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Unknown: For me,

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Jonily : the sequence is
division first, it's always

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division first, and then I teach
addition, subtraction,

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multiplication, always through
division.

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Cheri Dotterer: Good morning.
Welcome to tier one

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interventions with Jonily
Zupancic and Cheri Dotterer. So

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without further ado, I'm gonna
pass it over to Jonily. And

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let us get started. Hey,

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Jonily : Jonily Zupancic here JZ
in the house today. So when

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we're getting these kids ready
for learning, and being able to

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do that in an inclusive, least
restrictive environment, tier

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one, there are certain
instructional strategies that we

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need to focus on. If you're a
general classroom teacher,

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administrator, support
specialists, occupational

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therapists, speech therapists,
intervention specialists,

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instructional coach, whatever
your role is, in your school or

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district want you to think and
evaluate in your mind, the

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strength of your tier one. Now,
how do we do this? There are

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certain components in tier one,
meaning how visual is the

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content? How much do we adapt to
student visualization? How do we

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embed conceptual cognitive
stimulating multisensory

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approaches to our content? How
is our content leveled and

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adaptive? What connections and
associations are we making and

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supporting students to make tier
one interventions core

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instruction, we're really
unpacking all of the ways that

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we can improve student's ability
to function in the regular

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classroom. To avoid so much pull
out to small group. We want kids

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needs to be met in the regular
classroom. In the mathematical

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classroom. Our ultimate goal is
to improve number sense, having

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students gain a really strong
innate intuitive, natural

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understanding of number. Number,
meaning how large or small

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numbers are the size of numbers,
the value of numbers. The number

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one way to do that is through
counting and rote counting

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without meaning. And I'll
explain what I mean by that. One

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of our strategies is called the
numeracy cycle. The numeracy

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cycle is a four step process, a
four step linear process, but

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also a cycle. That is the key to
improving numeracy and number

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sense for all students. The
components of the numeracy cycle

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in order sequential are number
one count, just wrote count

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without meaning. The meaning
comes with Component number two,

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which is quantify. Quantify
means, do I know the value so

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non kids can oftentimes skip
count by 1010 20 3040 5060. But

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if I say, what's the quantity of
60? Tell me about 60. What's the

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value of 60? There's no
connection between that rote

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counting by 10s. And
understanding that 60 is six

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counts or six tenths. But that's
okay. Because if we go back to

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that, rote counting is the first
step. I've got to get kids good

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at rote counting, even if they
don't have an understanding of

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what they're counting. Because
rote counting alone,

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repetitively, with more and more
interactions, will build an

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understanding of quantity and
value of the number. The third

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component in the numeracy cycle
is compare. Once I'm rote

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counting by a number
1020 3040 5060. And I start to

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understand that 60 is 610s or
60. Ones, or 60% of 100. I can

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go really complex with this as I
start to quantify numbers. There

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are so many different
connections and associations and

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meanings. Compare Means, okay,
it's not about the number 60.

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Now, let's compare the number 60
to the number 90, which is

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bigger, which is smaller, how
much bigger how much smaller

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comparison is a higher level of
numeracy than just understanding

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the quantity or value and it's
definitely a higher level than

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rote counting. Finally, the
fourth component of the numeracy

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cycle is operate, add, subtract,
multiply, divide, exponents,

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square root, anything that I do
to compute numbers. Oftentimes

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what happens in the regular
classroom is there's a priority

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and emphasis on the operations.
I want kids to be able to add,

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subtract, multiply and divide
whole numbers, integers,

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negative numbers, fractions,
decimals. And so oftentimes the

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focus on intervention in small
group pullout, is on operating

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numbers. However, the
intervention cycle, the operate

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is the final component. If I
have students that are

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struggling with operation of
numbers, computation of numbers,

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add, subtract, multiply and
divide. Let's suppose I'm having

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kids add three fourths and four
fifths just says the example

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right now, that's an operation.
I'm operating. I'm adding two

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fractions with unlike
denominators. If students can't

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do that, whether I am pulling
them for intervention, or if I'm

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in the regular classroom,

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Unknown: I go back to the third
component, which is compare. Can

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I even compare three fourths or
forfeits, I take away the

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operation. And I look at three
fourths and forfeits and I say

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to students now remember, I'm
going back to my good

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instructional techniques. Tell
me about four fifths and tell me

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about three fourths. What do you
notice about four fifths and

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three fourths? For a struggling
math student, the number one

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thing that they will tell me is
those numbers are equal. They

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are not, but I'm not going to
fix it right away.

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Jonily : We have four fifths and
three fourths, we're comparing

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them they believe the numbers
are equal, which means I need to

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go back in the numeracy cycle to
number two component which is

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quantify, I need to separate the
numbers I need to look at three

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fourths by itself. Use
instructional strategies and

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approaches. To help students
understand the visual, the

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quantity and the value of three
fourths, I need to do that

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separately with four fifths. So
they can start to have a

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connection Association
visualization as to how large or

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small each of these numbers are
separately. And that's what

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comparing means. I cannot
intervene. I cannot do

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intervention on Operation
repetitively, procedurally over

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and over, I could say to
students find the common

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denominator, change the
numerator, blah, blah, blah. If

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they don't have a numerical
ability to compare those

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numbers, and if they believe
those numbers are equal, no

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matter what procedure I teach,
they are not going to remember

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it and they're not going to
retain it, the intervention. The

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tier one, tier two or tier three
intervention is to go backwards

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in the numeracy cycle by Matt
quantify and value, I'm looking

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at three fourths by itself and
four fifths by itself. And I'm

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not giving you a lot of
indication of the intervention

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that helps them understand that
value. Because I'm teaching the

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numeracy cycle right now. In
these sessions, we have tools

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and techniques that will help us
do that. But if students still

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struggle with understanding the
quantity and value or a lot of

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times I say the magnitude
magnitude is how large or small

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numbers are. For example, how
far away is three fourths from

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one hole? How far away is
forfeits from one hole? Which

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one is closer to a hole? Which
one is further from a hole? How

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much? So that's the exercises in
quantify. And as students still

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struggle with quantity, I go all
the way back to the first

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foundational step of the
numeracy cycle. That was the

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point I made at the very
beginning of this, and that is

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rote counting. How often do we
have kids rote count, other than

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whole number? So oftentimes, in
the earlier grades, we will rote

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count, skip count by 10s, skip
count by fives. 510 1520, did

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it. It's so essential. What
happens is as kids get older,

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and as we move into new number
systems, like fractions,

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decimals and negative numbers,
we skip the rote counting. And

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so kids are missing that
foundational step. So if you

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have kids struggle with
understanding numeracy, and they

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struggle with numbers and
operation and comparing numbers

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and numbers on a number line,
the number one key intervention

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is to go back to rote counting
of that type of number. So I

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might ask students, let's skip
count by three fourths, three

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fourths, six fourths, nine
fourths, rote counting is

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absolutely essential for
starting to understand quantity

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of numbers. Now, if they
struggle with that, let's just

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skip count by 1/4 1/4, two
fourths, three fourths

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4454647 4849 fourths 10 Plus,
that's it. That's it. It's as

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simple as rote counting without
meaning. I know kids don't

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understand that. But would then
I could start to ask questions.

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How many counts by one fourths
will it take to get to one 100

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Can you see how I just twisted
that perspective? And that

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question alone? Even my most
struggling student is going to

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say, oh my gosh, it's going to
take a lot of counts by 1/4 to

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get to 100. How many counts by
10? To get to 110 2030? Oh, it's

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going to take 10 counts by 10?
How many counts by one to get to

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100 100? How many counts by 1/4?
To get to 100? How many counts

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by 1/5? To get to 100? How many
counts by one eight to get to

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100. See, rote counting is the
foundation of moving into those

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higher level questions. And
without rote counting. And

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without asking those questions
to students, and without

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starting at the beginning of the
numeracy cycle, we are never

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going to get kids to the
operation level. So our math

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interventions are failing,
because we're not going all the

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way back to the rote counting of
the different number systems.

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Janet, you said you just said in
the chat, I noticed that some of

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my seventh graders had trouble
counting their hearts this week,

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because you talked about using
candy hearts to look at data

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distribution. It was so simple
one to one. Yeah, kids struggle

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with just counting individual
needs are what 12 year olds, 13

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year olds? Absolutely. When I'm
working with my high school

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students, I have high school
students that struggle or have

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never been exposed to rote
counting by fraction. We've got

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to take our math lessons back to
rote counting. And if you take

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away nothing else from this
segment of the teaching, it is

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rote counting by every type of
number, including fraction.

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Unknown: I know in my my sixth
grade classroom, we wrote count,

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I disguise it a little bit. So
that like when we're, we just

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got done with dividing fractions
with my Windblock. And they had

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troubles I'm like, Okay, well,
let's go back to the county. And

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I didn't say that to them. But
I'm like, Okay, what do we know

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about and they just started rote
counting, because sometimes it's

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hard to, they recognize rote
counting, as all this isn't

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something I should be doing that
sixth grade, at least my sixth

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graders this year. So I have to
sneak it in. But that's how I

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that's how I sneak it in. So

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Jonily : you make a beautiful
point. Because one of the things

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that I'll bring up with students
is what is six divided by two,

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and I'll do this with my high
school students as same as my

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fourth graders. And as a matter
of fact, my fourth graders do

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much better with what I'm going
to teach to you right now,

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because their numbers since
hasn't been schooled out of

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them. By the time kids get to
high school, they're all mixed

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up with all the math notation.
And I have to retrain them

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before I can move forward with
them. You can see here six

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divided by two equals what now?
No brainer, okay, for their like

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it's three. Okay. But that's not
the point. The point is not

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about solving. It's about skip
counting. Every single division

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problem is skip counting every
single division problem is skip

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counting. That's it bottom line,
when you're when we're teaching

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division, it's skip counting.
That is why 120 chart is so

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essential, because this number
to this second number here is my

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skip counting number. That's
what division means. I'm skip

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counting by two. And what am I
trying to land on? Not 100, like

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the 120 chart, trying to land on
sixth time skip counting by two

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to land on six. And the question
is, how many skip counts by two

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does it take to land on 6246? I
can use the 120 chart to do

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that. Or kids can a lot of kids
can just do that. Or I might

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need to get a manipulative out
with blocks. If I need kids to

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be more concrete manipulative
based, it depends on their math

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ability level 2463, skip counts,
here is where it gets

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Unknown: powerful in the upper
grades. If we're teaching

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division, if one of the ways
we're teaching division is by

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skip counting, and what a lot of
my teachers say is, they're

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like, Jonily. That's ridiculous.
That is not a strategy that we

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even should be utilizing.
Because if I have to 31 divided

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by seven teachers are like that
is not efficient. Why would I

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skip count by sevens all the way
to 231? Because if I want to

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improve number sense, it's not
about answer getting. It's about

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the process. See, and this is
where we fall short in tier one

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mathematics or even in tier two,
tier three intervention with

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mathematics. We believe that
intervention is more about

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answer getting than it is about
the process.

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Jonily : The process is what
improves number sense. And in

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the end when number sense
increases, then computation will

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increase as well. But if I want
to improve number sense, I want

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to think about this as 714 21.
Then what I want to do is start

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to chunk skip count. Gosh,
seven, I can get to 70. Right

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away. How many skip counts by
seven does it take to land on

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7010? I could count by seven
days to get to 31. See, this is

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the power in rote counting. Now,
why is this strategy important?

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It's important when we get to
the example that Krista

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mentioned, when I have the
problem six divided by a half. I

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know that one half is my skip
counting number. And if kids

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have had lots of interactions,
skip counting by half's that's

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not going to be a problem by the
time we get to this computation.

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One half is my skip counting
number one half, two halves oh

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two halves is one, three halves,
four halves. I skip count by

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half's to land on six. So the
question here is, how many skip

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counts by calf's does it take to
land on six. And I can do this

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with fraction by fraction. I can
do this with any division

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operation of fractions. So in
elementary school, what happens

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is Weepu sorry for the dirty
language here, we poo using this

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skip counting technique, because
we're like it's not efficient.

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That's a terrible way to do it.
But it is the most transferable

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to fraction division later on.
What we need to do is really

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prioritize the skip counting
strategies early on, and

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continue to refer to them,
because that is what's going to

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help our students with higher
level mathematics. And that is

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where we're falling short. Lots
of things right now I want us to

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reflect on. I want us to reflect
on what did I just do? And how

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was that responsive teaching,
because I skipped all the way to

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a different lesson. I want to
reflect on what I actually

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taught and what connections you
have. So let's pause for a

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moment. And just process
together with me everything that

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has just happened, because
there's a lot of power in what

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has just happened in the last 10
minutes. I think it's

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Cheri Dotterer: also happening
along the path of literacy. But

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they're starting to realize that
we have to understand the

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concepts. And hence the science
of reading and the structure

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literacy. Push is making its way
and will soon be mandated across

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the entire United States. But I
see a lot of parallels. I know

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you have always said to me that
there's no connection, but even

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looking at your numeracy cycle.
There is a lot of literacy

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connections that can be made
there. If kids can't are

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struggling with comparison,
which is usually one of the

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first things that they try to
introduce in the literacy. Okay,

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let's back up just a little bit,
to looking at counting and it

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might be that they're looking at
something else. But we're

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looking at talking

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Jonily : about this is where
your phonics is. Yeah,

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Cheri Dotterer: actually
counting is where phonemic

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awareness is there you would be
phonics would be the quantify.

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There you go.

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Teresa: So wouldn't it be
alphabet automaticity? Hmm.

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Cheri Dotterer: You're looking
at the writing part, I was

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looking at the

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Unknown: you know who I am.
That's both of you. That's a

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great point. Because oftentimes,
in literacy, we combine this

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reading and writing. And those
are two distinct, there's a

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cycle for reading and a cycle
for writing. I love it. Now. And

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this is absolutely parallel to
that I agree winning

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Teresa: feet from you. Jonily is
the fact that everybody's

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talking about a forward
progression for a shoe do add

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for a shoe do subtract, and you
do this, what's to say that and

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you said it you have in Division
mode, and that you already you

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only did actions, why are you
Why can't you revisit the way,

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Jonily at least talking is there's
always a revisiting, and there's

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nothing that says you can't
revisit. And the way she's

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talking is, if you're going
forward, there's no sense what

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did they forget what they did in
the past, so you have to go back

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to go forward. So we just say I
am the first one to tell my kids

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oops, I forgot something when we
just go back and we visit things

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or we just do something again.
So there's nothing that's says

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just because you want to try
something else that you can go

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back and revisit it. Teresa,

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Unknown: I want to stay on that
point for just a moment. And I

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think all of you on here have
heard me talk about this before

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and that is operation is not
sequential. Someone decided that

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addition should be done first
and then subtraction and then

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multiplication and division.
That is hogwash. There is no

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basis. There's no scientific,
there's no research basis. For

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that sequence me, the sequence
is division first, it's always

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division first. And then I teach
addition, subtraction,

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multiplication, always through
division with my five year olds,

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and in kindergarten, I don't
call it division, guess what I

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call it sharing. When kids are
two and three years old, we

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start to talk to them about
sharing. And kids develop a

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conceptual foundation of equal
sharing. They know that better

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than anyone, if you have more
than me, and I'm two years old,

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I know that and I'm going to
throw fit about it. We need to

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in preschool and kindergarten,
embrace sharing, which sharing

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is division. So that is how I
teach and how I sequence. I'm

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always in Division world, but I
call it sharing. And equal

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sharing means equal groups. And
equal groups means skip counting

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by the number in that group. And
Theresa, I'm glad you brought

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that up. Because I teach on this
all the time. That division

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should be the first operation,
and we disguise it as sharing

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and teach all other operations
through that. Now, Cheri, you

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have a lot to say about this.
The number four makes sharing I

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really cranky, at least it makes
me really cranky. And letters

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make Cheri and Teresa really
cranky when you're looking at

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fonts. I was using the font that
I liked the best, which Cheri

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Oh, I thought I was using lexan.
This is Arial. But anyway, I

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think there are certain fonts
that are cleaner for number,

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that when the typed font is
there, it connects best. But

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look at this for this isn't how
kids write a force, I have to

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search and search and search.
This was the best one I could

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find on Google. And it's
Pacifica, I went to lexan for

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nine, because nine had the best
I thought structure for how we

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actually write. But again, it's
just found Deco. deco on what on

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word I just found the

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Cheri Dotterer: desktop ins.
This is architects daughter,

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this is lexan. And this is deco
DECO,

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Unknown: we got go it is as a
general classroom teacher as I

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am, and I'm certified secondary.
So 712 Math, my bachelor's

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degree is in mathematics. These
are things that never came

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across my path. Until Cheri and
I began to learn from therapists

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from Cheri,oh my gosh, look at
all the things that were

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barriers to learning in my tier
one core classroom that I was

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just carrying on like it was
nobody's business, and these

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little minor things. We're
continuing to create these huge

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barriers for learning for kids.
Just by the way, the number four

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was typed.

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Jonily : And so this is what
tier one intervention is all

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about is for us to strengthen
these core classrooms. By

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utilizing these strategies,
these intervention strategies

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that combine the therapy world
and education world and better

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connect them to each other, even
though I've grown immensely in

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my math, instructional delivery
over the years because since my

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first year of teaching, I ended
up studying early childhood

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development, brain research,
cognitive science, I did

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everything I could to try to
relearn how kids learn. And I

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was able to create really great
experiential, adaptive

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differentiated multi sensory
mathematics in my classroom. But

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it wasn't until I met Cheri and
Teresa, and all of the other

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special support staff,
occupational therapists who have

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these techniques from the
medical world that have these

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techniques, that once I then
brought some of these adaptive

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techniques, non academic
techniques into my tier one

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classroom, it just glorified and
truly enhanced all of the great

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facilitation or transformations
I had already made. So when we

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look at both of these, when we
say tier one interventions,

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that's why we're not saying tier
one math interventions. We're

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saying tier one interventions,
because they are academic and

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non academic interventions. And
the only way you can get this is

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with the kids. action of both of
these worlds.

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Teresa: He's not a math person,
I think I'm one of the worst

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people, I hate math to a
passion. But I see where you can

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get me to help my kids advance
on other things like I can help

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with the visual perception, I
can help with the motor tricks,

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because my kids need that. And
they can take that back to the

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classroom. So I'm sitting here,
and as much as your trained

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people are sucking up stuff from
you, and they can go back from

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math, I'm still sucking stuff up
from you. And I've told you

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this, you came and talk to us, I
get stuff from you, every time

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you talk to me, that I can go
and say, Oh, I'm going to try

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that with my kids. Because it's
generic, I can go and take some

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of those same things. Not mad,
even though they're mad, I can

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work with them with my kids. So
even though like you're gonna

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you say, and people say, Oh,
poo, it's math. It's not like

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you're saying it's something
that can go across the board for

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general good teaching. And I
think that's very important for

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people to know that it's not
necessarily it's, yes, it's

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weighed heavily in math, but
it's not just math. So I think

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that's the push where a lot of
people need to know that it's

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good teaching.

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Jonily : And end today with
describing the best components

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that make for good teaching.

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Unknown: Me, but what has really
transformed my teaching with you

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is this this idea of
interactions over time, I think

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sometimes we get stressed about
trying to get through all of our

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curriculum, and these kids are
so far behind and all these

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gaps. But when you talk about,
they don't have to learn

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00:26:40,290 --> 00:26:42,180
everything, that first
interaction, and even with the

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00:26:42,180 --> 00:26:45,750
number are on Twitter, with all
these different interactions

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that happen. I think it's just
that pressure that's offered to

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the teacher, as a genetic
teacher, I feel that a lot I

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have to get through this
curriculum. And that's one thing

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00:26:54,540 --> 00:26:57,810
that has really helped me today.
Because I think sometimes when

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people get pressured, and they
feel like they have to get the

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00:27:00,600 --> 00:27:03,450
kids have to get it now, then
all of a sudden, sort of these

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00:27:03,450 --> 00:27:06,900
intervention strategies that go
away, at least they're like, I

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00:27:06,900 --> 00:27:09,120
just need to do procedural they
need to know it, and I need to

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00:27:09,150 --> 00:27:12,540
move on. So it's that
interactions over time that has

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00:27:12,540 --> 00:27:14,340
really changed. Maddix is

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Jonily : not a hot stove or a
busy street. I can let kids

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00:27:19,410 --> 00:27:24,150
explore. They're not going to
get hurt. And finally, as we

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00:27:24,150 --> 00:27:28,440
wrap up, this has been tier one
interventions. I want to thank

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00:27:28,440 --> 00:27:30,870
all of you for being here today.
If you're listening to the

401
00:27:30,870 --> 00:27:33,300
recording and you weren't here
live hopefully you got some

402
00:27:33,300 --> 00:27:38,100
takeaways as well. Thanks for
your attention, everybody, and

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00:27:38,100 --> 00:27:40,740
have a wonderful weekend.

404
00:27:42,420 --> 00:27:45,720
Unknown: Lima says tier one
interventions was a sensitizing

405
00:27:45,720 --> 00:27:49,530
workshop systematically thought
through put into an easy to

406
00:27:49,530 --> 00:27:52,290
understand framework that well
presented. Thank you to you

407
00:27:52,290 --> 00:27:55,920
both. Thank you and Halima.
You've been listening to tier

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00:27:55,920 --> 00:27:58,980
one interventions with Jonily
Zupancic and Cheri daughter.

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00:27:59,730 --> 00:28:02,400
Tier one intervention is
released on the first and third

410
00:28:02,400 --> 00:28:05,910
Tuesday of the month. The
podcasts are recorded live on

411
00:28:05,910 --> 00:28:09,990
the third Saturday of each month
except July 1 segment of the

412
00:28:09,990 --> 00:28:13,710
podcast is released to your
favorite podcast app. Here the

413
00:28:13,710 --> 00:28:17,130
entire workshop, go to tier one
interventions.com and register

414
00:28:17,130 --> 00:28:19,920
for our mailing list to get all
the news about the next episode.

415
00:28:20,940 --> 00:28:23,250
Be sure to subscribe so you
don't miss the next episodes

416
00:28:23,250 --> 00:28:27,750
release. Do us a favor give us a
five star rating and write a

417
00:28:27,750 --> 00:28:32,250
review. Every vote matters. I'm
Nicholas King, an intern for

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00:28:32,250 --> 00:28:34,140
cheri Dotterer educational
consulting