Power of Visual Perception in Math | T1I S1 E10

Power of Visual Perception in Math | T1I S1 E10

Unknown: Music. Hello and
welcome to tier one

interventions Podcast

with your hosts, jonily Zupancic

and me, Cheri Dotterer And I
like that you interrupted me

there because sometimes their
understanding of number and

their understanding of visual
perception are not aligned.

Hello and welcome to tier one
interventions podcast where we

share with you tips, techniques
and strategies to strengthen

your core. The core classroom
that is in the last episode of

tier one interventions, John Lee
was training on number sense and

how dots relate to number at the
end of what we've shared last

time, we're going to continue
that conversation with a

question that she asked me. So
tune in and find out what she


Sherry. I don't even know what
question I have for you, but

what are your thoughts on all of
that? What are the struggles

that kids have. What are the
deficits that kids have with

visual perceptual What are many
of the positive aspects of

classroom teachers using visuals
to gain access to the

curriculum, and specifically the
math curriculum? What is

happening in the brain that is
going to support what we're

trying to teach in tier one
interventions. I'm going to let

you take it away a little bit
and make some of these

connections for us through
cognitive science and


And there's another thing you
said, I'm giving you a lot right

now. I know that you always talk
about what the brains crave and

what toddlers naturally do like,
I'm asking you, like, 52

questions at once, but you just
take it away and give us your

insight on how cognitive science
matches what we're talking

about. Constantly, we were
having pre discussions about

what we were going to talk about
today. We've had discussions

about dots for a long time, you
and I, we've had conversations

with some of our students in the
past about dots, one of the dots

patterns that you utilize to
represent equation. We have some

samples from kids that we have
looked at in the past. But one

of the things that triggered me
earlier this week, we were

talking about representation of
dots in a different form. We

were looking at it with a board,
and one of the things that I was

thinking about was representing
dots on a pegboard.

We have these different dots
available. What I don't have is

one of those foam boards. I just
don't have any in stock at the

moment there at school, and you
know how that is. But they often

have this big knobby peg that's
three times this size. It has

that knob on the end, like this

was it? Those big knobbies are
going to be better for kids who

are struggling with fine motor
skills. What's nice about foam

is you can pop it in and out,
because looking at different

ways that we represent dots. The
other way is really a bigger

dot, but parketry also creates
patterns like dots. For those of

you listening to the podcast, I
suggest that you pop over to the

YouTube channel and look at this
segment so that you can see what

we're talking about, because the
dot representations and how the

kids represented the pattern
that they were copying is really


These dots represented on a
piece of grid paper. I don't

know if you can see the dots in
here, but she was trying to

mimic an image that she had seen
earlier that day.

Jason was trying to mimic the
image. Was a bit of a shot. We

can see the dots a little bit
better on on this image.

You need to know what the image
was, to know whether he's doing

a good job at representing that
the images, but he's keeping his

circles inside the dots. He's
doing a pretty nice job of

representing the fine motor

This little one, Lacey, she made
circles out of it. She got

started, but got stuck on
expanding Lane looks like the

top part of it is formed nice.
It's got nice circles, and the

nice hand form on the pencil
looks like he's got a pretty

nice pencil grip. And we come up
with something like this that

Zane did, and he knew he.

Was trying to make an X, but had
no idea how to represent the

blocks and the dots. Karen, it's
almost there's a left side and a

right side. They're all
separate. They're not blended.

She had the idea, but could not

write it and represent it. This
is what happens with a lot of

kids with writing skills, the
there's a disconnect between

what they see visually and what
they can put on paper. One of

the reasons that John Lee and I
really meshed when we first met

is we have in mathematics a need
to understand and relate some of

the disconnects there are
neurologically with what they're

seeing in the math classroom.

Chris is working. He's got an
okay pencil grip. He looks like

his. He could be doing a little
bit better with his grip. He's

loose on there, but he's making
circles. He started at the

outside, so he knew he had to
start wide and come to the


He may be processing it a little
bit slower than some of the

other kids. Then we have this
one. She knew she was making an

X, but that's all that she can

And here we have one is, oh,
this is wrong. Oh, this is

wrong. And doing a lot of
erasers. That's what happens

with kids with memory issues.
They'll do a lot of erasers. And

perfectionists also want to do a
lot of erasers and crossing out

and redoing things. Sherry, I'm
gonna say something here about

Jeb, that last one that you did
in looking at just without

knowing the context, you might
think that Jeb has a lot of

deficiencies and gaps. Jeb does
have some interesting brain


but from this picture, you can't
tell this. And I know who this

student is. He actually,
conceptually, is very high

achieving mathematically.
Sherry, this proves, on this

one, the disconnect between what
kids are seeing, what's in their

brain, what they can analyze
mathematically, which sometimes

is a higher level than the
teacher. And these kiddos were

in kindergarten at the time, and
he was actually teaching me

things about mathematics, but
then to show that on paper, it

is a huge struggle for him and
pushing on the pencil very

heavily. So he's got some other
issues. I'm going to say,

however, they're not with math
content. So I wanted to point

that out on this picture.

Then we have somebody like Ray,
who is not

maybe the fine motor, and making
the dot wasn't good, but he's

still doing three by three
squares that he's coloring them

in. Somebody Melissa thought she
did a fantastic job. Our friend

Randy. Randy had a real
difficult time with his visual


Whether he had initiation of
tasks, those executive functions

were getting in the way, or he
really had no concept, but he

knew he had to do something on
paper. I hope that represents

and answers a little bit about
where you wanted me to go.


look at visual spatial
dysgraphia. Dots are they

staying within the lines and the
bottom lines, are they able to

see the overlaps of the dots?
Are they able to

represent what they see
visually? And that's one of the

reasons I've like your what do
you see? Question, because if we

can have them verbalize what
they're seeing first before we

write it down, we can more

differentially analyze where the
disconnect is. Is it the visual?

If it's the visual, we need to
start there. Is it what they're

writing? Is it that motor skill,
is there some disconnect with

their memory? It's breaking it
down into its parts, looking at

it from a visual, a motor and a
memory standpoint,

we're looking at it to try and
differentiate where the

neurological gap is you're
looking at and then how do they

represent their understanding of

And I like that you interrupted
me there, because sometimes

their understanding of number
and their understanding of

visual perception are not
aligned. And.

Yeah, I like that you
interrupted me there, because

sometimes their understanding of
number and their understanding

of visual perception are not
aligned, that what you just

said, they're not aligned
creates, and I haven't talked

about this yet, but that false
negative kiddo, I'll explain

what I mean by that. Earlier I
talked about the false positive

kiddo that is appearing to
achieve high does well on tests,

can mimic the notation, but
doesn't have this deep sense of

conceptual understandings when
given something out of context,

or a more comprehensive test,
like an A CT, they don't score

well there, and we're confused
as the adults, because it

doesn't match what we typically
see from them in school. On the

flip side of that, we get these
kiddos that what Sherry just

said, the mathematics and the
visual perception, they don't

align. So we get a false
negative reading on kids when

we're asking kids to replicate
or use the visual to figure out

the mathematics. Many of them
struggle to do that on paper.

That's that misalignment that
Sherry's talking about. When

that misalignment happens, I
can't use that paper form to

truly assess what the kids
understanding is in that

specific example that she had
just shown we have to be really

savvy as the adults to know if
this is a misalignment, and not


target a child for math
intervention that actually has a

separate issue, and it's not the
mathematics. This is how we

expose conceptual understanding
in mathematics by using these

dots, and that's what I mean by
assessment of watching these

kids work. We had a session not
too long ago where one of our

participants, one of our
teachers on the session, said,

is what you're talking about,
like, when kids know the answer

but they don't show their work.
And that's absolutely what I'm

talking about here. Kids that
can look at DOT images or look

at mathematics and they're
accurate, they can actually

solve, they can actually count,
they can get the answer. And we

demand that they show their
work. This sometimes is a demand

that the kiddo is just not
capable of. They just physically

can't now that's what they need
the intervention for. But what

happens is, oftentimes, we give
them this lecture. If you don't

show your work, I can't give you
partial credit, so I have to

take all the points away. What
we're doing is we're reducing

the number of points they get
based on something they're not

even capable of doing. When
we're thinking about

intervention, whether it's math
intervention or therapy

intervention, we need to be able
to analyze and work with as

classroom teachers and
educators, be able to work with

our direct service providers to
make sure that we're assessing

the correct thing. If you have a
kid that's not showing their

work in mathematics, it's
probably because that is where

they need the intervention to
help them show on paper what

they're getting accurately.
Because, again, they probably

know more mathematically than we
do as teacher,

but where their deficit is being
able to articulate that and

those false negative kids, which
means they know more mathematics

than what we're giving them
credit for. Those are the kids

that we sometimes say, Oh, they
just don't test well, no, they

just aren't seeing the notation
and symbol, and they're just not

able to replicate that. And
that's where we need to provide

the intervention, which one of
the interventions is giving them

more experiences on creating
mathematics using dots. Picture

is not 1000 words. Go ahead,
Sherry, one of the things that I

want to emphasize to the
occupational therapists that are

listening to this is, please
include the symbols, math

symbols in your therapy
sessions, explain why a

parentheses goes to the right
versus goes to the left. Explain

it, and not just in literacy
terms, but also explain it in

its connection to mathematics.
What are three ways that you can

represent the divide sign. You
have the dots on the top and the

bottom. You have a fraction
which just has the line, and you

have a horizontal equation. You
can have it with the thing

almost looks like a square root
that line, you've got the dots,

you've got just a line. And what
are some of those other ways

that you can talk to your
students about the

representation of those symbols
and make connections for

mathematics? I think I just in
my brain, created a new

worksheet for my.

How many ways can you represent
the divide sign? I remember,

gosh, we were working together.
Maybe this was back in 2019

it was, I'm pretty sure it was
before covid, and you put up

something that to this day, I
still go, I

she went off on a crazy tangent,
and I still don't know that I

fully understand it, and I
represent it often, because it

made that much of an impact on
me. And you asked me, How many

ways can I write eight over 12?
And I looked at you and I went,

give me a calculator, because to
me, I automatically know what

the procedure is. I know how to
get the answer on the


Don't ask me, How many ways to
represent it. You did this thing

called 20 ways, and one of the
ways that you did it was with

dots, and that was different
ways to represent that

particular number, and I just
sat back

and I went, I have a long way to
go with understanding

mathematics. And I thought that
I understood mathematics until I

sat with you for a day.

But that really sums up my story
as well. I was that I'm going to

say false positive kid in K 12,
I achieved high I was always

told I was good at mathematics.
I always had this perception

that I was good at mathematics.
Got good grades in mathematics.

So I decided to actually major
in a mathematics area in

college, I started in Actuarial
science, but as a sophomore in

college, I failed my first math
class, and it really made me

question my own understanding,
just like Sherry said she came

to that realization at some
point that, wow, do I really

even know anything at all about
mathematics. So I failed that

math class, switched out of
actuarial science. That's how

much it affected me. Majored in
just pure math in college. Took

me five years to get the four
year degree, and then decided to

go on and get my certification
to teach. And I thought, oh, I

can teach eighth grade
mathematics because I at least

know enough to teach eighth
grade mathematics. What happened

was, in the first two or three
weeks of my first year of

teaching, I I thought, I'm a
brilliant teacher, and I would

give my quizzes and my tests,
and about half of my students

were not able to do what I
taught them. I was really

questioning where that
disconnect was, and the

realization I came to was I
really don't know math well

enough to be able to give access
to this mathematics. We did

almost full inclusion. We still
had some resource room for math,

where we had, like, pure tier
300% pull out for mathematics,

but we were trying to really get
full inclusion tier one core

classroom, and my we're
recording this live today, and

my intervention specialist who
helped guide me through this

realization of, do we really
even know the mathematics to

better support our students is
actually here. Live with us

today. You know who you are.
Thank you for being here. Would

you like this morning? Hello.

This is, this is a fun story.
Take us back, Christy, 1999

you saw this very young, early,
20 year old girl come in and

over the next five or six years,
as we collaborated and worked

together, you as intervention
specialist, me as math classroom

teacher. Give me your
perspective of this journey that

we actually took together, I
feel like I was in the same boat

as you, as a student, where I
always got great grades. I was

not necessarily a straight A
math student, but I could play

the math student. I could do the
math. Just show me what to do,

and I can follow the steps and I
can get the right answer. I feel

like when we first started
teaching together, we were like,

Okay, if I can give these kids
tricks and mnemonics to remember

how to do long division and how
do subtraction and how to do

different procedures, that it's
okay the kids have it. If I

write those mnemonics out and I
write the steps out, the kids

can go home and they can do it
for homework. Then in two weeks

from now, I give them a problem
again, and they have no idea.

How do we even start? I feel
like what we learned together is

that a lot of times we have kids
that can play the math game and

they can do the procedures, but
in the end, they have absolutely

no idea what they're doing and
why. They didn't really

understand the math. They didn't
have the.

Number Sense, that's the biggest
thing I felt. Was our journey

working together was, how do we
get kids to understand what

they're doing and why? Which is
that whole importance of number

sense? And how can we improve
number sense in kids? That's

exactly the neurological
philosophy neurodevelopmentally

gifted students will be able to
figure things out and understand

them in a few sessions, typical
kids a couple more, but kids

with disabilities and kids who
are truly struggling.

Initially, I had heard 60, but
lately, I've been hearing more

like 300

times you you need to represent
the number two, 300 times. How

do we get more interactions with
kids so that it increases their

memory and retention, and that
is through visuals. That's

really what the phrase a picture
is worth 1000 words mean. And

one thing I want to connect to
what Christy said is, and I'm

going to say this a different
way, but it's what we learned in

our journey, is that oftentimes
we can get kids to replicate

short term. Some of these kids,
we can give quizzes and tests in

our classroom, and they could
score very high, because it's in

that short term, they're able to
retain the information just long

enough to produce on my quizzes
and tests, but then we give a

midterm or a final exam, or the
end of the year assessment or

the state test at the end of the
year, where they have all of

these concepts all At once,
where they have to pull from

their memory and things that
happened five or six months ago.

That's where the breakdown is.
We have some of these kids that

achieve very high they get A's
and B's in math class, but then

they fail, or come close to
failing that end of year test.

And we're like, oh, they're just
not a good test taker. No, that

has nothing to do with it at
all. Their brain has not learned

in the way that increased the
memory of this content, and

they're not able to retain a lot
of teachers talk about this.

Also, when kids move through the
grades, they get to fifth,

sixth, seventh grade, and the
teacher says, These kids don't

know this. And the third and
fourth grade teachers are like,

Oh my gosh, we spent so much
time on this. We did this with

kids. The problem was they were
able to get it short term, but

without those visuals, we're
losing that long term memory and


So let's jump more into the
mathematics. If you want to hear

a little bit more about that
conversation, go to tier one

interventions.com sign up for
the workshop, and you'll get the

rest of the conversation. It is

inclusion. And when I talk about
inclusion, I'm talking full

inclusion. How are we going to

pull out sessions to zero? I
know it's in it might not be the

perfect for all kids, but the
full inclusion, if we're really

looking at the definition, it
requires professional

development. It requires

pull in sessions for all
disciplines. So inclusion is the

first one, metacognition,
thinking about thinking. And

that's all of these words and
all of these phrases and these

little nuances that jonily All
the time. What do you see? What

do you notice? Tell me about

number three is perseverance.
When we're toddlers, we're

running around, we're curious,
we're doing all these wonderful

things. We're always trying to
take the next challenge. How

often does it take a toddler to
learn how to walk? A few weeks.

How long does it take an 83 year
old, after they've had a stroke,

to learn how to walk again?

Not a few weeks. Takes much
longer. When we're looking at

perseverance, we're looking at
helping them create an innate

sense of drive and motivation to
accomplish something.

When we're looking at a we're
looking at adaptability.

Adaptability is more than just
physically adapting the

worksheet, adaptability is also
a change in a shift in your


When we're looking at See, we're
looking at curiosity.

I mentioned the toddler a little
bit ago, looking around and

doing all kinds of wonderful
activities and being absolutely

curious about their
surroundings. We put them in

kindergarten. Here you need to
sit in this seat. We can find


We teach them this structure
that we've created.

It in the system so that we can
get all kids learning at the

same time. I would love to see,

especially in middle school,
kids on treadmills learning


There's been a research study
that talks about it, where they

were had in this special ed
class of kids who were failing

math, they started putting they
put treadmills in the classroom

for these this particular set of
students. All six students, Aced

their state testing that year
because every time they came

into math, they had the
treadmill at a low rate of speed

so they could still hear the

and their math scores
skyrocketed, and they got the


before you say the last one, I'm
going to give the definition of

this last one before we say the
word that he is a new path that

doesn't yet exist, that Sherry
and I are Creating and hoping

that it catches on. This isn't
in addition to, it's instead of,

it's the better way.

It's the path unpaved that we
have all the research to back

it, and now we just need to take
the step so Sherry, give it to

us. What's that last word that
I've just transcendence. It's a


It's not transformation which
happens instantly. It's

transformation that happens from
this point all the way to this

point and beyond. It's that
concept of lifelong learning.

It's a concept of what we learn

we integrate into our base of
knowledge so that we can use it


All right, everybody. Have a
great weekend, great end of the

school year, great summer,

and we resume these tier ones,
September 21 the third, Saturday

of every month, I just go in, go
into disability labs and

register for September, October
and November, the date

that way you're registered in
your login so that you get all

the emails and the links and

Hello, everybody. Happy Summer.

Episode Video

Creators and Guests

Cheri Dotterer
Cheri Dotterer
Hacking barriers to writing success, dysgraphia No ✏️ Required. 30-sec@time Speaker | Podcast Host | Author | Consultanthttps://t.co/eM1CXSUIoZ