# 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.