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