Federation Spirit on the Internet

                               by Marc Maurer
     As Federationists know, I do not possess a great deal

of information about computers, but occasionally I turn my

attention to computer technology and equipment. Almost

invariably the telephone rings, somebody knocks on my door,

or the letters and messages from previous days begin to make

me nervous. I know that my prime responsibility is not to

understand the computer but to address the broad overall

needs of members of the National Federation of the Blind.

Consequently I don't spend enough time with computers to

become familiar with the way they work. Nevertheless, we in

the National Federation of the Blind have placed an

increasingly heavy emphasis on technological solutions to

information access for blind people. In 1990 we established

the International Braille and Technology Center for the

Blind (IBTC)--the only facility of its kind anywhere in the

world. In 1994 we established a Web site on the Internet. We

now distribute the Braille Monitor, Voice of the Diabetic,

and a number of other publications by electronic mail.

Shortly after we established the IBTC, we also created NFB

NET, our computer bulletin board service (BBS), and an

increasing number of our communications use our BBS and

indeed the Internet generally.
     Although I do not know how to use the Internet to

communicate, I review many of the documents distributed by

members of the National Federation of the Blind through this

electronic medium. Recently, Internet communications from

Jim Rebman and Christian Harris asked for help in finding

ways for blind people to study mathematics. As you would

expect, the response of Federation members was immediate and

positive. Not everybody will want to master the arcana of

advanced mathematics. However, some will. Of course, there

are many other topics which we in the Federation might

explore. If you want to know something, ask. Maybe we know

the answer. If we do, we'll make it available. If we don't,

we'll try to find out. Here are some examples of recent

questions and responses from the Internet.
Date:     Mon, 9 Sep 1996

From:     Jim Rebman jrebman@netcom.com

To:       Multiple recipients of list


Subject:  Introduction
Greetings list members:
     My name is Jim Rebman, and I'm sure many of you know

me, but some may not, so I'll give a little background.
     I lost my sight almost seven years ago as a result of

diabetic retinopathy, and just prior to that my kidneys

failed. In 1993 I received a kidney-pancreas transplant and

am no longer a diabetic.
     My formal training was in electrical engineering,and

from 1980 to 1984 I was a research assistant/engineer at the

Princeton University Plasma Physics Laboratory, where I

developed several microprocessor-based instruments and

controllers for a 12OKv 100 amp DC power system, as well as

several different 12-pulse high-current rectifiers and a

multi-pulse cycloconverter that was used to vary the line

frequency on the output of a 960 MVA motor/generator set.

Big volts, big amps, and an occasional big boom (grin).

Since that time I have been working almost exclusively with

computers on everything from compiler design/porting, to

application-development, to networks and MIS systems. I am

planning on going back to school to finish my bachelor's

degree and eventually to get my Ph.D. in computer science.

One of my big concerns at this point is how I am going to

handle the math--I really must learn it all over again from

intermediate algebra through at least four semesters of

calculus. Any tips on how to approach this would be much

     Under the heading of miscellaneous: I live just outside

of Boulder, Colorado; love outdoor activities like hiking,

rock climbing, and backpacking; am a board member of the

Boulder County chapter; and am also a graduate of the

Colorado Center (1995).
     I look forward to participating in the discussions and

especially to helping students with the tools, techniques,

and support they need to venture into the world of science

and engineering as blind people. Of course we can be

scientists and engineers--just look around.
                               Jim Rebman jrebman@netcom.com
Date:     Tue, 10 Sep 1996

From:     Mike Freeman mikef@pacifier.com

To:       Multiple recipients of list


Subject:  Help: teaching mathematics to visually impaired

          individuals (forwarded)

start of forwarded message:

From:          Christian Harris chrish@mercury.cs.albany-edu

Newsgroups:    misc.handicap

Subject:       Help: teaching mathematics to visually

               impaired individuals

Date:          07 Sep 1996

     I hope that this group is an appropriate place to ask

this question. I am a Teaching Assistant for a course called

Discrete Mathematics, which is sort of "mathematics for

computer science majors." The subject matter is entirely

mathematical; we don't do any programming in the course. The

work is all pencil-and-paper, theorem/proof work. It is

similar to first-semester calculus in the amount of work

that is assigned over the semester, and the subject is very

heavy on notation--the lecture consists of about 80 percent

board-work. Thus it is highly visual.
     I have a person in my class who is blind. I would like

to know if there are any people out there who have taught

visually impaired people highly symbolic, traditionally

visual subjects like mathematics and what methods you

employed to convey what was on the board. Also, if there are

any visually impaired persons out there who have taken

mathematics or computer science courses, I would really

appreciate hearing about what methods work the best and your

perspective about this subject.
     I have absolute confidence in my student's ability to

comprehend the material--just in talking to him after the

class, I got the impression that he is brighter than the

average student, highly enthusiastic, and very proactive

about getting help. I'm just worried about communicating the

material to him in a way that he can conceptualize. Also I

have to strike a balance with the rest of the class--I don't

want to be reading formulas off the board like: "OK, what I

wrote is open-paren, open-paren, open-paren, negation

symbol, x, close paren, . . ." because that will severely

limit the amount of stuff that can be covered and hence harm

the other students.
     I'm a bit out of my depth with this situation, I think.

I don't know the first thing about how to teach visually

impaired people. My rough plan is just to conduct the class

in the way that I would normally do and try to describe

what's on the board well enough to get the message across to

my student. But that probably won't help him do the

homework, or will it? Other than trying hard to be

considerate, nice, and communicative about the course, I

don't know what else to do. Could anyone help me out?


                                         Christian S. Harris

                                          Graduate Assistant


                              Department of Computer Science

                                  University at Albany, SUNY
           ------- end of forwarded message-------
Date:     Tue, 10 Sep 1996

From:     Mike Freeman mikef@pacifier-com

To:       Multiple recipients of list

     Good afternoon, Christian. I am responding to your post

to "misc.handicap" requesting help teaching mathematics to a

blind student. I have taken the liberty of forwarding your

post to the E-mail list of the Science and Engineering

Division of the National Federation of the Blind (NFB). The

NFB is the largest organization of the blind in this

country, and there are quite a number of NFB members

(including me) who have studied higher mathematics and the

natural sciences and/or computer science and who can help

you. Indeed the inventor of the current Braille mathematics

code used throughout most of the world, Dr. Abraham Nemeth,

is an NFB member and reads the NFBSE mailing list; I suspect

he will have something to say on the subject.
     I hold a B.A. from Reed College, Portland, Oregon, in

physics and an M.S. in physics from New Mexico State

University and have taken numerous computer science courses.

I took all the usual higher math courses so can give you

some ideas.
     First a question: does your student read Braille? If

so, is his/her math text in Braille (if you're working from

handouts, are these available in Braille)? While not

absolutely essential, use of Brailled math texts and notes

is highly desirable in that the student has the same

material in front of him/her as your sighted students are

privileged to have and she or he can peruse the material and

ponder it at his or her own pace. (I once took a topology

course from taped books alone; and, while I made it through

the course, it was tough! Physics texts, on the other hand,

were no trouble for me on tape.)
     As for a lecture style advantageous to the blind

student, I think you can follow a middle ground between the

literal "open paren, open paren, open paren . . ." style and

saying nothing about the equations. Often, especially in

fields such as set theory, Boolean algebra, math logic,

number theory, and the like, you can just read the equations

as you write them in the same manner you would speak them to

a colleague while engaging in a discussion while walking

across the campus. In some instances you will have to be

precise, but this is not as hard as it sounds. Proofs in,

say, linear algebra often go quite well aloud, especially if

the student has some familiarity with the material. Let the

student be your guide: ask him or her after class if things

were clear or not. It is, in the end, his or her

responsibility to see that she or he learns the material.
     Incidentally, I think you'll find that, if you just

relax and start talking the equations as you write them, you

won't be wasting much time, and your sighted students will

also find your presentations much clearer. I once took an

electricity and magnetism course from a very articulate

professor (the only person I've ever known who could just

read aloud any electronic diagram you put in front of him

off-the-cuff). I was late for class one day by five minutes

or so. According to fellow students, his presentation became

one-hundred-percent clearer the moment I walked in the door.
     In making certain concepts conveyed by diagrams come

across clearly, it is often helpful to use a raised-line

drawing kit (in which thin sheets of plastic are stretched

taut on a rubberized board and a ballpoint pen without ink

is rubbed along the plastic, stretching it to make raised

lines). In multivariate analysis, I once saw a wonderful

wooden model showing saddle-points and the like. Let your

imagination (and that of the student) be your guide. I got

quite good at doing all sorts of proofs in my head, and the

chief problem was getting someone who could write them on

the board for me fast enough from my dictation!
     Dr. Nemeth has invented a way of speaking mathematics

precisely and quickly. I do not think it is always

necessary, but it really works. You might wish to correspond

with him directly on this subject. His Internet address is:

     Good luck and feel free to ask as many questions as you



                                                Mike Freeman

                                Amateur Radio Calsign: K7UIJ

                                Internet: mikef@pacifier.com
Date:     Wed, 11 Sep 1996

From:     John Miller jamiller@qualcomm.com

To:       Multiple recipients of list


Subject:  Teaching math to blind students
                                          September 11, 1996
Christian S. Harris

Graduate Assistant


Department of Computer Science

University at Albany, SUNY
Dear Chris,

     My name is John Miller. I am the president of the

Science and Engineering Division of the National Federation

of the Blind. I received a posting of your message to

misc.handicap dated September 10. As you have no doubt found

from prior correspondence from the Science and Engineering

Division of the National Federation of the Blind, the

division is full of ideas on how to make learning math a

snap for blind folks. I will continue to forward the

discussion about teaching math to you as it develops on the

nfb-se.nfbcal.org list. I strongly encourage your student to

contact me and the members of the science division. The

brightest people and the ways they do math are right here.

The basic question of what alternative techniques will work

best for your student, your student will have to decide for

himself class after class and project after project on the

job. What has been written down from people's experiences,

of course, is just the tip of the iceberg. There is nothing

earth-shattering about the advice and experiences of

division members, but in the big picture I think they will

     I grew up totally blind since age three. Math has

always been my favorite subject. That's why I am doing

algorithm design and fixed-point implementation of signal

processing speech compression algorithms at QUALCOMM. I

received my B.S. and M.S. from Stanford University in

electrical engineering and have been taking graduate courses

at the University of California at San Diego ever since to

stay on the cutting edge. The discrete mathematics course

you are teaching sounds quite interesting because it has

some useful applications to what I am doing these days. I

have been attending similar courses specific to signal

processing at UCSD over the past year.
     Here are some personal experiences that have given me

the most from class participation. Braille helps. If your

student knows Braille and needs help getting handouts or

portions of a book into Braille, have him give me a call.

Places can do it with just a few weeks delay, although more

time reduces the cost and effort considerably. Preparation

helps. Usually the first day of class I make an announcement

requesting a copy of another student's notes. Usually I shop

around and keep several people's notes until I find one that

gets the details I think are important. That way the details

for rote memory I pick up later and only worry about those

that are pertinent to the discussion at hand.
     To get anything out of a lecture, I need a solid

context. I want to know down pat the postulates, the symbol

and graphing conventions, the basic framework ahead of time.

The best way I learn is to read the relevant material ahead

of time. Homework can be a pitfall. The trick is getting the

solutions in print. Sometimes I would just read my Braille

solutions to a grader line for line. No filling in with

"what I meant was." Today I would write solutions in print

or use Latex to laser print my solutions whenever possible.

I have found reviewing my professor's written comments on my

written solutions a useful learning tool. What's more, in

print is the way all work needs to be done on the job, so

sorting this out up front is a big help.
     These are the things I ask my professors to do to help

me out in the course: Tell me what in the syllabus will be

covered next lecture. Braille books are usually several

volumes. I bring the right one with me to class. If it is

possible to have raised-line drawings of graphs being used

in the course ahead of time, this is helpful too. Then the

only additional framework I need is "I'm now drawing figure

8.5 from the text." Speak the key equations as you go and

describe graphs as you draw them. The weight of

responsibility is on your student to ask when he is

confused. There seem to be two kinds of questions about

notation. "You lost me when you substituted the second

expression into the first," which means backtrack and

summarize a bit; and "read the right hand side of the

expression again please," which isn't a request to

resummarize the lecture. The error most professors make is

stopping to summarize here and resenting the interruption,

when they never said "the right hand side of the expression"

in the first place. Giving specific answers to specific

questions helps the flow of the lecture quite nicely.

Describe a graphic such as "this is a sampled decaying

exponential" as you sketch it.
     I have never found that my questions slowed the flow of

information in a class. As it turns out, on the heels of my

question always comes a related question from another

student. I sit in the front of the class. When the professor

loses the class, my question is usually the one that brings

the class back to where the professor is going.
     My learning style is my own. Your student may learn

completely differently. Use your own teaching style, the

tips that fit naturally with it, and be guided by the

requests of your student. I do believe that a good framework

will help your student learn the most from your class. I

look forward to hearing from both of you and wish you the

best with the course. You can reach me at E-mail:


                                      John Miller, President

                            Science and Engineering Division

                     of the National Federation of the Blind
Date:     Tue, 10 Sep 1996

From:     Dave Schleppenbach engage@sage.cc.purdue.edu

To:       Multiple recipients of list


Subject:  Re: Help: teaching mathematics to visually

               impaired individuals (fwd)
Dear Chris,

     The problem you are facing of teaching mathematics to

blind people is not a new one, and fortunately some terrific

advances have been made recently in the field. First of all,

let me recommend that you e-mail Dr. Nemeth, as others have

suggested, and ask his opinion.
     Second, I have written a paper, "Teaching Science to

the Visually Impaired," which deals with the topics of math

and science education for the blind. This, together with

other information on our home page, the VISIONS Lab home

page, may prove useful to you. The address is

     Third, we have developed custom software specifically

for teaching math to the blind. Specifically, we have

written a program that converts print equations into

Braille, which is available on our Web page. Version 2.0 of

our program, which we have recently finished, includes

support for Nemeth Braille output as well as MathSpeak

output, which is the spoken form of mathematics also

invented by Dr. Nemeth. This should be of great use to you

in teaching your student.
     Finally, let me mention that Dr. Mike Kress and Dr. Al

Blank have developed an AudioTactile beginning Calculus

course, which uses sound and tactile graphics to teach

calculus. This, along with some of our work in tactile

images, may be another route for learning for your student.
     Feel free to e-mail or call me if you have any


                                          Dave Schleppenbach

                                        VISIONS LAB director


     Deane Blazie, a member of the National Federation of

the Blind and president of Blazie Engineering, also

responded with additional information as follows.
Date:     Wed, 11 Sep 1996

From:     Deane Blazie deane@blazie.com

To:       Multiple recipients of list


Subject:  Re: Help teaching mathematics to visually impaired

               individuals (fwd)
     There is also a graphing calculator program called

Graphit that operates much like the graphing calculators you

see at stores. However, it is able to emboss the graphs of

up to ten equations on a Braille embosser. It can also

display in some fashion the information in an audio format.

This audio output is good for single equations.
     Graphit runs on any of the Blazie Engineering note

takers like the Braille 'n Speak. There is also a PC version

of the program. It works with most Braille embossers that

have a graphics mode.

                                                Deane Blazie