How Visuals are Changing Math Education: S2 E1

Jonily : The reason this is so
powerful for our students that

have any type of learning
disability or any type of

disconnect, such as ADD and
ADHD, is it's accessible. Hi.

Cheri Dotterer: I'm Cheri
dotterer Here at tier one

interventions podcast. Today's
episode was recorded about two

years ago in an evening workshop
that we did. I have taken an

excerpt from that workshop, and
I want to share it with you

tonight. The full episode, you
will get to know a little bit

more about at the end of the
podcast, so make sure you stick

around to the end to find out
how to learn more. For now,

let's listen in and hear what
jonily teaching about quick

DUTs.

Jonily : Cheri and I have been
collaborating on her expertise,

which is neuroscience and
occupational therapy, my

expertise, which is the
mathematics and what you're

going to get tonight from us, is
not going to be content that you

see on Saturday mornings, if you
come to Saturday math, or if

you've been a part of any of
those opportunities that we've

had, we are taking a deep dive
into how to enhance the

complexity of mathematics with
our most struggling learners.

Now we're also focusing on
students with disabilities,

dyslexia, dysgraphia and
dyscalculia, and what the

disconnect is in their brain and
how quick dots and we'll tell

you what a quick.is but if
you've been around me, you know

what a quick.is how quick dots
will connect that disconnection

in the brain through lots of the
therapies that Sherry's can

teach you and then enhance the
mathematics that I'm going to

show you tonight. We are excited
to combine both of our expertise

and bring to you a combination
of what we both teach, and this

is for K through 12, even
preschool and higher ed. So

we're going to extend the math
all the way beyond. And I will

also give you examples of how I
use this mathematics with all of

my levels, kindergarten through
high school.

Cheri Dotterer: I bring in the
neuroscience every time I look

at the purple X, all I see is
the visual perception and the

visual motor. It has been a
journey to try and learn how to

connect it to me. I had to slip
this one in tonight. Just as I

was getting ready to come
upstairs to my computer, my

husband flipped on Fox News
after we were done with supper

to this report that said, in
Philadelphia, 23% of fourth

graders are proficient in math,
and 29 are proficient in

Chicago, that was on the Bret
Baier show. I tried to look up

the link, but because he was
still alive and online and

didn't have chance to take that
anywhere else, that was what he

said. I don't know where he got
those statistics, but that's

what my husband told me. I
missed it, but that's what I was

told tonight. But when you
really think about that, 23% of

fourth graders are proficient in
math. What? All I gotta say is,

what? And

Jonily : I think if you look
nationally, urban versus rural

versus suburban, these I'm a I'm
assuming are urban numbers. I

don't know. I'm assuming these
are urban numbers, and typically

you get an average for suburban
numbers and rural numbers.

However, in any of the numbers
based on any reports that

typically come out, we are not
seeing steady increases in math

over time. And as a matter of
fact, there are inconsistencies

in the increases and oftentimes
decreases in the number of

proficient based on a wide range
of worldwide and national

assessments. Obviously, you're
here tonight. We have struggles

in mathematics. I'll give you
another statistic of students

that have dyslexia, of students
that have dyslexia, about 40% of

those students could possibly
have a math learning disability

as well. Math Learning
Disability being called

dyscalculia. Dyscalculia
research is 20 to 25 years

behind where dyslexia is. So
although we've made some gains

in reading, some gains in
reading, there's still some

controversy and some gains with
our dyslexia students. I don't

even think we've hit the tip of
where we need to be, and we

definitely have not done that in
mathematics. And I will say

until now, what Sherry and I
have done together with our work

has been leading. Leading the
way for dyscalculia,

specifically in this country and
we're hoping around the world.

What you're going to hear
tonight is very cutting edge,

very new and ahead of the curve.
So very exciting for you to be

here tonight. But I want to say
to preface this evening is I

myself have my own action
research statistics from

multiple projects I've done over
the past 18 years, and in our

statistics, I'll give you a
couple of examples with a sixth

grade cohort group. We took them
with the model that we're

presenting to you tonight. We
took those students in less than

a year, from 27% passing their
fifth grade state math

assessment to 60% passing the
very next year, and 92% showing

growth. We saw a significant
increase as they moved to

seventh and eighth grade. It was
a school that had a lot of

transient students, but of the
students that were still at the

building, it was a title
building, we saw a steady

increase from the kids of that
cohort. I also am a part of a

recent project with current
fifth graders that I have been

using this model with since
they've been in kindergarten.

This has been an amazing
project, and the data that we

have on standardized tests is
that this cohort of students has

broken the bell curve. When you
look at math achievement on a

standardized assessment, you're
looking at percentile rankings.

50th percentile is average of
this cohort of students that

started in kindergarten, the
lowest percentile on the math

portion of the standardized test
was 71st percentile. Now, if you

know anything about that, that
is all on the far right side of

the bell curve, past the peak of
the bell curve. If you look at a

bell curve, the peak of it, the
center, is 50th percentile. So

these students were all high
achieving. But when you look at

their cognitive ability scores,
their cognitive ability scores

ranged anywhere from 87 to a
couple of them in the gifted

range, at 132, 141, this is
exciting action based research.

What we're going to share with
you tonight is one of our

interventions, and that is a
quick.we have multiple types of

interventions tonight. We're
going to focus on the quick dot,

and we want to know how to
expose more mathematics out of

these struggling students so
that it becomes habitual and a

way of life for them. We are
just excited to bring this to

you. If you've not seen a quick
dot before, we're going to show

you the next set of dots for
about four seconds. We're going

to show you in two different
ways, one with the grid behind

it, one without the grid. So two
seconds each, and at the end, I

want you to type in the chat.
How many dots Did you see? Is

Cheri Dotterer: everybody ready?
Here we go. How

Jonily : many dots Did you see?
Do the reason this is so

powerful for our students that
have any type of learning

disability or any type of
disconnect, such as ADD and

ADHD, is it's accessible. One of
the takeaways I want us to have

by the end of today is I want
mathematics to be accessible yet

complex at the same time. It's
very purposeful that I use the

same quick dots over and over
again, because when we use the

same task over again with
multiple grade levels, with the

same students. That's how we're
going to get our students with

disabilities, interactions over
time. Our gifted students need

one to two interactions before
they have forever learning. They

know it forever. Our bright kids
who play the school game, they

achieve well, but they're not
necessarily identified as

gifted. Might need five to seven
interactions before they know it

forever. And our students with
disabilities and our struggling

students are at risk. Students,
mathematically, might need 66

zero to 100 interactions. How do
we get more interactions over

time? By using the same quick
dots again and again, tonight,

we're going to show how the
complexity of mathematics can

happen much earlier than middle
school, specifically in first

and second grade. You're going
to be blown away a little bit

with the mathematics. However,
it's important that you

understand the mathematics. You
are telling me 72 you see the

overlaps. You see the three by
three grids. That is beautiful.

One of the deficiencies for our
students that have learning

disabilities is the struggle
with estimation and math facts.

When we're facilitating a quick
dot, you're going to do it

exactly like I did. I'm going to
show you this for four seconds.

Take it away. The. Reason you
have these facilitation slides

where these the border is light,
is to remind you that at this

point you could do a turn and
talk for students to talk to

each other about how the dots
were arranged. For all of you

right now, go ahead and type in
the chat. Kate already did this,

but type in the chat how you saw
the dots arranged. I want to

share why this is so essential
with students. We're not

necessarily solving anything
here. What we're doing here is

we are extracting student
perspective. Part of student

motivation and engagement is
about feeling a sense of

belonging and feeling like I'm
able to achieve what an exercise

like this does is changes the
mindset. I don't have to teach

fixed or growth mindset or
whatever climate and culture I

want to create in my classroom.
I don't have to teach that. I

can just provide a task that's
going to give kids a sense of

belonging, a sense that she
cares, what I think, a sense of

accessibility. Most importantly,
aside from the mathematics, we

want to tap into those positive
emotions, this reaches over into

Sherry's expertise, which
negative emotion hinders the

ability to learn? The quick dot
you saw was the image for stage

three. What we're going to show
you now are images for stage

two. I get this question many
times, and the question is, why

don't you start with stage two,
with students with disabilities?

Because there are fewer dots and
it will be easier for them. I

want to answer that in a couple
of different ways, because

that's an important question.
Number one, if we begin with

something too trivial, and
students feel like they get it

incorrect, then their mentality
is, I can't even get the easy

one. In my experience delivering
a more complex but easily

accessible stimulus, like this
quick.in stage three, and

especially if I'm giving this to
a whole class of students, and

not just my students that I
pulled for intervention, I can

naturally differentiate, because
with the complexity of stage

three, my gifted or higher level
students really have equal

access with My lower level
students, if the higher level

students are struggling with it,
then look at the mentality shift

that takes with our lower level
students. Oh my gosh. Johnny

always gets these problems, but
this time, Johnny wasn't quite

sure. This is really cool,
because I may have guessed

better than Johnny. This is a
complete shift in prompting to

level the playing field for all
ability levels of students, and

I can't stress that enough. I

Cheri Dotterer: love what Nicole
puts in the chat. Some of my

lower special education students
get quick dots right away,

Jonily : and Nicole, if you want
to unmute and expand on that,

I'll expand first, but I'd love
to hear your testimony on Nicole

is actually one of our certified
coaches who has been heavily

implementing but the one thing
I'll Expand on Nicole's comment

is that this changes the outcome
of the game, or the question of

who's good at math, because our
students with disabilities are

actually better in general than
our higher achieving student

With these specific quick dots,
it completely changes where

students position themselves
mathematically within their

cohort. Nicole, do you want to
add on to that, in your

experience with your eighth
graders,

Cheri Dotterer: I would say with
my experience, it's because it's

a visual. That's why so many of
them catch on quicker than some

of the you could say higher
students.

Jonily : Absolutely, there is a
disadvantage for many of our

high achieving students when we
represent math visually, it's

exactly what our students with
disabilities need. However, it

becomes a struggle for our high
achieving students, because what

are those students good at?
Those students are good at

symbols and notations and
mimicking and memorizing when we

change it to this visual aspect
and make math visual first we

change. Who has the better
access to it, and that is our

students with disabilities.
Great point. Nicole,

Cheri Dotterer: my daughter is a
gifted student with a struggle

in writing. She will tell you, I
can do integrals and what are

the what's the other one?
Integrals, derivatives,

derivatives. Thank you. In my
sleep, but don't ask me to add,

subtract, multiply and divide.
What

Jonily : I'm going to ask you to
do is and some of you have seen

this before, and this is also
purposeful. Some of you have not

seen this before, and this is
purposeful. I want to show you

an analogy right now of how our
students with disabilities

intake and perceive mathematics
and what a challenge it is to

them, because what I'm going to
show you next is a visual, but

it's not a connected visual, and
I'm going to talk about what

that means, this disconnect with
students that struggle with

pattern recognition and making
connections, which gifted Kids

can do very naturally and
innately and not even be able to

explain how they're doing it.
And it's absolutely brilliant.

The way that our students with
disabilities see mathematics is

very disjoint, disconnected in
our typical traditional

delivery. And I'm going to show
you what they feel right now.

Now if you are a mimicker and
memorizer, you're going to do

better on this exercise than if
you are someone who doesn't

mimic and memorize we're going
to show you nine symbols. The

nine symbols are listed
vertically and they're in

different orientations. We're
going to show you these symbols

for about five seconds. Once we
take it away, we're going to ask

you to write down the nine
symbols vertically in the same

order, in the same orientation.
So don't write until the slide

comes up that says, right, and
we take away the images. So in

whatever brain capabilities you
have, whether it's seeing

patterns, making connections, or
just simply memorizing. I want

you to use the strengths of your
abilities to remember as many as

you can. And then, once the
slide is taken away, there'll be

a slide go ahead and write down
those nine symbols

in the same order, in the same
orientation that you saw them. I

have to tell you a story before
I have you check your work. I

was doing a professional
development a couple of years

ago, and there was a teacher
that had been in a professional

development of mine eight years
prior. I had done this exercise,

and I was relating it to
something a little different,

because the topic of the
professional development was a

little different. After I showed
this, he got all nine Correct. I

didn't remember exactly who he
was, but at the end, when we

were sharing, he reminded me
that he was in a professional

development seven or eight years
prior I had done this exercise,

he hadn't had any interaction
with me since. He hadn't seen me

anytime since, and got all nine
correct because of the

connection that I made in the
delivery of my instruction when

I did this with his group eight
years prior, what I want you to

absorb is that when we can
explicitly and directly create

mathematical experiences that
are visual and help students

recognize patterns and make
connections, because students

with disabilities have a
disconnect with recognizing and

using patterns, which is why
they sometimes make the same

mistakes or the same core
behaviors over and over again.

They're not understanding the
connection of whatever

consequence it was. They truly
don't remember and relate, and

aren't able to see the own,
their own patterns of behavior,

and how that's negatively
affecting the interactions with

other students and adults.
Pattern Recognition is extremely

important, and it's one of the
things that students with

disabilities lack. So not only
with soft skills or social

skills. Do we want students to
improve their pattern

recognition? We also want them
to be able to do that

mathematically. So that carries
over to socially and quick dots

again is one of the ways to do
that. Let's check our work. I

want you to type in the chat how
many you have the correct

orientation and the correct
position. I'm going to show you

the alternative in how to
deliver and instruct mathematics

and how students can perceive
the connections and the

recognizing of patterns. And
this is exactly why. I this

person that I told the story
about that remembered these

symbols, this teacher had no
interaction, had no studying,

had seen this one time and
retained it forever. Now I did

ask him, the first time you did
it, how many did you get

correct? And he said, three.
What I want us to think about

is, how do we deliver
instruction mathematically so

that kids don't have to mimic
and memorize? They could, if

that's their skill. Like many of
our high achieving math kids,

they have a great ability and
skill to mimic and memorize, and

I do not want to take that away
from them. That's how I got

through math. I could save on a
mimic and memorize, and I was

high achieving. Now later on, I
found out I knew nothing about

mathematics or numbers. However,
I was able to achieve high

because I was able to mimic and
memorize. But how do we deliver

instructional experiences
mathematically for students so

they don't have to remember,
they don't have to mimic, they

don't have to memorize, they'll
just know it. It'll be ingrained

and become an innate part of
their understanding. And that's

the question that we're going to
answer for you tonight. We

Cheri Dotterer: have two
comments. They're saying that

they remembered all nine,
because they've done this with

you before. I wanted to ask
Debbie to unmute and can you

relate to the story that jonily
expressed? Is that how you

remembered this? Or was there
something else that happened

that helped you recall this task
I did? You see this with me. I

want to say three or four. How
about you? Nicole?

Jonily : Only can remember one.
Even though I have seen this

before, my brain is mush. I love
the examples that we have here

with previous interactions and
not previous interactions. I'd

like to hear from someone who
has not seen this with me

before. I'm going

Cheri Dotterer: to go with
Beverly.

Unknown: I have not seen this
before. I was in the few seconds

that we had. I was trying to
figure out a pattern, but I

really only got to correct
there. I'm looking forward to

finding out what the mystery is
how to solve this. I was the

same way Beverly. I'd

never seen this before, either,
and I was able to do the first

two in the last two, and that
new idea how to connect the rest

of them. I could do things full
on the pit too.

Jonily : What I love about this
is almost all of you have had

interactions with me before and
my teaching, but at different

phases. What I mean by that is
some of you are recent in the

last year or two. Some of you
it's been two to three years.

Some of you, it's been four to
five years. Some of you, it's

been seven to eight years since
we have had some major

interaction. What I'm delivering
to you has been the most

essential and most impactful and
most powerful impact for

students with disabilities, but
this point, everything that I've

done that has not been impactful
has been filtered out, and what

you're seeing tonight is the
evolution of what sticks. Just

to make that point, I think if
you guys walk away with nothing

else, it is to not start with
the most trivial example.

Because when students can't even
do the easiest one, and we don't

even have to say it, I can put
something up there that that

looks simple, but say, Oh, this
is a tricky one, like I'm trying

to insult their intelligence.
They know when things are

trivial and when they're
complex, because your frequent

flyers in the classroom that are
always answering every question

are going to be able to do it.
When that happens, that's when

students with disabilities
internalize, gosh, if I can't

even do the easy one, so we
might as well do the complex one

so that, gosh, I couldn't do
that. But she told us that was

really difficult, and I believe
her, that it was really

difficult, and I think that is a
counterintuitive approach to

delivering mathematics
instruction that has been a game

changer. I think it also is
counterintuitive for the

research that we have seen in
special education. Let me talk

about that for just a moment.
All of the facilitation and

instructional guidance that I'm
giving you is based on improving

student number sense and
conceptual understanding. Number

Sense is defined as the innate
intuitive understanding of

number, or the size of number.
It's inborn, and it's common

sense. And. I don't want to say
common sense in the fact that

everybody has it. It's a common
sense meaning if you have it and

if you don't, number sense
cannot be explicitly taught, but

it can be learned through
experiences. All of the Special

Education Research concludes
that students with disabilities

need explicit, direct
instruction in mathematics to

close gaps. However, in all of
that research, it is based on

the opposite of what I've just
described, the opposite of

improving number sense and the
opposite of improving conceptual

understanding, the explicit
direct instruction for special

ed students using line paper,
grid paper to line up numbers,

etc, etc. All of the research
has only been done on the

procedural and fact based
efforts of mathematics. I

completely agree with that. If
we're teaching the long division

algorithm, or we're teaching
subtraction with stacking and

regrouping, if we're teaching
solving linear equations, if

we're teaching solving
proportions, whatever the

content is, whatever the skill
is, if it's a procedure that

we're teaching, then students do
need direct, explicit

instruction. I don't want them
to create that procedure. Here

are the steps. Here's how to do
it. Now, try a few that has

typically been 100% of what we
teach in mathematics and 100% of

what we put on IEP goals. But if
we want to improve the

procedural and the fact based
abilities mathematically, we

will gain more leverage in
improving the procedures and the

facts if we, at the same time,
improve conceptual and number

sense. So I want to state that
tonight, I'm not focused on the

procedures. I am going to be
focused on the facts later, I am

focused on facilitation
strategies to create experiences

in which number sense and
conceptual thinking.

Cheri Dotterer: Today's episode
of tier one interventions was

brought to you by disability
labs. One of the courses that

they have contained in
disability Labs is the purple X

mini course. Click on the link
in the show notes, and if you

want to know the answer to that
symbol. Also click in the show

notes and download the purple X
mini course today. I'm Cheri

dotterer, one of your co hosts
here at tier one interventions

podcast. You.