Rethinking Math Education Part 3: S2 E26

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. This week we're going to talk about part three of the background to the paint problem.

Anybody who's out there listening to the podcast that Not only do we need to help kids with letters and numbers, we also need to help them understand the symbols that go with mathematics, the symbols that go with social studies, the symbols that go with music and science, because they don't make the connections.

over and over again and make those connections to the conceptual. But kids aren't just gonna figure out a parenthesis. They're not just gonna figure out a square root. That must be explicitly and deliberately taught. I say it, they hear it, and then they tell me what I just said and they learn it. So very important to understand this as we're moving through the science of math. That is up and coming.

The differences between what needs to be explicitly taught in mathematics and what cannot be explicitly taught in mathematics. With the science of reading, the collection of research on how students learn to read.

Reading must be explicitly taught. That's what the collection of science says for reading. My fear when we move into science of math is we're going to try to parallel that for everything. But what we're missing in schools is a high level of number sense. And that can never be explicitly taught. It must only be experienced through these things.

That experience is what is going to provide The functional aspects for students to be able to individualize where they are and be able to work independently on mathematics. We seem to not be able to ever get to a point in any classroom at any grade level where students can independently work on mathematics.

Because we're not focused on iterated and repeated reasoning. Using reference tasks and bringing them back again with a different number, kids already have been explicitly taught the process. Now they can independently repeat the process with other numbers. This is also how we individualize and build independence in mathematics.

What are some of these other non academic functional pieces? That's the question that we're going to answer here in this, in Part 2. Part 2, what are some of the non academic functional pieces that need to be included in Tier 1 general? Core instruction so the kids don't have to be pulled out of the room to go to a separate small group, a separate teacher to learn how to function, behave, regulate and manage their learning.

And I say this has to do with rate because one of the examples of rate is. Speed. How fast? That's innate and intuitive right there, because as Teresa mentioned, when we go to the gym and we get physical and we do movement, we could have short distance running races and use a stopwatch, because what we're measuring is distance.

Per time, and that is the pure definition of rate. I don't have to teach it as rate in second grade. We can just do these short distance runnings, and we can document the distance to the finish line, and then the time it took for each student to get there. And we're collecting data, we're experiencing it, we have physical movement, and then we're going to use those numbers for mathematics. Now, not only can I improve my number sense by seeing number as shape, like with a quick dot.

to start to give meaning to number. Now I can physically feel number. Because I can see who is faster, and whatever number that is, is going to be a smaller number as far as time. Because if I have the same distance, finish line is at the start and finish line.

I have the same distance for every race. But the smaller the number, Why does that mean? The faster they got there because the definition of rate, one of the definitions for rate is distance per time. So I can take my younger kids and do these things and collect data and now they can physically feel rate. This is what we're missing in mathematics. So that's a, that's an example of a functionality. A non academic way to put movement into mathematics.

But also be able to improve number sense experientially. So let's talk about some other functional non academic features of interventions that can be done in the regular Tier 1 classroom.

But I, had these two students and we one of the questions I would ask is like how estimate how many rolls of their wheel they thought it would take to get to like our finish line, which was marked off. But this one. This one brother and sister we got to talking about the number of rotations for the the wheels and I think this this would relate to paint problem, right? Because it's the inverse relationship, right?

And I asked Or they came up with a statement like the bigger wheel has less rotations because of the length of it. And the smaller wheel would have more rotations. Because of its length. And so it's just really exciting to have that rate conversation without using any math We were just talking about what we see, what we know, that kind of thing.

So that's more an observation comment. My question though, was hold off on that question

When that number is the denominator of a fraction, the more pieces, but the smaller the piece, and that's really difficult for kids to overcome unless they experience it contextually and conceptually, and one of our, I'm going to put this up here, another reference task is paper folding that we need kids to experience, which is really connected to what Sarah's talking about with the rotation of the wheel, because it's that sort of counterintuitive inverse understanding

when I ask kids, which is bigger?

1 8th or 1 4th? 1 8th is always the answer. It's wrong, but it's very popular. Okay, so kids need to understand that the larger the number of the denominator, the smaller the pieces, and they only can do that. I can tell them 500. 86 times. And we do this in schools. We tell them and tell them and tell Guys, we've told you this! We've told Yeah, you know what? That's the problem! Ding! Insanity! Doing the same thing over and expecting a different result!

That's why we need to unlearn, relearn, rethink. These contextual, conceptual, experiential ways of delivering math instruction so that kids can figure it out on their own.

Then we can explicitly teach the association and the connection to the symbol and language. Sarah, question though.

And one of the students did get to that point.

We're using a smaller Teaspoon. So we need more of them to and which is what you're saying about that fraction, right? The like smaller, the denominator, the more we're going to need to like get to that. So think about it

See, that's right. But Sarah, let's talk about this for a minute. You teach in a cyber school. So were you guys all together on site

Love it so much. Okay. What's your question? Sorry. My question is back to the symbols. Okay. Because this comes up consistently with the sixth grade teachers the, Multiplication can transition to dot and parentheses from the like little X. And my question is, like, how early on is it okay to start introducing the different symbols to elementary students like Okay, so like from the get go, just interchange them and know it means the same thing.

Okay, all right.

3. 50. So I'm introducing and exposing that way early, starting in kindergarten. By second grade, kids should be able to see that My bi number, my

rectangle notation, and this is what's important about calling that blank multiplication chart the dimension chart. I can use the word bi, I can use a dot, I can use parentheses, and it really has nothing to do with multiplication, it's a notation of dimensions. Follow up question on that.

Okay, other functional non academic aspects. Sherry, talk to us a little bit about what that looks like in your setting and how it can be done in the regular classroom. Sure,

It's called the autonomic nervous system that turns on and turns off. It'll increase or decrease blood heart rate, depending on how much activity we are needing. I think I am sharing. Oh no, I'm not sharing any screen yet. The other part of it is feelings. And that's what I want to share the screen for. And that is That we have eight senses or eight emotions, joy, trust, fear, surprise, sadness, disgust, anger, and anticipation.

We have about 4, 000 feelings, but the difference is that emotion is that first seven seconds before we even think about it.

It's that gut response that our body. It does without us even thinking about it. It is part of the subconscious. It is part of our innate nature. We talk about numeracy cycle being innate. We've got eight core emotions that are innate. So kids that are refusing mathematics or handwriting or whatever task you're asking them to do, one of those eight, most likely fear, is the Is overcoming their ability to engage in the task.

So the emotion I said, there's eight is a neurobiological response to that initial gut reaction before we can even think about it. Once we can think about it. Once it brings up into our conscious, then we can evaluate it, and that's when it becomes a feeling. But there's also something else that I haven't really ever talked about before, and that is called mood. And that is our disposition. That is the kind of that thing that lasts forever.

That's why people can get be in a depressed mood or a sad mood. That's different than emotion. When it becomes this long drawn out Disposition. It's the way we're feeling over time. That is our mood and we can change those moods and that is going to change that emotional response.

That in itself is the best way to reengage kids in their education is changing their mood. It's the most difficult part of. education. But that is the key. The key to making that change is motivation. So we need to change how they're motivated to engage in the mathematics. And what Jonily is teaching. About engaging kids in mathematics is a way of circumventing those moods and remotivating kids into their education

Educators and administrators, but I'm telling you, if you want kids to be motivated intrinsically, if you want kids to be able to function at a very high level, if regardless of disability or ability, if you want kids to be able to engage in the task at hand.

and work independently. You'll hear many focus triggers on this kindergarten audio. I'm going to tell you about a few of them right now. So whenever I teach a class of kids, no matter the age level, in the first three minutes, I can find out how, who our special students are. Okay, it's not rocket science. Ended up finding out yesterday, and you'll hear how I do this on the audio, because what I will do is, I will give some prompts to gather student perspective to get a feel for the classroom.

And I might say, so yesterday I introduced myself, I say I'm Mrs. Zoo Panzick, Zoo, like where animals are, Pan, like frying pan sick, like you're not feeling well, say that. Zupancic. Boom, there's a focus trigger right there. I give an association for my name, then I make them say it. That's actually two focus triggers. Creating an association, my last name, Zupancic, it's a little difficult. Make an association. Zoo, where animals are. Pan, frying pan. Sick, like you're not feeling well.

Okay, so that's one focus trigger is to make that association. And another focus trigger is make them say it. Make them repeat it. Wrote. Okay, so you guys say it. Zoo, pan, sick. Okay, so focus triggers. There's two right there just very subtle and you'll hear that in the audio and now that I pointed it out to you, it'll be very intentional. You'll see that. And so as I'm having them do this, I watch for the kids that are laying on their desks or being like, THE PIZZA! Okay?

Hey, come on, I'm not exaggerating at all. Okay, so then I go on and I start telling them that I used to have a classroom like this and I just like to go in different math classrooms and do math with them. And then I went on. Another focus trigger is to share the purpose.

Okay, another focus trigger is to share the purpose. I went on to say, How do you guys exercise your body? Oh, we work out. You lift weights. You can run. That's all exercise for the body. But what do we do to exercise the mind? And they were like, We work out. We lift weights. We run. I'm like, No. I said, No. No, that's, we exercise the body. And then another little lady, she raised her hand. I called on her cause she plays school really well. And she's math. I'm like, that is exactly right.

We do math to exercise the mind, the brain. So that is a perspective in and of itself. So when I'm teaching kids, I tell them, I don't teach math. I teach thinking. So when they ask gosh, when are we ever going to use this? Probably never. You're never going to have to think. Okay, the thing is, thinking is my content, like I teach thinking through the vehicle of mathematics. See that's an unlearn, re, relearn, rethink right there.

So if you are an educator, intervention specialist, or instructional facilitator, of mathematics. You teach thinking. You just use mathematics to teach that thinking. Couple other, and then then I found out my good friend Jace. I thought it was Chase, and then I was like ch, and they were like, no juh, Jace. I'm like, ooh, because my first name is Jonaly juh, and then they were like, oh, but we have juh, James, and Jesse, and juh, and it was just a whole thing, and it was fun.

And But the kid beside Jace kept speaking for him, so I picked up on that, and I said, Oh, are you his secretary? He's yes, and I'm like, okay, I need to keep this kid near Jace. You pick up on these things, but what I'm doing is I'm using focus triggers. I'm getting kids to hone in and focus on one thing so that they can give me their perspective so that I can teach to their perspective. Okay, making a lot of associations and connections.

So once I find out who Jace is, we come to carpet, I make sure Jace is near me and his secretary on carpet.

So that was beautiful, okay. We go back to our seats, but I make Jace stay with me. Because I knew this kid needed to wonk the willies out. Okay, I knew explaining what we were going to do with the 120 chart and starting that facilitation with the kids before I mini lessened to that small group. I knew Jace needed to just be up and moving and not at his table. He wasn't going to get anything out of that anyway.

So he was beside me and then he started spinning and I'm like, Jace, you keep spinning. He would spin and then he'd jump and then he'd spin and then he'd jump. And then. He was behind me and the whole class was attending to me and ignoring Jace because they know Jace is special. So I move strategically to another area of the room. Jace stayed over there doing his jumps and spins and whatever. And then I finished explaining and I said okay so now go ahead with your 120 chart.

I'm going to come to your group, so I'm going to help you. And I said, Jace, come on back. And I said, Jace, No, sorry.

This was before they were making squares with blocks. Blah. Jonily, you got the whole story messed up. Anyway, doesn't matter. The point is, while I was explaining that we're going to make squares and what that means and equal sides and da, I totally screwed this up. We should re record this, but we're not going to because I'm out of time. Anyway. So then, he comes back, before I went and observed other groups, when he came back I said, Hey, do you know what we're going to do right now?

And he's we're going to make squares. I didn't expect him to say that, because he was off over in La Land. But do you see, he needed to do all that, and it didn't bother any of the other kids. They didn't ask why he was doing that. They probably intuitively know why he's doing that. He came back, and I wasn't expecting him to say, we're making squares, but he did. And I'm like, do you know what a square is?

And he was getting a little weird and I was like, you know what, here's your blocks, go ahead and make squares. And then he, for the next 10 minutes, was so focused and engaged and in tune and working independently. See, focus, a focus trigger for him, he's got to spin and jump. Then he can attune to the task. And he was listening to every word you said. Why?

Tune in next week where I answer the question, why?