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Teacher's Corner Podcast: Graham Fletcher and Tracy Zager

Posted by admin on Oct 28, 2019 11:04:15 AM

Our latest episode of Teacher's Corner features a fantastic conversation between Graham Fletcher and Tracy Zager about the development of the Fact Fluency Toolkit, available next year. Click the image to listen!

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Nate Butler:  This is Teacher's Corner from Stenhouse Publishers. I'm Nate Butler.

Graham Fletcher:  When we're building understanding, there needs to be both number knowledge, and there has to be strategy, and so what happens is eventually we hit a number knowledge plateau to where we can't build on our strategies, but then if you don't have the strategies, then you can't build new number knowledge.

Nate Butler:  That's Graham Fletcher, maths specialist and author of the Fact Fluency Toolkit scheduled for release in 2020. Graham's work with the math progressions and problem-based lessons has led him to present throughout North America and beyond, including the recent NCTM Regional Conference in Boston where editor and author Tracy Johnston Zager caught up with him for a great conversation about the thinking behind the project.

Tracy Zager:   I'm Tracy. I am one of the math editors at Stenhouse, and I'm here with my friend, Graham Fletcher.

Graham Fletcher:   Yeah, I'm super excited to be here. I guess we're here talking about something that's true to both of us and something that we're both super passionate about, so fact fluency.

Tracy Zager:  Fact fluency.

Graham Fletcher:  Yeah, I guess when you ask, "Hey, let's talk about this." It's nice to just sit here, chill, chat and just talk about some of the things that we've come across over the last couple of years.

Tracy Zager:  Totally, because Graham is the author, I'm the editor, and we're buds and have been for a while, so this project is a happy place for the two of us. This collaboration is so fun, and we wanted to let people know how it's going and what we're working on. Let's talk about what it is. What is the project?

Graham Fletcher:   Basically, it's going to be like a fluency kit, so one of the first things like why? Why do we need this fluency kit? I guess one of the things that we've been talking about for a long time is it doesn't matter what grade you're in. Both of us have been all over the place, and no matter the number of teachers that we talk about, it always comes back to fact fluency like, "Our kids just don't know their facts," and it doesn't matter if you're in second grade, or you're in sixth grade, or if you're in high school, we still have kids that are using the same counting on strategy that they were using back in the '80s, that they were using back in the '50s, but we keep doing the same thing.

Tracy Zager:  Totally.

Graham Fletcher:  It's definitely what can we do that's different that's going to help support this move?

Tracy Zager:   I think one thing we both have noticed is that it doesn't really matter what curriculum people are using. When I go present, people say, "Okay, that sounds great to me, but what do I do about my facts? The kids don't know their facts." I say, "Tell me what you're doing," and I hear a whole range of things people are doing from more prescriptive stuff to more inquiry-based stuff, and nobody feels like their kids are getting to a place of automaticity.

I think some people wonder like, "Should the kids get to a place of automaticity?" They're worried that it's a bad thing to talk about automaticity. I think you and I both agree like, "No, actually, they should, but how we get there is the key."

Graham Fletcher:   I think we have so many good resources out there, but they're all in different places, and so there's no coherence, and I think the true key to building automaticity is through coherence of understanding. One of the biggest misconceptions that I've encountered, I know we both have, is how to learn our facts. Most of us, as adults, we're taught to just memorize our facts.

I can even remember my dad saying something way back in the day where it's like you need to memorize harder, like for real. You just can't memorize harder. It's like, "Go faster. Go harder. Memorize harder." You can't do it. I would be that kid that would always be like with my multiplication facts I could never get past the threes and then with the Sunday I'd only get the [inaudible 00:03:42]. A lot of our students feel as if they're not good at math just because they don't have their facts, which is totally crashing to me, and I know you as well, especially when we want our kids to feel safe in classrooms.

Tracy Zager:  I think people haven't known what tools are there. There's a lot of talk about not using a stopwatch anymore to teach math facts.

Graham Fletcher:   Amen.

Tracy Zager:   That's what we had. We had stopwatches and flashcards and mad minutes. There's a lot of really good research saying, "We don't want do it that way," but then people are saying, "Okay, well, what do I do? I care about conceptual teaching, I care about sense-making. How can I teach facts?"

Graham Fletcher:   Yeah, I think one of the big changes for me was my daughter who's now in seventh grade. When she was in third grade, at the end of the year all the kids in third grade who knew their multiplication facts got a certificate at the end of the year. My daughter she gets it, and so she got her multiplication facts, and there was about eight of them, but then I'm thinking about the other 15 kids in her class who don't get the certificate, and now in third grade they think that they're not numerate like they don't understand numbers, so now I suck at math, and now they're done all because of a time test, which is crippling.

Tracy Zager:   Totally.

Graham Fletcher:  Some kids will be okay. Some kids can memorize their facts, but the majority of kids need to build it properly. Even with memory, if you forget your eight times seven like, "What do we do?" Fall back to rote counting and skip counting.

Tracy Zager:  When we first started talking about this project, I told Graham ... He gave an ignite talk a long time ago about the difference between knowing something from memory and memorizing it, and that's what came to mind for this kit. Can you explain what the difference is?

Graham Fletcher:   Yeah. I start thinking like when you hear the terms memorize and then from memory, yes, they both have the root word memory in there, but a lot of the times if kids ... When we all learned our facts, we learned them from memorization, which is just that rote process. When I look back now, and I think about it, we're asking six, seven, eight, nine-year-old boys and girls to memorize 100 facts. Just take a step back and think about that. That memorization it takes a lot of brain capacity in order to memorize, and it can be really tedious to some kids, but then how does that look different from memorization from memory?

Well, if we build fluency from memory, it's built through a learned experienced. It's where a student might go ahead and understand a strategy, but that strategy is used repeatedly over time to where it can appear as if it's memorization to so many on the outside, but what it really is it's rapid retrieval of a strategy that they've used over, and over, and over, and over again.

Tracy Zager:   Totally. So then it's hardwired, and they can recall it at will, but it's because they understand it. They learned it by understanding it.

Graham Fletcher:   Right, so then that student who doesn't know their eight times seven fact, if they forget it, they can go, "Well, I know that seven sevens is 49, and then I can just go ahead and add on another seven to that," because they have that flexibility. I think that whole idea from memory really gets at what the heart of fluency is. I think we could ask 20 people what the definition of fluency is, and we'll get like 75 definitions, right?

Tracy Zager:   Yeah, totally.

Graham Fletcher:   It's all out there, but when we go to what NCTM talks about and how they define it, it talks about looking at a student who's accurate, flexible and efficient as well.

Tracy Zager:   Right. Susan Jo Russell coined that way back, and it's still my favorite ... I think about it like a triangle. You got to have all three parts, and we just focus on that accuracy so much but not inefficiency. We care about speed, but that flexibility piece is ... You don't have understanding if you're not flexible with it.

Graham Fletcher: Absolutely. I think about all of the times when we're building understanding there needs to be both number knowledge, and there has to be strategy, and so what happens is eventually we hit a number knowledge plateau to where we can't build on our strategies, but then if you don't have the strategies, then you can't build new number knowledge.

Tracy Zager:    This is making me think about number talks because one thing we talked about earlier is those of us who I think would call ourselves ... I don't know what we call ourselves. Progressive in the math movement. I'm not talking politics.

Graham Fletcher:     I got you.

Tracy Zager:    I'm talking within math education. We want kids to understand and have agency and feel good and develop strong identities in math. When people say, "Okay, if I'm not supposed to do timed test, if I'm not supposed to do that mad minute anymore, what should I do?" The answer has kind of been number talks, and we both love number talks. But we talked early on about it's not enough to get the kids to automaticity. Why is that?

Graham Fletcher:   I even know. I was a third grade teacher for so many years. I think students will know the strategy, but what ends up happening is they only will ever use that strategy in number talks, so one of the things that I've realized over time is that as much as we both love number talks, number talks is a piece of getting to automaticity. It's one of those pillars.

 I would have kids that would be able to go ahead and know their make a 10 strategy, and they could use that with their number talks, but then second that we put it in some kind of contextualized situation they would completely forget, and I'd be like, "What are you doing? You didn't use your number talks strategy?" Well, the problem is that they never really build that to a point ... They never practice it in context, so it's just that naked number talks, and the strategies only ever live in number talk world. It doesn't live in math world.

Tracy Zager:   When we started brainstorming what should go in this kit, we wanted to keep that conceptual stuff from the number talks but to have enough practice for kids to get to a place from memory. Why don't you talk about some of the things that are going to go in the kit? What are the core pieces for kids?

Graham Fletcher:   One of the things that I'm most stoked about like super pumped about is number talk images. One of the things that I love with you and your Twitter feed is how you always just show these bright, beautiful pictures, and you and Pierre Tranchemontagne from Montreal with Number Talk Images, phenomenal website, those colors, and it's just so vibrant. Now kids don't get bogged down in numeral. They get bogged down in context because they can talk about what's there. It also comes back to Christopher Danielson's book with How Many? like, "Let's just show a picture, and let's just talk about what we see." Now numbers are not just numbers on a board. Numbers are now in the screen. They're in that image, and so now it's mathematized.

Instead of just having one single image, well, we know how number talks has a number string where there's a sequence of expressions. What I'm doing is creating these number talk images where it's a series of three to four pictures that actually build on one another. One of the examples that I think we both like is the lemonade.

Tracy Zager:   It's the lemonade. It's so pretty.

Graham Fletcher:  Yeah. It starts off to where there is one yellow and one pink glass of lemonade, and then the next image will be two yellows and two pink glasses of lemonade, and the next one will be three and three. They're using that context of lemonade to help build an understanding.

Tracy Zager:  We both are super passionate about access to math for kids, so one of the beautiful aspects of the images is there's no text and there's no language that's a barrier to access those pictures. Where I teach there are a lot of languages spoken, and the teachers they're really excited as they're trying this out. That the very first picture is just so simple, and you can start with, "What do you notice, and what are you wondering? What are these things?" And come up with the words for kids who might not know what lemonade is or whatever the context is.

We were really careful to pick accessible context for everybody, but you might have that conversation and build a vocabulary before there's anything formal or symbolic introduced. What are some of the other contexts? We have lemonade.

Graham Fletcher:  We have marbles. One of my favorites as well is apples. Just seeing green and red apples together on an apple mounting thing that you'd see in the grocery store. They're just so bright that kids they want to talk about them.

Tracy Zager:   That one is in the doubles plus one strategy, and it's so beautiful to see. As the number of apples grows, you see this thing about when it's a double the rows are filled, and when it's a double plus one, there's one sticking out. I just know it's going to lead to a great conversation about evens and odds as part of doubles plus one. That's so exciting to me about where that might go for teachers.

Graham Fletcher:     Yeah, and I think that's a really important piece. That's always a good reminder. A lot of the times we dive into the math per se without ever making sure that every kid has access to the math before we even start talking about it, so having the images there and say, "Let's just talk about what we see, and then now once we have an understanding of what a marble is," because we have so many kids that are from all over the place, and maybe they've never seen a marble before, but now if we show them a picture of a marble, the word marble no longer becomes a language barrier for them.

Tracy Zager:   That's right.

Graham Fletcher:   And they're picturing those images. You'd have the number talk images, but then you also have an anchor problem, so we'd launch each week. The way that the kids actually worked out is that we're going to have an addition and subtraction kit, and then we're also going to have a multiplication and division kit. For each of the strategies, there's going to be three different contexts. Within each context will be the theme for a week, and with that there'll be the number talk images that we were just talking about but then also an anchor problem, so a very rich problem.

But now when kids are working through this anchor problem what they'll be able to do is go back to the number string images, and they're now picturing those glasses of lemonade, which is awesome, because so many times, you know as well as I do and I think for everybody out there, we drop word problems on kids, and the first thing that kids do is they go right to the numbers because they can't relate to the context. Well, now that we've primed the pump with this number talk image, now kids are picturing those glasses of lemonade, or they're picturing the apples, or they're picturing the marbles as they're working through the context.

 And then one of the things that I'm really excited about with the kit is the contextualized purposeful practice to where ... I guess CGI has been an absolute game-changer for me.

Tracy Zager: That's cognitively guided instruction. We love the book Children's Mathematics, first or the second edition, where they talk about the problem types, and their problem types are baked right into the common core standards and others standards so that we should be asking kids all the different problem types like a joining problem where we don't know the total at the end, or a joining problem where we don't know what we started with, but we know the change. I'm thinking about folks listening that might have heard different words for it, but those are the problem types that we're talking about.

Graham Fletcher:  Right. We're really good as teachers asking A plus B equals that unknown number, but we're not very good at asking will the unknown number plus A equals B but having those. Now what we'll do is, say, if our theme is doubles for the week, the number talk image string will go to the theme of lemonade, and then the anchor problem goes to the theme of lemonade, and then the entire problem type table from the cognitively guided instruction.

Every one of those problems in there is grounded in the context of lemonade, so you can use those throughout the week as just that purposeful practice to where now kids are taking the number string, but now they're actually practicing that double strategy in context, which is really missing. I think that's been a big missing piece in many of the resources that are out there, which I think really created a big need for this.

Tracy Zager:   Totally. Well, and you're so thoughtful. I mean, this is why I knew Graham would be amazing with this project because he's so great with multimedia and context, like if you've done any of the three-act tasks. You're just so creative at thinking about what situation might surface a particular piece of math. I just want to make sure it's clear about what's a strategy and what's a context. If the strategy is like making 10, that's a strategy we really want kids to have. You've chosen three contexts to photograph, right?

Graham Fletcher:   Yeah.

Tracy Zager:  Do I have this right?

Graham Fletcher: Yeah.

Tracy Zager:   So, that there are three unique times where we have a whole week's worth of stuff around making 10 with three totally different contexts, so we get to come back to it all year long. We get to interleave that practice and have a variety of contexts. It's not just lemonade for doubles. It's also a whole bunch of other things. We've got eggs, and we've got markers, and we've got all these other things that Graham has been filming, seashells, so that there's a whole variety of real images that kids can connect to for each strategy.

Graham Fletcher:  Absolutely. Even for like pizza, the example for pizza is I've cut up two pizzas both into 10 slices. I leave one pizza with nine slices in it, and on the other pizza there's six slices of pizza, so now when we say how many pieces of pizza are there, well, kids will say, "Well, I take one slice from the six slice. Give it to the nine slice to make a whole pizza, and I've got 10 and some more now."

Tracy Zager:   Right, which is such a great way to build that 10 number structure.

Graham Fletcher:  Unitizing.

Tracy Zager: Yeah.

Graham Fletcher: 10 pieces make a whole pizza.

Tracy Zager:   Totally.

Graham Fletcher:   We just have way too many kids that are leaving kindergarten, first grade and second grade without this understanding of unitizing, which is why they have a really difficult time applying that make a 10 strategy or pretend a 10 strategy.

Tracy Zager:   Totally.

Graham Fletcher:   I'm really pumped about the contextualized problem types, but then also somewhere in the middle of the week what we do is I strip away the images of the lemonade, and now I replace the lemonade with like red and yellow counters, so now kids when they look at red and yellow counters they're going to image those red and yellow counters as the cups of lemonade that they saw on Monday, but then on Friday instead of using images now, now we go to a number string.

What's beautiful about this and what's great, as I start messing around with kids and seeing this, is we start with the glasses of lemonade on Monday. On Wednesday we represent the lemonade with counters, and then on Friday we represent it with numbers, and so we're gradually stripping away the context so that when kids see numbers they're actually really still seeing those lemonade.

Tracy Zager:  We're making all those chances for connection from the symbolic to the context, but also kids are building a much more robust mental set of images around what's going on.

Graham Fletcher: Yeah, and then just the application of the same understanding in multiple different venues, I guess, just allows for that flexibility that memorization doesn't allow for.

Tracy Zager:    Totally. Also, we keep mixing it up. To be clear, if a kid used a different strategy ... I don't know. I can't think of ... That doesn't seem like one where they would. Often with make a 10 if it's-

Graham Fletcher:    Like nine plus nine.

Tracy Zager:     ... nine plus nine, they might make a 10, or they might think of that as a double. In this kit both of those are great.

Graham Fletcher:  Absolutely.

Tracy Zager:   It's not like, "This is doubles week. You're only allowed to double."

Graham Fletcher:  Yeah, and I think that's a really big piece because a lot of the times ... Let me be crystal clear here. I'm super guilty of this as well. I'm like, "Today we're going to work on our double strategies," and then everybody has to do doubles, and it's almost like we brainwash kids to see doubles, but it's us owning the doubles understanding, and it's never them having ownership of it, so there's minimal retention there as kids are working through it. I think that's definitely a really big, big piece about it. As much as you might want to see doubles, we should never tell kids what they can't see.

Tracy Zager:  Totally.

Graham Fletcher:  I think that's a big piece.

Tracy Zager:   Totally. We want to just keep building bridges from their strengths to other new concepts. Some kids really love doubles, and other kids they want to go to those tens faster, and both of those are correct and having them discuss, "Well, I did it this way. Well, I did it that way." You can have really productive relationship building.

Graham Fletcher:  Absolutely. And then what's nice about it is as kids are working through all this, sometimes their problem-solving here. They're looking at images, but then there's also a game for every single week.

Tracy Zager:   That's amazing.

Graham Fletcher:     Kids love games, right?

Tracy Zager:    Yes.

Graham Fletcher:  ow we have a doubles game, so the kids will work through the anchor problem. They'll work through the number image string. They'll work through the number image string with tools. Then they'll work through the CGI problem type tables, the contextualize problems, and then they'll do the numbers string, and then you have a game. It's that game that you could even send home with your kids to where now like, "What's homework?" Games.

Tracy Zager:  These are real games, by the way. It's such a pet peeve when we call a worksheet a game. We're like, "Oh, it's supposed to be fun," but it's not actually strategic, and the games that I've been reading that Graham has been making are genuinely fun. I have to tell you a story. I didn't even tell you. Cassie saw the doubles games, and it's this board with all these different numbers on it, and you're trying to get four in a row or three in a row.

Graham Fletcher:  Four in a row.

Tracy Zager:   Four in a row, so you have to be strategic, and you roll and you can double the number or keep the number.

Graham Fletcher:  You can double the number. You can roll. Say you roll like a 10, you can either go doubles 10, you can go doubles plus one, doubles minus one, doubles plus two, or doubles minus two depending on what number you want to cover on the board.

Tracy Zager: Totally. In one of these games there was a number on the board that wouldn't have been possible to roll, and my friend Cassie [inaudible 00:21:44] she said, "Why would that be on the board? You can't get that." I was like, "Right, because it's actually a game. It's not just a worksheet that you're filling out like coloring in four in a row." You're like, "Oh, the 17 or whatever it was, was going to be hard to get. I'm going to try this part of the board," so it's actually engaging for the kids. There's rote-thinking going on.

Graham Fletcher:   Yeah. One of the things that I've really tried to be intentional about when creating the games is I am not ... I know you did a talk a while back in Boston, and one of the things you talked about was student choice. I think student choice needs to be applicable multiple different things. I'm going to just go ahead and say. I really hate the games where kids just roll and move. Kids don't need to play Snakes and Ladders, but we have so many Snakes and Ladder like games like, "Roll and do this."

 What I've tried to do is kids roll, but then they have to apply a strategy to it, so there always is a choice built within the game to where now there's a strategy, so it's not just roll and do this with a rote thought.

Tracy Zager:  Roll and record.

Graham Fletcher:  Yeah, roll and record games. We want them to roll, and then we want them to have to apply a strategy. And then what that does, which I really like, is it opens up as the questioner to say, "Huh, can you tell me why you did that?" A lot of the times we don't ever allow ourselves the opportunity to climb into student thinking when they're playing games, but it's very telling.

Tracy Zager:    One thing I love about the games is they're introduced within the strategy of the week that we're working on, but those games can stay open all year, and so they make this great opportunity for mixed practice because one thing Graham and I have talked about is we tend as teachers to want to say, "Right now we're working on doubles plus one," and everything is doubles plus one, and then we drop it, and then we don't do it again for months, and months and months, and the kids forget it, and when they see it in a while they don't do it.

We're looking for mixed review and things to circle back around all the time so that the kids aren't just doing it the way they think the teacher wants them to because it's written on like, "Students will be able to double." You know what I mean?

Graham Fletcher:   Right.

Tracy Zager:  We tell them which strategy to use, we take all the fun away.

Graham Fletcher:  Absolutely.

Tracy Zager:  By keeping those games alive and reentering some of the games throughout the year, kids will have to keep on their toes, which is how they actually build that retrieval if they have to think about it harder.

Graham Fletcher:   I think that's an important piece to consider because a lot of the times no matter what resource you're looking it, and this is where I think sometimes we need to be a wise consumer with the resources that we're bringing into our classroom. You have one lesson for doubles, and then the next day you go to doubles plus one, and then the next day you go to make a 10.

Tracy Zager:     Whiplash.

Graham Fletcher:   Yeah. Kids they're mucking about with all these strategies in their head, and they never make sense of any of them. It can never be like a one-and-done. My wife has to tell me things like 40 times for me to automatize her thinking.

Tracy Zager:  Poor Whitney.

Graham Fletcher:    Yeah, absolutely. I think one of the things that's really nice, and we went back and forth with this conversation, is do we want to keep those three contexts for doubles? Do we want to do them back to back to back? What we're ending up doing then is we're going to do it spiraling, and so we're not expecting ... And now when I look back at it would have been nidicolous to go three weeks of just doubles. As much as-

Tracy Zager:  So, it'll be interleaved. We'll kind of scramble the strategy so that they keep coming back around, and they keep shifting, and the kids keep-

Graham Fletcher:   Spiraling.

Tracy Zager:   ... having to think about it as it goes.

Graham Fletcher:   Absolutely.

Tracy Zager: And there'll be spaced also. If all the doubles are at one time ... I read this book, Make It Stick. I know some people have read it. It's so interesting. They talk about M-A-S-S-E-D like massed practice versus spaced practice. It's really important to space it out so that you have to kind of almost forget a little and come back to it because if you just cram, it's like in college. We would cram for the test in a really short amount of time and then forget it.

 But if you space out that practice, if you studied better than I did in college, you would get to finals and not have to cram much because you had been really laying it down, so we're going to be spacing and interleaving. One thing I love about that we owe mobility in our district, and so I don't want a kid to have missed a strategy if they join school in November. You know what I mean? We'll becoming back around all the time. If kids are coming and going, that's okay. They'll get opportunities.

Graham Fletcher:    I guess we could look at it as kind of like an automaticity muscle. If you're working out at the gym, you don't go, and you just don't go pump iron one time, and you've got bulging biceps.

Tracy Zager:    I tried that. It's not working yet.

Graham Fletcher:  Well done. Nice play. What I think then what you're doing is you're stretching them, but then you've got to give it rest. I mean, you stretch it a little bit more, and then you give it rest. Each time that we come back and we're spiraling we stretch their automaticity muscle just a little bit more, a little bit further to the place to where they're Arnold Schwarzenegger, and they're just bulging with muscle.

Tracy Zager:   Totally. One thing we've been talking about is how a teacher ... Definitely, teachers are going to use this. It's definitely laid out. If you're a first grade teacher, and if you want to use the addition and subtraction kit, you can be using it every week really all year. How many days a week? How much time do you think? What are you thinking?

Graham Fletcher: As we start playing around with it and field-testing it, I think what we found is that I would hate to go ahead and say it has to be done this way because no one resource knows your students that you're working with better than you yourself. You're the expert of your kids. What we want to try and do is leave as much flexibility and autonomy at the building level, at the school level, in the classroom level, at the intervention level, however you want to use it, so I really see the scalability of this. It could be used in first grade, and you could do a little bit every single day.

                                                                           If you're in fourth or fifth grade, maybe this is something that you do one day. You have a day where you're building that purposeful fluency, but then also in middle school we've talked to so many middle school teachers, and it's the same thing in high school. But I think what we've done to not be really intentional about this is that it's very grade-neutral, so it's not cute for first grade.

Tracy Zager:                       28:07                    No, we will not be designing this with crayon and googly eyes.

Graham Fletcher:             28:10                    No.

Tracy Zager:  Middle school teachers will say, "I cannot teach my content standards because the kids lose track of the problem. They have to go back and re-derive five times four every time." They're like, "What can I do?" There'll be a short effective intervention to get kids up to speed on their facts. They really need them. We didn't want to design something that would make that sixth grader feel like they're put in baby math. You know what I mean? That's very demeaning.

  We wanted something that would ... As we're designing the project, we're thinking about how to make it accessible for kids across grades so that the pictures are warm and inviting for those first graders but also kids of different ages or who've had interrupted schooling. I think intervention teachers ... A first grade teacher might use it for 38 weeks, but an intervention teacher might do it quick like six week intensive in small groups, which is part of one of the things.

  We could talk about some of the pieces of the kit. These beautiful images are going to be projectable so that everyone can see it in a large group, but we also are going to make a tabletop flip display chart. Those are all the words I can think to describe it so that you could pull a small group wherever you are, and they could all see the image, and you could talk about it there, so we're thinking a lot about usability. We want it to be user-friendly.

Graham Fletcher:    Like a little tent where they can flip the images over, because we know sometimes if you're an intervention teacher, you get stuck in a room that doesn't have a projector.

Tracy Zager:   Totally, or the hallway.

Graham Fletcher:  Or the hallway. That's your superpower. You do what you have to do wherever you have to do it, right?

Tracy Zager:  Right.

Graham Fletcher:We don't want anyone to say, "Well, I can't do that because." I'm trying hard to make sure that there is no because.

Tracy Zager:   Totally.

Graham Fletcher:   As much as we want to make learning accessible to kids, I'm trying to make this as accessible to kids and as many teachers as possible as well.

Tracy Zager:     I could see teachers using this in push in situation in a small group in the classroom, in a pull out situation. I could see people in summer school, in tutoring, at home. There's so many different ways people might use it. As we write the user's guide, which Graham is working on right now, he's thinking about there might be some example schedules like, "If you have this much time, you could do this. If you have that much time, you could do this." I think we'll try to generate some ideas, but none of those will be rigid because we both believe so much in teachers being decision makers.

Graham Fletcher:    Absolutely.

Tracy Zager:  Some suggested pacing guides maybe with some flexibility, but our field test teachers right now are saying, "Wow, it's working well. What are you trying? Are you finding it's better to start with the number talk image, or is it better to start with the contextualized problem? Try both ways. Try different open questions." We're getting great feedback from them on how they're using it. They're really excited.

Graham Fletcher: Yeah. We're basically finding all the glitches, screwing up, seeing what works, seeing what doesn't work. That way by the time that it gets to you we can say, "Listen, we truly wholeheartedly believe that this is what works, and it's up to you, but you still have that flexibility and the autonomy to do however you want to do it."

Tracy Zager:    We've talked a little bit about the student facing materials. We got the images that they'll see. We have anything you would need for the games. We'll have whatever dice or cards you need, the game boards and all the problems and all that stuff, but there's also a whole teacher facing component, so there's going to be videos, user's guides, help with assessment, so let's talk about some of that.

Graham Fletcher:   Yeah. I think about a lot of the times we get so many resources, but the problem is it's the support, so a lot of the times the support resources that come along with what we're trying to put into our classroom are either too wordy. It's not enough. It's not clear enough. I am writing this as if I would want to read it as well, so there's not going to be a whole lot of print. My goal is there will be a user guide kind of how to use it, but then the big piece for me is I'm going to go and capture videos.

One of the things that I loved about this when we were teaming it up, and I'm super thankful to you and the Stenhouse team, is I don't want to go and have some basically fixed video. I want it to be as raw as possible, so if a kid's picking his nose in the video, we're not editing that out-

Tracy Zager:  No, we're not.

Graham Fletcher:   ... because that's what happens in a first grade classroom.

Tracy Zager: Totally.

Graham Fletcher:   It's going to be-

Tracy Zager:   Hands down the pants, man. That's what happens in a first grade classroom.

Graham Fletcher: Absolutely. That's like a go-to for sure. But that's it. Here's the thing, you don't have five hours to read a user manual, so I'm not going to write a five hour user manual. You don't have 20 minutes to sit down and watch a video. You have three minutes to watch a video as you're leaving basketball practice going to gymnastics. I'm trying to create as much to where it can be consumable by you on your end. You're like, "Okay, well, what does a number talk image lesson look like?" Boom, pop open the video, check it out, "Okay, great, I've seen Graham do it. Now I can go ahead and do that."

Basically, what we're trying to do is lay just the supports that you need to just basically take this thing and go with it. I'm hoping that you're not going to be selfish once you do try it. You will come back and share with us because we're super excited about this.

Tracy Zager: Yeah, we've talked about ... Graham's going to have videos where he teaches how to play all the games. You might watch that video and then teach your kids the way you want how to play the games in a small group, or in a big group or however you want to do it, or you might just show the video and say, "Mr. Fletcher is going to teach us how to play this game now," and just a quick two minute video is enough to get the kids started on the game.

Graham Fletcher:  Absolutely. You know what, whenever possible I might just step aside and shut up and let kids talk and let kids teach kids. Imagine that kids teaching kids how to play a game. As teachers, sometimes we just need to set it up and just get out of the way, and kids will do a lot of the driving of their own learning.

Tracy Zager: Do you see why I have the most fun job in the world? Look at that. I love that idea. Let's do that.

Graham Fletcher:  Okay. There's something that we just got to. It's going to be kids teaching kids how to play the game. I just need to shut my fat mouth and let six and seven-year-olds go ahead and do it because-

Tracy Zager: Totally.

Graham Fletcher:     ... that's what we want. That's it.

Tracy Zager:   We want that agency. We want kids to feel ... We're contrasting this with how humiliating it was with the mad minute or the march across the room. Christopher has told me this story of-

Graham Fletcher:   Christopher Danielson.

Tracy Zager:  Christopher Danielson. There's a clothespin across his classroom, and your name was supposed to move across the clothespin as you mastered your facts, and he got like 30% on the way there and never got all the way across because of the way that they were assessing the facts. The man has PhD in mathematics. It never slowed him down, but he likes to think about relationships, and he didn't care about quick free call, and so he didn't do well on that teacher's test. Thankfully, his identity remained intact, but lots of kids get crashed by that. We're trying to do the opposite of that everywhere we can, so I love kids teaching kids in the video. That's awesome.

Graham Fletcher:   Yeah, and I think that's a big piece. I think one of the nice things that will also happen is as kids are playing, it comes back to that opportunity to engage kids in questions. To be honest, if I screw up in a lesson, I'm not going to delete that, but what I'm going to do is then I'll follow it up with like a metacognitive thought after that, "You know what, I'm leaving this video as it is because I want to show you where I screwed up, so you don't have to make the same screw up."

Tracy Zager:   Totally.

Graham Fletcher:   I think one of the biggest things that I've learned is being vulnerable has really allowed me to grow. Basically, you tell me a lot of things that I do wrong, but that's the thing though.

Tracy Zager: But I say it in a nice way.

Graham Fletcher:    You do say it in a nice way. But I think about it like I would much rather screw up publicly in front of adults than screw up privately in front of kids. I think for too long we've been okay screwing up in front of kids, and we don't make ourselves vulnerable enough to learn in front of our peers. I think that's part of the community that we're of now like, "Let's screw up before we get to kids." If I screw up, I'm not going to delete it. We're not going to run the video 17 times, so it looks super polished because you know well as I do you see super contrived videos, and you're like, "That's not how it really happens."

Tracy Zager:     Totally.

Graham Fletcher:    These are not going to be contrived. They're going to be raw. They're going to be ruthless, but it's what really happens in a classroom, and I think that's how we all learn and grow for sure.

Tracy Zager:  Yeah, that's awesome. That makes me so happy.

Graham Fletcher:  Who knows what we have? We'll start videotaping here, I guess, in the next month and a half. Start putting together all the teacher resources and supports and things like that.

Tracy Zager:  Yeah, and we're like deep in the logistics of ... Even the other day the production team said, "Okay, what kind of container are you thinking for this whole thing?" Because there's a lot of multimedia, there's videos, there's the table display. What we think we're going to do for the game boards is we'll have a nice permanent game board that's durable for teachers, and then each person will have a unique access code where they can get the PDFs, and they can print multiple copies, so kids can mark up them up if it's a game board where they write on.

We're just thinking a lot about ... It's so fun to think about what would be everything a teacher would need to teach addition and subtraction. One thing we talk about a lot is curriculum, so people have this whole range of curriculum. Some curriculum has fluency practice as like a separate thing, 12 minutes a day or whatever fluency practice. Some it's supposed to be emerging. We're hoping to design something. I mean, we are designing something.

Graham Fletcher:    We are. We're knees-deep in the work. There's no turning back.

Tracy Zager:   It doesn't matter what curriculum you have. You might swap out a fluency thing, but also thinking about those CGI problems, this is your contents. Also, you're teaching addition and subtraction, conceptual understanding. It's going to be something that ... I think teachers will be like, "I have time for this. This is really so many of the things that I need to teach." We're going to think about how to make like ... I think what we'll do is we'll look at some of the common curricula that's out there, and we'll say, "If you're using this, you might want to swap it in here." We'll make crosswalk document for folks.

Graham Fletcher:    Absolutely.

Tracy Zager:  We haven't even talked about that too much. It was something that came up at editorial last week. We were talking. I think teachers will need that. We're also hoping to equip teachers to have the research base so that they can prove why these materials are research supported, and so they can use them in title and intervention situations. We're just trying to think about all the work we can do so that teachers don't have to.

Graham Fletcher:   Basically, my goal is for it to be like the one-stop shop. You open it up, and what will happen then is when you open this up you're going to be like, "Well, my resource doesn't do this." And then what we're going to find is that there's a lot of holes in terms of how we build fluency. As I said, there's lots of good things out there, but in terms of having it all in one place with fresh ideas to the context.

What I love about this the most is we're building fluency through context, and for too often fluency has just been a bunch of naked numbers on a card or on paper, but nowhere in the world do you see a five floating around. You see five apples. You see these things. Why are we trying to have kids build understanding with just number when there's number everywhere around us? And it doesn't look like a numeral.

Tracy Zager:  We're already starting to cook up ideas for the multiplication division one of like things that naturally come in arrays and things that naturally come in groups, and how will we be ... It's going to be so much fun to dream up that one.

Graham Fletcher:   I think that's funny because you've been really bugging me for a long time to write a book.

Tracy Zager:  Which you loved. You loved that.

Graham Fletcher:  Yeah, I guess that's what editors do. I've always said from day one. I'm like, "T, I'm not writing a book." I am the guy that skipped typing class in high school, and I suck at typing, and so it would take me years. This would be a lifelong project.

Tracy Zager:  Two finger typing.

Graham Fletcher:  I can throw a third finger in there sometimes. The big thing with that is I said like, "I'm a project guy. I like creating. I need the creative juices going," and I think this really just hits the nail on the head.

Tracy Zager:   It plays to all your strengths. It's such a good match for you.

Graham Fletcher:   We're having fun. See, here we are laughing and talking about fact fluency. Normally, that's tears for a lot of people. I'm super excited about it.

Tracy Zager:   Normal people don't talk like this?

Graham Fletcher: I don't think so. Weird is normal in our world.

Tracy Zager:   That's totally true.

Graham Fletcher:   I think one of the big pieces where I think we also miss out that I'm excited about is the whole idea of assessment.

Graham Fletcher:  Yeah, I think it comes back to the story of my daughter, Emma. These time tests they're a crippler. I know Jo Boaler has done so much work on how time tests and mad math minute build math anxiety in our kids. At the end of the day, we shouldn't have kids crying in math class. That, to me, is the most mortifying thing in the world. I'll be honest. My first couple of years of teaching I did it. If I could just go back and hug and love on those kids and say, "I'm sorry. I screwed you up so much."

Tracy Zager:   I feel just the same. Cathy Seeley wrote a great essay called Faster Isn't Smarter, and she talks about sitting next to this kid who breaks the pencil tips off during the mad minute and can't get it all done in time, but then later on, in a word problem, totally knows all their facts. It's one of the things that's frustrating about those time fact test is we don't get quality assessment because of the anxiety level. We don't even know what kids know. We think it's an assessment, but it's not because they choke.

 My younger daughter says like, "Everything just goes blank in my head, and I'm just looking at the clock. I can't think about math at all." We are thinking a lot in this kit about how will you know what facts your kids know without that kind of stress?

Graham Fletcher:  Absolutely. I think anyone who knows your work and my work is we are obsessed with student thinking.

Tracy Zager:  Totally.

Graham Fletcher:  The only way to move student thinking forward is to look at what they can do like looking at their thinking. Once you find out where their thinking is, it makes it so much easier to move their thinking forward, but too often it's like throwing spaghetti to a wall just hoping that something sticks, but we want to be super intentional and super purposeful. You're not going to learn from a number being written on a paper what a kid's thinking.

 With the assessment, I'm creating an interview. But here's the thing, you have 26, 27 kids in your class. You don't have a time to sit down there with every kid for 15 minutes doing an interview in a real world, so for me one of the things that I want to try and do is I want to be able to sit down with a kid and know within two minutes how they're doing on their fluency through five, how they're doing on their fluency through 10, and how they're doing on their fluency through 20.

   I guess that's another thing that we also have is there's a lot of differentiation built into within the kit, which is solid, because let's be honest. If you teach fourth grade, you don't teach fourth grade. You teach 10-year-olds who function at a kindergarten through eighth grade level, so it becomes really important to just sit down and listen to a student thinking so that you can move it forward. It's going to be a quick, little interview that you can sit down just maybe putting two addition facts in front of them and just saying, "Tell me what this would be."

Tracy Zager:  Totally.

Graham Fletcher:   And so there's no pressure. You know what, sometimes some kids don't talk to an adult at home, and they don't talk to an adult at school. They get spoken to from adults, but sometimes when we can sit down one-to-one with a kid, I always think about some of the pictures that I've seen of you with your book where you're just sitting down and you're listening to kids. I think too often we do too much talking and not enough listening.

Tracy Zager: Absolutely. But I love that we're making it practical. I was just giving a talk about workshop, and in it Nancy [Attwell 00:44:18] talks about how her knees gave out after a while of crouching down next to kids, so she had like a kindergartner sized plastic chair that was really light, and she would carry it around the room, and she'd pop a squat next to kids' desks and say, "How is it going with the writing?" I think about that kind of level of confidence of a minute, two minutes you ask a few questions.

 Maybe they come to you, or maybe you go to them and you circulate around and you listen to six kids that day or something like that, and it takes you literally eight minutes to do all of those. You've checked in with kids, and you're getting good data, and you know where they are, but it's actually part of the learning and the work. It's not extra, and it gives that information that we need without extra worksheets. Oh my God. We assess through worksheets in math facts, and we've got to move away from that.

Graham Fletcher:   I found the more that I talk to kids, the more addicted I become to talking to kids. It's beautiful just listening to their thinking, and so that's what we really want to do, but let's be honest. If you have a class of 27 kids, it's hard to talk to every single kid. There's a lot of good resources out there that assess, but what it does is it requires that you sit down for like half an hour with each kid.

 Now, you're going to learn a lot from that, but realistically, that just turns a lot of teachers off and say, "I can't do that," so how do we make accessing student thinking more attainable for us as teachers? I think that's our goal.

Tracy Zager:  Then it's genuinely formative assessment. You're listening to kids, and it's guiding your instruction, and it's building the relationships with the kids. It brings joy to your life and connection. That's the money right there.

Graham Fletcher:  That's it.

Tracy Zager:   That's it.

Graham Fletcher: Find out what they're thinking, so you can move it forward for sure.

Tracy Zager:   Totally.

Graham Fletcher: It's definitely exciting. One of the things that I'm pumped about, I guess, the kit's going to be ready in 2020, so we're shooting for next fall like August or September of 2020, and then we're going to-

Tracy Zager:   We're going as fast as we can. I mean, I know people want this as fast as possible, so we're hoping to get it in production by the end of the year this year. There are all these pieces to manufacture, but we'll be going as [inaudible 00:46:26] as we can. We know people want to start the year with it, so we will try as hard as we can to get it for the start of the year. When you were in Atlanta, you started in, what, July?

Graham Fletcher:    Almost. Pre-planning starts the second last week in July. We start the first week in August.

Tracy Zager:   Yeah, that's tough. But we'll try our hardest, and then while that's in production, we'll be working on multiplication and division. It'll follow during the school year.

Graham Fletcher:   And then that will definitely follow up within the school year, but my goal is that you might not have to wait until next year, so my goal is I'm going to start dripping out some content. If you're anything like me, if you see something and you want it, and you can't wait. But I'm going to go ahead and create some other ones, and I'm going to throw it out there so that you can just even go double into it yourself and give it a whirl. I think that's it. You can get a taste, and then you're going to want more for sure, but we're super excited because whether it's addition, subtraction, multiplication, division, some things got to change, but we keep doing the same thing. That part's tough.

Tracy Zager:     When I think about the impact this project is going to have, it blows my mind. I can't think of anything we could do that can make such a measurable difference in kids' lives in math class. You talked about Boaler and Fluency Without Fear. I did a lot of research on math anxiety, and it comes up like 40% of the time. People when they have math anxiety they talk about math facts.

For all those kids, if we can have this be a positive, it'll go throughout the year. It'll be varied, it'll be engaging, it'll be interesting. There'll be learning. There'll be conceptual. There'll be getting enough practice to get to that automaticity without pain.

Graham Fletcher:   Absolutely.

Tracy Zager:    I'm just really excited about the potential for what we're doing together.

Graham Fletcher:  Yeah, it's nice when you get to team up with your best friend and start knocking your heads together and winning.

Tracy Zager: I'm so glad I kept nagging you, buddy.

Graham Fletcher:   Yeah, I'm glad you didn't make me write a book.

Tracy Zager:    No, I never would. It'll be user's guide. We'll call it the user's guide.

Graham Fletcher:  Absolutely. I can do that. I can write a user's guide. That's definitely attainable for sure.

Tracy Zager:     Yeah, with lots of video. It'll be good.

Graham Fletcher:    Nice.

Tracy Zager:       Thanks for hanging out.

Graham Fletcher:   Yeah, absolutely. I'm super excited. Thanks for the opportunity to you and the whole Stenhouse team. It's going better than what I could have ever imagined. For us to be just sitting down at a table chatting two years ago, and then, boom, look what we got right now. I think we're both super proud of the work, and we just can't wait to get it out in front of kids and teachers.

Nate Butler:                       48:59                    And that's Graham. The Fact Fluency Toolkit is on the way for 2020. Until then, check out his site, which is loaded with materials for teachers at Graham is also active on Twitter @gfletchy, G-F-L-E-T-C-H-Y. We'd love to hear what you think. Please send your questions and comments to

                                                                           Next time on Teacher's Corner Gravity Goldberg and Renee Houser go deep with the teacher's toolkit for independent reading and all in one conferring system to help teachers in grades three, four and five. Thanks for listening.


Topics: Math, #StenhouseMath