Course Design

• Course Overview.
• Disclaimer.
• Choice of a Text.
• Basics of Braille.
• Tools to make Braille.
• Tools to make tactile graphics.
• Student's Tools.
• Daily Nuts and Bolts.
• Course Pluses and Minuses.
• Acknowledgments and Links.

Overview

Support for a Blind Student

Disclaimer

The first thing to be said is that neither I nor Earlham are experts at this topic. Earlham is a college of about 1100 students; the student involved in this course was the only blind student either I or the College has taught in the past 20 years. I'm therefore describing a situation in which both individually and institutionally we were starting from zero and learning as we went along. This discussion is therefore one personal and anecdotal account for beginners, and nothing more.

I should also stress that everybody is different, and that what I'm describing here was aimed at one particular student, not a fictitious generic blind student. Like sighted students, blind students have varying skills and interests. Some are tactile learners, using Braille heavily and comfortable with the special Nemeth codes needed to put math into Braille. Others prefer to work in a more purely auditory environment, and are not fluent in Braille/Nemeth. For some, geometry provides insight; for others, it confuses. Some are serious about math; others are just trying to get through a course. They differ in what technological tools they have available, and in how interested they are in learning new tools as part of a course. In all these respects, they are just like any other student. Conversations about what resources would make the class work and what would just get in the way, and about how the class is going and what could be changed, are just as helpful here as with any student.

In my case, my student was fluent in Braille/Nemeth, and asked for material to be made available to her in that form. She thinks about mathematics rather geometrically, and found it helpful to have not only the equations, but the figures available to her in real time in class. A Spanish major, she was taking what may be her last math class, and was not particularly interested in learning new technology like MathTalk, which integrates voice input, a computer algebra system, and print and Braille output. She preferred to submit homework to me on audio tape, as she had done in past math classes. She was willing to reply on a student assistant to act as her interface with Maple. The choices discussed below were aimed at supporting her as an individual, not at providing a general framework for a large population of blind calculus students, which Earlham does not at this time have.

Text

It was a surprise to me when I started into this project to learn how few books are available in Braille, and how expensive Braille publications are. As an example, just about everything Jane Austen wrote is available in Braille, but at a cost of about $150 per novel. Only a few calculus texts are available in Braille, typically the largest volume current texts. We used Larson, Hostetler and Edwards' Calculus with Analytic Geometry,, not because it's my favorite text, but because we were able to borrow a copy in Braille belonging to my student's former high school. Larson et al. is a standard fat calculus book in print. In Braille, it costs over $1000 and comprises something like 60 volumes. It was shipped to us in 8 large cartons. For all of us to be using the same text seemed very important to me, and I couldn't justify asking one student to purchase a $1000 text; so we graciously accepted the offer to lend us Larson et al., and I used this book in the class.

A Note on Braille

Starting into this project, I knew, like most people, that Braille is an alphabet used for writing with raised letters. Converting material to Braille seemed like it should therefore be an easy exercise. This isn't true.

First of all, it's slower to read by touch than by eye. Proper (Level 2) Braille therefore incorporates a large number of phonetic contractions - far more than a casual user can learn. Here's an example. In print, Lincoln's Gettysburg Address begins,

"Four score and seven years ago, our fathers brought forth on this continent a new nation, conceived in liberty and dedicated to the proposition that all men are created equal."

In Braille (but in printed characters), the same text looks like this,

,f\r score & sev5 ye>s ago1 \r "fs br"\
=? on ? 3t95t a new n,n1 3cvd 9 lib]ty &
d$icat$ 6! proposi;n t all m5 >e cr1t$
equal4

More concise, isn't it, but obviously not easy to produce. The contractions are phonetic, not orthographic; it's claimed that a couple of years of study are typically required to do Braille translation.

Mathematics is not displayed 2-dimensionally, but is written in a sort of mark-up language called Nemeth code. The formula that a² + b² = c² and the quadratic formula look like this:

a^2"+b^2 .k c^2

x .k ?-b+->b^2"-4ac]_/2a#

Tools for producing Braille

Good tools now exist for turning math into Braille under Microsoft Windows. I have not found similar functionality on other platforms. The starting point is DBT, the Duxbury Braille Translator, which offers bidirectional translation of plain text between print and Braille. If you're not writing math, this is all you need.

If you are writing math, then you also want one of 3 products from Mackichan Software. Scientific Notebook is a $150 product incorporating the Maple and MuPad computer algebra systems with WYSIWYG math editing into LaTeX. Scientific Notebook uses LaTeX as a file format only; it has its own simple print engine, and doesn't actually do LaTeX formatting and typesetting. If you don't care about whether your output is beautifully typeset, then this is all you need. The output is quite readable; this is what I used. If you do care about beautifully typeset print, then you want to spend $650 instead and get Scientific Workplace, which includes a full LaTeX implementation.

Either way, you can edit math in a very comfortable environment, incorporating plots for your students who read print. Current versions of DBT can then take the resulting files and produce Braille/Nemeth, ready to send to an embosser. When I was teaching this class, DBT didn't yet have this functionality. I used instead a beta version of a Scientific Notebook to Nemeth translator graciously made available by the people at NMSU's MAVIS project, providing mathematics accessible by visually impaired students. To get the Nemeth translator to accept my Scientific Notebook files, I needed to remove all the figures. Wide tables also had to be manually split into strips of a width that would fit on a Braille page.

The other tool you need is a Braille embosser, a printer that pounds the little dots into heavy paper. Like everything in the assistive technology business, they're expensive; Earlham owns a fairly basic model that cost around $4000.

Producing Graphics

There are two solutions here. Software can be gotten to enable Braille embossers to print graphics, but the quality is said to be rather limited. We instead produced tactile graphics using a special rubberized paper which bubbles up to form a ridge when you write on it with a heat pencil like a small soldering iron or wood-burning tool. Remember that you can't feel as much detail as you can see, so make the figures as simple as possible. My student could read large raised letters written in print characters, so I labeled points and axes this way ("A" or "x"). Longer labels like "y = f(x)" were typed in Scientific Notebook, converted to Nemeth, embossed, and fastened to the figures with rubber cement.

The Student's Tools

Now that I could communicate with my student, how did she communicate with me? For daily conversation and questions, we used the phone and e-mail. Her screen reader software turned e-mail into voice; I suppose it could also have been turned to Braille and printed.

For homework assignments, my student wrote for herself using a Brailler, a small computer with a 6-key Braille keyboard, and obviously without a monitor. These devices typically have a single line of Braille display, and can output either to voice or to a Braille printer. They are the PDAs of the blind world, except for the cost. You would think that what amounts roughly to a Palm Pilot minus the display would sell for less than one with a display, but in fact a base model Brailler starts at around $1500, and the fancy ones for cool executives range up to about $10,000. I cannot help thinking that there is a business opportunity here. In any case, the Brailler let her take notes and write for herself. At the end of each assignment, she would dictate the answers to an audio tape. She produced figures using a special film paper that wrinkles up when written on with a ball-point. It's a little rough and ready, but it works.

As mentioned above, there are alternative technologies like MathTalk that might make more sense for a student intending to major in math, but this set of tools were the familiar and comfortable ones for my student.

As a personal comment, I found it surprisingly emotionally difficult to deal with math homework on audio tape. My student was quite good, and her solutions were generally remarkably clear and precise. There was no difficulty following her answers. But lots comes through on tape that one doesn't experience with a written assignment. You get to hear the student sounding exhausted late at night. You hear the long sigh before she starts another complicated calculation. Instead of a blank problem, you get to hear her say, "I guess...I don't have anything on that one." For the student, all this was just the equivalent of a routine written assignment, but to me, it felt much more intimate than math papers normally are. I loved her work for the quality, but I found it hard to listen to someone doing calculus homework.

Daily Nuts and Bolts

In order to make sure we were all involved in the conversation in class, I prepared fairly complete written lectures each day. Minimally, these needed to include all the equations I planned to present in class; in fact, I embedded the equations in a context. The lectures on this site are slightly modified versions of what I distributed. These lectures were converted to Braille and distributed along with tactile copies of the figures; print copies were available for the students reading print. In this way, when dissecting complicated algebra, everyone had it in written form, and the figures were available as we talked about them. In past math classes, the student was used to having to get the equations by ear, and to having copies of the figures written by an assistant during the class, which meant that she got the pictures only after they had been discussed. She felt that getting figures and equations along with everyone else made a big difference in the whole experience. I also wrote up solutions to all the written assignments, and distributed these to everyone

The College also paid for an assistant who could act as a tutor, and who accompanied the student in class. The assistant could make copies of figures at those times when conversation and questions led me in unexpected directions. She was also the interface between the student and computer algebra systems and graphing calculators.

Pluses and Minuses

For the blind student, I think the course worked pretty well. She had taking calculus in high school without having it really connect at all; this time she finished near the top of the class. There were frustrations about the nonexistence of graphing calculators for the blind, and about the fact that much of her electronic equipment was old and erratic. We also had to work a bit to fend off the good people in our publications office, who wanted to write up the miracle that the blind can do mathematics.

For other students, the written notes were a clear plus, and the added detail I went into in describing figures and arguments mattered. On the down side, they were forced to use a more expensive text than I would otherwise have chosen. The classes were also much more scripted than they would otherwise have been - I was reluctant to follow digressions that I thought not everyone would follow. Also, the professor was busier and sleepier than they might have wanted.

For me, the course was a wonderful learning experience. I got a glimpse of a world I had never had much exposure to. I met wonderful people. On the down side, I had to work for my education. I wrote and typed something like 400 pages of typeset mathematics during the 15 weeks. Although Donna Keesling of our Academic Supportive Services office was enormously helpful and encouraging, we were breaking new ground locally. We were therefore scrambling to figure out what software and hardware we needed, and to get everything authorized and ordered and delivered and installed and understood before the semester actually started. Try to allow more time than we had to get the kinks worked out; try to get enough lead time that you are not always coming home late at night after making the tactile graphics you need for tomorrow.

Acknowledgments and Links

As threatened above, this has been very much a personal account of one class, nothing more. I hope something in it may help others, though.

This course would never have worked had it not been for the hard work and encouragement of Donna Keesling, our Director of Academic Supportive Services. Eliza Navias-Bell was splendid as an undergraduate assistant.

The people at NMSU's MAVIS project and at Purdue's TAEVIS office generously shared their software and expertise. They kept me going.

Kathy Simon at Houghton Mifflin provided tremendous support, locating and lending me copies of out-of-print versions of their text so that I would have access to the editions being used both by my print and Braille reading students (which were not the same). I've repaid Kathy badly by not using Houghton Mifflin calculus texts subsequently, but that's a pity. She is a real partner in education - by far the best publisher's sales representative I've ever had the pleasure to work with.

The software of the folks at Duxbury, Mackichan, and Maple has changed the world for both sighted and blind mathematicians.

To all of you, thanks.

Tim McLarnan,
Assoc. Prof. of Mathematics
Earlham College,
Richmond, IN 47374 USA

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