Cognitve Science Meets Counting: S2 E16

The conversation on Saturday Math was about cognitive science of math. And what are some of the terms that Jonily and I use when we are teaching the instruction methods that we are teaching, and that is spaced repetition, interleaving, spaced practice, and cognitive feedback. I hope I got them right. Jonily's shaking her head. Close enough.

And in Impact on Impact Wednesday, we followed up with What parts of the brain turn on when those types of instruction are provided and what parts of the brain shut off? What we discovered in that second part was that anything that has to do with executive function shuts off. How are kids going to learn and make connections if those parts of the brain that kind of put things together get shut down? If we're not teaching using a cognitive science method.

Go back, listen to the episodes from the second week in January. I will have the information in the show notes as to which episodes they are. And look forward to some more sessions that correlate to the science of math. And for anybody here at Tier 1 Interventions Workshop today, I have the slides tuned up here that we can take some time and look at those as as a group and go into them a little bit deeper here in Tier 1 Interventions. Rise and shine, good morning ladies!

to tell them about interleaving and I want to tell them about all those good things, it's just, it doesn't flow out of me as quickly as, As my brain wants to say it. So those are the things I need to work on.

What I do is I basically script all of my mini chunks for the first two or three sentences, so that when someone brings that up and I'm going to be responsive teaching and I'm going to teach on that chunk, I already know the two or three sentences that I'm going to say first, because really our hang up when we're speaking and presenting Our hangup are the first two or three sentences. Once we get the first two or three sentences out, then everything else flows. The intro is what's difficult.

So those are the sentences that I practice and memorize so that when I'm teaching on that topic, it flows really beautifully. So that's just a little piece of how I do it. When I say I plan in chunks and not sequences, What I do is I document about 30 different chunks of topics that I present on. And for each of those, I write my best three sentences. That's an exercise that I do, and then I literally memorize those. Then I can ad lib after that.

That is a really great question, and these are the things at the end of the month when we jump into certification, these are the things that I want to pull back the curtain and tell you exactly what I do. I used to not know what I did because people would say to me, Jonily, how do you do that? But how do you say it that way? And how do you get people on the edge of their seat? And how do you Make sure that you don't pause and it sounds awkward.

How do you make it sound like you're not reading off a PowerPoint? And I used to not know, but what I've done in about the last eight to ten years is I've unpacked the processes that I use to speak clearly, change my tone, change my facial expressions, watch my hand gestures, and figure out what language comes through my lips. Teresa, you are so insightful and asking the exact correct questions, and that is what I have analyzed for myself so that I can better help others.

Again, I never used to be able to do that. That's what we're going to focus on as we go into the end of this month. Great question. Other thoughts or questions on that topic? And you'll notice that I haven't gotten there yet. Tell us more about the let's talk about this for a moment. Sarah, good morning. You have your hand raised. Go ahead. Good

And I know I'm not there yet with what you have shared with me and taught me. And I and I think to Cheri's point, like sometimes, again, I know you know what you're doing, but my mind is like definitely more linear. And I'm like give me the book. Give me the And here's, kindergarten, first grade, blah, blah, blah, like all the like chapter by chapter.

And I understand that's not like always the most beneficial way either, and we've talked about that, like brain development, like going here, then going there, then going here, coming back here. And so anyway, it's just taking time, but I think in some ways time is just time and experience. Helps to develop a little bit better understanding, and then when you really own something, then you're able to communicate it, if that makes sense.

When people say to me, I want to do what you do, I want to do it how you do it. First of all, I don't want you to do it how I do it. I want to teach you to be the best you. Because the way I do it, You can't pull off. The way Cheri does it, I can't pull off. The way Teresa does it, I can't pull off.

And so we want to make us the best that we can be, but on the other side of that, I think that as we start to Analyze, we do that through Sarah, and I'm going to stamp exactly what you said because this is really good. Just watching it over and over and over again. This is a really exciting group we have here, and I'll tell you why. Actually, you all know why, because I think you all know each other. But a couple of things I know, Kirk, We were you, we'd wanna be you too.

I tell my family all the time, if I were you, I'd wanna be me too. I'd wanna be me too. I'd want, and my kids are like, mom, please, come on. So yeah, let's just face it. No, anyway Natalie and Amy are certified coaches. Amy, I have not gone back and looked through all your texts. You know me. I will get to it and I will focus on it, but I need the time to do it and I appreciate you so much, but so much has happened. Amy, I did see your one question. What year were you certified?

I think it was 2019. I think it was 2019. Natalie, do you remember the year you were certified? Was it 2021? I think

I think you know some of our Certified Coaches, Natalie, Amy, Krista, that have been here.

Life gets in the way and but when we talk about the first session of Certified Coaching and we start with the phrase, I'm the nation's leading expert in, certified coaching can be more than just math achievement formula. It can be thinking about lots of things that you want your face to be known for. Think about that also. Cheri I'm always hijacking our topic for today, but it's very exciting.

If we look at this group, we've got current certified coaches and we've got people jumping into the program and We are all just so committed and move in this movement so that so many people can experience it and grow from it. Thanks for being here.

One of the things that we were thinking about is I've created these quick start guides for the different reference tasks. Would that be something that you would find value in if we did a digital subscription that Just highlighted those that you could print them off yourself digitally. Would that be something, you would pay for ? Because I was thinking about putting those together. I can start, I can set it up and do that, but I wanted to ask before I did it.

That is because NumberSense is the foundation of understanding concept. Not, NumberSense doesn't necessarily correlate or doesn't correlate with procedures. Procedures are a different animal. Today, we're going to be looking at NumberSense and the staircase. Jonily, take it away.

Cheri talked about the two podcasts, she talked about our intro opinions of Science of Math and Cognitive Science of Learning, and how we need a cognitive science method. If we zoom out, today is part of what we call Tier 1 Interventions podcast. The bigger umbrella of Tier 1 interventions is the Mastery Math Model. The Mastery Math Model is the cognitive science method Cheri was talking about. So Tier 1, and I like to write as I talk, so I want us to get a visual of this.

If I have that bigger umbrella, and if we want everything focused within cognitive science, COGSci, we call that the Mastery Math Method, which is a core Tier 1 general classroom structure and approach to teaching and learning. That is when we talk about Tier 1 interventions, that's the big idea. If I go to a different color on this, one of the Tier 1 interventions topics is today's topic, and that is staircase. We also know that above and beyond Tier 1.

We also have Tier 2 and Tier 3 math interventions that depend on a strong core Tier 1. That's not anything we're talking about today, but I want you all to see the big picture of where all of this falls, and all of this is grounded in cognitive science. And as

And the regular math teacher, and the tier one math teacher, and the instructional coach and, we need all of these stakeholders to understand all of this, and Cheri, that is, I want to, yes, special ed, paraprofessionals, all stakeholders need to understand And I'll put a bigger umbrella, big cloud here. All stakeholders need to understand the entire vision and process. The entire vision and process.

And the reason that I back us up before we jump into this part of the session is often when I present a topic, people get really amped up about it. We have some really good game changing takeaways and people send me testimonials all the time about, look at what my kids did. Look what they said. Here's a picture. They were so excited. It was so fun. It was so impactful. I uncovered this. But many times, what we're missing is where that fits into the big picture.

Now, remember, in Tier 1 interventions, there are 12 of these. There's a dirty dozen set of tasks. Now, within all of this, I have to actually put a bottom umbrella.

A bottom umbrella. Because, again, all of this is grounded in cognitive science. But the goal of everything is improving number sense and understanding of number, which I just said a few minutes ago is all about counting. So the whole board is about counting, like counting is the key. So this vision and this mission, and I'll move that away for a moment because I don't want us to get distracted by it. is really all embedded in a bigger picture of where all these pieces fit.

I think that's important to say. The other important thing that I want to say, and I want to pull this up and draw it for you today, I want two different ways of visualizing big picture, and I thought I had it up, but I didn't, so give me just four seconds to do this. In order to make certain that we don't take a new model and implement it with our old beliefs, we have to talk about a new belief system. When Singapore math came to the United States, Singapore math is powerful.

The strategies, the techniques. But they're grounded in a certain instructional philosophy. So when quote unquote Singapore math came to the United States in the form of a textbook, we as Americans completely butchered it because we were implementing this really powerful model without the inner philosophies and beliefs and frameworks. So we were Americanizing the Singapore math method. And it completely crashed and burned.

In order to implement a new model, we have to invest in a new belief system. We call this belief system the Five Seasons of Mathematics. So if we start our year in August, and let's say we go to June, here's our entire year, In a typical traditional system, we have Unit 1, Unit 2, Unit 3, Unit 4.

Some of the spacing is a little bit bigger, a little bit smaller, and that is our mastery way of thinking, but we need to have An implementation model that is an exposure way of thinking and it's what I call an exposure map. The mastery map is such that our district creates this pacing guide or our textbook becomes the pacing guide. If we have a mastery map, which is actually it's fine. I'm not telling us to get rid of The Mastery Map, which I'm going to list in pink here.

We have Unit 1, Unit 2, Unit 3, Unit 4, Unit 5, and then what happens is the end of the year gets near and then we're like, oh, we have to fit all these in. And so we shortchange a lot of our curriculum. And it happens every year. By the time March 1st comes, we're in this panic mode, and it's because we've tried new things, we've used a new textbook, we've tried to implement a new model, but we have not transitioned our mindset and our philosophy about the delivery.

This new model This exposure map is the five seasons of mathematics throughout the year. The first season is the most essential. This first season is called First 15 Days. In the first 15 days, we expose every single one of these dirty dozen in an intro, very quick exposure, maybe in 12 minutes. And just get a taste of what that is. But for every single task, that we do. Kids get a little piece of it.

Now, I'm going to stop sharing there because I don't want to share the whole five seasons. I want to go right into what Staircase looks like in season one and what our purpose is for this, which is, let's go back to our Staircase slide. You guys are going to be proud of me today because what I've done is I have about four linear maps going on right now. I'm teaching to you very linearly today. I want you to notice that I've done this for you. You're welcome, okay?

But I actually have four linear presentations today. It's the staircase, Which is the counting and the number sense and all that. The second is this cognitive science brain base that Cheri is going to keep like bringing in as I present. The third is the model and then the fourth is The belief system of the model, which is the five season of mathematics. I've got four linear topics that I'm presenting today, but I'm going to be bouncing around between each one.

Tier one math interventions, reference task number eight of the dirty dozen is the staircase, and the staircase is like a quick dot. The QuickDot module is another module. If you want to watch and listen to that before, if you're watching the recording of this, you might want to pause the Staircase recording and go listen to the QuickDot module because you'll get the foundation of what a QuickDot is. I'm not going to re explain that here, but I want to make that connection.

Also, in this Staircase chunk, I remind us of all of the Dirty Dozen. The 12 reference tasks are exactly the same from preschool through high school for every grade level and every course. They're the exact same task, but they vary depending on the standards of the grade level and the ability level of the students in that grade level that we are exposing the task to. And for our non math and our non academic and our support staff. And for our parents and our interventionists.

And those of us that are trying to improve executive functioning with kids, improve fine motor, improve visual processing, for those of us that are trying to just help kids function, and that is our main objective and goal for our students, not necessarily the math, these four focuses that we're going to go through today in presenting the staircase problem are exactly what those stakeholders need. Cheri has already mentioned these, but the first is How do we increase focus and engagement?

Now, I will tell you, of the stakeholders that I mentioned, the regular math classroom teacher has been asking this million dollar question for years. My kids are not focused, they're not engaged, they're not on task, they can't work independently, there's no perseverance, there's no this is the complaint of everyone. How do we use Staircase to increase focus and engagement? In Season 1 We present a drip of it and here's what that looks like. In a moment I'm going to show you a pattern.

I want you to tell me about this pattern. Now you guys play along with me because this is not a reference task that I teach on a lot. The most frequent reference tasks that I teach on are paper folding, 120 chart, Jesse and Kay, pizza problem, making rectangles. Because those ones actually teach more mathematics than the staircase. So let's play along with me for a moment. Tell me about this pattern of blocks that you notice. Tell me about this pattern. How many stages are missing?

Each column is one less than the column before. And Sarah, that's a great comment because I'm going to tell you what I experience with students. When I show this to students, Amy, your first graders usually say the first one is included in the next one. That, I don't think we, let's sit on that for a minute before I go back to Sarah's comment. I don't think we realize how brilliant that is for a first grader.

And we never, in mathematics, we never give kids time to think and process and share their perspective. So if I go back to the question, how do we increase focus and engagement? We help kids feel like they belong and that they matter. And how do we do that? Here are the exact steps. Use my favorite three words. Show them a stimulus, something that's going to stimulate mathematical thinking, reasoning, and sensemaking, like what I've just shown you, this picture of these blocks.

Do not ask a content related question. Use my favorite three words, not I love you, tell me about, and let kids share. What that tells them is, I care what you think. I care about your thinking. You belong here. You matter. Your perspective is important. So how do I get kids focused and engaged? This is the first step of the process. Now the stimulus, you notice, can't have a lot of noise. Not the noise we hear, but the noise we see. Words, questions that get in the way.

Our stimulus cannot prompt answer getting and solving. My responses, go back and listen to the recording of this. What were my responses to the comments? Love that. Now we're fancy. Okay. I'm not confirming or denying anything. Now I'm gonna go back to Sarah's comment. Each column is one less than the column before. Many of my middle school, upper elementary students, even high school students will say, because of Sarah's comment, each column is one less than before.

They'll say that as the pattern grows, there's one more each time. Therefore, it's a linear function. I'm going to tell you right now, I don't tell this to kids, but because I'm presenting to adults right now, this is not linear. There's not a constant rate. I just wanted to give that. I don't do that in the classroom with kids, but I say that in my trainings with adults, just So that I can continue to stimulate your thinking.

I'll go back to what Natalie has said here, how many stages are missing. What I typically do next is I will define some things for students. I will say, look, in a moment we're going to get blocks and we're going to build. So in a moment you're going to get some blocks and you're going to build and play. Now this may happen the first day that I introduce it. If this is season one, the first 15 days of school, I might spend 30 minutes on this. It's okay.

But if I don't want to spend a lot of time, I will say, the next time we come back to this problem, we're going to use blocks and you're going to get to play. And then I may not come back to this until season two in mathematics. Let me go back to that. Okay. So season two in mathematics. I want to get a different, I want to get blue here. Okay. Season 2 in Mathematics goes from about October to December. Season 2 in Mathematics goes from about October to December. to December.

And this is where, after we have a very intense first 15 days, because we're exposing all of our curriculum we have to be on our game. We have to be creative, we have to be intense, we have to be the best facilitator we can be. During this season two, from October to December, we can chill out instructionally.

This is a lot of times where people are like, okay, Jonily, I've done your first 15 days, I need to jump into my textbook, I need to get back to linear, I need to go to my pa This is where you can really do whatever you want. However, if you have done part of Staircase in Season 1, maybe mid October, you might bring Staircase back and say, We saw this pattern about a month ago. We saw this pattern about a month ago. What do you remember about this?

Tell me about this pattern again, and today we're going to play with it. We can roll this out throughout the year, not in one sitting. That is the power of the model. And if we go back to what Cheri is talking about with the neuroscience and the cognitive science, what I've just done are two of them in, actually three of them, interleaving, spaced repetition, and retrieval practice.

When I come, when I do a hint of staircase here, then I do my second interaction of staircase, I've left space I've left space between that, and I've done a lot of other mathematics unrelated to staircase. That's interleaving, out of context. It's also spaced practice because I've left space between the first interaction and the second interaction of the same chunk, of the same task.

Then, if I grab a different color here, Then, when I'm at this point, instead of jumping in and me reminding students of what we've done before, I go back to my favorite three words. Tell me about this pattern and what we talked about the last time. That is the prompt for retrieval practice. The reason retrieval practice is so essential is because we need to forget.

Kids are either going to say, Oh, I remember you were wearing that pink shirt because I loved it because the bottom was like a U and I kept looking at that. And then you had pink shoes, but they were a different shade of pink. It's going to be insane what kids remember about the moment. And memory is about the moment and the emotion. We, I'm going to trigger you Cheri, so be ready to say some things.

Memory, deep memory, deep core memories are about the experience, the moment, And the emotion of that moment. So a month later, kids are going to remember the strangest things. Now on the flip side, some kids are going to be like, I forget, I don't remember doing that. Or they're going to be like, Oh, I was absent that day. I was absent. See, this model doesn't matter if kids are absent. If you have kids that are absent, 30 and 40 days every year. This model negates their absences.

This does everything. It does everything. Kids will remember this, but that is retrieval practice. And when kids say I forget or I wasn't here, I will then celebrate forgetting. Forgetting is necessary because the process we do immediately after, the re remembering, is what deepens those grooves, deepens the neural pathways in the brain, and makes long term memory and retention of content.