NARRATOR: The name “Perkins”

carved in stone. Below a gothic tower,

a boy navigates with a cane. A title… I actually started

in the fall of 1978. I did have a background

in teaching mathematics. I have a bachelor’s degree

in math, a master’s degree

in mathematics education, and I have a Texas certification

to teach secondary mathematics. But I had no knowledge at all of teaching blind and visually

impaired students, and I just kind of happened

across… There was an opening, and I

decided to just check it out and basically I went in for,

I thought, my first interview at the Texas School for the

Blind and Visually Impaired in Austin, Texas. Actually it was TSB

in those days, Texas School for the Blind. And they kidnapped me. (laughing):

No, they wouldn’t let me go. You know, I walked in and the

principal who interviewed me said, “We need you desperately. Your credentials are fantastic.” And I was there… you know, normally when you’re

in interview you’re supposed to be telling

them the best things about you, and I’m going, like,

“But I’ve never taught the blind and visually

impaired.” “No problem,” you know. “You will have to go back to

school, get your certification, but you can do it.” And so I said yes, and here it

is 36 years later, so I must have liked it. I really thoroughly still enjoy,

you know, what I did. But again, I knew, you know,

virtually nothing about teaching the blind

and visually impaired. And, in fact, in those days,

unbeknownst to me, a lot of people really didn’t

feel that a blind person could go on into higher

mathematics… Let me put it this way,

the average person. We have our geniuses, you know, that just happen to be blind

and so forth. But the average student who was

blind was thought to, you know, not really have any hope of going into higher mathematics

and so forth, that it was such

a difficult subject. Well, anyway, I didn’t know that

and so I just jumped in. And bottom line, when I started

in 1978, the highest level of mathematics taught

at our school, at least, was a kind of a two-year,

I’d say equivalent to pre-algebra nowadays. And now we have students taking

calculus, scoring fives– five, that’s the highest you can

score on an AP calculus exam. So we proved them wrong,

those other people. NARRATOR:

Fade to black. What I had to do was, first,

I had to learn braille. I didn’t know literary braille,

much less the Nemeth code. The Nemeth code is the braille

for learning mathematics and science notation. And so I had to start there. I had to learn Nemeth code, and I’ll tell you a little story

about that. I came to the school for

the blind, and again, I thought I was told, you know, get all

kinds of help any assistance I needed. We had a lot of teachers

who themselves were blind. So I’m asking

for the teachers’ help. I go to the braille teacher,

she is the teacher of braille, and I ask for help and she goes,

“I don’t know Nemeth.” And I went, “Okay.” And then I went to the social

studies teacher, who had… He was a social studies teacher but he had to have taken math in

college, so I said, “Can you teach me

Nemeth?” and he laughed. And I went, I said,

“What’s going on here? I’m missing something.” And what he told me was that

they were too old. I was young for them. NARRATOR: We see a page

with column headings, “Symbol” and “Nemeth.” In the “Symbol” column

on the left are common math symbols such as

plus, minus, multiplication and division signs, greater

than, less than and equal signs. In the column to the right are

the symbols as they would be displayed in Nemeth code

using six-point braille cells. OSTERHAUS: And so a man named

Dr. Abraham Nemeth decided to create

this special code, and he was a professor

of mathematics himself and he wanted to be able

to read and write, you know, in all these symbols

in a code. So he invented the Nemeth code,

and I ended up teaching myself, my students and the rest

of the staff the Nemeth code, and as I was teaching myself

and learning, I saw how beautifully it was

done, how logical it was. NARRATOR: We see a photograph

of Dr. Nemeth on the occasion of his induction

into the Hall of Fame for Leaders and Legends

of the Blindness Field. Dr. Nemeth is holding a bronze

plaque of his likeness. OSTERHAUS: And Dr. Nemeth

has passed away now, but I want to say,

“Thank you, Dr. Nemeth,” because I just don’t know how I really could have done

what I did without the Nemeth code. I’m not saying that I feel

like I’m a good teacher, but having that Nemeth code, that ability to give

these students the higher mathematics using

these higher-level math symbols was just a real necessity. And so I think that’s

the main thing that has really expanded

this world of mathematics to, I’m going to just say,

the average student. I’m not saying I didn’t have

some very brilliant students, but the average student can now

take mathematics and enjoy it and, I hope, have as much fun

with it as I have over the years. NARRATOR:

Fade to black. OSTERHAUS: So I’m going

to actually start with the low-vision students. Remember, this was 1978, okay? I had to enlarge something

by hand-enlarging it. So I would just get out

my large print paper or, you know, lined paper,

whatever, and make everything large

and then copy that, because we didn’t have copying

machines that would enlarge. So we had to do all that

by hand, and then all the tactile

graphics, again, had to be done by hand. So there I was, with my… I had a Sewell raised line

drawing board. It’s just a clipboard that’s got

a little rubber padding on it. And I would put braille paper

on top of that. I would use a Howe Press

compass, by the way, which is from Perkins. And I would go ahead and draw

my tactile graphics using that and just a ruler

to guide me. NARRATOR: In a photograph,

we see a person using a Howe Press compass to trace and produce

raised-line drawings on a sheet of braille paper. The braille paper is

on a raised-line drawing board. OSTERHAUS:

So very, very basic. Now, I’m not going to say that

some of those tactile graphics are still very good. I don’t want to throw out

all the old stuff. But basically everything was

done by hand. All the brailling was done,

again, on a Per… I feel like I’m advertising

because… for the Perkins Braille Writer. We would put everything… And so it was one copy,

and then we had a machine called a thermoform machine

that would make our copies, the kind of plastic paper. That’s how it started, okay? That was the original method. And then over the… And if you’re thinking, well,

why wasn’t I using high tech? It’s not… believe me, if there

was any higher technology, I would have been using it, but at that time,

that’s all we had. And then later on, you know, there were many, many

improvements. NARRATOR: We see displayed

on a black background several thermoform pages depicting a variety

of geometric shapes, such as triangles and circles,

as well as a page with plot points

of intersecting lines. In addition, there are two

green plastic protractors with raised lines

and markings. OSTERHAUS:

But there’s so many… there’s just so many more tools that you can create tactile

graphics with these days. When you create

a tactile graphic, let’s say with Microsoft Word,

you get a nice print copy… And by the way, again,

I’m always thinking in terms of low-vision students

and the braille student. So I make one graphic, let’s

say, on the Microsoft Word, and you can do it any way

you want. Some people are more artistic

than I am, so they’ll use Corel or some

other type of drawing program. But you create a black line

master, and then you can go in and where

you would normally put print, you can still put print– you can put large print font

for your low-vision students, but then you can change the font

to a braille font, and then what you have to do

with the copy that is in braille,

it’s not really raised… It’s just, you know,

you’re printing it out and there are braille dots. So what you have to do is copy

that onto this special paper called swell-touch paper

and it does what it says, swell. So everywhere there’s black,

including the braille, you put it through

this special machine and there are like three

manufacturers of these machines and… three vendors,

and you put it through and it comes out the other end and all of the black lines

are raised and the braille is raised. So that’s probably… I would

say that is about the fastest method of getting a very good

quick graphic. NARRATOR: A photograph shows

a sheet of thermal paper coming out of the machine

that heats the paper, causing any black line or image

reproduced on that paper to swell and become

a raised line, dot or shape. In this case, a line arcs upward

on raised graph paper. OSTERHAUS: Now when I’m

preparing my math materials, I actually use… I’m not saying everybody has to

use, but this is my method, I use a product

called Scientific Notebook. And it’s a software that’s kind

of like Microsoft Word. When you look at it you think you’re maybe

in something like that except it has a special little

extra icon that you switch back and forth

between text and the actual math. So, anyway, I just get on my

computer and keyboard and I type in all of my math, and the description or the text

portion is one thing and then the mathematics

is in… actually even in a different

color when I’m looking at it. And I can change that font size

to any size font, any type of font, so for my

low-vision students, they get a perfect copy

in the font… If they want Comic Sans 24,

they get Comic Sans 24. And then I take that particular

document after I’ve created it and import it into something

called Duxbury, and that’s DBT Win. I think we’re up to 11.2 now. And it translates it into

very good Nemeth code and then I do need to do

a little formatting. So that’s how I create, you

know, all of my math work now. So we’ve come a long way

in 36 years. NARRATOR:

Fade to black. OSTERHAUS: I was teaching

very much like I teach today even when I taught sighted

students. In fact, I’ll go back

to my student teaching days. They used to have a nickname

for me. I hope it was… (laughing) They called me

the Tinker Toy Lady, because I was teaching geometry

and I would come in and I would make all these 3D

models and come in… for the sighted students. So truthfully, I want to say,

when people ask me how do I think mathematics

should be taught, I want to say, I think all

students should be taught like I teach blind students. And I’ve learned this

over the years. When I was, you know,

growing up, I was taught totally visually, I think,

mathematics. And I thought I was

a visual learner myself. Now that I’ve been teaching

for 36 years, I think I’m more of a

multisensory learner myself and I’ve learned so much while, you know, teaching

these students. NARRATOR: In a video clip,

we see a boy who is blind in a math class at Perkins. Today, he and his teacher

are working on fractions using segments of wood

in various sizes that are labeled both in marker

and with braille tape. BOY: Four-twelfths

equals one-third. TEACHER:

You got it. Nice job. OSTERHAUS: The way I approach

everything, I found out that it’s called

the multisensory approach. When I started out, I just did

my own thing, but then people later on

told me, “Wow, you use the

multisensory approach.” I said, “Oh, I do? Glad to hear that.” “And you believe

in universal design.” So let me explain a little bit

about that. As far as multisensory approach, when students are

in my classroom I really try to get them, at

least, if they have some vision to look at it. Basically, we use

as many senses as possible. If they can see a little bit,

some of them, even if they’re a braille

student, can have a little vision and we want them to use as much

of that as they can, even if it might just be color. And then we want them to,

you know, of course, if they’re a braille student,

to feel it. But even if they’re

a low-vision student, I still have them in there

doing a lot of tactile work. With the… I’ll even

have them eating math. You know, if you make a pizza and they have to cut it

into pieces, into fractions, all kinds of things. I can still remember doing,

you know… I don’t think they do them

anymore, they do too much work

for us now, you used to be able

to break the crackers into four pieces, and so we would do the fractions

that way and then I would say, “Okay, eat one-fourth of your

big cracker” and so forth. And it’s amazing. They learn a lot better when

they get to eat their math. NARRATOR:

Fade to black. So I was desperately constantly

telling people, “Find me a better calculator.” And again, over the years they’ve had several of the basic

calculators. You can buy them anywhere

these days. But finally, I was really

in need of a… at least a talking

scientific calculator, and I started doing a lot

of research to find the perfect one. Went all over the place, had the students evaluate each

one of these. And finally we found, just as I was about to make

a bad decision, a new calculator came out,

and it was from Orbit Research and it was called the ORION TI-34 talking

scientific calculator. It was, like, a third of the

price of all the other ones and had more functions, and again, it was based

on Texas Instruments’ product. So I have… I am from Texas,

so I have confidence in Texas Instruments. And that ended up being

our calculator of choice. NARRATOR: We see displayed

a photograph of the TI-34, a Texas Instruments

talking calculator. OSTERHAUS: However, at a certain

point, TI decided to stop making the TI-34, so then we went to… and actually Orbit Research

asked me, by that time I had gotten

involved and had helped them actually

with the TI-34, so they asked me for my input. And I am actually the one who

put the stamp of approval on them doing the TI-36X. So currently we have

the ORION TI-36X, which has, as I said,

many more functions. I think it has 122 functions. And then ViewPlus came out with

the audio graphing calculator, which was a software product

that was on… basically used on a PC. And I, you know, learned

how to use that and again asked them to, you

know, continually update that. And we used that for many,

many years. Bottom line, I was involved, and we got this fantastic

collaboration between Texas Instruments,

Orbit Research and the American Printing House

for the Blind, and we now have the ORION TI-84 Plus talking

graphing calculator. APH came out with something

called Math Flash, which is a cute little program

of teaching… helping… Well, it’s not really so much

teaching, it’s giving sample problems,

but it’s in such a cute way. If a student gets the problem

correct, you know, it gives them all this great

talkative feedback and praises them and so forth. And if they get it wrong, it does things like

flush the toilet. The people that I worked

with were Touch Graphics, who do the Talking Tactile

Tablet, and since I field-tested that,

you know, that’s the one that we got

to keep. The IVEO is the competition. It’s ViewPlus. I just want to mention them,

though. You know, but it’s the fact that

Touch Graphics got to us first and we field-tested that. And the Talking Tactile Tablet, I thought what

we were going to do is that it was going to mainly

be for my blind students. NARRATOR: A raised-line graphic

of a right triangle sits within the frame

of a Talking Tactile Tablet. The tablet is connected

to an open laptop computer that displays an X-Y axis on a

background field of graph paper. OSTERHAUS:

But that particular year that we were first

field-testing it, I happened to have a student

who had achromatopsia, which is basically

real color blindness, no… just seeing basically

in black and white and grays. And he also had dyslexia. And it turned out that this was the most fantastic

thing for him. As it turned out,

the contrast was best black on canary yellow– not

that he could see canary yellow, but the contrast was the best. So I did his graphics that way

with the black line masters but on the canary yellow paper. I did the whole

Talking Tactile Tablet with him. I was so pleased. He was absolutely ecstatic. The iPad, yes. What had happened there… I’d been working with

the University of Arizona, and they are taking

AnimalWatch Vi Suite, and they are basically opening

it up to the Vi population. And this is, I think, one

of the first apps for the iPad that is truly, you know,

accessible for our students. It has the… again, it’s on the

iPad, so you can listen to it and so forth, but in addition

to all of that, we have a braille script

that goes with it– a hard-copy braille script– hard-copy tactile graphics… We even have

three-dimensional objects. NARRATOR: A fourth-grade boy

who is blind is using the AnimalWatch app

on an iPad. This particular math problem

involves determining the amount of weight that

a cheetah gains per month over its first year of life. The boy can hear the problem

read to him using the voiceover feature

on his iPad. He also has a refreshable

braille display that allows him to read

the problem. On the screen of the iPad,

we see the text of the problem and a picture of a cheetah. On the desk to the right

of the iPad is a small three-dimensional

plastic figure of a cheetah. COMPUTER VOICE: …to find the

average weight gained per month. (boy laughing) BOY: 60 divided by… COMPUTER: Divide 60 by 12 to find the average weight

gained per month. OSTERHAUS: And the little

three-dimensional objects are the actual animals

themselves. We came up with, I think,

good tactile graphics, but there’s still nothing better than they really need

to kind of feel… even though it’s, of course,

a much smaller version of what it’s going to be. NARRATOR:

Fade to black. OSTERHAUS:

My first… and this was old. This is the oldest tool I… Well, maybe not. But if not the oldest,

one of the oldest tools. In my closet when I got there there was something called–

it’s got a long name– Graphic Aid for Mathematics. We just call it

the rubber graph board. It looks like a coordinate

plane, and you put the X and Y axis on

with rubber bands and you use push pins. And I’m going to tell you

that we… It’s changed over the years. They’ve made adjustments

and so forth. But it is still

the greatest thing. So I don’t believe in throwing

out the old with the new. We keep the old that is good

and add the new is what we do. So we still have that and I

still just absolutely love that particular tool. NARRATOR: We see a photograph of

a Graphic Aid for Mathematics. In the lower left corner, three

push pins with rubber bands stretched between them form

the X and Y axes of a graph. Two other plot points are

noted by push pins, and a thin piece of flexible

black plastic describes a line that passes from the 0,0 point

on the graph through the other plot points. To the upper right on the board, rubber bands stretched

between push pins create a triangle shape. The thin, flexible black plastic forms a circle

around this triangle, intersecting at the points

of the three angles. OSTERHAUS: Some people complain

that we’re, like, “Well, Susan, you know, you can

only do one graph at a time” or, you know, “and then if the

student has 12 graphs to do, what do they do?” So I was, like, thinking

very hard, “How am I going to do this?” And the light bulb finally went

off because I have a motto that anything I can do

my students can do better. So I had been taking

digital pictures. I would do something and I would

take a digital picture for a presentation,

for a PowerPoint. And I thought, “If I can take

a picture, they can take a picture.” So we teach blind students, our totally blind students

and the low-vision students, they can take a digital picture

of their graph and put that in their math

teacher’s shared folder or however they want it

and hand their homework in. So I have brought an old, old

tool into the modern world. There’s something

called Geometro that has not been around

as long. It is a Canadian…

a Canadian vendor created these. They’re… if you can imagine,

polygons with a Velcro edge and you can make something

we call nets and then you take the nets

and you fold them up to this three-dimensional model. They are the most fun thing ever

for geometry. There’s something called

a braille print protractor that… actually I had something

similar to it in my classroom but we didn’t have a vendor

for it anymore and I asked APH to kind of

reinvent it. And this braille print

protractor has braille and print on it, so again,

it’s universal design. And it’s got this little wand, and it’s really what people

out there, a geologist, would call a goniometer. They would use it for measuring

the angles on crystals because it has this wand, and you use it in a very

different way. It’s kind of like you turn it

almost upside-down and you actually, the wand actually forms

the angle that you want and then its supplement. So it’s another teaching tool. You get such a good tool for

teaching supplementary angles. NARRATOR: We see an example

of the braille print protractor with the APH logo as described. The wand portion, which pivots

from the center of the compass’s

horizontal base, comes to a point on the end

that sweeps over the compass arc just below raised markings

that denote a distance of five degrees on the arc. This allows the student

to measure an angle. OSTERHAUS: And then if you think

about, as I mentioned, like just a ruler. So we have at least… we have an English measurement

flexible ruler that’s both braille and print. We have a metric one. We have a braille print

yardstick. So all of those kind of tools. And I know I’ve… Oh, there is another one that’s

another one of my favorites. It’s called Omnifix Cubes. This is not available

at the blind store. This is just something

you can purchase at Didax, which is one

of the math education type online stores that you can

buy from. And they’re just these cute

little… Actually they come as a net. You fold them up into a cube. But the cubes fit together

and they’re not unifix cubes. They fit on all sides. NARRATOR: In a photograph,

we see many Omni cubes stacked in various

configurations. In the center of the picture we see one of the cubes

unfolded, its six sides flat on the table. OSTERHAUS: So when you’re trying

to create this three-dimensional drawing

of squares or cubes… which they love to put

on standardized assessments. This is the real big thing. And we used to try to do this

with regular cubes, and the kids…

if you can see it and maybe keep the cubes

together, you’re okay. But to explore them tactilely,

your cubes would all fall apart and so forth, so this was just

a wonderful thing, again, to have, and so I use

that with students. NARRATOR:

Fade to black. OSTERHAUS: There are obviously

problems with online testing, but that’s where they

would like to go. And I think that they’ve been

more successful in, let’s say,

with English language arts. Now, so what are the problems

with math? Okay. Well, I’ve already addressed

a little bit about that talking about the iPad and needing that extra hard copy

additions. So as far as what we can do and whether we think

it’s good or bad, first of all, you can listen

to math, but listening to math… what I

try to tell sighted people is, “You try to do it.” Because a lot of these testing

organizations say, “Well, they can just listen. “They can just listen

to the math. “I mean, they can listen to…

they can listen “to an English passage, a

nonfiction or fiction passage. Why can’t they just listen

to math?” Well, what I like to say

then, “Okay, if you think listening

is the way to go, “then everybody takes

their online test in math “by listening. “There will be no print. “There will be nothing visual. You go ahead and take a math

test just by listening.” And then they kind of go,

“Oh, I get it.” The other thing is with… let

me go to low-vision students. The way that these online folks

are doing it, they are incorporating

a zoom feature so people can enlarge things. They are coming up with

calculators that, again, you can zoom them and they are

actually on the test itself. They have contrast. You can choose. Do you want black

on canary yellow or black on white

or white on black? You know, you can do

that type of thing. So, they are coming up

with a lot of features, that type of features. And even math tools that these

low-vision students are going to be able to use

and manipulate. Again, when you get

to the braille reader, some of them have said to me, “Well, what about

refreshable braille”? And that’s… and basically

a lot of students are using

refreshable braille now. But I’ve heard… not everyone. But, you know, just about all

of the students that I know, they have some type

of a refreshable braille. However, at the present time, they get one line

of refreshable braille. Well, when I do math, yes,

I may do one line at a time, but I look back at the line

before. I want kind of this bigger

picture. And there are some things that

you can create in math that require your looking at

more than one line at a time. For instance, a number line

graph can be created, and in fact this is

the standard way. Now it is considered

the standard way in the United States and Canada

that we make number line graphs. And they require three lines. You can’t do that on

a one-line refreshable. But again, I’m going

to tell you right now, teachers are still saying, “We still need the hard-copy

braille, the hard-copy tactile graphics

for now.” They don’t feel that the

technology is there yet. NARRATOR:

Fade to black. You know, when you’re studying

orientation and mobility, they do put us

under the blindfold and we kind of simulate it and I was amazed how all my

other senses started kicking in, things that I had never bothered

to notice, never heard before, never felt before,

never, you know… the sun coming in the…

just all of these things that I had never heard

or felt, et cetera, before until we blocked out

the vision momentarily to where I actually had to use

my other senses. So again, I’m not going

to say… there are certain aspects

that are more difficult that are just easier

to grasp if you can see it. But I still think that

there is no ceiling. I mean, and now with all

the new technology, it’s just becoming

much more accessible. Everything is still…

like I said, we’re behind. You know, the technology

continues to be behind, but from 36 years ago, boy, have we come a long way,

baby, as they say. So I really encourage

many students… You know, not everyone is

going to be a mathematician, but certainly at least explore

mathematics. I’ve had a lot of students

who were fantastic in math and, unfortunately, they didn’t

go on to become mathematicians, but they certainly went on

to do other, you know, fantastic things

and used their math. NARRATOR:

Fade to black.

How how far we have come with technology! Susan is truly an amazing person!

nice video. I want to ask a question, when a VI person search for solution for any mathematical equation, in that condition teacher who is explaning the question, he sad that we put the X here. he is explaning for a sighted student with the help of hand waving or text. how can a blind student gain where he is pointing x.please suggest me any link, YouTube channel and app which is accessible for Blind users. for maths solution. thanks sir

Good for you.

I’m visually impaired I Went to public school all through high school I HATED math with the ever living breath of me. Couldn’t see what teachers were doing up there and as for nemeth I thought it was just evil because like she said the Braille teacher could not teach me so I was just clueless. I graduated in 2016 with barely a C in math

My cousin is NLP ( completely blind) and excelled in math. She's gone on to a career as a chartered accountant. I want to both say that technology has helped the blind and visually impaired immensely but…braille is still important. My cousin learned Braille and Nemeth Code and teaches it to her kids.