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@example.com To: Multiple recipients of list firstname.lastname@example.org 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@example.com
Date: Tue, 10 Sep 1996 From: Mike Freeman firstname.lastname@example.org To: Multiple recipients of list email@example.com Subject: Help: teaching mathematics to visually impaired individuals (forwarded) start of forwarded message: From: Christian Harris firstname.lastname@example.org 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 email@example.com Department of Computer Science University at Albany, SUNY
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Date: Tue, 10 Sep 1996 From: Mike Freeman mikef@pacifier-com To: Multiple recipients of list firstname.lastname@example.org
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: email@example.com
Good luck and feel free to ask as many questions as you desire! Cordially, Mike Freeman Amateur Radio Calsign: K7UIJ Internet: firstname.lastname@example.org
Date: Wed, 11 Sep 1996 From: John Miller email@example.com To: Multiple recipients of list firstname.lastname@example.org Subject: Teaching math to blind students
September 11, 1996
Christian S. Harris Graduate Assistant email@example.com 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: firstname.lastname@example.org
Sincerely, John Miller, President Science and Engineering Division of the National Federation of the Blind
Date: Tue, 10 Sep 1996 From: Dave Schleppenbach email@example.com To: Multiple recipients of list firstname.lastname@example.org 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 email@example.com 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 firstname.lastname@example.org To: Multiple recipients of list email@example.com 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