Internet
Internet
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 [email protected]
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
appreciated.
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 [email protected]
__________
Date: Tue, 10 Sep 1996
From: Mike Freeman [email protected]
To: Multiple recipients of list
Subject: Help: teaching mathematics to visually impaired
individuals (forwarded)
start of forwarded message:
From: Christian Harris [email protected]-edu
Newsgroups: misc.handicap
Subject: Help: teaching mathematics to visually
impaired individuals
Date: 07 Sep 1996
Hi,
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?
Thanks,
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
desire!
Cordially,
Mike Freeman
Amateur Radio Calsign: K7UIJ
Internet: [email protected]
__________
Date: Wed, 11 Sep 1996
From: John Miller [email protected]
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
help.
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:
Sincerely,
John Miller, President
Science and Engineering Division
of the National Federation of the Blind
__________
Date: Tue, 10 Sep 1996
From: Dave Schleppenbach [email protected]
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
http://www.chem.purdue.edu/facilities/sightlab/index.html
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
questions.
Regards,
Dave Schleppenbach
VISIONS LAB director
http://www.chem.purdue.edu/facilities/sightlab/index.html
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 [email protected]
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
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