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 released on the first and third
Tuesday of the month. The podcasts are recorded live on
the third Saturday of each month except July 1 segment of the
podcast is released to your favorite podcast app. Here the
entire workshop, go to tier one interventions.com and register
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Be sure to subscribe so you don't miss the next episodes
release. Do us a favor give us a five star rating and write a
review. Every vote matters. I'm Nicholas King, an intern for
cheri Dotterer educational consulting