Rethinking Math Education part 1: S2 E24

Special Service Provider, Occupational Therapist, Speech Therapist. How can kids get exactly what they need in the Tier 1 Core Regular General Classroom? Too often we have kids leaving the room to be pulled out for small group Tier 2 or Tier 3 intervention. By today, in 2025, The amount of pullout 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 1 Regular Core General Classroom.

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, public, private, and any school should be able to meet their needs in the Tier 1 Regular General Core Classroom.

We can do this with Tier 1 Interventions Mathematics, Mastery Math, based on 12 reference tasks. Reference tasks are such that they are presented, the same dirty dozen, to students. 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.

These tasks are sensory based, multi sensory, neuroscience, cognitively science, strategized. To help teachers and specialists as well as support specialists and school leaders create learning environments and experiences in the regular classroom. I know that's a long introduction, but as we have been presenting each module of tier 1 interventions, oftentimes we jump right into the content and I want to make sure that we review. And restate and make known what our purpose is.

And our purpose is for all students to get exactly what they need in the regular classroom so that we can. Minimize the number of times and the number of students that are pulled from the regular classroom. Basically, we need to reinvent education. We are going to look at a few different parts today. At a few different Today I'm going to back up because although our reference task today is the paint problem is not about the paint problem at all.

We are going to break down today's module into What is the most essential concept for math learning? Because the paint problem is a vehicle to get to that most essential concept. That's the first thing we're going to talk about is the most essential concept. If students just knew this math content piece, They could do almost anything mathematically. And this essential concept is in the standards subtly, not explicitly, from preschool through high school.

Our first part today, and to launch into that, I'm going to say part one is looking at the essential standard. What are the essential standards for math? And then we're going to talk about how the paint problem facilitates that. Big part two are direct service providers. At one point in this session today, I'm going to say part two. How do we meet students functional needs? What are the most important functional needs that kids have that we can bring into the regular core classroom?

Because what benefits, what is necessary for some, benefits all.

Math essentials. Special Service Essentials, Functional Essentials, Non Academic Essentials. And then finally, we are going to unpack the paint problem mathematically. I'm going to write that down because I want to keep track of our checklist today. And I'm going to write this on the top of here because this is just going to be our, like, when we go back to this, I will section this into Part 1, Part 2, Part 3. Part one today, math essentials, and actually there's just one essential. That's it.

There's only one thing. What's the one thing? There was a movie with Billy Crystal. The name has slipped me. We'll think of it, but the premise is. The idea is he's trying to search for the one thing. What makes humans happy? What's the one thing? Because I want, he goes on this journey to find this one thing. And it's the secret of happiness. What he finds out in the end is it's not as profound as what he originally thought. And he also found out That, City Slickers, thank you. City Slickers.

He also found out that the one thing may be slightly different for others. In mathematics, there is a one thing. There's a one thing and it's not as profound as what you think it's going to be. I'm gonna say it and you're gonna be like, that can't be the one thing, that doesn't even make sense. But also paralleling the movie. That one thing looks different at every grade level. So what we're going to unpack today is the one math essential, and then how that progresses through the grades.

What does that look like at first grade? What does it look like at fourth grade? What does it look like at seventh grade? What does it look like in tenth grade geometry? Because what we're missing in schools mathematically is a progression of experiences. That kids can build upon the previous year. Now we think we're doing that. We think we're doing that because the fourth grade teacher will say you guys, I know you learned this last year.

It's not about the content and the learning, it's about the experiences they were engaged in. And that's the pure essence of reference tasks. We're going to break down the essential, but it's not always about the math in the math classroom. Now, secondary teachers, hear me out. I'm going to pick on you for a minute because I am 712 secondary certified. I am one of you. We have to be humbled. We do not just teach mathematics. We teach life and functionality. And through that, mathematics evolves.

Because mathematics is thinking, it's reasoning, it's sense making. Mathematics is a training and exercising of the mind. Mathematics! is how we start to think logically, conceptually, contextually, and then we use those skills to our advantage in life. The second part of today is going to be the non academic.

The functional and we have two of our amazing experts here today, Cheri and Teresa from the medical world, from the occupational therapy world that are going to be able to give us insight on what some of these key functionalities are. What are these subtle things that we can teach that are going to help our human beings in our classrooms? Function and live life better because we as the adults in the room have control over doing that through our content and not just through the math content.

We're going to talk about through the math content specifically with Tier 1 interventions, but not just through the math content. We could do this through phys ed, through the arts, science, social studies. And then Part 3 today is unpacking the reference task. The paint problem and referring to how it relates to our academic and non academic standards.

Now, in addition to that, in addition to that, there are 4 questions that we always like to answer, but our session today is not going to be broken down into these 4 parts. I'm going to put the 4 questions that we. Answer through this, like what's our why? Like, why do we care about this? I'm going to put that off to the side because other modules have been structured in that format. But today we're just going to keep those four things in mind as we go through each of these parts.

Each of these parts will connect. To these other structures and one is how do we and I'll call this a how do we increase focus and engagement in the classroom. Because we talk in each module about how reference tasks do all 4 of these things that I'm going to list and then B, how do we individualize? With one lesson, less prep and less stress for the adult. That's the key. We all know ways of individualizing that take 17 hours to plan.

No, we want to minimize the planning time, prep time, and stress time, and be able to do one lesson for an entire group of all ability levels. And be able to individualize this. The third piece is, How do we make math accessible? This is why I don't write these because I don't know how to spell accessible. I think that's correct, but chat me if not. And we cannot make math accessible by stripping the complexity and simplifying it. Because that's what we do. And it's not working.

How do we increase the complexity and rigor of mathematics, even for our most struggling student, but also increase the accessibility at the same time? These are outcomes that we want from Tier 1 interventions. techniques. And then finally, how do we improve memory and retention of content? Here are all of the pieces that if you go back and watch any other module in Tier 1 Interventions Level 1, Year 1, different pieces of this are focused on depending on the reference task.

There's our overview, and part one, right now, part one, is what are the math power standards. And I'm gonna make that singular and not plural. What is the standard, the concept, the content piece that if I had to pick just one to teach at every grade level, this would not only build fact fluency, automaticity, improved number sense, it would do everything that we want kids to have mathematically. In the chat right now, go ahead and type what you think. The one thing is. One. One concept.

That's it. See, you all are well versed. Counting and skip counting is a part of the concept. Yes. Relationships. What is the big math concept that means relationships? There's a math term for understanding relationships. Mathematically. Function. Good. Okay. There is one important concept that is completely indirectly related to function, but is actually more important than function, and it's the pure essence.

Of counting, Natalie, the only topic that we ever need to teach to improve all mathematical understanding is rate. But here's where we argue with ourselves and maybe our admin and maybe our curriculum people. This part one of this session is essential for all stakeholders in a school or district to hear. Because you're not going to see the word rate in a kindergarten set of standards.

What you will see in the kindergarten standards is, we want kids to be able to count to a certain number by ones. 10. Maybe it's to 100, maybe it's to 120. Some states in the United States have varied what that final number is for kindergarten. Doesn't matter. Me, I like 120 for all kids. And I like 120 charts.

The other thing that I want to mention today is when I said the paint problem is not about the paint problem, Today is going to be a combination and connection of a few different reference tasks. And the reason I say that is because when you listen to this podcast or you're listening to this recording in this module of Tier 1 Interventions, I'm going to refer you back to some other podcasts and some other modules that you can get the connections.

To rate and the 1st 1 is the module or any podcast. that has anything to do with 120 chart. I was in a kindergarten classroom yesterday. I had never met these kids. It was in a high poverty building and it was absolutely a beautiful experience. I walk in and I knew in my head I had four things, four reference tasks that I wanted to do in 35 minutes with kindergartners that I had never met. In a high poverty school with very high needs.

I audio taped this and in tier one interventions on this module. If you are a member, I will put this kindergarten audio and it will be named kindergarten multitask. And rate you will have access to that audio. I just recorded it yesterday, it's not been uploaded anywhere before the four stimulations experiences. I wanted kids to have. were quick dots, fact based quick dots. There are two types of quick dots, fact based and function based.

Fact based, and I'm going to show you right now the quick dot that I gave. Fact based is when each stage of the quick dot has the same number of dots. Each chunk of the quick dot has the same number of dots. This was the quick dot, and this will be uploaded into this module as well. For those of you that are listening to the podcast and not watching, there are seven chunks, and each chunk is a rectangle of eight dots, so two by four arrays. with eight dots each. This is a quick dot fact.

This is to build fact fluency. This is to build single digit multiplication automaticity. A quick dot is, I show this to the kinders for a few seconds, I take it away, I have them raise their hands and tell me how many dots they see, and then how did they see the dots arranged. That is the one experience I wanted kids to have. Now because Each of these chunks, each of these stages, have the same exact number of dots, 8. The goal was to skip count by 8.

We were at carpet, and we were just having conversations about this. What do you see? What do you notice? I show them the dots again, and I have kids talk about what they see and what they notice. What do they know about 8? How much is 1 8? How much are 2 8s? And then we practice a technique called whisper counting. Whisper counting helps toddlers, primary school kiddos, How to skip count by numbers that we would typically not have them skip count by like the number eight.

At carpet, we started learning this whisper counting technique. We point to each dot in one chunk and we whisper two, three, four, five, six, seven, eight. When we get to the final dot in that chunk, that's our loud number. That's how many dots were in that chunk. Then I say to students, how much is one eight? Eight. And that's a phrase I want kids to know. Because this is what function is. One eighth is eight. Then how much are a hundred eighths? Do you see?

That jump, that efficient counting, that explicit rule is all about function. Being able to figure out what the explicit rule is to be able to do higher numbers. with a certain pattern. Then we say, okay, what was our loud number? Eight. Let's whisper again. Nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen. Sixteen is our loud number. How much are two eights? Sixteen. Then we whisper count. And then I say to students, I wonder how much four eights are. I had never met these kids.

They had never done this before. They'd never done a quick dot. They'd never done a whisper counting. And right away, I release them to go back to their seats. I give them a 120 chart that I'm going to show you a visual of right now. There are many adaptations. Cheri, I want you to talk about this when we get to the function. Oh, talk about, let's talk about it now. She's got it right there. This girl is on. This is why she's our brain boss, okay?

This is why Cheri is our classroom coach, brain boss, partner in crime. You name it, the girl's got it all. I like four 120 charts on a sheet, and my kinders didn't have too much trouble with this. But, an adaptation when we start utilizing the 120 chart for other exercises. Cheri has taken the 120 chart where I put 4 on an 8. 8. 5 by 11 sheet, and she has enlarged one 120 chart to put on two sheets.

Cheri, talk to us a little bit about this adaptation, which these are the things we're going to talk to you about in part two of today, which is some of those adaptations and functionalities, non academic things that we can support kids with. Cheri, tell us about what you did here.

The other thing I did was created 1, 1 20 chart on four pieces of paper because Amy, one of the teachers we have in the classroom today had a, has a student who was had difficulty, I can get the words out, who has had difficulty with his vision and needed things even bigger. One of the adaptations that you can do for the one 20 chart is in making it bigger. I won't know if I'd go much smaller than what. Jonily has there. Agreed.

But one of the things that I am working with, I have a student that I'm tutoring right now in mathematics, and one of the things that we have been talking

about is taking the four on one page, but she wanted the full size, so she's using full size one 20 chart. And she's highlighting her multiplication tables, and then we are laminating them so that she has them available. And because they're full size, as she's having to struggle with being able to see the smaller Smaller ones. It had, we've been working on that and trying to link that back to what it looks like when she has a problem in front of her in the classroom.

Mom tells me that she is starting to use the 120 chart in her digital math program. It is, she is starting to carry it over into other instruction.

A stimulus, and when we prompt it, we say, tell me about this. What do you see? What do you notice? Just like I did with the quick dots. When we do that. Our goal is to extract student perspective and extract student thinking so that we then can help them apply. And what Hattie says in his research is we need techniques and strategies that are transferable. If we have instructional facilitation strategies that allow students to transfer that experience.

Just like Cheri said, this child now is using the 120 chart from math tutoring session, but applying it, transferring that strategy and technique. to her digital program. So when we can get transfer of knowledge, that is the highest level of learning and understanding. And that's what we want students to be able to do. Transfer of knowledge does not happen when we teach algorithms and procedures. I'm not saying don't teach algorithms and procedures. We need to teach algorithms and procedures.

But just understand that is not going to elevate understanding of number. It's not going to elevate number sense. It's not going to elevate math achievement. It's not going to increase thinking, reasoning, and sensemaking. And it's definitely not going to create a transfer knowledge application opportunity. So just keep those in mind, depending on what your goals are. The other reason I like what Cheri said about the much larger spaces is, then we have room to put a physical manipulative.

I like cubes. I like block cubes. Those are one of my favorites. Don't like the teddy bear. The teddy bear has no mathematical structure. I'm not in love with teddy bears as manipulatives. I'm in love with blocks as manipulatives because we can transfer the block to a lot of other math concepts and skills. That comes back to that transfer technique.

What I also like about what Cheri said is, Now, one of the reasons that Cheri actually enlarged the 120 chart is another one of our reference tasks and another one of our tier one interventions modules is locker problem. So in the locker problem, we use a good solving problem solving strategy. Use a smaller number. So a locker problem. We have 100 students in 100 lockers and they go through and play this game. Through this problem, we want to generalize patterns with a smaller number.

So we make a game board with 24 lockers.

But if you want to extend that and look at the complexity of what happens in the phenomenon mathematically of the locker problem, Cheri's I want to look at the 1 20 chart and I want to use. Pieces that are TR two color and she has purple on one side, white on the other, and she's gonna show that to us right now. She actually took the whole one 20 chart and she's acting out locker problem, not with the game board of 24 lockers. Now that. that we've had a lot of interaction with 24 lockers.

What if we have 100 or 120 lockers? We can do the same repeated reasoning. We can do the same iterations, but now we need the chart to be bigger to include more numbers so that we can see how that experience, how that locker problem creates this natural math phenomenon. So the point of all this is that We have in tier one interventions, not only the answers to all of your math troubles, but we also provide the adaptations so

that all students can be successful. That's the accessibility piece. We want to continue to increase the rigor and complexity, but we want to make it accessible for all students, all levels, all ability levels, all of all functional levels. Even our most struggling students, but you can also see how this one lesson can enhance and stimulate our most gifted student, which oftentimes they get shortchanged because we're trying to keep everyone up.

They never get as far as the gifted child's thinking. And so the gifted child never gets to go above and beyond. But with reference tasks and our instructional delivery strategy, we're able to do that.

Tell us what you like. Tell us what you don't like. We want to know.