by Al Maneki
From the Editor: In the February 2011 issue we published an article by Al Maneki containing a survey, the results of which Al reported to the parents division in July. Because we know how many jobs, both current and future, require proficiency in math and in order to provide some context for Al’s report, we are again including his survey. We strongly urge everyone who can do so to complete the survey now so that we can understand more clearly what separates those who succeed at mastering mathematics and those who have concluded that it is simply beyond them. Here is the survey, followed by Al’s report based on initial responses to his original request:
Who Should Complete This Survey?
We would like to hear from any blind or visually impaired person who has taken or is taking at least one math or math-based science course at the secondary or post-secondary school level. We would also like to hear from any parent or teacher who has advised or assisted a blind or visually impaired child with at least one math or math-based science course. Furthermore, we are interested in students' experiences learning geometry or elementary school arithmetic.
There is no restriction on when or how long ago you or your child took a math course. We want to learn about the methods of handling math that worked best for you. We are equally interested in methods that were not particularly successful or useful.
If your child or you are considering taking math courses at any level, you should read these survey questions. They may help you get the information you need to complete your courses successfully.
In your responses please provide contact information (name, address, email, phone) so that I can reach you for possible clarification and follow-up interviews. Please also include your age (closest to 5-year multiples, i.e., 20-25, 25-30, etc); the highest level of education you have completed; your primary reading medium; your current employment status and job title.
You need not answer all of the questions, since some of them may not be relevant to your experience. You do not have to answer questions separately. You may provide a narrative summary as your response to this survey.
If you require additional information about these questions please get in touch with me. You may contact me by email, phone, or snail mail. My contact information appears at the end of the survey.
You may submit your responses by email or snail mail (Braille or print please, no audio) to the addresses shown below. Please complete this survey by April 15, 2011. Those taking courses after this date may respond later, since I anticipate a continuation of this survey.
Your answers will not be used to judge your mathematical strengths or weaknesses. Any personal information you may reveal in your responses will remain confidential. Names, mailing addresses, email addresses, and phone numbers will not be distributed.
Here are the questions to consider:
1. What math or math-based science courses have you taken (elementary, secondary, community college/university, graduate school)? Specify the level of each course, and describe the subject matter that was included.
2. Were classroom lectures useful to you? Since mathematics is generally communicated visually, tell us as specifically as you can what you actually learned from these lectures. If lectures were not helpful, tell us what you did to compensate for the missing information.
3. Were you able to take classroom notes? If so, tell us what method you used: large print, hardcopy Braille, electronic or live notetakers, audio recordings, etc.
4. How did you handle reading assignments? Tell us about your use of Braille textbooks, recorded textbooks, large-print textbooks, or live readers or tutors.
5. How did you do homework assignments and take tests? Describe your use of large print, notetakers, hardcopy Braille, mental arithmetic, or dictation to a live reader. If you used Braille, describe your method of translating Braille into a medium accessible to instructors who do not know Braille. If you used Braille/print reverse-translation software of any kind, describe how this worked. In your answer to this question, tell us about any additional devices and technologies you have used, i.e., older devices such as the Taylor Slate, Cube-a-Rithm Slate, Circular Slide Rule, and Cranmer Abacus; and newer devices such as talking calculators or specialized learning software.
6. Have you written papers containing mathematical content in an academic or professional setting? Describe how you did this, especially the use of human support.
7. How did you work with line drawings, graphs, or charts? Explain how these were described to you or produced in accessible formats. If you had to construct these items, tell us how you accomplished this task.
8. How familiar are you with the Nemeth Braille code? Describe the extent to which you use it for reading or writing.
9. Are there any tools/devices/aids that you wish you had had that would have enhanced your mathematical experiences?
10. How satisfied are you with your mathematical experiences? Would you like to make other comments about how blind and visually impaired people may read and do mathematics?
This is an informal survey. I am conducting it with the intention of using the results to help others who will be taking math and math-based science courses in the future. The results of this survey, after they have been compiled, may also prove useful to people who are accustomed to doing math in their own ways. These folks may find new ways of working more productively. It could further turn out that these responses will suggest altogether different ways of doing math, either by refining methods already in use or by suggesting the development of new techniques and technologies. I fervently hope that over time this survey will make it possible for blind and visually impaired people to learn and do mathematics more efficiently and with greater ease.
I plan to compile the first set of responses (received by April 15, 2011) into an article, ideally for publication in the newly established Journal of Blindness Innovation and Research. It is also my hope that this survey will be a continuing investigation. Additional articles pertaining to this survey will be published if they are warranted.
In preparing this article and survey, I received valuable help from Deborah Kent Stein, editor of Future Reflections, and from Mark Riccobono and Judith Chwalow of the NFB Jernigan Institute. Although they have left their marks on this article and survey, I assume responsibility for all shortcomings, errors, and omissions. I thank you in advance for helping me with this survey. I look forward to hearing from you.
(443) 745-9274, cell
9013 Nelson Way, Columbia, MD 21045
Now here is Al’s preliminary report to the parents:
As I said in my article which appeared in Future Reflections and the Braille Monitor, the seed for this survey sprouted from the workshop “I Survived Math Class,” which I moderated at our convention last year in Dallas. I’m pleased to come before you today to report that the responses I have received so far have been most gratifying. We received messages from several people saying that this survey was much needed and that, even though they were not part of the survey population, they were very interested in the results. We heard from a few teachers of visually impaired students, and we are keeping track of their responses. We even heard from a sighted professor of mathematics who expressed an interest in what we are doing.
Dr. Abraham Nemeth was kind enough to respond to my survey. He listed his age range as 90-95, is obviously retired, but went into some detail about his work experiences. Although he did not directly answer the question concerning familiarity with the Nemeth code, I thought that it would be safe to include him in this category. I understand that he is attending this convention.
So far we have received fifty-three responses. Of these
Thus far we haven’t heard from very many people who had unsatisfactory math experiences. While it is often embarrassing to reveal one’s unsuccessful experiences, we need to hear about more of these to gain an accurate picture of the state of math education for blind people. Whether your math experiences have been successful or unsuccessful, please continue to respond to this survey. We need to hear from more of you.
While we must be wary of drawing conclusions from small samples, I want to share some of the impressions I have gathered up to now:
Some of our responders were fortunate enough to have Braille textbooks. Those lacking Braille, used recorded textbooks or live readers. With recorded texts, they had to cope with the inconsistencies in which mathematical material was read and the ambiguities of having diagrams and charts described orally. The most successful responders did not hesitate to seek clarification from their instructors and to get help from classmates, live readers, or tutors. The most successful responders were keenly aware of the way they used class time to ask their questions and the creative strategies they used to communicate their solutions in homework assignments and tests.
Responders commented about the significant amount of extra time required for their math classes. If they did their homework assignments and tests in Braille, time had to be spent on transcribing their work into print. If they received assignments and tests in print, these had to be read to them, and they had to read their solutions back to their readers.
A disconnect often develops between the functions of math instructors and TVIs or DSS staff. Some responders complained that too many instructors ignore the needs of their blind students, making the assumption that it is the job of the TVI or DSS office to teach the math, even though it is not. We want and need a true partnership here. The math instructor should creatively think of nonvisual ways to teach because these methods could also help sighted students. TVIs and DSS personnel should know enough math to ensure that materials are properly transcribed.
The vast majority of Braille readers claimed a degree of familiarity with the Nemeth code. I gained the distinct impression that Nemeth code has been taught as it was needed. This is as it should be. Some of the responders said that, given rudimentary knowledge of the code, they proceeded to invent Braille symbols for their own use. This practice should be encouraged because writing correct code can be cumbersome in note-taking. For personal notes we should use any shortcuts we like. For reading textbooks produced for general distribution, we must use correct Nemeth code.
More important than reading math texts is the need to work on exercises and problems to firm up one’s mastery of the concepts. This area proved to be most difficult for the responders. Electronic Braille notetakers don’t work because math solutions require the simultaneous examination of multiple lines of calculations and expressions. Writing with slate and stylus was also unsatisfactory. Most Braille readers have found the best success with mechanical Braillewriters, such as the Perkins, because embossing is right-side-up and paper can be shifted from line to line without disturbing the position of the embossing mechanism. Large-print readers, even the few who know Braille, used large print to write their solutions. Anyone who has developed sufficient mental abilities may simply dictate solutions to a live reader. None of the responders, except a few large-print readers, expressed confidence in their ability to construct diagrams and charts.
Technology, no matter how good, can only go so far in helping blind students learn math. By itself it will not make learning math easier. It will not turn any of us into brilliant mathematicians. But I think technology has a place in education. The people who responded to my survey share my belief that:
I hope to get more responses very soon, and I hope these responses will shed more light on our experiences with math courses. I’ve not yet decided how best to display a summary of responses while maintaining individual confidentiality. I’m thinking about editing the more substantive ones and posting them on my own web page with links from the NFB website. I also believe that with additional responses other articles will be forthcoming.
To conclude my report to you today, I want to quote the response from Sandi Ryan, a retired dietitian from Ankeny, Iowa, to survey question 10, giving her comments about how blind and visually impaired people can read and do mathematics.
I have her permission to quote her answer in its entirety. Here is what Sandi says:
I feel that, as I approach my sixties, I understand a lot more about math and science than I ever thought I would. I had always been given to understand that blind people couldn’t do math and science. I was fortunate to know a couple of blind electrical engineers, and they obviously had to do math. If I’d known, going in, how difficult my college career would be, I’d have backed out before I started. But I am glad I didn’t know. I learned a great deal from surviving math and science classes. I learned the concepts, of course, but I also learned that I can be pretty creative and innovative when it’s needed, and so can some sighted people who agreed to tutor me and used solid objects and hundreds of drawings to make sure that I understood what I needed to know. Incidentally, my tutors were always students—not in my class, but in the discipline I was studying—and they took their valuable time to do things, for which my payment was meager, to ensure my successful education. Several of them bought into my education as much or more than my teachers, and I am grateful that they believed in me when I wasn’t sure I did. I have had a wonderful career as a registered dietitian and look forward to the future because I have been successful.
A woman at my university who ran the Handicapped Student Office stated, in a talk during Woman’s Week, that not many disabled people are interested in math, science, technology, or engineering. I challenged her, and I still believe she is absolutely not right. I think many disabled people avoid these disciplines because they fear they cannot succeed. And I believe their well-meaning advisors and instructors encourage them to go another direction. I would love to be around when there are so many blind and otherwise disabled science, technology, engineering, and math professionals that we aren’t even pointed out as unusual. I doubt that will happen in my lifetime, but math and science are rewarding, and blind people shouldn’t miss out on the reward because they lack tools and education.With thanks to all of you here today, and with thanks to our collective efforts in the NFB and the Jernigan Institute, we are turning Sandi’s vision and our vision of a brighter math and science future into reality.