, I’m like, this is my strategy. I use, like, okay, I’ve figured this is how many that were in the bottom, and then I was like, ah, I think, I’m looking, and I was just making some sort of estimate based on what I could see spatially, because obviously, it’s not a regular cylinder, or anything like that. And I was like, I think it’s this, but I know I’m way off, so I’m going to double it.

Kyle Pearce: And that was it, and everyone was like, oh, boo, they were all booing me at the table and everything like that. But that’s my go to, and you nailed it. Estimation is something that we all, as adults, are not that great at. So, just imagine our poor little ones who, we’re trying to help them think of reasonable answers, or at least, to consider looking at their solution, and try to figure if it’s reasonable. And yet, we don’t give them enough opportunity to actually make estimates to see whether that can actually be reasonable, or not. So, that to me was a shock.

Kyle Pearce: And something else that I’m reminded of, and I wanted to hit on it in this interview, was from that particular workshop, it was a whole day workshop, a great workshop, I learned a ton. Everyone there was really happy with how everything went, and how much they learned. Something that I really wanted to touch on was the idea, and you spent a significant amount of time unpacking some of the number sense trajectory after a few of the different tasks you did that day.

Kyle Pearce: And I’m wondering if you can share a little bit of the background. What research were you basing some of that number sense trajectory off of? Do you have any particular resources that you could share here, for those who are interested? Anyone who’s in that pre K, to all the way into the later primary grades of counting in quantity, and just share some of your background in there. Because I thought that was fascinating, a lot of teachers felt like they learned a ton from it.

Graham Fletcher: Yeah.

Graham Fletcher: For me, my go to for all things mathematics, for quite some time, is I was a classroom teacher was leaning on the work of John Van de Walle for a lot of teaching students that are mathematics. I used that book a lot, but then as I realized, whenever he was referencing PK2 students, he kept on referencing Doug Clements and Julie Sarama.

Graham Fletcher: So, the number sense trajectory, for our K2 students, is really, primarily, based off the work of John Van de Walle, Doug Clements, Julie Sarama, and then also the common core standards that are here in the United States.

Graham Fletcher: And so, just taking those and just… Because, I think the learning objectives, and learning objectives whether you’re in Canada, wherever you are in the world, a lot times, they can get wordy, and it can be really hard to be consumable for a teacher. So, the goal was to take a word like, hierarchal inclusion, and… Let’s make sense of it. What does this mean?

Graham Fletcher: Because at the end of the day, when you’re sitting down next to a kid trying to assess, if you don’t know what you’re looking for, you just don’t know what you’re looking for. And in that case, you can’t, they’re thinking forward.

Kyle Pearce: Yeah, you nailed it. And I mean for me, not only do I need to make sense of words like hierarchical inclusion, I need to actually practice how to say them first, because that one was definitely a tongue twister for me.

Kyle Pearce: But I spent a lot of time as well, and I had a funny feeling Mr Van de Walle would pop in, I’m so happy that you shared Doug Clements and Julie Sarama. Their work is actually quite, quite fascinating, and I had an opportunity to hear Doug speak at NCTM, this pass go around as well. And not only is he amazing with the early number piece and the whole trajectory there, but he’s also a really, really animated presenter. So, anyone who’s listening, if you have the opportunity to go see Doug, definitely, definitely do it.

Kyle Pearce: And then I also want to pitch, Alex Lawson. If you don’t know what you’re looking for, then how are you actually going to assess it? She’s got a great resource, and she’s based out of Ontario here, called, What to Look For. So, that’s a great resource as well. And Graham, you may or may not have come across that one, but definitely one to look at.

Kyle Pearce: And for me, that John Van de Walle book is actually what my good friend Yvette Lehman and myself have really spent a lot of time digging into the chapter on proportional reasoning, from John Van de Walle’s book that you cited, teaching student center mathematics. And we have learned so much, and we’ve had to reread it, probably a good 50 times each. But we’ve learned so much from it, and it’s helped us to unpack so many different concepts.

Kyle Pearce: So, three really good resources there. So, folks, make sure you check out John Van de Walle’s work, Doug Clements, and Julie Sarama, and Alex Lawson’s, What to Look For. Definitely, definitely something cool to check out, for sure.

Jon Orr: Graham, we’re wrapping up here. It’s almost been an hour already.

Jon Orr: And we are wondering, where our listeners could learn more about you, and what kind of resources they could get their hands on from you?

Jon Orr: I know so many teachers have taken advantage of your progression videos, and your 3-act math tasks, you’ve been working with Christina Tondevold on a online course on fractions. You want to share a little bit about where everyone can find that kind of stuff?

Graham Fletcher: Yeah, for me, I guess the biggest space is really on my blog, where I share a lot of things that come to my brain. My brain’s been on overload here for the last little while, so it’s not been where I’ve been able to share a whole bunch. But I’ve been following along on Twitter.

Graham Fletcher: But things are really going to start ramping up here, again. There’s a lot of, I’d probably say I’m close to 20 tasks right now, that I’m going to be putting together over the next couple months, that have been sitting in the crock pot and it’s time to get them out to make room for some new ideas.

Graham Fletcher: So yeah, anything that I have, anything that I create, I just share it in that space, and if we can ever connect with listeners, at conferences or on my webpage there, it says where I’m going to be, and I’d just love to connect, get together, and let’s be math soulmates.

Jon Orr: Right, so that’s at GFletchy.com. And we’ll put all that in the show notes.

Kyle Pearce: Beautiful.

Kyle Pearce: Well, thank you so much Graham, it’s been a pleasure having you. Thanks for spending the time with us this evening. I know folks at home, the Math Moment Maker Community are thankful that you’ve taken this time, and I’m sure they are going to be looking you up on your blog, on Twitter at @GFletchy, and I’m sure they’re going to be reaching out to see if you are the math soulmate for them.

Graham Fletcher: Nice.

Kyle Pearce: Have a great night, my friend, we’ll talk to you soon.

Jon Orr: Take care.

Graham Fletcher: Appreciate it, thank you both, all the best, take care.

Kyle Pearce: We want to thank Graham again for spending some time with us to share his perspective on math education with us, and you, the Math Moment Maker Community. In order to ensure you don’t miss out on the new episodes that we release, every Monday morning, be sure to subscribe on iTunes, or on your favorite podcast platform.

Kyle Pearce: Also, if you like what you’re hearing, please share the podcast with a colleague, and help us reach an even wider audience, by leaving us a review on iTunes, just like Shaun Hershey did in this particular episode, at the beginning, and by tweeting us, at @MakeMathMoments on Twitter.

Jon Orr: Show notes and links to resources from this episode can be found at MakeMathMoments.com/Episode64. Again, that’s MakeMathMoments.com/Episode64.

Kyle Pearce: Well, until next time, I’m Kyle Pearce.

Jon Orr: And I’m John Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high fives for you.


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