teaching math to blind students

From: John Miller (jamiller@qualcomm.com)
Date: Wed Sep 11 1996 - 10:22:25 PDT

John Miller, President
Science and Engineering Division
of the National Federation of the Blind
8720 Villa La Jolla Drive #118
La Jolla, CA 92037
phone: (619) 587-3975
 e-mail: jamiller@qualcomm.com

Christian S. Harris Department of Computer Science
Graduate Assistant University at Albany, SUNY
chrish@cs.albany.edu (518)-442-4286
September 11, 1996

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 a bevy 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
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 BS and MS from Stanford University in
Electrical Engineering and have been taking graduate courses at
University of California at San Diego every since to stay on the cutting
edge. The discrete mathematics course you are teaching sounds quite
interesting as 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 of my 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 brl, 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 wrote 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 how 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 cylabus will be covered next lecture.
Braille books take several volumes. I bring the right one with me
to class. If it is possible to have raised-line drawings ahead of time
of graphs being used in the course, 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 seems 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
righthand 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 it when they never said the righthand
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 down the flow of information
in a class. As it turns out, on the heel of my question always comes a
related question from another student. I sit in front of 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

John Miller
John Miller, President
Science and Engineering Division
of the National Federation of the Blind
E-mail: jamiller@qualcomm.com
Phone: (619) 658-2689

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