Re: help : teaching Mathematics to visually impaired individuals?

From: Mike Freeman (
Date: Tue Sep 10 1996 - 13:15:23 PDT

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). NFB is the largest organization of the blind in this country and
there are quite a number of NFB members (including myself) 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 ths 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 a 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
s/he can peruse the material and ponder it at his/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.)

Insofar as a lecture style advantageous to the blind student is concerned,
it is my view that you can follow a middle ground between the literal
"open paren, open paren, open paren ..." style and saying nothing of the
equations. Often, especially in fields such as set theory, Bulean
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/her after class if he understood
everything or if things were unclear. It is, in the end, his/her
responsibility to see that s/he learns the material.

Incidentally, I think you'll find that if you just relax and start
talkinng 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
off 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!


MIke Freeman                    |       Internet:
Amateur Radio Calsign: K7UIJ    |       */ PGP Public Key Available */
... Experience varies directly with equipment ruined.

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