Room to Grow - a Math Podcast
Room to Grow - a Math Podcast
Intervention for Middle and High School with Kevin Dykema
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In this episode of Room to Grow, Curtis and Joanie welcome Kevin Dykema, new President of the National Council of Teachers of Mathematics (NCTM). As a practicing classroom teacher, Kevin brings practical knowledge to his NCTM leadership. He reflects on they ways that most school systems have historically addressed students who are struggling in math class, to give them more-of-the-same, or a slower-and-louder approach, and how these typically don’t result in resolving students’ struggles.
Kevin suggests how to decide which mathematics topics are worth intervening on, recognizing that if we worry about student mastery of every single standard or topic of the grade level or course, we overwhelm the students and ourselves. Instead, if we focus on fewer, more important topics, we can support students’ future learning. He suggests that we use timely and relevant data to determine which students need support on which topics, and anticipating and planning for supports that come just-in-time to support new learning.
Acknowledging that intervention structure looks different at the middle and high school level than for elementary school, Kevin shares his thoughts about intentionally targeting math interventions that will support students for the long term, and finding time to intervene that doesn’t take away from their regular math instruction time. He shares the problems behind teaching “tricks” or gimmicks for helping students get answers quickly, but not understand the meaning of the mathematics behind those tricks.
Ultimately, building relationships with our students and attending to building their mathematical identities and agencies is what matters most. We know that every student brings “math brilliance” to the classroom, and finding and tapping into that creates wins for all of us.
This episode is packed full of important ideas and resources – we think you are going to love it!
We encourage you to explore these resources, mentioned and referenced in this episode:
- Rules that Expire blog and link to full article from NCTM journal (membership required)
- Nix the Tricks by Tina Cardone, free online book and resources
- Productive Math Struggle, Kevin’s book co-authored with available for purchase
- The Math Pact series of books by Barbara J. Dougherty, Sarah B. Bush, and Karen S. Karp, available for purchase
Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.
You know, I often say in in professional development sessions I lead that my favorite sound in the math classroom is the oh sound. And that's what I live for. And that's why that's why I keep going back year after year, day after day into that classroom. Because you get to see that and you get to work with those kids and help students who are currently struggling start to recognize, oh, I really can do this thing called math. And this thing called math isn't really as bad as what I thought it would be.
SPEAKER_02Welcome to Room to Grow. I'm Curtis Brown. And I'm Joni Fenderberg. We work together at Texas Instruments, and we're glad you're here.
SPEAKER_01We're looking forward to continually improving our practice, and we understand that you are too.
SPEAKER_02We hope that you'll find this podcast as a room for you to grow along with us as we wrestle with and explore ideas about teaching math even better. In this episode, Curtis and I share conversation with NCTM's president-elect Kevin Dykema. As a classroom teacher himself, Kevin has a passion for and understanding of the day-to-day struggles and celebrations of current classroom teachers. We focus our conversation on the importance of intervention in mathematics class. We talk about what mathematics warrants intervention, what strategies are effective for supporting students who are struggling, and how intervention might look different across the different grade bands. Kevin's enthusiasm and can-do attitude is contagious. You're gonna love this one. Let's get growing.
SPEAKER_01Well, Joni, it's really exciting to have you in the office again today. So hello.
SPEAKER_02Hi, Curtis. It's great to be in person. I love, you know, we're growing fond of this little office space that's, you know, what is this room? Like eight by eight. But um, but it feels kind of like our room to grow home. We should maybe like put a little picture of our earth on the room.
SPEAKER_01Maybe we need to put our bar nail up on the corner. That would be really fun. Well, today we have a wonderful guest. And uh, Kevin, I'm gonna give you a chance to introduce yourself um and just kind of tell us a little bit who you are and what's going on.
SPEAKER_00Yeah, thanks so much for having me today. I'm very excited to be with you here this afternoon and and talking about math education. So my name is Kevin Dikeman. I've taught eighth grade math in Southwest Michigan for 26 years. This year I'm actually out of the classroom doing some district level math supervision as I'm also the president elect for the National Council of Teachers of Mathematics, taking over as president in October and looking very forward to that. So I taught eighth grade math for many, many years, liked it most days. It has its moments every now and then, and the kids are middle school kids are middle school kids. But I'm very passionate about helping increase math education for each and every student, and what can we do to really make math not that dreaded subject? And I ask all my students at our open house in our district, we have the the meet the teacher night before school starts. Sure. So when I introduce myself to each kid as they come into the classroom, I say, Hey, what's your favorite subject? What's your least favorite subject? It's okay if it's math. Nice. And I start every single day saying, Good morning, welcome to math. That's the best class of the day. And I was just in the high school a couple days ago, and and I had several students who said, What was your little tagline that you said every single day? And it's those little things that they remember. They may not remember what they learned, but they remember those relationships that you that you build. And as we talk about intervention a little bit, I think so much of it's about those relationships that we build with the students. So thanks again for having me here today. I'm very excited to share some ideas.
SPEAKER_01Wow, we're we're really excited to have you here. Honored that you'd take your time and come and visit with us and do a little bit of a chat. So we've got a few questions that we've we've got together, and we'll ask you some questions. I think uh let's go ahead and get started. You said we were gonna be talking about intervention today. I'm really excited actually to hear um your thoughts on that because this is kind of a this is a big topic. It's a big topic in math.
SPEAKER_02Every math educator thinks about it. And really, I I kind of want to circle back for a second because part of why I was so excited to invite you to join us and why I'm so thrilled you're here today is you know, it's not all the time that the president or president like an NCTM is a classroom teacher who like is actually living it every single day. Um, and I think, you know, Curtis and I own on the podcast that although we both have classroom teaching experience, we've both been out of the classroom for a while. And um, you know, we continue to support educators and try our best to stay in touch of what does it really feel like on a day-to-day basis with with uh for a teacher, but you know, you're bringing that to the table. So we're really excited to hear your, you know, very real, like, hey, you were just living this months ago, right? Like how this feels.
SPEAKER_00The good, the bad, and the ugly. For sure.
SPEAKER_02Exactly. And and again, we the three of us kind of collectively came to this topic of intervention, particularly intervention at the secondary level. And what does that look like? And what does that not look like? So um I think uh let's let's kind of go ahead and jump in. And maybe you can, before we get into some formal questions um around what we want to talk about, maybe you can just talk a little bit about why intervention is a topic that you're passionate about.
SPEAKER_00Yeah, I think when we look traditionally at who we've served well in math, it's those who are already identified as good mathematicians. Those who either feel like they're good at it, those who may have an interest in it, those who may have parents at home who are saying, you must be good at this because you need to do that. And I don't think as an as a math education community, we've done as well of a job as we should with some of our students who experience struggles at times. And so often I think we start to label them and say, oh, it's a struggling kid, and we try to just put the blame on them if they would have tried harder, if they would have paid more attention, if they would have done the homework, if they, if they, if they maybe it's me. Maybe the way that I presented that lesson just didn't work for that student. And I need to be confident enough in my teaching abilities to say, hey, you know what? That didn't work. Let's try it differently. And it can't be the slower and louder approach. And you know, I think we can all think back to when we were in school. You know, you have classmates who struggled, none of us, of course, and nobody who's listening to the podcast, because we're all math teachers. So the this whole math by memorization worked for us rather than the math by understanding. But we can all think of a classmate who had to go with that slower and louder approach. And, you know, I still distinctly remember, you know, you get the worship with 20 problems. If you don't get it, the next day you get a worship with 40 problems, and the teacher just sort of holds your hand and goes slower and louder with it. And and I'm not sure the pure repetition works for every single kid. Now, we do need to acknowledge it's gonna work for some kids. There are some kids at the 18th time you explain how to add a positive and a negative number, something finally finally clapped there. But for most kids, purely repeating it slower and louder is not gonna work. And you know, so I've always had a heart for students who don't get it the very first time. And I think that's one of the that's that's my favorite part of teaching middle school math is when you keep working with that kid over and over and over and try different things, and all of a sudden you see that little light bulb goes on, and you see that that whole facial demeanor just changes and they get excited. And you know, I often say in in professional development sessions I lead that my favorite sound in the math classroom is the oh sound. And that's what I live for, and that's why that's why I keep going back year after year, day after day into that classroom, because you get to see that and you get to work with those kids and and help students who are currently struggling start to recognize, oh, I really can do this thing called math. And this thing called math isn't really as bad as what I thought it would be. And and when we push them past that memorizing, get into the actually understand some stuff, magical things start happening. That's awesome.
SPEAKER_02I want to point out what something you just said, because I think it could get lost, and you know, oh, he just said this whole big string of things. But at the very end there, you said students who struggle. And I just think about the shift of that language from struggling students to students who struggle. People might be like, why is she even pointing that out? Don't those mean the same thing? But I think your your point at the the beginning where you said we blame the kids, right? So when we call them a struggling student, it's sort of like we're putting them in this bucket. You know, you're a struggling student and you're a successful student. And that that then becomes intertwined with their identity. Um, and we're really setting them setting ourselves up and setting them up to not have success. But when we say a student who struggles, now we're talking about this is a temporary condition that this student is experiencing, and we can do something to alleviate that, and that kid will go back to you know, fully engaging in the learning in a different way. So I just want to point that out. I think that's a good idea.
SPEAKER_00Yeah, and I think you said a temporary thing that so often the path, I think, we've identified as a struggling student. Right. If you struggle in September, you're gonna struggle all year long. And I love that you that you pointed out it's that temporary thing that I may struggle temporarily looking at adding fractions with unlike denominators. But you know what? When we get to that geometry unit, I'm gonna kick butt in there and I'm not gonna struggle there. Right. And that's why I love to have that students who are currently struggling rather than that struggling student, because it really puts it on, you're not gonna be struggling with every single thing. And I think when we call it a student who struggles, you know, in the past we've had our good kids, our struggling kids, those good kids, the kids who are understanding everything, they reach a point where they don't understand something and they haven't memorized it. And then what does that do to their identity? We can all think of a time that it that it hit us, and it may be at different points in time. You know, it was in college when I had the oh my goodness, can I really do this anymore? Yeah, oh my gosh. Yeah, real analysis. I thought I was this stuff. Yeah, right. And we all reach that point, and yeah, so it's it's the labeling that we put on students sometimes that does them a disservice and does us a disservice.
SPEAKER_01Yeah, yeah, I really appreciate that pointing that out. That's a really that's a good way of kind of you know, switching the order of words. We've done that a few times on the podcast, right? We've talked about how that how important just even the order of things, the way we say things, helps our mindset uh change and and the way that we think about uh things change. So that that is a really good thing that you pointed that out. I can see your eyes light up too when we asked about why is this a passionate thing for you. Just that I mean, I was thinking about this is the place where we uh as teachers, as we move away from the math as memorization piece and into the math as concepts and understanding piece, uh, it's where we get to be creative. Absolutely. Uh with, okay, so I'm presented with a student uh who happens to be currently struggling. What are the things I can do now uh to be able to help this student uh move past that that struggle? And so as a matter of fact, uh we've got a good question, I think, that that plays off of that. What are some of the math tap topics that we typically intervene on? Uh, because maybe not every topic is worth it.
SPEAKER_00Absolutely, yeah. And I think you know, it comes down to identifying those big key ideas for your grade level and recognizing where is it coming from, where is it leading to. And you know, if you look at any set of state standards, if you look at the common core standards, whatever, there's so much there. And if you try to intervene on each and every one of those topics, you're gonna drive yourself crazy. And you're not gonna, you're not gonna feel validated as a teacher. The students aren't gonna feel like they're doing that. So I think you know, you've got to look at those big key ideas. What do I want them to gain? Knowing that what we do in whatever grade happened prior, there's some foundational work. And so we need to have some more of that vertical articulation and and really looking at what we can do. Now, one of the things then, you know, when this idea of you know the essential standards at a grade level, some people I think understand the essential standards as those are the only eight to ten things I teach all year long, and that's doing our students a disservice. And you know, our our assistant superintendent, when that question came up, phrased it very nicely. He said, You're still teaching everything, right? But those eight to ten essential standards for that grade level, that's what you are committed to providing those interventions on. That we can't intervene on 25 different things, but you can intervene on eight to ten really big overarching things. And those big overarching things, you know, depending on your grade level, it looks different as what they are, and you know, a lot of the work with the numeracy and the fluency and you know, in the early grades, the adding and the subtracting, and you know, bless those young five teachers' hearts. That you know, I worked with a young fives teacher a couple of weeks ago, and and she was talking about, you know, we never get to double-digit numbers. We deal in our district just zero to nine. Yeah, and she said, it's so easy for adults. And I said, but so hard for those kids. And the whole idea of you know, the conservation of a number we put five beads out, shuffle them up, how many beads, and the kids have to count all over again. And yeah, you know, so at the early grades, those are the things that we need to be intervening on as we progress through the grades, we've got to look in, and it can't just be our pet project. We all have our things that we just absolutely love teaching, right? And we think are the most important thing in the whole wide world. But if we if we take a little step back and start to look at, hey, what am I doing in eighth grade and how does that get built on again in algebra, in geometry, in algebra too? Not that our job at any grade is to prepare kids for the next grade level. We're teaching them that grade level's content, but we also need to be realistic that part of teaching math is to get them ready for that next level. But notice I said part of it, not the sole thing for it. So I think it's important to look at what are those big key ideas, what are those big essential understandings that you want your students to walk away from whatever grade that you are teaching and not try to intervene in every single topic. Pick those, and then you have that flexibility, you have that time to really intervene well. Although I think the intervention becomes the slower and the louder when you're trying to reteach, reinforce every single topic.
SPEAKER_02Yeah. I think that's great. So so once you've identified, I love how you framed what the, you know, the topics for intervention are those big ideas. Once you know what they are, how do you decide who needs intervention, when they need intervention? Talk a little bit about that side of it.
SPEAKER_00Yeah, that's the tough thing. And you know, I think in the past, especially at the secondary level, you know, we like to have an exit ticket and we make a snap judgment based on one day's worth of stuff. And as much as we can, we have to get multiple data points. And just because an eighth grader at the end of the class, when there's four minutes left and they're looking at the clock and they're thinking about what am I doing in language arts class next hour, oh my goodness, I forgot to do that. Oh, but first I got to quick do this math problem, but I want to quick finish up some other homework. The data we get may not be accurate data. So we've got to be careful then that we're not looking at a single piece of data that we're looking at over the course of a couple days. And that's why when we're looking at those eight to ten, it gives us then that flexibility that day one I teach it. I don't need to start intervening on it day two. That's still the that's still a continuation of it. We're looking at if I'm teaching a brand new topic on day one, maybe the intervention's day eight, day nine, whatever the topic is, that we've had time to develop that concept in class, we've had time to work with that topic in class. Otherwise, I think so often we feel like we have all this intervention, we have all these students who are are currently struggling after that first day. Well, of course. When you're learning a new skill, when you're learning a new concept, it's gonna be there. So, you know, the multiple data points, give yourself the flexibility to wait a week or two before you start doing some of that. That doesn't mean we're not teaching new things in there, but there's so many spots that you can do a quick little refresher and uh building it upon that, and and give those students then that extended exposure to that topic and give them that time to work on it. And try doing a variety of ways. You know, when you get down to where you have four or five kids, you're like, oh, I'm not really sure they get it, just giving another exit ticket may not be the the most efficient way of it's it may be the most efficient way, but not the most effective way. And I think so often, especially, you know, and I've only taught eighth grade, but when you have 150 kids in front of you, so often we sacrifice efficiency at times for effectiveness at times. And when we're when we're getting down to those last few and trying to make some decisions, we have to do what's most effective, not what's most efficient for the students. And maybe it's you know, have a quick little interview with them and talk to them. And you know, you can find time in a classroom as they're walking in the door, have a quick conversation with them, as they're walking out the door, have a quick conversation, find those spots to see once, hey, my gut says you don't really fully understand this yet. What is your guts telling you? And and asking those, hey, talk to me about whatever and and really get to hear their voice. I love that. I love that.
SPEAKER_01That's man, that I wish I would have had some of this conversation, you know, when I was back in the classroom and really thinking about the stuff. So do I, you know, like so do I, and so do many of my students.
SPEAKER_00Yeah, and I'm just not in the classroom, and and that's one of the beautiful things that as the president elected president, I had time to stop and think. Yeah. And in the district level support role, I had time to stop and think and reflect and to to look at different teachers and do that. Where in the classroom you don't have that time because you know it's always Mr. Dykeman, Mr. Dikman, Mr. Dykman. There are times I feel like in the first two minutes of class, I've already answered 80 questions, mostly have nothing to do with math. But I mean, there's all those other things you just don't have the time as a classroom teacher often to sit and reflect back and say, oh, I wish I could do that. And that's one of the parts I'm most excited when I go back in the classroom at the end of my presidency. That all this time thinking that I've done these last four years, at that point it'll be four years, I'll be able to bring all that thinking back into the classroom, and it'll be interesting once what I do differently post-presidency is what I did pre-presidency.
SPEAKER_01What are some other strategies, you the ideas that maybe you have on top for us that you can kind of give us some tools and things? One of the things that Joni and I do often in the podcast is give our listeners something to think about. Yeah. We have, you know, the the here's something we don't have a solution. We don't know that we have the solution, but go back and consider this thought process or you know, here's this thing. But I think uh in here, uh I've I've heard you talk a little bit, and I know that there's you've got some really great ideas. And so what are some other really good ideas we can pass along?
SPEAKER_00Yeah, I think private the recognition there is no silver bullet. Okay. And if there was a silver bullet, whoever invited or whoever invented that silver bullet discovered it would quit whatever they're doing and make millions and millions of dollars sharing that.
SPEAKER_02And all of us would have no jobs left because it'd be easy. Absolutely.
SPEAKER_00Absolutely, absolutely. But I think that destroys the magic of teaching. Then the fun part of teaching is figuring out what works for each kid. So I think part of it's the flexibility, the grace that you have to give yourself to try a variety of different things. I still remember when I interviewed for my current eighth-grade position, the principal said we don't want people who never fail. If you're not, if you never failed at a lesson, we don't want you in the school because we want people who are trying new things. And when you try new things, that means you're gonna fail sometimes. Now we don't want somebody who fails all the time, of course, but you've got to, and that was that was just so eye-opening for me as a fifth-year teacher that here's my administrator, potential administrator, saying, fail at a lesson, please. Yes, because that means you're trying new things and you're and you're pushing there. So I think about you know, how do I meet different kids' needs? You know, for some of them, it's using graphing calculators, for some of them, it's using manipulatives and giving them some hands-on things. For some of them, it's having them do some writing with it, and not necessarily the writing out your explanation of something, but you know, for some of them, you know, with an exponential curve. For sometimes I'll have students that when I really want them to really get the idea that it starts out kind of small and all of a sudden just zooms right the end. Describe what it'd be like to walk on a graph of an exponential relationship. Just given some of those things. Yeah. For some kids, it's whatever. We've just got to, we have to be willing to try a whole variety of different things in order to get our students there. And and for some of them, it may be reading a picture book. And I like to read picture books in eighth grade, even with mine. And you know, you find them, and sometimes they're a little quirky with that, but you can find ways to to hook them, and you don't know what's gonna hook a student. And so often, especially when we start to look at those middle grades and high school grades, they view themselves when they look at that math identity, the oh, I'm just not good at math. Right. We've got to find ways to hook them in, to get them going, to get them excited about math, so we really can see, hey, what do you understand? What do you only have a partial understanding of with all that?
SPEAKER_02I think what I'm hearing you talk about are things that a, you know, a regular classroom teacher does during regular classroom time, right? So like the the sort of per the paradigm that I'm thinking of from my classroom days was intervention was pull out, right? Like, okay, you're instead of what the regular, regular classroom is getting in terms of instruction, if you need special supports, you're getting something different in a different space with, you know, a different, maybe a different teacher, or maybe it's just a different time of day. But you're talking about things we can do, sort of working into our regular classroom routine as a teacher to expand the reach of students who are understanding that first time instruction. Absolutely. And not getting to that, like, okay, you're you're um a student who is struggling so much that we need additional time outside of that. So I'm really intrigued by that.
SPEAKER_00Well, so often that additional time is in replacement of the existing math class. Right. That you know, if we're thinking in the elementary grades, oh, we have a math interventionist, we're at a math time, let me send you to go work with a math interventionist. No, you need to find different times that you're that you're doing that, and you know, and it's it's always comes back to that time. There's never enough time to do everything you want. But if there's a student who's struggling currently, they need to have that core instruction and then some additional instruction as well. The same thing happens at the in the you know, the middle and high school grades, and it gets a little bit tougher there sometimes to figure out with with different structures, but you've got to find time. Sometimes I mean before school, at lunch, after school, that you can do that that targeted intervention. And you know, sometimes districts have the when the what I need time or whatever the district's calling it, but we have to do our best to keep our Kids in for that core instruction because they need to have that good solid core instruction, and we've got to try a variety of different strategies as we're doing that good core instruction.
SPEAKER_01We've talked a little bit about what this looks like um in in general. Um, and we talked at you know some of the grade levels, and and you I love that you brought up, okay, so when are we gonna do this? The time of the day, how are we gonna fit this in? Because I think that's such a big uh deal. And the importance, I was just thinking as you were talking about this, the importance of of uh keeping the student in for instruction, the general instruction, because my son, uh my older son, is in an intervention program uh often. And so he uh he has some some uh some things that um they do with him on a regular basis. Um and for a while he was being pulled at math time. Uh, and it breaks my heart. That that's just it's so sad to see that happen if he's gone during math instruction time, because it does really two things to his identity, right? I mean, it it says, hey, I'm different than everybody else. There's some reason why I'm not with my classmates when they're learning math. I'm learning math too, but I'm not learning math that they're learning. Uh so that's that's a big, that's a big deal, especially early on, and just thinking about, okay, so but I'm I'm really pleased to see that now his in his interventions that they're doing, he does so much now uh in person, uh in the classroom with his teachers, and they do things a little bit different in the classroom, which is really, really cool. So um maybe let's talk uh about what is different. So different types of intervention from elementary to say high school. What is what is different uh maybe about those two?
SPEAKER_00Yeah, that's a that's a great question. That's one of those things that you know I constantly ponder in the elementary when I have those kids all day long that allows me some of that flexibility that I don't have in the middle school and high school where I don't have that kid all day long, where you have that hard, fast 50 minutes, 55 minutes from start to end, the elementary have a little bit longer, and you know, you can find during free choice time or whatever you call it in your classroom when they're working on different centers that allows you some of that. And that there, so I think you know, the elementary is sometimes it may feel a little bit easier to find time for the intervention. But I also want to acknowledge elementary teaching is hard work because you're not just you're not just teaching math all day long. You're teaching math and you're teaching reading and you're teaching writing and you're teaching communicating. And oh yeah, there's a thing called science and social studies that we've got to try to squeeze in there. So there's so many different things that you're you're doing in there. And I think sometimes secondary folks forget that how much work it is to teach those six different things there. And and we grumble sometimes if we have three different preps in there, and you know, and when we have our district-wide meeting, somebody, a high school teacher usually sometimes will complain, Oh, I have three preps a shear, and a veteran kindergarten teacher says, I have seven preps a shear, and that really shuts it out of the way. Yeah, yeah. So we just need to acknowledge that the structure is gonna look different. So one of the things, you know, in the middle and high school, there is no real easy solution. So, you know, so some districts, you know, have a semester-long math intervention class, which if it's done correctly, may really help support those students, but it really sort of can't really be in place of that math class. So, you know, in our district, unfortunately, it's in place of the PE or the art or the music, and it gives the kids what they what they probably need, but it takes them away from that fun class that and the what they perceive as that fun class, that class where they don't have to think as hard and and do some other stuff. And we're looking at intervention sometimes, you know, if I don't feel successful in that, why do I want to have it two classes a day? Yeah. So it really comes down to what are you doing in that intervention time. And I think in that intervention time, there's what the students want to do, and there's what the students need to do. I think so often the students want then the extra little bit of support to be help me with my immediate needs, help me do my homework, help me get ready for that quiz or test. And as interventionists, we have to take that little bit longer approach. Yeah, maybe I can do a little bit of that. But we also have to look at why you are currently struggling and what can we do to backfill some of those concepts that you just don't fully understand yet. And I think in way too many school districts, if we have the self-contained intervention classes for middle school and high school, a sixth grader who's in math intervention is probably in seventh grade math intervention, is probably in eighth grade math intervention. And I think that that really defeats the purpose of intervention. The intervention really needs to be we need to target those concepts and really get them up to that grade level so that we can we can teach them with that grade level. And one of the other things that you know as I work with teachers throughout the US, so often teachers sort of unfortunately resort to teaching them tricks. And teaching them tricks isn't helpful. Number one, I think it sends the wrong message about math. Math is not a set of tricks that you need to memorize. And it comes back to that memorize, memorize, memorize, and that doesn't work well for many students. But I think it also does our students a disservice because sometimes the tricks that we teach them, the next year that trick no longer works, or in three years down the road, that trick doesn't work. Or we have this beautiful story. I had a colleague one time who had a beautiful story for how to solve equations. It's something to do with castles and kings and queens. She had this big elaborate story. Well, nobody else knew it. So then when they went to that next grade, they would ask the teacher, Oh, is this one of those castle problems? And the teacher would be like, What are you talking about? There's no castle problem in there. So I think you know, when we resort to those tricks, we we hit that. And you know, there's a fantastic set of articles from NCTM called The Rules That Expire. There's an elementary, middle school, and a high school version. There's a Nick's the tricks from Tina Cardone out in the Massachusetts area. You can just Google Nick the Trick, Nick's the Tricks, and it's a free PDF. There's a series of books called The Math Pact by Karen Carp, Barbara Doherty, and Sarah Bush, and those are the authors of The Rules That Expire. But those are really eye-opening for me as a teacher because I could see myself saying some of those things. I see myself telling my students, for instance, the square root of a negative number doesn't exist. Well, it really does. Yes. It's just called an imaginary number and later on down the road. And you know, when we first teach our kids to add, we say adding always makes your answer bigger. Well, it does when you're in early elementary. But as soon as we start to get negative numbers, all of a sudden then the world changes for that. And we don't do it with bad intentions, but we have to keep in mind we can't just tell our kids these tricks to try to get them through the content. There's a difference between getting them through the content and having them learn that content and building that into that confidence level. And I want to do whatever I can to help my students build their math confidence so that they become good, solid problem solvers and they can start to understand all the math in the world around them. And, you know, and that's really over the last few years, as we've dealt with this thing called COVID. And you look at all the graphs and all the misinformation, all the way that people are skewing things. It's time that we really spend some time focusing on we need to have highly math literate people in the in the world so they can make good judgments and not just listen to whoever is screaming the loudest at any point in time, and they can identify all of those things that we want them to be able to identify. For sure. For sure. That was beautifully said.
SPEAKER_02That was so well said, and I want to just connect some dots of some of the things that you just said to what you had said previously. You know, the whole conversation around teaching kids tricks. Um, and again, I'm drawing my own experience here. I think it can be satisfying as a teacher to teach a trick or a little mnemonic device or something because then kids are able to be quickly successful and you go, like, oh, you get it now, right? So like the kid feels good, the teacher feels good, but really if they've been taught a trick, it's not something that will make sense as they move on to expanding those mathematical ideas. So it's like starting over from scratch. So it's one of those things that it feels like a good solution because you feel like there's success in the short run, but it's actually causing issue in the long run. And I love that, you know, we'll link those resources that you mentioned in our in our show notes so that people can access them easily. Because oftentimes, like you said, no one's doing it on purpose. Um, you know, you just might not realize as an educator that you're contributing to a problem down the road. And and the other thing that I kind of just want to circle back to, you know, we talked about the importance of language and so much of what you're talking about from identifying to approaches to time. All of all of what you're sharing, Kevin, just does such an amazing job of supporting students' identity and agency in mathematics. And I think that, you know, doing that with intent and really thinking about all of the ways that we engage students in learning, and particularly, you know, there's some vulnerability in being a student who struggles and treating them with the respect and the care of knowing like this is not about your value. Like you still are perfectly capable of doing mathematics, even if you haven't found success with this mathematical topic yet. So I just love how you we've we've really talked around that kind of idea at the very center of everything you've shared today.
SPEAKER_00Well, thanks. Yeah, and it's and it's one of the goals that I always that I always try to have. You know, I I shared at the beginning, I always said, welcome to math classes, the best class of the day. What I didn't say at that point in time, you know, at the beginning of the year, when I asked them what's your favorite subject, what's your least favorite subject, and I know half of them say math is their least favorite subject. I always tell them my goal at the end of the year is that there's one subject at least that's that you like less than math. That I want math to sort of move up that totem pole. And by golly, for many of them, at the end of the year, they're like, oh, I really do like math a little bit more than I did at the beginning. And to get an eighth grade to admit that they like math a little bit more now than what they used to, that's an that's a huge thing. So I think we're looking at students who struggle. I mean, the identity of the agency is so important, and we've got to build relationships with those students. We can't give up on a student who struggles. And, you know, it gets to the middle of May, and every year we're like, oh, what am I gonna do for those last two weeks of school with with whatever kid? And you know, not talking about that, but so often, you know, I hear colleagues sometimes in December, I don't know what to do with that kid. And I just I have no idea. There's a lot of school left after that point in time, and we've got to just keep fighting and keep fighting and and have that belief in ourselves that every single student brings some math brilliance to the classroom, and just identifying what is their their math brilliance and what is what is that big thing that they're doing, and find that strength and build off of that student strength. And you know, so much about being successful in math. However, you define success, for most students it's I'm getting good grades in math. So if you define it as getting good grades, so much of it is then the student's confidence level. Right. And a student who's feeling good about math is willing to keep going and persevering when they hit that little roadblock. A student who's not feeling successful in math isn't gonna keep persevering when they hit that roadblock. So so much of it really comes back to that working with the identity and the agency for each and every student, but especially we just double down on those students who are currently experiencing a little bit of frustration with something. And we never know what's going on in their families' lives and their home lives, and students deal with so much more stuff than I've ever had to deal with. And you know, you get little glimpses into some of their home lives, and you're like, oh, it's amazing that you're as put together as you are, because I'm not sure as a as a well-educated 40-something year old person, I could handle all of the trauma that's going on in your in your family right now or in your community right now.
SPEAKER_01Yeah, it's amazing. It is, it is. Well, Kevin, you've given us some incredible things to think about uh today and shared some wisdom with us. I really appreciate uh your thoughts and and the comments that you've had uh today. I've enjoyed this interview. Um, sitting here just I don't know if our listeners can't see it, but I've been sitting here with my mouth open, just kind of this whole time trying to draw in everything that you've been talking about. Um, because it I think there's incredible wisdom there. I'm gonna go back and listen to this a couple of times to make sure that uh I've got uh those things well seated. Um so um, but really, I so appreciate you coming by uh and uh hanging out with us, doing answering some questions, talking about this incredibly important topic um uh uh of intervention. And so really appreciate it.
SPEAKER_00Well, thanks for having me. And it's it's hard work teaching. It is hard work teaching math, and it's hard work teaching math to students who feel like they're and they're not doing well who are currently struggling, but we can't give up. We've got to do it, and we don't have all the answers, and we all have our good days, we all have our not quite as good days. And there are other times that what I try may not work with a student, and God would be willing to tell the kid, no, let's try something different than next time. And you know, they've they acknowledge that and they they appreciate that and recognize oh, my teacher's not always perfect. Yeah. So I encourage all of us to to keep working hard at meeting the needs of kids.
SPEAKER_02Yeah, and you know, just some the positive attitude you bring to this. And I'm so excited for you to move into the leadership role at NCTM. I think we're gonna be learning from you for lots of years to come. So thanks.
SPEAKER_00I'm gonna learn from from each and every person as well. And you meet lots of wonderful people and and hear lots of different stories.
SPEAKER_02Yeah. All right. Thanks so much, Kevin.
SPEAKER_00Thank you.
SPEAKER_02Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us, consider leaving a review to help others find us and share the podcast with a fellow math educator. See you next time.