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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: "anameth@ece.eng.wayne.edu".

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

Cordially,

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

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