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Math Teacher Lounge
Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer)dive deep, with guests, into the math and educational topics you care about. Interact with us on Twitter (@mtlshow) or join our Facebook group (facebook.com/groups/mathteacherlounge) for more content.
Math Teacher Lounge
S6-E06: Nurturing fluency through student strengths
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Join us for Episode 6, where we discuss how to take an asset-based approach to building math fluency with John W. Staley, Ph.D., who has spent decades in math classrooms. In this episode Dr. Staley shares his experiences and research to provide strategies on how to utilize student strengths to encourage growth.
For more from Dr. Staley, check out the following resources:
- Follow John on X at @JStaley06.
- Learn more from John by checking out his NCTM articles.
- Read John’s book, High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice.
- Read John’s book, Middle School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice.
We have to look at mathematics as a story that we tell students across the grades K to 12. And what we are all is the conveyors of a chapter in this progression of the story.
Speaker 2Welcome back folks to Math Teacher Lounge. I'm one of your co-hosts, Dan Meyer,
Speaker 3And I'm your other co-host, Bethany Lockhart Johnson .
Speaker 2And if you folks notice a little extra charisma or vibe between Bethany and I this recording, it's because Bethany and I got to hang out in person, a real rare occurrence for us. Uh , yeah . Bethany was up here with , uh, fam and, and my home. And , uh, yeah. Bethany , what was your , uh, what was your take on the , uh, on the whole situation? You know, I gimme a thumbs up, thumbs down. How was it neat enough for you? You know , talk to us about it. <laugh>
Speaker 3On the Meyer household. Well, you know, anytime I get to see you, Dan, which is usually at conferences, this was like a whole nother level. You invited me into your home to hang out with your wonderful family. Uh , the only thing missing was that I really did, like, I was serious. I told you this beforehand. I really did think I was gonna get to play some of those like fluency math games with your kiddos. Yeah. Yeah. And that did not happen. In fact, I think once I gave them some Halloween stickers, they were done. They were like, but you know. Yeah . You said, actually, could you stop calling them math games? Is I believe what you told me, <laugh>.
Speaker 2You <laugh> , yeah. You, you served your purpose in delivering a fantastic little treat for them. And then they were off scurrying into their, you know, their rabbit's den or whatever to go GNA on it. And , uh, yeah. And we had, we had, we had, we had aspirations for like, doing some social content, you know, to try to make our producer Martin happy. Yes . You know, we had some reels ideas. I thought I was gonna have, you know, figure out all my fluency stuff. 'cause I had a , you know, KA legit K five specialist in my home. So I was gonna put Bethany to work with my kids. But really, we just like , had a, had a good time just hanging out, talking, talking shop, talking family, that kind of thing. It was a real treat to hang out with you. Hey ,
Speaker 3Thanks. And if I come to your home and you immediately present me with a fall cocktail and then feed me an amazing dinner, I probably will get a little distracted off the fluency stuff. Sorry. But I will tell you. Okay. Dan had a really fun idea for a reel . Do you wanna share it? Dan?
Speaker 2I'll , I'll , I'll share it 'cause it probably won't get made. Okay. And I wanna clarify on the front end. Okay. I'm, I'm a secondary guy, so I'm , I want to like set the bar real low for myself so low. I can step over it with this right here. So I had this idea, all right , which was that , um, I got a ping pong table in my backyard, right? And I learned about coral counting recently from Bethany and other folks on the call, right? Where , you know , you can start at any number and go up around a circle by a fixed amount maybe. So one kid says six, next kid says nine, next kid says 12, and so on. So here's what I was thinking is me, Bethany pinging pong in it, all right ? Table tennis in it. And , uh, we start just doing choral by ones. So like, I hit the ball over one, Bethany hits two, three. And whenever someone misses that, then is the new starting number. And the new, the new what , what do you call it? You know, the new skip amount. So if we make it to four, then we go 4, 8, 12. If I blow it there, it's like 12, 24, 36, whatever's after that. Who even knows <laugh> ? But you gotta like, kind of , there's a little bit of time pressure, you know? 'cause the ball's coming, the ball's coming and uh , you gotta hit the , gotta hit that back. So I was feeling pretty good about that. Never . We never did it. But you can all imagine how funny and heartwarming and a little bit profound the reel would've been on a , on Insta. You can , you can imagine in your mind's eye,
Speaker 3I did not see this pinging pong table you speak of. But if you had like, greeted me with paddle in hand, I would've been ready to go. I've been like, let's go. And also, I wanna clarify that in coral counting, one of the beauties is the coral nature of it, where you're counting together. So like you have, so it's not like a popcorn, Dan has to tell me
Speaker 2Person on the spot.
Speaker 3Yeah. Okay . I know it's that we're counting together. So if I don't know what like a multiple of 12 is, because you missed the ball, love that on the , you know, I mean, just in case you missed it, I would , you know, I would then we're doing it together so there's no pressure and it's just joy in counting. So let's, let's take that pressure off that we would've been counting together. Mm-Hmm. <affirmative> ,
Speaker 2I love that. That like, if 24 plus 12, I'm like, ah , I know it's 30 some , you know, but not 36. Then like, there's like, I can kind of like get , get happy about, we all said 30 and I , I said 30. I was a part of that. And I was like, you know, not quite at six yet, but can contribute. So, hey , I'm learning here. Thank you for that, Bethany. It's
Speaker 3All about learning Dan Meyer , it's all about learning. It
Speaker 2Is about learning. I wanted to offer one quick thing, fluency wise has been happy in our lives around here. Got kids in k and one, as I've mentioned before, they're like in the official, you know, learning math thing in , in formal school environments. And, you know, I'm so grateful to have a little bit of time and energy at the end of my day. I'm not working two jobs. I can sit down and do a little, you know, work with them, homework of different sorts. And , uh, we're doing some, some mathy stuff. And they said to me, can you time me? And I was like, wait, what? And it kind of hit me a little bit and , uh, come to find out that like, they get timed in school and they wanted to kind of like do the timing thing at home. I just wanna say, you know, I felt a little bit of conflict here. I wanna say just straight up, my kids' teachers are incredible, love them , could not do what they do. And obviously over the course of this, our season here, I've been working issues out about fluency and, you know, how to balance a kid's joy in math and their ability to work the mathematics fluently. Anyway, I'm, I'm still thinking about it. I was glad if nothing else, that they weren't like traumatized by the timing. Yeah. Uh , you know , that , that's nice that they weren't freaking out about that or, or shrinking back. But it did raise questions for me about like, is this part of the nature of math? Or like, is this extra?
Speaker 3Yeah, I mean, we, we had our whole season about math anxiety and you know, the time test came up a bit and we had one of our guests who was like, there's a space for time test . We kind of like, thought about that and we're like , uh, but will teachers do it in a way that's not traumatizing? You know, I have some questions. Yeah. I would maybe ask like, how does timing show up in AK or first grade classroom? Like, what is the, the goal there? And again, your kiddos seemed excited, wanted you to time them, but is that the experience for all kids? We don't know. But it might be interesting in a very, like, Hey, I respect what you're doing sort of way . But I'm also curious, can we talk a little bit about how this shows up in the classroom? Because that seems Yeah, that is, that's, maybe it's just because you usually time them in every other aspect of their life, Dan, you're like, you know,
Speaker 2Do the potty stuff faster, fast . Um , Bethany, I , I love your confidence in me, but do you, what part of our experience together makes you think that I could gracefully thread the needle between being encouraging and respectful and also asking a sincere but interested question about why you're timing my kid <laugh> . Uh, I'll do my best at some point .
Speaker 3Do your best, do your best or, or , um, le why don't I met your wife? Why don't we leave that to your wife? Because she is charming. She's fabulous. Yeah . There . So let , we'll leave it to there . There you go . But you know what, though, this is a really great invitation, Dan, to like, for our listeners to be listening to what kinds of conversations are coming home. You know, what kind of language, how are kids talking about math, talking about reading? Because once our kiddos are in that more formalized schooling environment, we don't really know what's happening, right? So how can we even just tune in a little bit to hear, are they saying things that kind of great against the way we're hoping to think about math or have conversations about math in our home? And how can we make sure we're not having our kiddos traumatized by that, that language, by the , those exercises. So I, I wanna , I wanna hear more. Please keep the stories coming. Dan will
Speaker 2Do. And I, I think we should like , uh, we're lucky enough to have , uh, really smart guests on the calls , uh, in the , in the season, who can help us sort some of these issues out. So I might just like be selfish here and ask about my own situation of our, of our current guest. Um, to tee up the current episode here. Just to recap where we've been in our season, you should hit the back catalog if you haven't. We've talked about assessment of fluency with Dr. Val Henry. We've talked about how to balance fluency and use that to develop enthusiasm for math and problem solving with Dr. Art Brody . And we've talked about developing fluency in a classroom setting that also really prioritizes listening and conversation between students with , uh, with Lauren Carr. It's been a fantastic season. We also had, of course, Jason Ziba on , uh, to talk about the nature of fluency itself. Been a, been a whirlwind. And we have on the call today Dr. John Staley , who's gonna talk with us about how to develop these kinds of skills we're talking about in teachers at a system level. John has seen it all. Um, John has worked with the Baltimore County Public Schools for nearly three decades in roles such as teacher of middle and high school, math coordinator of secondary mathematics, director of math, pre-K to 12, and currently the coordinator of special projects. So we're excited to talk all things fluency with John here. Uh , but especially right now , uh, about my own children. You know, what's up, what , you know, how , how <laugh> welcome and how would you handle this? What should I do here? <laugh> big welcome to
Speaker 1John . Hey , hey , hey, Dan. I'm , I'm taking notes from you on this one 'cause we have a grandson who's , um, okay, he's almost 20 months and we're not quite doing that time fluency with them yet. But I'm hoping the same thing that you're hoping that as teachers think through what that does for students. The question I ask on the front end is, how does that impact their confidence? And so, K 1, 2, 3, as you keep moving across the grades, when do students who aren't as fast as the other ones begin to believe that maybe they're not as good as math at math? Mm-Hmm . <affirmative> with doing it because they can't do it within this certain time limit, this certain speed. They're not the first one to finish. And so that's always the minute that timer goes on, that's always a, I'm wondering what's gonna happen as far as not whether or not they can do it and get there, but how it begins to chip away at a student's sense of confidence and willingness to go try and do and show what they can do. So all of that is what I'm thinking about with you for your kids that are in kindergarten, first. Our grandson is not quite there yet, but , um, you know, just thinking about how that has played itself out even with our own children.
Speaker 3Thank you so much for being here. Dr. Staley and I, I got John <laugh>.
Speaker 1Yeah , yeah , please. John
Speaker 3<laugh> , thank you for being here. I, and I really appreciate you saying that. I, I have a two and a half year old , so you know, K one and I'm a kindergarten teacher. So you think about our kiddos, we're trying to help them build language of the discipline. We're helping them like make sense of what is math and seeing math all around them. And if we are bringing in that timed nature, I love how you put it, like, at some point for some of our students, it's, they're gonna make meaning out of that, right? If their time either goes down, doesn't improve or does improve, like, we don't know how they're gonna make meaning of it. And, and so thank you for saying that, and thank you for being here. Yes. You're coordinator of special projects, so little did you know your special project is Dan Meyer . So <laugh> , he , he's got, he's got a doozy of a , a question for you, right? <laugh> ?
Speaker 2I am a project. Yeah ,
Speaker 1I understand that .
Speaker 2Could I ask you a question? We've asked some guests and found really illuminating here, John , which is , uh, you know, we talk about fluency in math and a lot of ideas flood into the mind for a lot of math folks. So we wanna take it outta math for a second. And we're curious, is there an area of your life as personal as you wanna make it here, that where you feel like you've been developing fluency yourself? What is it? How's that, how's that process been for you?
Speaker 1Um, yeah. The , the one area is , um, I would just put it, and so let's go personal. My quiet time with God. You know, I , I try on a, on a regular basis, daily to have quiet time when, you know , um, that might entail a whole bunch of different things from listening to music, to reading the Bible, to journaling, to just prayer, to just sitting and being quiet. So I've got different things that I can do within that quiet time. But as I think about from day to day to day, it's always a growth in process for me. So, in other words, there are days when I'm thinking I'm doing well with it. There's days when I'm light. And the consistency of doing it across the days is something that I continue to myself step back and look at. And, and I take that time personal because there are days when I know, okay, man, I didn't give much time. And there's days when I know, okay, I put in time. And so the goal is how do I think about continue to build, grow, and develop? I've got multiple strategies that I can bring into it. So as I think about quote unquote building that fluency, I'm thinking about which strategies do I need? Which ones do I want to use that day? And quite often from day to day , it depends on what's happening with me in life, what's happening with me and my, my wife Karen, and our children, our grandchildren, and the situations that have come our way. So fluency will vary, but that idea of my time with God helps me with dealing with situations that come up.
Speaker 2I appreciate you sharing that. It's , uh, it's real personal. And I'm , I'm thinking, you know, about how often in fluency development, there's an element of feedback attached to it. You know, like, I wanna, if I'm developing fluency, you know, in the, in the, in the kitchen, it's like, well, how do people receive my fall cocktail, let's say? Or, and , uh, when you're talking about , uh, you know, discipline that's spiritual and you know, how you get feedback on how you're doing , uh, feels like a real interesting part , uh, takes a real sensitivity to know like, how am I doing with this , uh, this process on developing fluency? And that's really interesting.
Speaker 3I also wanna to flag that. Like, it's that consistency, right? You talked about that consistency. And when we're thinking about fluency like that, we're doing it consistently. And not only the feedback, but that growth, right? That growth with, like, it's gonna change, it's gonna evolve. Now here, Dan Meyer , what if Dr. Staley, what if you put a time pressure on that? What if you said <laugh> , you have to get it down by this time, or you have to get an ice cream scoop to show that you have mastered these verses or whatever your walk is looking like. Hmm . Is it , is that gonna change your relationship with your journey? I wonder, see , I'm still thinking about this question, Dan <laugh>
Speaker 1And that idea of feedback , um, Dan and time, when you put both of those together, 'cause you think about days when I'm thinking, okay, I need to be spending 15 minutes, 20 minutes, 30 minutes, and I spend three minutes, or I spend five minutes. It's gotta be a nonjudgmental zone, especially as you think through and process self. So as you think about your children, Dan, as they process what they're doing , uh, when they no longer enjoy you, timing them at home, Ooh , I wonder what's going on. And it's not because of something that you've done that's changed it, but it's because of some kind of interaction with something in the space of where it's happened. So like, what I don't do is run around saying to my wife, Hey, you know, I spent 15 minutes with God today, 10 minutes, 12 minutes, two minutes, because I, I don't want it to be in a judgmental space. And so that time element of how much time do I spend or don't spend, that's, that's, that's me. That's an individual piece that I have to internalize. So
Speaker 3Thank you so much for that perspective, John . It's so, it's not only helps us get to know you better, but it's also like in my brain, all these little connections are zing. And, and thinking about how that, that evolution, your journey with that, how that's gonna impact the way you approach it tomorrow, right? The way you approach your conversation or you walk tomorrow. Yeah . And anyway, thank you for that. Um, you know, you, you identified a potential risk when it comes to fluency development that oftentimes fluency can be used as an excuse to hold kids back from progressing in math. And I'm wondering if you can talk a little bit about that concern, because I don't know if folks even sometimes see it. They may say, oh, well kid's not fluent, therefore they may not have access to a certain aspect of the material as quickly. But you're talking about on an even bigger level, like actually holding them back from their, from building a further relationship with math or progressing in math. Maybe you can give an example of how you've seen that in your career.
Speaker 1Um, here , easiest part, let's continue with Dan's story. This time testing, this time testing of facts. Um, which quite often really is people linking this idea of fluency to automaticity, to recall, to memorization. So how many facts do I have memorized, especially if I'm going through and I'm doing it so quick that I have to be boom, snap, snap, snap right there. If I'm a student who processes, I need time to think a little bit and process. When I'm put in those situations where that kind of fluency is, is elevated, that's where, man, I could be all over the place. I can shut down the anxiety's kicking and things like that. But that one fluency is about fact, fluency about the memorization. The automaticity, quite often it's addition type problems. Um, it's your quote unquote your addition facts. It might be some subtraction facts that might be held to within 10, within 20. Um, and later on it becomes your multiplication facts. So my students don't know their multiplication facts or types of words that you hear. And that's quite often about the middle of thir third grade, fourth grade, fifth grade, where that becomes a dominant set of importance that people chase. And when that's happening, you start to see groupings. You start to see people grouping students who can't quickly and fluently recall them, AKA memorize them, right? But often sometimes you see memorization without understanding of what they mean. Memorization or multiplication facts can happen for students with some drills and practices and games and things like that. But if students don't understand what the multiplication means behind that fact that they just spit out, that's another piece of it. So as you think about how that plays out in groupings in elementary schools, then it changes into identification for students to go into different math courses, especially as they go into middle school, which is when I say different math courses, we're talking about tracking beginning to happen based off of can I fluently recall? We're not even talking really about procedural fluency yet. Can I do addition and subtraction and do it within a timely manner? Do I have a strategy that I can use? So a lot of it's fact then it shifts to computational fluency. It leads into who we see as who can and can't because they get put into different groups. Some of those groups get identified early, third, fourth, fifth grade, next thing you know, they're in different sixth grade classes. And that leads into, ultimately when you step into high school, people looking at what came from fluency in elementary leading into who you're deeming as being ready or not ready for algebra. It just has that trickle up effect that really is mindful of not what students can show and do. And also it impacts their confidence. You see students coming into middle school and their confidence begin to crumble and begin to be shaken. I haven't gone out and studied this, but I would almost say it's connected to this idea of what they can do and how fast they can do it in grades three, four, and five. Prior to that man they're doing, doing , doing . They're trying, trying, trying. Then when they stop showing that willingness to try, that willingness to raise their hands because they're not fast enough, we gotta step back and say, what's going on here?
Speaker 2Yeah. It's interesting. You're really describing a , a , a self-fulfilling prophecy as it were, where like, students who are told you are not this or that will wind up living into those expectations, be they, you know, higher or lower for kids. Um, and it all seems to start from these assessments that humans flawed, wonderful humans are making about the kids in front of them , uh, evaluations and , and judgments that are in inflected with every kind of, of bias and history of the person, but also their ideas about what fluency is. And you've, you've spoken about , uh, you put a name to this, I think is , uh, really effective, which is , uh, fake fluency indicators. I think you kind of hovered a little bit over some of those in your answer just there. Um , but it's interesting to me that like the fake fluency indicators like hurt both kind of kids. They hurt the kids that get advanced who don't have the understanding that you described. Mm-Hmm . <affirmative> . And they hurt the kids who have the understanding, but don't measure up against this quote unquote fake fluency indicator. So I'd love if you like, could you put a few under that umbrella of fake fluency indicator, what are some of the ways that systems and teachers evaluate students as fluent or not that you think should be reconsidered or considered more deeply?
Speaker 1Um, man. Okay. How much time do we have today, <laugh> ? No, let's , um, let's start with just one, the first one thinking about and connecting to this idea of how fast can students recall these facts? So let me, maybe it's a 32nd, maybe it's a one minute to reproduce these facts. That right there, when you start thinking about fact recall and I'll, I won't call it fact fluency, but fact recall within a certain time limit, that right there begins to be one indicator that says are are they doers or math or not doers or math. The idea is, are they thinkers of math? And the question we have to ask ourself about that practice of timing them is how does that help support their thinking and making of sense in mathematics classroom as people who do work in math, when was the last time you were asked to reproduce or do something within a 32nd timeframe? And the question becomes, is that a practice that mathematicians have to do on a regular? And people will say, oh, they have to be able to recall certain facts. So when you think about what comes up sometimes as the faked math indicators or these readiness indicators, that piece right there, computational fluencies. So when you think about can students add or subtract and let's say with additional subtraction , um, it's a continuum for computations. And so when you think about the computational continuum, you have to think about where are students in the space? How do they have strategies that help them with adding and subtracting and doing problems that involve additional and subtraction so that they're able to accurately and efficiently produce an answer, produce a solution, develop a , uh, a problem solution to a problem that you put in front of. So as you think about whether or not you wanna say, yes, they're ready, or no, they're not, and this is a place where I need to slow them down or not slow them down. You have to ask yourself that question quite often with these indicators I've seen in high school or middle school, when you start to say algebra readiness or students ready to quote unquote study the formal course of algebra. Now how are we gonna define that formal course? It's often words like, my students don't know their facts, my students don't have good numbers since , well, the questions that I ask in those questions, what we have to push in on, and what I've pushed in on with teachers and teams is, okay, tell me which number facts or what facts don't they know , um, so that we can work on them . Oh, well , uh, and sometimes they don't have their multiplication facts memorized. They don't have those down pat . Sometimes it's their work around fractions. And so we have to dig in up underneath of it . So what's important about fractions when we talk about algebra readiness? Is it because they can't do the operations or they struggle with doing the operations or they take time to do the operations? Or is it because they don't understand how fraction sense goes into proportional reasoning? And that right there for algebra readiness is more important because when you don't understand proportional reasoning, ooh , that hurts you later on when you start to talk about slope and rate of change and everything along those lines, which have nothing to do with the computations of adding, subtracting multiple or dividing fractions or have very little to do, I won't say nothing because you use some of that skillset there also. So we have to think about what we wanna label as those gatekeepers that will keep students from progressing along their math trajectory. They're in a pre-K to 12 or AK to 12 math learning trajectory. And so we really have to think about how we can continue to move students forward and build their skills, their knowing, their depth of understanding when it comes to content versus using these as stop gaps . And the stop gaps might not be in the way we design courses, so we put 'em in this course or that course, but it's about the mindset that we as the teachers, we as those supporting teachers bring into the classroom. When we talk about students, when we talk about their skillsets , when we talk about what they can and cannot do, and how do we shift that language from talking about what they can't do and what they don't have to, what they can do and what they bring with that we can build from
Speaker 3That . I love the way that you're framing that it's not just about the students, right? What the power that teachers and the educators have and taking the results of a times test or taking what they're seeing, like you said, as an indicator that they're not ready, that power that they have, and how can we help teachers have a deeper sense of where students are at or, or more, maybe not deeper, but a , um, a broader look at what mathematics can look like. It's not just about the speed, it's not just about this number on the test. Like you said, my, that student may be able to recite six times seven , you know, they may have memorized the verses to the fluency lyrics, right? But they mm-hmm . <affirmative> don't have the understanding of what that actually means. And how can you as a teacher use your knowledge to help hone into like, where is that, where's the actual gap? Where's the actual space that they need support in? Rather than just send 'em home with more time tests or say practice these flashcards more. That feels really huge to me, and it feels like a, a call an invitation to teachers.
Speaker 1True. And, and Bethany, what you mentioned about that space. So we have to think about with our students, we have to stop thinking about just, I have them for this one year is I have 'em from a one year and it's a handoff process I'm getting them from and they're going to. So that idea of where's the space and where's the handoff and what do I need to work on is really critical. Especially I will say now here we are in 2023 and we are what, a couple of years out of schools having responded to the Covid pandemic. And we know over the course of that pandemic students had different learning experiences, let's just put it that way. So we're still thinking we need to still be thinking and still working. We cannot have fixed all the different things that happened during that pandemic for some students who got richer learning experiences and some students for which that learning experiences was not as rich as we would like for it to be. So we have to keep thinking about what's the vertical nature of mathematics and how from year to year, especially when it comes to, and I'll go to computational fluency, how we go about building and developing that computational fluency from year to year. So when you said teachers need to step back and recognize where students are so true, so true. Because if this is where you are, that's where you are now, how do I help you go to your next? What's your next? And that's the importance of me understanding the vertical nature of how computation grows and develops for addition, for subtraction, for multiplication, and I'll say for division also. But really if you think about addition and multiplication, those two are so powerful and lead into algebra readiness. It's so key and critical in elementary school when you think about decomposition of numbers versus just going with this quote unquote a standard algorithm that we teach procedurally sometimes, but just decomposition of numbers. Just one tens , hundreds, thousands placed . And students understanding how to take a number and and decompose it into those three. And then adding that, that sets them up for later on when they're simplifying algebraic expressions, when they're adding like terms and everything. If I understand constants , if I understand linear and then quadratic terms, I can equate that to what we did with one's tens and hundreds. And so this is the importance of me as a teacher and those who are supporting teachers providing that space and time for vertical work to happen that allows us to connect with what they learned earlier grades and how they learned it. Now, I don't need to know all the problems in the procedure , but I need to know how the conceptual understanding was laid that led to the procedural at that grade level so that as I'm building in the later grades, I can build from it . Multiplication is another example. In third grade, when you start to introduce it, if you rush to the fact fluency of multiplication, multiplication facts and the procedural piece, which really is not really quote unquote in many places required until fifth grade, but if I just rush at the procedures, I overstep the ability to use place value and a grid method in grade three to introduce it. Well, it's a nice visual, it also helps 'em with place value. But then later on when I get to algebra and I'm teaching multiplication of polynomials, if I use a grid method there, the , the connection of those two just from what you did. I remember working with some third grade a team at a school years ago, and the third grade teachers sort of wanted to skip that method. And I shared with them where it goes and said, you're laying a foundation for later on when I'm using algebra tiles to really use algebra tiles or a different kind of manipulative tool that visually shows them. And I can easily just layer in numbers or algebraic expressions. And so the importance of understanding where you begin and where some of the foundational pieces are beginning in grade 3, 4, 5, and grade one and two also, if addition is attraction especially and how that plays up into the upper grades and prepare students with their algebra readiness, it gives teachers something to build from. No, as a high school teacher, I'm not gonna totally activate prior knowledge from doing a one sense hundreds addition problem, but I have, because the place value piece is so critical with understanding the terms within an expression.
Speaker 2Yeah, definitely. I think it's really easy for me as a teacher, like , uh, to imagine my grade is a silo or the end of it is a is a gate. And my job is to give students everything they need to get through that gate. And it's harder to see students as me equipping students with resources that they will carry with them through K to 12. And I'm really curious, you've mentioned several times about this kind of this vertical understanding of mathematics in different domains as being really essential for helping students develop fluency and for not holding students back unnecessarily. I'm wondering , uh, we have administrators who listen to this show. I'm curious, do you have ideas for how to create those moments of vertical understanding both within a building like say K 5, 6, 8, but also, and especially like across buildings, like getting those K five teachers talking to nine 12 teachers saying, Hey, here's what we got for you. We're giving these students this decomposition skills. If you know that's there, draw on that. Don't ignore that. When kids get to algebra and they're combining like terms, are there structures you put in place from your vantage point that have worked?
Speaker 1So some of the structures have been around the, the teams that schools have built and developed. Sometimes it's from a professional learning community. Sometimes it's just from grade level teams. Sometimes it's just , um, content teams. So when you think about the opportunities to provide space for teachers to grow in this area with vertical nature, you have to set environments where , um, it's non-threatening. You have to set an environment where all teachers, so let's go with AK to five team. When they come together, you are bringing in math that goes across the grade levels and helping the teachers see examples, problems, problem sets, and the strategies that play themselves out. Especially if you're using a curriculum resource. And I, I'll say that because what you wanna see is the design in the curriculum resource and how that's exposed. Especially like in a lot of , um, schools who are using a curriculum resource have access to it online also. So it's no longer this , you gotta give each teacher, say K to five, you gotta give 'em six teacher edition books for them to see it, but also focus it. So don't go try to do all of the domains in math in one year, you know, focus this year say, or a year on, let's look at the addition and subtraction. 'cause subtraction, additions sort of go together. But just look at how addition and subtraction grows and develops across our curriculum. In AK to five structure, if you have a pre-K to five curriculum structure across that structure, what are the key pieces that get elevated each year? So don't talk about every single little nuance. Don't go to like every single lesson the way we tend to , um, take our curriculums and lay it out and got a hundred plus lessons and this many on this. But think about the big idea of what's happening at each other , the grade levels. And so what's the big idea of addition that happens in K 1, 2, 3, 4, 5 ? What's the big strategies that we elevate at that space? What are the strategies that we spend more time on ? What's the representations that are used? What's the tools that are used? So if we're using number lines in grade K or one or two, how do we use that number line across the grade levels? Because later on it goes from whole numbers on the number line to fractions on the number line to decimals on the number line . So how does it show up and how do we as a teacher team see it show up with just the use of a number line? I'll just use that as one tool. If we're just using a number line , how do we work with that later on so that we're consistent? We're building from not tearing down what teachers in prior grades have done. And the reason why I say pick one space, don't, don't go pick multiple domains to study in one year because you say you gotta try to do it all by trying to do it all. You get very little done , um, that has meaning and that students can hold onto that teachers can hold on to . So that's, that's one, you know, when teachers have that time to really look at the vertical nature of adding numbers across K to five. And then how do I take a document? How do I create some kind of resource? Maybe it's a one page or a two pager that I can hand off to my middle school so that they can see the key strategies and how they've been built and developed. And how do I develop this If I'm working as a system, how do we develop a vertical tool that shows from K to five additional cross and where it grows so that my high school teachers can see, hey, here's where it comes from, here's where it came from, here's what they were doing in elementary that I can connect to, that I can build from, that I can reactivate. And maybe the space that I reactivate is a space where they were finding joy in math, third grade, fourth grade, second grade. Oh, wow. They boom, a problem like that. They found joy by the time they got into middle school where maybe their confidence started to shake. They weren't finding that joy again. And now that they're sitting in high school, they're really like, man, am I a doer of mathematics? Am I not a doer? Mathematics? Sometimes you gotta pop that back in with a , Hey, this is a problem y'all did back in second grade. Remember y'all did it with X, Y, z and this and that. Okay, let's go. We're doing something similar. But now with algebraic terms,
Speaker 3It feels too like it's just so worth it. Like we, as a teacher, I, I know how pressed we are for time and especially when like, let's say we have just a few meetings with our team a week. If we're lucky, we get to see our team, right? But if we focus, and like you're saying, I think you're inviting us to zoom in on something, let's say addition and really understand the story, the progression and how that grows and builds. Like if each teacher is holding their grade level knowledge, but how much richer it'll be if they're, like you said, able to see the just, there's their piece , a piece in the story because they're gonna get students that come in at all different points on that trajectory, right? Yep . And so that feels really powerful to me as a teacher to think the more that I know about that story, the more, even like when I'm working with my students with fluency, it's gonna change the way I teach those additions, subtraction, multiplication, division facts, right? Mm-Hmm. <affirmative> . Because now I wanna put it in the context of a bigger story, right? I want to teach them how these number facts or being able to decompose and compose numbers and use strategies, the power in that, right? I feel like it's gonna really change the way I teach my students. And it's gonna mean hopefully we're printing off less , uh, you know , cutesy time tests and just saying, here, memorize this. But instead we're weaving it into the story of mathematics because it's one piece and it can serve us well. And like you said, or be a gatekeeper, if we don't have that,
Speaker 1Bethany, the word story is , is key and critical. We have to look at mathematics as a story that we tell students across the grades K to 12. And what we are all is the conveyors of a chapter in this progression of the story. If we look at it as an isolated chapter, then the question really becomes, what am I doing to my students and for my students? So if I'm, if I'm that teacher and I gotta , it's gotta be about me staying in that space. And maybe that's where my comfort level is at this time. I invite you to begin to grow a little bit, and I invite you to begin to look at small chunks of it. You might think that students need help in everything. Okay? But what I would offer is that you step back and say, okay, where are my students' strengths that I can begin to build from and that I can begin to help them with making more sense of the story of mathematics that I have to tell them this year. And by building from that perspective, it allows me to continue to keep going if I'm trying to build from your deficits what you've been struggling on for years. Um, I think even us as adults, if you try to say, John , man, we're going to help you be a , um, run five miles a day. And I would say to you, yeah, okay, help. I would tell you after a little bit of time, and if, if I'm not sure what magic you have, but I gotta find the time, the space, the energy to really want to do it. And if I've been struggling at that for a number of years, I'm not sure if I'm going to keep on wanting to do it. And so if students have been struggling for a number of years or perceived that struggling, and that's always the lens that we come at versus a lens of, Hey, here's what you can know, here's what you can do, man. I like the way you were working with your number work . I like the way when we studied the domain of geometry, wow, you really got a sense of spatial reasoning and you can really push in on those parts. Hmm . Okay. I , I see how you were connecting what we do in number to algebraic thinking. And so I'm thinking about their strengths in the content area. Boom. When I elevate that I can build from that. When I elevate your deficits, it's almost like, yeah, you're strong in this, but you can't do this. And so which do we as adults trigger to help us wanna keep going and trying? I'm not sure if it's every time you turn around you saying the, but you can't, but you still can't do this. That helps me keep going and wanting to go. So you got content strengths, you got process and practices, and then you even have disposition strength. That's , you have to think about for your students. And here's the hard part of all this work. We often think we wanna do it for all of our students. And when we begin trying to do it for all of our students, I'm trying to figure out logistically, how do I do it for this student, this student, this student, this student, da da da da da . What I would offer you to think about in some cases is how about if I pick three students? How about if I get pick three students to really begin to understand what it means to build from their strengths and asset-based approach. How to identify what their strengths are, how to think about how I activate prior knowledge based on their strengths, how I use their dispositions to help them grow. 'cause if I can figure it out for three, then I can begin to grow it more. But it's, how do I go about figuring it out first with a , a manageable way that I can do it. If I'm an elementary teacher, I got 20 students, 30 students, and I'm trying to do it for all 30, it might become overwhelming, let alone once I move up into middle school and I've got, or if I'm content specific in elementary school , fourth grade, fifth grade, quite often you see that happening and I've got all the fourth graders, and maybe that might be a hundred of them . You're asking me to do something for a hundred students. Hmm . Can I do it for three students first? I think I can,
Speaker 2We talked a lot about asset orientation and various , uh, episodes of this podcast, and you've talked about the ways that we can artificially and incorrectly label someone or something not good enough, right? And I think your description of , uh, the runner and the teacher I think are a great moment to draw those ideas in where like, someone you would not wanna see a running coach say to someone like, you are a runner if, and only if you are able to run five miles. Like that coach is gonna be looking at like, okay, so what do you got? What are you bringing here? Like, can you do, can you do four laps, two laps? Do you have like grit? Do you have, are you able to like, push through those moments? You feel absolutely gassed? Mm-hmm <affirmative> . And in the same way a teacher listening might say to themselves right now, oh, like what we're talking about here. Like that's, there's the good teachers and then there's the other teachers. And I'm not , I don't know if I'm one of the good teachers, but what you're describing here I feel like is interesting to me of like figuring out what you've got on a smaller scale before then saying, okay, like the , like the , the three kids is, you know, the two laps, so to speak, around the track and the five miles is like the entire class. And we can just easily communicate to ourselves a deficit orientation of who we are based on the enormity of the challenge, challenge at full scale . Anyway , it's just been a fantastic to chat with you about all these ideas at a system scale. Before we go, is there a final thought or idea you'd like to leave with listeners?
Speaker 1I think two things. One thing is this idea of where do I begin? Especially let's start thinking about my student strengths and building from there , um, is the first for us to look in the mirror and look at our beliefs when it comes to computational fluency. And when it comes to this idea of fact fluency and, and what are our beliefs around it . Quite often what we are doing is what we've learned and what we believe in . And I'm gonna say beliefs . Sometimes it's what we've seen for some students, for pockets of students. But when we look at those students who have not been successful, take a quick look at that, take a deep look at that and identify your own biases. When it comes to, oh, if a student by this grade doesn't have this, they can't spit off their facts. What does that mean? Well, what does that really mean? And so think about those biases and think about how we look at students and how we speak about our students and what role does speed come in there versus not come in there. So that's one piece. The other part is really go and take some time to gain an understanding of computational continuum, the computational fluency across the grades. I think that part right there helps you at any grade level, K to five, six to eight, nine to 12, understand where the math is coming from and where the math is going. Why don't I teach certain tricks? Because I know those tricks don't work when they get to X, Y, Z. And so think about that and enroll and, and work there as you keep going and think through things. And just really the bottom line with fluency and everything related to fluency, I think we have to really be critical of ourselves and think about what impact does it have on students' sense of identity as math doers, you know, their self-confidence. What does it do to them When we think about and how we execute our work with fluency, be it facts. And I'm gonna keep going back to facts because I think that's the a piece that automaticity piece is something in there that people speak about with fluency, but computational fluency. So how does it impact their self-confidence, their identity, and then their sense of agency, their willingness to show you what they know and they can do in multiple ways. And I think that's the biggest thing. The bottom line message is fluency will impact students' identities and agencies as math doers. The question we have to ask ourselves is, and as we watch our students grow across the years, when does it start to chip away at their self-confidence? And when does it continue to help coat their self-confidence and build it even stronger? And how do we shift our process from a, in many cases, identifying struggling students, a deficit mindset to more of a strengths base in a assets-based approach? So I'll leave it right there with that.
Speaker 3So wonderful. You have such a perspective, you're able to zoom in, but you're also able to give us that bigger picture and help us see the importance, like you said, of that vertical understanding. We really, really deeply appreciate your time and your perspective. I think it's really gonna help us and hopefully our listeners, like you said, to look in the mirror and to help reframe the way that we might be thinking about it and if we're subconsciously or not using that fluency as a gatekeeper. Thank you so much for your time, Dr. Staley . John. Well thank , thank you ,
Speaker 1<laugh> . Thank you, Rob . Thank you for the opportunity to share.
Speaker 3Dan , I am so happy that we got to hear Dr . Sta , John <laugh>, that we got to hear his perspective on this. It also reminded me like, because sometimes I think when folks think about that vertical understanding of like mathematics, for me anyway, it can start to feel really overwhelming, right? Like, there's so much to know, how do I learn? But it's also about that zooming in, right? On those particular topics. And it made me think of like how Val said, like, where is gonna have the most impact? So she was talking about if we're focusing on doubles, well that's only gonna get you so far. But if we're really thinking about like 10 compliments and we're thinking about decomposing and composing 10 and working with 10 , like the power that's gonna have over the course of a student's mathematical career, right? Talk to me Dan.
Speaker 2Yeah. The vertical continuum, that kind of work was really interesting to me as was this idea that as you get higher up into like middle and high, maybe even elementary, it feels, I think like easier to say kid doesn't know it.
Speaker 3Yes.
Speaker 2In ways that like, especially with fractions for instance, it's like the kids just don't know 'em , you know? And it's like, well, I , I appreciated John's, you know, broadening of that perspective saying no and doesn't know that's a binary lights , which kind of measure. It's more like, what do they know? And there's some things that you don't know, like the operations which can be developed throughout, for instance, algebra. Whereas ideas of scale and proportionality, if you don't know those, that's gonna create some real fundamental limitations, right? So I just appreciated that. I , I , I can think at elementary, I just find it hard to imagine a teacher saying, ah , that kid, you know, doesn't know number. It's like, well, no , there's like a lot going on there. So I , I appreciated the check on making that kind of binary evaluation of a thing that's really a continuum and a and a very vast space. So that was very interesting to me.
Speaker 3But I think that is happening kind of more often than we think that like, even he was talking even like third, fourth, fifth, are we, yeah . Are we already starting to say that about students? Oh , they don't understand that, or they don't get that, right. And one other thing that I wanted to flag too is the way that he was, I can just imagine him talking to teachers and to students and just that asset lens of like, pulling from what they already know to say, well, you know this, well then yeah, use that to solve this as a teacher, I wanna be able to facilitate those connections Yeah . And help students see this bigger picture of mathematics and how it plays together. And I, I just, what a rich conversation and I'm, I'm really, really glad that we had that opportunity. And I wonder what would happen, Dan, if you asked your kiddos like, sure, I'll time you, but why? What, what do you wanna be timed for? Tell me more. Like, why are we timing? Tell me, you know, and just see what they say. What do you think about that, Dan ? Mm-Hmm . <affirmative> .
Speaker 2Yeah, they , uh, they , they already, they're starting to roll their eyes at me . Like, I don't dunno who taught them that <laugh> , but I'm getting some, I'm getting some periodic eye rolls and I can definitely see some eye rolls happening there, but I, I might give it a try. It hasn't happened a whole lot, the whole timing request. But I'll , I'll keep you posted. Believe me, I'll keep you posted. Just wanna say to you all out there, thank you for listening to our conversation with Dr. John Staley, coordinator, our special projects with the Baltimore County Public Schools. You folks can check out the show notes for links to connect with Dr. Staley on social media here and there. Um , get in touch with us by joining our Facebook discussion group, math Teacher lounge community. And I tell you next time on the show, we're bringing you a special episode that I recorded at NCT nm , the National Council of Teachers of Mathematics annual Conference with Dr. Jennifer Bay Williams. It's all about games, games, more games, and using games to develop fluency in particular. Here's my question. It's an annoying one to start with here to debrief this. But like, what is a game? You know,
Speaker 3Make sure that you don't miss the special episode recorded at NCTM or any other episodes in this season. And you can do that by subscribing to Math Teacher Lounge on the podcast platform of your choosing . And, you know, while you're listening, go ahead and we hope you'll leave us a rating. Let us know what you think and let other folks know what you think of the show. If it brought value to you, we hope you'll share it with , uh, educator in your life. You can find more information on all the Amplify shows at our podcast hub . Go to amplify.com/hub. Thanks so much for listening.
Speaker 2Bye.
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