Rethinking Math Education Part 2: S2 E25

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Hey everybody, welcome to tier one interventions, where we work on helping you gain the core in your classroom. I am Cheri Dotterer, your classroom coach. That's Cheri with a C and dot with a stutter. I'm here today with Joni zupanzik, your instructional coach on mathematics, and we are here to help learn. Help you learn how to deliver your math instruction in a very unique way. Today we're going to talk about the pain problem. Jon Lee, get us started. Hey everybody. I'm Jay Z. Jay Z in the house. Jonily Zupancic and tier one interventions is, as Cheri said, strengthening your core regular classroom. So this is for specifically the classroom teacher, partnering with the intervention specialist, instructional coach, curriculum leader, Principal, special service provider, occupational therapist, speech therapist, How can kids get exactly what they need in the tier one core, regular general classroom? Too often we have kids leaving the room to be pulled out for small group tier two or tier three intervention by today in 2025

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the amount of pull out that is needed or necessary, so to speak, is astronomical. We need to either avoid or severely reduce the need to pull students out of the tier one regular core general classroom.

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The strategy for doing this is strengthening the core we must unlearn, relearn and rethink how we operate in the regular classroom, how instruction is presented and delivered, so that kids, all kids, regardless of disability, ability, any type of spectrum, neurodiversity, neurodivergence, whatever students are dealing with internally or externally,

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public, private and any school should be able to meet their needs in the tier one regular, general core classroom. We can do this with Tier One interventions, mathematics mastery, math based on 12 reference tasks. Reference tasks are such that they are presented the same dirty dozen every single year, the exact same tasks from preschool through high school. They are presented multi times a year and every year, and the complexity increases over time.

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Let's tune in to part two of

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the background behind the paint problem. They never get as far as the gifted child's thinking. The gifted child never gets to go above and beyond, but with reference tasks and art instructional delivery strategy, we're able to do that. So this is a great activity for this coming Easter season. So if you're using the 120 chart and the picture that I show you, use these stickers. They have the white on the one side. They're the foam stickers. So they're, what, a millimeter or so thick.

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Here's pink one. So all they, all those are, were the eggs in the foamy stickers that you can get at Michael's.

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But don't take the sticker bath, because take the sticker back off. I just happen to have a whole bag of them,

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and I was trying. So this all came down from something that I was trying to use an eight and a half by 11 piece of paper to demonstrate something to one of my students. And I was like getting so frustrated. I went, hold on a second, and I came back, and I created the two page and then moved on. And while I was doing this, I had the most amazing experience with an adult.

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My husband was watching me work, and I introduced him to the 120 chart and how it helps kids with counting. And he's genius,

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so he actually helped me pull out 120

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purple ones, rather than having them mix and match the colors when I was doing that project. So

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this is a great opportunity to utilize a 120 chart coming up here.

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In the Easter season.

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And I'm going to put locker problem on our board, even though that was just an aside today. We also have a module for the entire locker problem. But what I also want to say that in our 120 chart module and some of the other modules.

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Oftentimes we will use a larger 120 chart and cut off the horizontal rows and move them beside each other so that you can see the 120 chart become a linear horizontal number line or a linear vertical number line. And it's important to do both, because coordinate plane is the combination of a vertical number line and horizontal number line, so we want kids to see them separately,

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each individual. But what we also do so that kids can cut and have a better accessibility with fine motor and cutting is we make the 120 charts bigger, but we also make the lines thicker. So that look, this is what they do in occupational therapy as an intervention, but we can just provide these adaptations in the regular classroom. They are already ready made in our tier one interventions program. Sarah, comment,

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I have a question,

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and I hope that this, I don't think it was detrimental in any way, but just curious your thought on it. So I have a lot of teachers who work with their special education students who are really strongly attached to the multiplication table. We've talked about 120 chart. I have a few people who are moving in that direction. I do love what Cheri said about having the students almost create one of those with a count by two or a count by four to create a multiplication reference sheet, if you will, for each of our like count bys. But I was also wondering. So we had a conversation one day, and I was like, if you're, if you're going to use the multiplication chart, maybe you could turn it into because I know something you say a lot is number as shape. And I said, Maybe instead of just, oh, what's three times five and just looking at that intersection point, okay, my answer is, 15. Could you have them like, draw the rectangles that, like encompasses that area in a sense, right? So three by five versus five by three, then I'm getting still that 15, but that they look different depending on like, the lead factor. If that makes sense, you make beautiful sense. And let me go back to my Kinder story for the 120 chart. So when we did the skip counting, by eights, and the kids went back, because that's where we stopped the story, because then we have these adaptations for the 120 chart. So remember, kids are at carpet. We're doing the eights. We're doing the whisper counting. We come back, they go to their seats, they get 120 charts, and on one chart, their goal is to skip count by eights. Now the Kinder teacher, I told her before we started,

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just trust me,

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Famous last words. I said, we're going to have kids skip count by eights today. And she's there is no way, but I'd like to see this happen. Okay, so they go back, they have they pick a 120 they all have a paper. So as they go back, I start to talk quieter, and they just get to work.

Unknown Speaker 8:40
And some kids are like, so then I start to like mini lesson at smaller groups, because they're in table groups. This is just some instructional technique. Sarah, I'm going to get to all of your questions. This is just some instructional technique. I go to smaller groups. I talk a little softer, but not too soft, because then the two groups beside them start to listen. So I'll mini lesson at one table group, and it's really at three, because some of the kids are like, what she's saying. So I'll go to one table group. I won't try to do this whole class, because I just released them. Okay, I don't make every single table get on task at the same time. Okay, so I'm at one table group, and I'm like, Okay, guys, we're going to circle the numbers on our quick dot pattern. When we were doing eights, how much is 181

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I'm like, oh, let's look at the quick dot again. How much is one eight? Let's whisper again. 123, I just make them do it. And they're like, one, eight is eight? I'm like, perfect. What's the first number we're going to circle here, eight. Do you guys know what an eight looks like? Oh, we know what an eight looks like. And they were fine. They circled eight on the 120 chart, and these are even the small versions. And no, nobody had any issue. But then I said, Okay, how much are two eights, nine?

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You know what you guys are, so amazing, so amazing. Let's look at our quick dot again. How much is 188 Okay, so let's whisper with me. Back.

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1011, 1213, 1416,

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and I said, perfect. So how much are two eights, 16? Now this is what we talk about as wrote, counting without meaning.

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I don't care that kids know what 16 means, but by doing it with this quick dot pattern, they start to understand quantity, value and magnitude and size of number.

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So we're taking root counting to a little more sensory level. So I said, Do you guys know what a 16 looks like, and the one kids? Oh, is it a one and a six or a six and a one? I'm like, it's 1616, so I just tell them these things so that there's I'm like, Oh, how much are three eights and then one kid's 24 and I'm like, Oh my gosh. And the teacher, Oh, you were right. So then I'm like, I don't know, let's check him. Our loud number was 16. Here we go. And now, remember, I'm doing this with one table group, but the two table groups beside them are listening in. So then and then two other table groups are going back crap, crazy. But who cares? Okay, it's y'all. If we focus so much, please hear this. If we focus so much on compliance

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completion,

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we will never create good, complex math experiences that are conceptual and contextual. Not 100% of kids need to be 100%

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on task 100% of the time.

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So stop. I'm gonna get to those kids. Look, they're not throwing chairs. They're not dancing on desks. Okay, that's not what I'm talking about here.

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They're talking about how, Hey, your right pocket, the white parts out on your jeans here. Let me help you. I'm going to stick it back in. Don't touch me. That's what's going on up there.

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Just let it go. Let me finish this. All right.

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16 is our loud number, 1718, 1920, 2122 2024 24 you were right. 24 loud number. What is it? 24 two and a four. All right. Then what I do is, at that one table group, I leave a copy that I made. See, I have a copy of the images of the quick dots. I leave it in the middle of that one table group, not the other two. And then I go up to there's two other table groups. I go up to one of the table groups that were much more off task, and then I do that same exact mini lesson there. So this is how I facilitate and support without telling kids what to do, I help them figure out what to do. When they figure it out, they learn it when I tell them, they only hear it so as they're doing this now, kids are equipped with this whisper counting technique. I mini lesson it twice. Other kids pick up on it.

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And now they can do this iteration and repeated reasoning with any number of eights, and I can just leave them alone, and I can let them mess up. They're all busy and on task. They're not all accurate, but I'm not going to fix that, because I need a break. Okay, the pocket outside the jeans conversation was too much for me. Okay, I finally reeled them in. It doesn't matter if they're accurate. They're in kindergarten. Okay, so

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Earth, where you go? Too, farther? Yes, go ahead.

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So you were talking about adaptations. I'm bugging in the adaptations given on us, one of the things that you will find in the tier one interventions work course, in the in that particular module, for the 120 chart, we've created the a worksheet similar to this that has all of the the spaces in between thickened. So why do we do that if we have kiddos that are struggling with cutting skills?

Unknown Speaker 14:12
But research is showing that if you give them thicker lines so that they can cut through the black area and be successful, they're going to engage more in the classroom. So we can even make them thicker, if we have to. But for the case of trying to get it on an eight and a half by 11 piece of paper, we made them that thick, and we also made the numbers a little bit bigger so kids can see them.

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So I wanted to share that with you that we have a complete 120 chart in the course. So if anybody is out there that's listening to this podcast and wants to know more about all of these adaptations that we've created.

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Already for you, give us a buzz at

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info, at Disability labs.com,

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and we will get back to you. And we will share with you more information about how to access this course called The 120 chart.

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You're muted now,

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the entire course is made up of 12 reference tasks, just like the ones we've mentioned and K 12 preschool through high school math standards all fall into each of these 12 reference tasks. We've simplified the process the entire tier one interventions course, which is the mastery math method,

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is an adaptive, condensed curriculum that can be used parallel to your current textbook, curriculum resources. So we teach you how to use your resources and deliver them in these strategic, brain based technique way. Just a little add on there for what Cheri said. Now. So I'm in my kindergarten class. We do the quick dot fact. We do the 120 chart. Kids are going and going, and they're just starting to learn about skip counting by eight.

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Now I'm going to pause for a moment, because then we did another skip, another quick dot, and the other skip counting number we did that day was twelves. Yeah, the teacher was like, I thought eight was a stretch. Now you're doing twelves. I'm going to tell you about that in a moment.

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Now, let's back up for a minute. I'm telling you all this, and I'm sharing my kindergarten story, because this is exactly what rate looks like at kindergarten

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or even second grade. You could mimic this whole thing at second grade or third grade or at eighth grade, but it would go a lot faster. You're going to do things a lot quicker.

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So I'm going to pause that Kinder story, and I'm going to go to one of Sarah's questions, and that is

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as we are looking at numbers and trying to make sense of numbers and see numbers. Another one of our reference tasks is called Making rectangles.

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The way that we can improve number sense and math Fact Fluency is to help students see numbers as shape. And that's one of the things that I do with the quick dots. And I try to make many of the shapes a basic rectangle. Rectangle is the most simple of shapes. Triangle is fairly complex, and the circle is the most complex shape, mathematically and with number. So we try to have students see number as rectangles or combinations of rectangles or extensions of rectangles.

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This, in and of itself, builds single digit multiplication Fact Fluency prior to third grade,

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when it needs to be mastered, the way that we're currently teaching multiplication facts, kids still don't have them mastered by seventh and eighth grade or even in high school. So we just have to agree it's not working. We're telling you what does work. So one of the other things that I have students do, Sarah, you talked about the multiplication chart. I like a blank multiplication chart, a multiplication chart that doesn't have any numbers there.

Unknown Speaker 18:52
We know that if students can see number as shape, specifically as rectangle, it starts to connect and associate that experience, which leads to long term learning and increase in memory and retention of content. So if I have a blank multiplication chart, and I've got five times three, and I outline five times three, I actually have a rectangle that is a five by three, and we call this the dimension chart. Yesterday in my kindergarten class, we began to make squares, which is a type of rectangle. They used blocks,

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and I talked about the dimensions a square, the dimensions meaning how tall, how long, have to be equal and the same number. So we can just count the number of blocks here, and in the final connector block, this connector block right here, we can write the number 15, because.

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Because the 15 shows that my array number for this rectangle, the number of unit blocks, is 15, hence three times five is 15. Hence, what is my skip counting number? It's either five three times or it's three five times. So another one of our modules goes through the entire progression of making rectangles, and this is one example of how we can do that to improve number sense and make shapes, thoughts, comments, questions on that. I want to just add to that I had my kids do now, Sarah, I don't know it was one of the things, and I ended up having my kids do it. I had two dice. So I'm not sure if my case did it. I know my first second and third graders did it. We had two dice, and you can look it up. It was a multiplication page. It said multiplication, and the page didn't have numbers on top and bottom like us did, but when they rolled the dice, they could take like you say three or five, and they could go across three down five. But they that's how we did it, and what they did is, and I did it with them, and they colored in their box because we used we colored as a the OT so we colored in the box, and I told them they could place it wherever they wanted. They were making their rectangles, and I said, Oh, three times five. What is that? And they counted out the box, and they counted their numbers, those that didn't know it, and my older kids that didn't know it would tell me the numbers. But I did it as coloring, but, but they I said, it also looks like a Tetris. You know what I'm saying. So they were trying to fit in whatever they Oh, we need to roll one times three, because I can fit in a long rectangle. They were trying to tell me what they needed, but two dice, roll it out, pick the number, put it where you want it. So that's how I did it with my kids. And when you roll the dice, let's say we rolled a three and a five. We did this, here's my next facilitation question,

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what other box will 15 go in?

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There's another place where 15 can go,

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because I can either do five on top and three on the side, or three on top and five on the side. So the other box that 15 can go is here. So we're constantly creating in k1, two. We're we're building with blocks. I left this out, but we're building with blocks, rectangles, and then we're charting and modeling the rectangle we build, and then putting the array number, meaning how many blocks did it take to make a five by three, or a three by five? That's our array number.

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And then in third grade, all of the array numbers turn into Oh, that number is our area. Do you see the progression of associations and connections to rectangles understanding number using skip counting? This is how we teach rate in primary. That's the whole point of this. And we can use these tasks to do other follow up, thoughts, comments.

Unknown Speaker 23:30
This is just like, maybe a bit of a critique, or a point where I'm like, Ooh, I wish this was a little better. I don't know. I think Cheri said you have that PDF in the course. What I tried to look for, though. Because if I want to do square is like square blocks for each number, so that then they can like you to your point. If I want to move to squares, then they're going to see that square shape compared to the rectangle. Yeah. U T full. And I will get one of those templates made. Sarah, you are a rock star now you just know it's not going to show up anytime soon, because you'll have to email me and there's like, free ones that you can like Google and download or whatever. So no, no shade on getting that done. That's not I'm just saying no, but I am that is top priority at this point, because that makes a good point. Cheri, the connection to centimeter grid, if it's actually on centimeter squares, then we can have physical centimeter blocks to go on top of it. Do you see why we need each other? Because all of these apps adaptations just increases the complexity and the rigor of the mathematics being able to use these manipulatives in a way that is going to create the foundation for so many of our math standards. Other thoughts.

Unknown Speaker 25:00
I'm going to add. Now, here's more accessibility. You take him to the gym, and you do your 120 chart in the gym, and do it big and physical. Let the kids, if they want to do lockers open and close, you stand and squat however you want to do it. But you can do it in the big physical modality as or come up with big thing, I don't know you come up with, you got teachers. Get all the classrooms in there together. Do the whole thing however you want to do it, but do it in the big physicality kind of thing, because some kids need that physical mode to learn things as well. Let's get physical. I want to get physical.

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Let's get Theresa. You got her singing? Oh no, hey there. There's always a song breakout, Cheri Teresa. Talk to us a little bit about the cognitive the neuroscience, aspect of physical movement and why it's necessary.

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We have hidden senses. I bet you thought you only have five. We actually have several more. And those hidden senses that we have are called proprioception. You may have heard that word somewhere along line, but don't really understand what it means. There's also vestibular, there's interoception, there's thing, and a lot of you people use the word kinesthetic, but don't really understand what it truly means. So let's go back. Proprioception really is an a sense sensation inside your joints that tells your brain what that joint is doing. So when we're holding a pencil, the little joints inside your fingers, as you're moving to write letters, is telling your brain how to move that finger to make that particular letter. Kids with disabilities lack that sense. We need to find other ways to get that deep pressure into that joint so that they can understand what to do to get that letter written.

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When we add movement like Teresa was talking about, we add vestibular, which is generally any movement pattern that moves our head around, what the vestibular system is doing is trying to keep our head perpendicular to the floor, to the ground.

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That's why, when you get off a roller coaster, your head's going, I don't know where I am, and you're walking all over the place for that first moment or two, till your brain

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and your eyes and your ears and your brain all go, oh, that this is where the ground is again. This is where I'm supposed to be.

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Gymnasts learn how to negotiate the vestibular system in a hyper

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sensitive hyper Wow way, because they're able to flip themselves on all different kinds of directions that kind of take the brain to a new level. So they learn that a lot of sports will do that with the with kids, and that's why movement is so essential, because they can take that movement that they have the and that improvement in that nervous system, bring it back to the classroom, and they excel better in their

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in the classroom.

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I also mentioned interoception, and that is like intuition. It's that feeling inside that tells you when something's not right?

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There's more to the story, but let's just go with that simple explanation of it. We talk about this periodically here on tier one interventions podcast, but today, it really is hitting home, because

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we're able to take the mathematics, the sensory stuff, and we're all we're putting it all together, and we're showing you how the whole picture works today. It's real blessing. Thank you. Jonily, no, this is really beautiful. Oh, go ahead. I was just trying to attach to that saying the kids that are not like you've always talked about, the kids that have that innate math, the kids that do not have the innate math need multiple inputs. So because they don't have that, because they need that multiple inputs, some kids need to see it and hear it and touch it. That's why we need to address those. They may be smart kids in other ways, but they just need extra inputs. And then we have the special ed kids who need and then they need extra exposure so they may get it from the extra exposures that we do. And that's why we as the OTs and the PTS have to give them that extra exposure and come up with clever ways of doing that. And in my again, research Bell.

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Movement and math come together, and that's another reason why you want to give some extra movement with the math.

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And this is really beautiful. This is a later module in the course, for a lot of reason, because what ends up happening is see, in order to do the paint problem?

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Kids need all of these other experiences before the paint problem.

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However, what I'm going to tell you is paint problems should be one of our tasks the first 15 days. So that means in the first 14 days of school, kids need experiences with all of this. So when we talk about first 15 days of math, they get their first exposure of experiences. Now, as Teresa made a great point, kids need extra exposures interactions over time, our truly gifted kids only need one to two interactions before they have forever learning. Our bright kids, whose parents think they're gifted, they still need five to seven exposures, but our most struggling kids might need 40 to 100 to 200 exposures before they learn it and they before it's ingrained in them before it's lifetime learning.

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And so the way typical, traditional mathematics is set up to be taught and delivered, there is no way to get extra exposures. There's no way. So this is where I say we have to unlearn, relearn and rethink how we're delivering math instruction. And we do that in 15 day cycles. We take each of our reference tasks. You might pick five, there are 12, and we expect Kirk,

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Kirk, Kirk.

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We just had a comment here isn't homework, extra exposure? Yeah, don't get me started on that nonsense. Anywho.

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So to get extra exposures, we think in 15 day cycles through our math year. So anything that is absolutely essential, I'm telling you today, the only thing that's essential is rate. What I'm doing today is giving you all of these examples of what rate looks like.

Unknown Speaker 32:27
Kids need exposures to quick dots, 120 chart locker problem, making rectangles, seeing number as shape, blank, dimension charts, blank multiplication charts, array numbers, everything I've already mentioned, they need exposures to, I would say, every 15 days of the school year, because once we put it out, there are so many levels to it that as they get these constant exposures, our struggling kids get learning that sticks, and our highly gifted kids get to increase their complexity every time they see the new exposure, the goal is different for different students, and then, because the reference tasks are the same every year, we give the same exposures to those tasks and continue to increase the complexity. So it's a very unique, counterintuitive, brain based cognitive system of delivery of math instruction.

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If I go back to my kindergarten story,

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we did the 120 we did the quick dots the 120 chart. 120 chart has a lot of uses. We talked about the locker problem as an extension, use of the 120 chart, making rectangles, seeing number as shape. What I next did with these kindergarteners and you guys, this was all in 35 minutes.

Unknown Speaker 33:53
35 minutes I did all this. Okay, what I did next with the kindergarteners is, I said, we're going to do another quick dot. We're going to do another one. I said, Okay, here we go. How many dots raise a quiet hand?

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Boom, okay. Then we go through the process below, I'm going to skip all that

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now on your 120 chart, you are going to, instead of skip counting by eights. You're going to pick a second 120 chart, and we're going to skip count by twelves. What shape is this? Now, some of the kids were like, Oh, that's a square this time. So we said, Okay, wait a minute.

Unknown Speaker 34:34
How many dots tall? Three, how many dots long? Four? Oh, it's three. The same as four. Is that the same number? They're like, No, I'm like good, because it's not, in order to have a square, you must have the same tall and the same long, you must have the same number for dimensions, you must have an equal so I use all these different words so they can hear it. They're not note taking on it. They're just getting exposed to all these words over and over again. Okay, don't make a big deal of it. They don't have to make.

Unknown Speaker 35:00
Master. It's kindergarten. We just use these exposure languages so that kids hear it and hear it again and again. So then I sing my song.

Unknown Speaker 35:11
Okay? So we whisper Cal and we do the whole thing we did with eights. I'm not going to get into that. But then after that, I was like, we're going to sing. It's not we're going to learn a song. Ready? Here we go. 1220, 430-648-6070,

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280-496-1081,

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2132,

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let's do one more. It's 144

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now, when you hear this on the audio, okay, the kids are gonna be like

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but it's kinder. We start the 12 song in kinder. We sing it multiple times a year. They start to pick up on it. Wrote counting with no meaning. That is exactly how we enhance the opportunity to understand rate later on, okay? And then we sang it again. And sang it again, did it up. So I'm like, Okay, that's it, moving on. The last thing that we're going to do today, my little peeps, Okay, last thing we're going to do today is we saw a lot of numbers. We skip counted by numbers, and we saw these numbers as rectangles. Here's the final thing we're going to explore. I want to know what numbers we could make that would make squares. And I had kids predict and guess. And then I gave them blocks, and I said, your only goal right now is to make squares, because there's this pizza company and they only make square pizzas.

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Boom. And then you can hear on the audio how I facilitated it. The point of all that is

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I purposefully wanted to give kids as many exposures to different reference tasks in 35 minutes at the primary level, at a high poverty school with students that have many issues and struggles, and they engage beautifully and on the audio, you can Hear what they're coming up with mathematically, and it's absolutely uncharacteristic of a kindergarten classroom, even if you are a ninth grade algebra one teacher, I want you to listen to this kindergarten audio, because you are going to pick up on these techniques. Are you going to present it the same way I present it? No, please. Are you going to talk the same way I'm going to talk. No, please. Are you going to do the same tasks? Yes, please, the eights and the twelves and the quick dots and the 120 charts. But it's going to happen much quicker

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for these older students,

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thoughts, comments, questions, before we deliberately and intentionally. Jump to part two, and we're going to talk a little bit about some of the functional pieces, which we've already done, but I want to make it a point to be like, why are we doing all of this? And then I'm going to make a functional connection to rate. But any thoughts, comments, questions, to close out part one, i.

Transcribed by https://otter.ai