# The Numeracy Cycle: A Four-Step Process to Mastering Mathematics: T1I E4

Unknown: For me,

Jonily : the sequence is

division first, it's always

division first, and then I teach

addition, subtraction,

multiplication, always through

division.

Cheri Dotterer: Good morning.

Welcome to tier one

interventions with Jonily

Zupancic and Cheri Dotterer. So

without further ado, I'm gonna

pass it over to Jonily. And

let us get started. Hey,

Jonily : Jonily Zupancic here JZ

in the house today. So when

we're getting these kids ready

for learning, and being able to

do that in an inclusive, least

restrictive environment, tier

one, there are certain

instructional strategies that we

need to focus on. If you're a

general classroom teacher,

administrator, support

specialists, occupational

therapists, speech therapists,

intervention specialists,

instructional coach, whatever

your role is, in your school or

district want you to think and

evaluate in your mind, the

strength of your tier one. Now,

how do we do this? There are

certain components in tier one,

meaning how visual is the

content? How much do we adapt to

student visualization? How do we

embed conceptual cognitive

stimulating multisensory

approaches to our content? How

is our content leveled and

adaptive? What connections and

associations are we making and

supporting students to make tier

one interventions core

instruction, we're really

unpacking all of the ways that

we can improve student's ability

to function in the regular

classroom. To avoid so much pull

out to small group. We want kids

needs to be met in the regular

classroom. In the mathematical

classroom. Our ultimate goal is

to improve number sense, having

students gain a really strong

innate intuitive, natural

understanding of number. Number,

meaning how large or small

numbers are the size of numbers,

the value of numbers. The number

one way to do that is through

counting and rote counting

without meaning. And I'll

explain what I mean by that. One

of our strategies is called the

numeracy cycle. The numeracy

cycle is a four step process, a

four step linear process, but

also a cycle. That is the key to

improving numeracy and number

sense for all students. The

components of the numeracy cycle

in order sequential are number

one count, just wrote count

without meaning. The meaning

comes with Component number two,

which is quantify. Quantify

means, do I know the value so

non kids can oftentimes skip

count by 1010 20 3040 5060. But

if I say, what's the quantity of

60? Tell me about 60. What's the

value of 60? There's no

connection between that rote

counting by 10s. And

understanding that 60 is six

counts or six tenths. But that's

okay. Because if we go back to

that, rote counting is the first

step. I've got to get kids good

at rote counting, even if they

don't have an understanding of

what they're counting. Because

rote counting alone,

repetitively, with more and more

interactions, will build an

understanding of quantity and

value of the number. The third

component in the numeracy cycle

is compare. Once I'm rote

counting by a number

1020 3040 5060. And I start to

understand that 60 is 610s or

60. Ones, or 60% of 100. I can

go really complex with this as I

start to quantify numbers. There

are so many different

connections and associations and

meanings. Compare Means, okay,

it's not about the number 60.

Now, let's compare the number 60

to the number 90, which is

bigger, which is smaller, how

much bigger how much smaller

comparison is a higher level of

numeracy than just understanding

the quantity or value and it's

definitely a higher level than

rote counting. Finally, the

fourth component of the numeracy

cycle is operate, add, subtract,

multiply, divide, exponents,

square root, anything that I do

to compute numbers. Oftentimes

what happens in the regular

classroom is there's a priority

and emphasis on the operations.

I want kids to be able to add,

subtract, multiply and divide

whole numbers, integers,

negative numbers, fractions,

decimals. And so oftentimes the

focus on intervention in small

group pullout, is on operating

numbers. However, the

intervention cycle, the operate

is the final component. If I

have students that are

struggling with operation of

numbers, computation of numbers,

add, subtract, multiply and

divide. Let's suppose I'm having

kids add three fourths and four

fifths just says the example

right now, that's an operation.

I'm operating. I'm adding two

fractions with unlike

denominators. If students can't

do that, whether I am pulling

them for intervention, or if I'm

in the regular classroom,

Unknown: I go back to the third

component, which is compare. Can

I even compare three fourths or

forfeits, I take away the

operation. And I look at three

fourths and forfeits and I say

to students now remember, I'm

going back to my good

instructional techniques. Tell

me about four fifths and tell me

about three fourths. What do you

notice about four fifths and

three fourths? For a struggling

math student, the number one

thing that they will tell me is

those numbers are equal. They

are not, but I'm not going to

fix it right away.

Jonily : We have four fifths and

three fourths, we're comparing

them they believe the numbers

are equal, which means I need to

go back in the numeracy cycle to

number two component which is

quantify, I need to separate the

numbers I need to look at three

fourths by itself. Use

instructional strategies and

approaches. To help students

understand the visual, the

quantity and the value of three

fourths, I need to do that

separately with four fifths. So

they can start to have a

connection Association

visualization as to how large or

small each of these numbers are

separately. And that's what

comparing means. I cannot

intervene. I cannot do

intervention on Operation

repetitively, procedurally over

and over, I could say to

students find the common

denominator, change the

numerator, blah, blah, blah. If

they don't have a numerical

ability to compare those

numbers, and if they believe

those numbers are equal, no

matter what procedure I teach,

they are not going to remember

it and they're not going to

retain it, the intervention. The

tier one, tier two or tier three

intervention is to go backwards

in the numeracy cycle by Matt

quantify and value, I'm looking

at three fourths by itself and

four fifths by itself. And I'm

not giving you a lot of

indication of the intervention

that helps them understand that

value. Because I'm teaching the

numeracy cycle right now. In

these sessions, we have tools

and techniques that will help us

do that. But if students still

struggle with understanding the

quantity and value or a lot of

times I say the magnitude

magnitude is how large or small

numbers are. For example, how

far away is three fourths from

one hole? How far away is

forfeits from one hole? Which

one is closer to a hole? Which

one is further from a hole? How

much? So that's the exercises in

quantify. And as students still

struggle with quantity, I go all

the way back to the first

foundational step of the

numeracy cycle. That was the

point I made at the very

beginning of this, and that is

rote counting. How often do we

have kids rote count, other than

whole number? So oftentimes, in

the earlier grades, we will rote

count, skip count by 10s, skip

count by fives. 510 1520, did

it. It's so essential. What

happens is as kids get older,

and as we move into new number

systems, like fractions,

decimals and negative numbers,

we skip the rote counting. And

so kids are missing that

foundational step. So if you

have kids struggle with

understanding numeracy, and they

struggle with numbers and

operation and comparing numbers

and numbers on a number line,

the number one key intervention

is to go back to rote counting

of that type of number. So I

might ask students, let's skip

count by three fourths, three

fourths, six fourths, nine

fourths, rote counting is

absolutely essential for

starting to understand quantity

of numbers. Now, if they

struggle with that, let's just

skip count by 1/4 1/4, two

fourths, three fourths

4454647 4849 fourths 10 Plus,

that's it. That's it. It's as

simple as rote counting without

meaning. I know kids don't

understand that. But would then

I could start to ask questions.

How many counts by one fourths

will it take to get to one 100

Can you see how I just twisted

that perspective? And that

question alone? Even my most

struggling student is going to

say, oh my gosh, it's going to

take a lot of counts by 1/4 to

get to 100. How many counts by

10? To get to 110 2030? Oh, it's

going to take 10 counts by 10?

How many counts by one to get to

100 100? How many counts by 1/4?

To get to 100? How many counts

by 1/5? To get to 100? How many

counts by one eight to get to

100. See, rote counting is the

foundation of moving into those

higher level questions. And

without rote counting. And

without asking those questions

to students, and without

starting at the beginning of the

numeracy cycle, we are never

going to get kids to the

operation level. So our math

interventions are failing,

because we're not going all the

way back to the rote counting of

the different number systems.

Janet, you said you just said in

the chat, I noticed that some of

my seventh graders had trouble

counting their hearts this week,

because you talked about using

candy hearts to look at data

distribution. It was so simple

one to one. Yeah, kids struggle

with just counting individual

needs are what 12 year olds, 13

year olds? Absolutely. When I'm

working with my high school

students, I have high school

students that struggle or have

never been exposed to rote

counting by fraction. We've got

to take our math lessons back to

rote counting. And if you take

away nothing else from this

segment of the teaching, it is

rote counting by every type of

number, including fraction.

Unknown: I know in my my sixth

grade classroom, we wrote count,

I disguise it a little bit. So

that like when we're, we just

got done with dividing fractions

with my Windblock. And they had

troubles I'm like, Okay, well,

let's go back to the county. And

I didn't say that to them. But

I'm like, Okay, what do we know

about and they just started rote

counting, because sometimes it's

hard to, they recognize rote

counting, as all this isn't

something I should be doing that

sixth grade, at least my sixth

graders this year. So I have to

sneak it in. But that's how I

that's how I sneak it in. So

Jonily : you make a beautiful

point. Because one of the things

that I'll bring up with students

is what is six divided by two,

and I'll do this with my high

school students as same as my

fourth graders. And as a matter

of fact, my fourth graders do

much better with what I'm going

to teach to you right now,

because their numbers since

hasn't been schooled out of

them. By the time kids get to

high school, they're all mixed

up with all the math notation.

And I have to retrain them

before I can move forward with

them. You can see here six

divided by two equals what now?

No brainer, okay, for their like

it's three. Okay. But that's not

the point. The point is not

about solving. It's about skip

counting. Every single division

problem is skip counting every

single division problem is skip

counting. That's it bottom line,

when you're when we're teaching

division, it's skip counting.

That is why 120 chart is so

essential, because this number

to this second number here is my

skip counting number. That's

what division means. I'm skip

counting by two. And what am I

trying to land on? Not 100, like

the 120 chart, trying to land on

sixth time skip counting by two

to land on six. And the question

is, how many skip counts by two

does it take to land on 6246? I

can use the 120 chart to do

that. Or kids can a lot of kids

can just do that. Or I might

need to get a manipulative out

with blocks. If I need kids to

be more concrete manipulative

based, it depends on their math

ability level 2463, skip counts,

here is where it gets

Unknown: powerful in the upper

grades. If we're teaching

division, if one of the ways

we're teaching division is by

skip counting, and what a lot of

my teachers say is, they're

like, Jonily. That's ridiculous.

That is not a strategy that we

even should be utilizing.

Because if I have to 31 divided

by seven teachers are like that

is not efficient. Why would I

skip count by sevens all the way

to 231? Because if I want to

improve number sense, it's not

about answer getting. It's about

the process. See, and this is

where we fall short in tier one

mathematics or even in tier two,

tier three intervention with

mathematics. We believe that

intervention is more about

answer getting than it is about

the process.

Jonily : The process is what

improves number sense. And in

the end when number sense

increases, then computation will

increase as well. But if I want

to improve number sense, I want

to think about this as 714 21.

Then what I want to do is start

to chunk skip count. Gosh,

seven, I can get to 70. Right

away. How many skip counts by

seven does it take to land on

7010? I could count by seven

days to get to 31. See, this is

the power in rote counting. Now,

why is this strategy important?

It's important when we get to

the example that Krista

mentioned, when I have the

problem six divided by a half. I

know that one half is my skip

counting number. And if kids

have had lots of interactions,

skip counting by half's that's

not going to be a problem by the

time we get to this computation.

One half is my skip counting

number one half, two halves oh

two halves is one, three halves,

four halves. I skip count by

half's to land on six. So the

question here is, how many skip

counts by calf's does it take to

land on six. And I can do this

with fraction by fraction. I can

do this with any division

operation of fractions. So in

elementary school, what happens

is Weepu sorry for the dirty

language here, we poo using this

skip counting technique, because

we're like it's not efficient.

That's a terrible way to do it.

But it is the most transferable

to fraction division later on.

What we need to do is really

prioritize the skip counting

strategies early on, and

continue to refer to them,

because that is what's going to

help our students with higher

level mathematics. And that is

where we're falling short. Lots

of things right now I want us to

reflect on. I want us to reflect

on what did I just do? And how

was that responsive teaching,

because I skipped all the way to

a different lesson. I want to

reflect on what I actually

taught and what connections you

have. So let's pause for a

moment. And just process

together with me everything that

has just happened, because

there's a lot of power in what

has just happened in the last 10

minutes. I think it's

Cheri Dotterer: also happening

along the path of literacy. But

they're starting to realize that

we have to understand the

concepts. And hence the science

of reading and the structure

literacy. Push is making its way

and will soon be mandated across

the entire United States. But I

see a lot of parallels. I know

you have always said to me that

there's no connection, but even

looking at your numeracy cycle.

There is a lot of literacy

connections that can be made

there. If kids can't are

struggling with comparison,

which is usually one of the

first things that they try to

introduce in the literacy. Okay,

let's back up just a little bit,

to looking at counting and it

might be that they're looking at

something else. But we're

looking at talking

Jonily : about this is where

your phonics is. Yeah,

Cheri Dotterer: actually

counting is where phonemic

awareness is there you would be

phonics would be the quantify.

There you go.

Teresa: So wouldn't it be

alphabet automaticity? Hmm.

Cheri Dotterer: You're looking

at the writing part, I was

looking at the

Unknown: you know who I am.

That's both of you. That's a

great point. Because oftentimes,

in literacy, we combine this

reading and writing. And those

are two distinct, there's a

cycle for reading and a cycle

for writing. I love it. Now. And

this is absolutely parallel to

that I agree winning

Teresa: feet from you. Jonily is

the fact that everybody's

talking about a forward

progression for a shoe do add

for a shoe do subtract, and you

do this, what's to say that and

you said it you have in Division

mode, and that you already you

only did actions, why are you

Why can't you revisit the way,

Jonily at least talking is there's

always a revisiting, and there's

nothing that says you can't

revisit. And the way she's

talking is, if you're going

forward, there's no sense what

did they forget what they did in

the past, so you have to go back

to go forward. So we just say I

am the first one to tell my kids

oops, I forgot something when we

just go back and we visit things

or we just do something again.

So there's nothing that's says

just because you want to try

something else that you can go

back and revisit it. Teresa,

Unknown: I want to stay on that

point for just a moment. And I

think all of you on here have

heard me talk about this before

and that is operation is not

sequential. Someone decided that

addition should be done first

and then subtraction and then

multiplication and division.

That is hogwash. There is no

basis. There's no scientific,

there's no research basis. For

that sequence me, the sequence

is division first, it's always

division first. And then I teach

addition, subtraction,

multiplication, always through

division with my five year olds,

and in kindergarten, I don't

call it division, guess what I

call it sharing. When kids are

two and three years old, we

start to talk to them about

sharing. And kids develop a

conceptual foundation of equal

sharing. They know that better

than anyone, if you have more

than me, and I'm two years old,

I know that and I'm going to

throw fit about it. We need to

in preschool and kindergarten,

embrace sharing, which sharing

is division. So that is how I

teach and how I sequence. I'm

always in Division world, but I

call it sharing. And equal

sharing means equal groups. And

equal groups means skip counting

by the number in that group. And

Theresa, I'm glad you brought

that up. Because I teach on this

all the time. That division

should be the first operation,

and we disguise it as sharing

and teach all other operations

through that. Now, Cheri, you

have a lot to say about this.

The number four makes sharing I

really cranky, at least it makes

me really cranky. And letters

make Cheri and Teresa really

cranky when you're looking at

fonts. I was using the font that

I liked the best, which Cheri

Oh, I thought I was using lexan.

This is Arial. But anyway, I

think there are certain fonts

that are cleaner for number,

that when the typed font is

there, it connects best. But

look at this for this isn't how

kids write a force, I have to

search and search and search.

This was the best one I could

find on Google. And it's

Pacifica, I went to lexan for

nine, because nine had the best

I thought structure for how we

actually write. But again, it's

just found Deco. deco on what on

word I just found the

Cheri Dotterer: desktop ins.

This is architects daughter,

this is lexan. And this is deco

DECO,

Unknown: we got go it is as a

general classroom teacher as I

am, and I'm certified secondary.

So 712 Math, my bachelor's

degree is in mathematics. These

are things that never came

across my path. Until Cheri and

I began to learn from therapists

from Cheri,oh my gosh, look at

all the things that were

barriers to learning in my tier

one core classroom that I was

just carrying on like it was

nobody's business, and these

little minor things. We're

continuing to create these huge

barriers for learning for kids.

Just by the way, the number four

was typed.

Jonily : And so this is what

tier one intervention is all

about is for us to strengthen

these core classrooms. By

utilizing these strategies,

these intervention strategies

that combine the therapy world

and education world and better

connect them to each other, even

though I've grown immensely in

my math, instructional delivery

over the years because since my

first year of teaching, I ended

up studying early childhood

development, brain research,

cognitive science, I did

everything I could to try to

relearn how kids learn. And I

was able to create really great

experiential, adaptive

differentiated multi sensory

mathematics in my classroom. But

it wasn't until I met Cheri and

Teresa, and all of the other

special support staff,

occupational therapists who have

these techniques from the

medical world that have these

techniques, that once I then

brought some of these adaptive

techniques, non academic

techniques into my tier one

classroom, it just glorified and

truly enhanced all of the great

facilitation or transformations

I had already made. So when we

look at both of these, when we

say tier one interventions,

that's why we're not saying tier

one math interventions. We're

saying tier one interventions,

because they are academic and

non academic interventions. And

the only way you can get this is

with the kids. action of both of

these worlds.

Teresa: He's not a math person,

I think I'm one of the worst

people, I hate math to a

passion. But I see where you can

get me to help my kids advance

on other things like I can help

with the visual perception, I

can help with the motor tricks,

because my kids need that. And

they can take that back to the

classroom. So I'm sitting here,

and as much as your trained

people are sucking up stuff from

you, and they can go back from

math, I'm still sucking stuff up

from you. And I've told you

this, you came and talk to us, I

get stuff from you, every time

you talk to me, that I can go

and say, Oh, I'm going to try

that with my kids. Because it's

generic, I can go and take some

of those same things. Not mad,

even though they're mad, I can

work with them with my kids. So

even though like you're gonna

you say, and people say, Oh,

poo, it's math. It's not like

you're saying it's something

that can go across the board for

general good teaching. And I

think that's very important for

people to know that it's not

necessarily it's, yes, it's

weighed heavily in math, but

it's not just math. So I think

that's the push where a lot of

people need to know that it's

good teaching.

Jonily : And end today with

describing the best components

that make for good teaching.

Unknown: Me, but what has really

transformed my teaching with you

is this this idea of

interactions over time, I think

sometimes we get stressed about

trying to get through all of our

curriculum, and these kids are

so far behind and all these

gaps. But when you talk about,

they don't have to learn

everything, that first

interaction, and even with the

number are on Twitter, with all

these different interactions

that happen. I think it's just

that pressure that's offered to

the teacher, as a genetic

teacher, I feel that a lot I

have to get through this

curriculum. And that's one thing

that has really helped me today.

Because I think sometimes when

people get pressured, and they

feel like they have to get the

kids have to get it now, then

all of a sudden, sort of these

intervention strategies that go

away, at least they're like, I

just need to do procedural they

need to know it, and I need to

move on. So it's that

interactions over time that has

really changed. Maddix is

Jonily : not a hot stove or a

busy street. I can let kids

explore. They're not going to

get hurt. And finally, as we

wrap up, this has been tier one

interventions. I want to thank

all of you for being here today.

If you're listening to the

recording and you weren't here

live hopefully you got some

takeaways as well. Thanks for

your attention, everybody, and

have a wonderful weekend.

Unknown: Lima says tier one

interventions was a sensitizing

workshop systematically thought

through put into an easy to

understand framework that well

presented. Thank you to you

both. Thank you and Halima.

You've been listening to tier

one interventions with Jonily

Zupancic and Cheri daughter.

Tier one intervention is

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Nicholas King, an intern for

cheri Dotterer educational

consulting