Transforming Math Instruction Using a SIMPLE Counting Problem: S2 E6

Speaker 1 0:00
Welcome everyone. This is tier one interventions podcast. I am one of your hosts. Jonily Zupancic, math specialist, and my co host is here, co author, partner in crime, all of those things. Cheri Dotterer and occupational therapist and neuroscience expert. Our topic today is pattern recognition, and talk about how this affects the learning of our students in schools, typical traditional mathematics instruction. Typical traditional mathematics instruction elicits that fear response every day with students, they don't get it. We're harming them every day. Now we can be like, Yeah, but I showed them six times, or we get the email from a parent. The kid took home the homework, and the parent is they have no clue. The teachers, oh my gosh. We went through three examples. It didn't work. It didn't work. That's their perspective, that's the student perspective, and perception is their reality. That is schema. We can't change that by just saying, I did my job now they need to do theirs. That's not how teaching works. We're going to take a look at the locker problem. The way that our instructional delivery system works is through what Sherry mentioned as an interleaving process. It means that typical traditional instruction. Another reason it doesn't work is because we teach one thing at a time, one standard at a time and one unit at a time. What we need to do is much more interleaving. What that means is out of context experiences that are not strung together linearly. Now you can still teach your linear textbook or your linear this, but on top of that, we want to bring in out of context exposures, to enhance student experiences. On today's task, the locker problem. I'm not going to do a locker problem unit. That's not how this works. I don't do four days of the locker problem all in a row. I don't do two weeks of a locker problem. I do multiple interactions over time with space in between. Cognitive Science says in order for the brain to retain any information, create core memories and have long term learning, we have to utilize interleaving, which is out of context, nugget dropping that is disassociated from what we're currently teaching, but will ultimately be connected. That's a very difficult way to teach, but it's the way that it's going to work. We also, as we drop these nuggets of experiences. We need to have space in between each of the interactions the way the structure of our delivery is set up, and you'll see this in the slide decks. When you have that access to these modules, you're going to see it explicitly stated. Interaction one, here is what you do. Interaction two, here is what you do. Each interaction has to have just our regular general instruction. Some people are like, when do I teach my textbook? If you do locker problem one day for 20 minutes, you teach your textbook the other 20 minutes of that day and for the next two weeks, then you bring back locker problem again for 12 minutes two weeks later, you bring back locker problem again for 40 minutes, then you start making connections to your content. It's a very counterintuitive way of thinking how to deliver math instruction. Another question I get is, when am I going to teach my standards? Here's what I'm going to show you. I'm going to show you this on a task we're not doing today. We are not doing this task today, just the staircase problem. But I just want to give you some shock and awe for a moment. We haven't even recorded the staircase mod module in our course. At the time, we're recording locker problem. But if I look at all of the standards that the staircase problem can teach here are kindergarten, first grade, second grade, and I'm just scrolling. If you can't see this, you're not getting the shock and awe value. Don't worry about it. But if you're seeing this, I just want you to see all of the standards from each grade level that can be taught through one of our tasks called the staircase problem. Now I also did this for the locker problem. Do. But the locker problem is a little different type of problem. The locker problem is so foundational for habits of mind that it's not going to hit as many standards. What we as teachers will often think is, oh, it's not important. But actually the locker problem is even more important because it directly relates to pattern recognition. The locker problem will teach every single mathematical practice. The locker problem is an innate, intuitive experience that will force students to persevere without us forcing them to persevere. The locker problem will naturally and organically create an experience where kids are able to reason abstractly, quantitatively, argue, debate with others, understand the reasoning of others, and be be able to explain their own reasoning. I'm going to show you how the locker problem in our model is using tools that are visual, that model the mathematics. The locker problem is one of the very few tasks of this model that actually teach the mathematics for you earlier grades, the locker problem creates a foundation and a front loading for math content in the later grades, it's used as an intervention tool. The locker problem has a very different purpose. In our K 12 school, every single grade level should be utilizing it, and should be utilizing it to improve pattern recognition, number sense. And then the biggest, or the highest leverage we get from the locker problem is repeated reasoning. There are fewer standards that we can teach. There's still a lot with the locker problem. However, the magnitude of the standards that we're teaching is very impactful for students. You know what we're going to I'm just going to introduce you, and we're going to play today with the locker problem. With my students, I'll even say to them, this is interaction one. We're going to do this today. We're going to throw a lot of stuff out. We're going to play with it, but we're not going to answer hardly anything today. You may answer, but I'm not going to confirm or deny what you're answering. The reason we call these interactions is we have a variety, yes, students. When we are teaching kids, if we have very gifted kids, we're talking cognitive ability and IQ above 130 kids that have an innate pattern recognition, they have an innate, intuitive understanding of number. These are all very distinguished through cognitive ability scores, IQ scores, those students only need one to two interactions with something before they know it. Forever, with only one or two interactions, they don't necessarily get the depth we need. And we talk about depth of knowledge in mathematics or in any of our content areas, our gifted kids oftentimes are missing the experiences that are going to get depth in the mathematical content. They already have an innate, intuitive depth of the content, but it's our job as teachers and facilitators to let the to facilitate the mathematics so that they get a deeper knowledge. But honestly, to have a good knowledge, they only need one to two interactions our bright kids, who we often may miss, identify as gifted, because our bright kids play the school game. They do well on achievement tests. They have high achievement our bright kids are typically the hard workers, the school players. Those kids, though, need five to eight interactions before they know it forever, but oftentimes they don't get the interactions from the school or from the teacher or from the classroom. They get it from themselves because they work harder, they do more homework, they do more interactions on their own. So some with identified gifted kids, but they're not. They've just given themselves more interactions because they've practiced things more on their own, because they know that they want to play school so that they can do better, because their motivation is higher grades. Gifted kids motivation is not higher grades.

Speaker 1 9:35
My point on all of this is our most struggling students are kids that don't have pattern recognition, have a low number sense. Our kids that struggle to access the math content might need 60 to 100 or even up to 200 interactions with the same thing before they know it forever. This is why we use a few tasks to hit a lot of standards, which is counterintuitive. Of from the way that a textbook allows us to teach our content. When we talk about various interactions, every level of student is going to get something else out of the new interaction. But if we use the locker problem three or four times during our school year, if I'm teaching my third graders and I use the locker problem three times in the third grade year,

Cheri Dotterer 10:27
if the school has deemed

Speaker 1 10:29
this philosophy worthy, the second graders and first graders have also seen the locker problem two, three or four times each of those years. Then the fourth graders, they're going to see the locker problem two or three times by the end of fourth grade. Look at how many interactions we've provided and not and these are actually more powerful and more impactful interactions than a textbook interaction, because it's experiential. It is hands on, it's visual, it's sensory, it's it includes all of those things which actually one interaction can count, sometimes as five or six interactions, because of all of the other sensory experiences that we're providing in this lesson. Let's get to it. I'm going to share the problem, I'm going to show you how it works, and then I'm going to get some of your feedback, and I'm going to allow you all to process out loud, because we've been yacking at you a lot. But that is, that is the structure of these modules is, I hate to say they're sitting yet, but they're very seminar style, so you can get as much information as possible. We are teaching you in a little bit of a different model than what we promote teaching kids. I just want you guys to understand that because you need information, you're an adult, this is how you need to access the information. The locker problem is stated as this. I tell my kids, whether they're first graders or high school students, if they're high school students, I'll say at Canary High School, whatever. At Canary Middle School, there are 1000 lockers and 1000 students. These silly students play a game of opening and closing lockers. So I tell my kids, look, don't try to make sense of it. We're not unlocking locks. We're not doing No, they're not locked. We're just opening and closing lockers in a certain pattern. That's it. Don't overthink it. Just bear with me. All right, in a moment, we're going to act this out, because one of the greatest problem solving strategies is for kids to act out the situation in order to solve it. Experiential learning, learning by doing, we have dropped so many phrases for initiatives that have come in and out of schools in the past 30 years, just in the last hour and a half that we've been here, I hope you see the power. I hope, I hope you see the power. Period. I'm not even going to add to that, okay, the rule is the lockers all begin closed. As I talk about this with students. I show them what that looks like with a visual. Now this is where Cheri expertise comes in, where I like to use these two color counters. Sometimes they're red on one side and yellow on the other. What you're going to see digitally is red and yellow. These are foam counters. They're a little thicker than the plastic ones, which are going to help kids that struggle with fine motor. But you're going to want something that has two sides. It's different on each side, because one side is going to be the closed locker, the other side is going to be the open locker, because we want this very differentiated, very therapy based. Cheri, you offered a lot of other ideas. Yes,

Cheri Dotterer 13:48
you mentioned the word Othello, almost you cut off there, but, oh, sorry, Othello has the black and white. Black and white are much easier visually to see the contrast than possibly yellow and red. They're closer in contrast, one of the things that you may see is the kids not able to see the difference with the one side to the other. White and red might be better, but red is an awkward color, especially for those kids who are colorblind. It's red and green are two in the main colors that you want to avoid. If there is a kid who has issues with the contrast, Othello pieces might be something that you can use, or you can take checkers, and sometimes they say the same thing on each side. I just happen to have these wonderful little smiley face stickers right here in front of me that I can stick on one side of the checker to make it so that both sides are different, and they can then feel it, which even if they have trouble with the vision of seeing it, they can feel the text. Tactile part of the inside of the checker, and then the smooth side of the sticker on the other side. Hopefully the sticker stays on there, because with it being bumpy, it may not stick. But you get the point is, if you haven't a student who's having trouble, change the object. Okay. There's also something else I want to share with you, with kids, from this perspective, is another thing that you can look for when we're doing flipping watch the kids, are they bringing the penny or the Othello piece or the foam piece to the edge, getting underneath it, and then flipping it and putting it in place. Or can they manipulate with their fingers enough to make the flip? If they are bringing it to the edge and flipping it, I recommend that you take a closer look at their manual dexterity, and that will be a hey, OT, I noticed this with my student. Please take us. Take an OT. Can do a screen of that student. It's going to be especially important for those of you who are doing those k1 and two era kids. Then it is going to be later on, hopefully by later on, they can do that. One of the tasks that you can do before you get the OT screen is to put dice in their hands and have them manipulate the dice or small objects, get the dice, bring it to their fingertips and put it down in a cup or something like that. Manipulate their hand, get the dice, put it down, getting and getting used to manipulating those fingers, and what they're doing with their fingers is going to help, not just flipping the coins, it's also going to help their writing skills. Y'all,

Speaker 1 17:03
let's not just slide past this. Okay, that is flipping brilliant. See what I did there? Flip flipping. Ha, wow. But in all seriousness, I I want us to not just like, rush past this. Okay, oftentimes my k1 teachers will say, You know what, I love the idea of that problem, but my kids just can't do that. They can't this, they can't that. This is the reason we have adaptations, because we have to have our k1 kids experiencing Walker problem, even if it's just playing the game and there's no other intentional mathematics that's being taught from it, they have to have the experience. Remember, we're building their schema without the experience. If kindergarten or first grade teachers say no, we'll wait until they're older to do the locker problem, we've now not. We've now just said we're not we don't have any desire to develop their schema. That is going to be detrimental down the road, mathematically, when you listen to these adaptations that Cheri is talking about, instead of not doing the task, because the kids are going to struggle, we do the task, we make it messy. We analyze it. We tell kids, you're going to struggle, this is going to be a mess. And then we assess where kids are. Then make these adaptations. See, we have to make the math accessible. This is why. And I'm going to say this and say what you will about it in Asian countries, their kids can do more complex mathematics than we can here. When the Singapore curriculum was adopted in the United States, it miserably failed. It failed, and so will tier one interventions if the training is not there to change the instructional delivery and the mindset of the teacher. It shouldn't have failed those kids for no difference than our kids cognitively, their brains are no different than our kids brains. Their situations might be different. The how people feel about education might be different. Okay, you can say what you will, but the brain structure exactly the same. If their kid can do it, our kids can do it, the way that they get their kids to do it, the way that they get their second and third graders thinking algebraically, is through tier one interventions, tasks. This is the answer. You expose kids to experiences that are high level complex mathematics, like the locker problem, and you just have them play with it at that level. You don't push the mathematics. All right. Cheri, give up. Us an unveiling of what you have been working so hard on and what we have to offer people that's just fun. Yes,

Cheri Dotterer 20:11
this came totally out of left field and totally not in my thought process until I got something on Facebook one night that said, why don't you do this? And I'm like, but I can't there's nothing we have to offer. We do. The first module that we recorded was called the pizza problem. What I've done is I've taken the pizza problem, and I've turned it into one page, quick, quick start guides that you can just take the ideas and I'm working on all of them. Okay, that's not it. That's not everything. I've also had to incorporate some ideas for writing. There's some ideas for writing. On the back of that, there is a checklist on what to look for when you've got kids who have writing struggle, where the core issues might be. But that's not all. We have some presents for you. Inside this little package is a little gift for you. We have gifts like this for you. Everybody needs stickers, right? One of them says, Be kind. Where are they? Here. They are. Can you read it. Can you back it up a little bit? Maybe, because it's the wrong way. There we go. I am brilliant. This goes along with we're gonna put it. Why do short pencils help our kids? If the kiddo, you gave a kiddo a pencil that says, I am brilliant, who's struggling, what does that tell them? Locker problem magnets. Found this amazing game. Found this amazing game. It has all of these colored stickers that are made out of squares, and there's a game that goes with it. We give you one copy, and we tell you how to find some for the rest of your classroom, the teacher survival kit, so you can use this bag for whatever you want. Plus, just for the holidays, we got some socks for you because you always want to come warm up by the fire, right? I'm wearing them along with a bangle. And we have, we're I'm still working on getting the right necklace to go with it, but we're working on that. What is this? This is a buy one, get one. Buy one, gift, one offer for you. And let me share my screen.

Speaker 1 23:03
Premise as she's getting to share her screen is, teachers are going through a lot right now. We're struggling. Sarah, you had the question of, what are the best adaptable resources? We've combined that question for each of the tasks. Like, what are the best adaptable resources for each of the tasks. We have a quick start guide. It's all based on the tasks, but it's also based on teachers need to just take care of themselves. There's a combination of this, and it's called 3d 3d the three disabilities, dyslexia, dysgraphia, dyscalculia, it's relief in 3d so that we can get some relief for our struggling students, and then just fun relief for us, like good, fun gift for us. You could actually get the subscription box for yourself, and you get a box every month with something new related to a different time. This is

Cheri Dotterer 23:59
just the holiday box that's buy one gift, one. We definitely started the subscription yet,

Speaker 1 24:04
but in but this is, like, the what is this whole thing? But what Cheri has right now is and take it away, Cheri, because you've got this. Like, how would you launch this, not only for yourself, but for someone else? Here's just a special packaging. So yeah, tell us about this. Cheri, you have how many

Cheri Dotterer 24:28
other seventh grade teachers? And I don't know if you guys do a gift exchange, but you are secret Santa. Gift could be right here right now, and it could have stuff for your fellow teachers, as well as something for you. We have a lot

Speaker 1 24:44
in store, a lot coming up, a lot to unveil. It's going to be an amazing year, not only with tier one, but also with all of these additional things that we will have to offer. Some of the things we come out with, you guys will be gifted some of that for being tier one members. Hours, and some of it will be additional, but you will be in our wheelhouse for all of the unveiling. Do.

Transcribed by https://otter.ai