The following essay is reproduced with permission of Dr. Charles E. Hallenbeck of the University of Kansas. It was written in 1996, shortly after his retirement, but has lessons that are still applicable. For more information about Dr. Hallenbeck and his work with computers and mathematics, you are referred to his excellent
Learning and teaching are cooperative social acts. While each may benefit from the current proliferation of technological aids, they remain a fundamentally human process in which capacities, motives, and attitudes play crucial roles of greater importance than technology. While technology is a potent catalyst, it is neither necessary nor sufficient for this process. The triad of teacher, student, and subject matter is central. The student acquires from the teacher not only knowledge and competence in the subject matter, but also a passion and reverence for it. Technology often originates in this process and is evidence of its vitality, as well as serving to foster and promote it. This paper describes low- and middle-tech aids to one blind student become blind teacher over a five decade period.
Both Sides Of The Teacher's Desk
The following is a personal retrospective in which I report some factual information, and offer some generalizations. While I am not a professional mathematician (a friend has even told me I do not know math from a hole in the ground), Mathematics has always played an important part in my education, as well as in my research and teaching in psychology and cognitive science. Having lost my eyesight in 1945, at age 15, in the tenth grade of high school, and having recently retired at age 65 as Professor of Psychology, my experience spans five decades and includes perspectives from both sides of the teacher's desk.
(1) Before losing my sight in high school, I was a somewhat above average student with a mixed record. I was probably capable of better grades than I was earning, but which of us is not? My grade in ninth grade elementary algebra was, in the language of the times, a "circled 65," which translates to "we gave him a passing grade of 65, even though technically he did not earn it." Elementary algebra and I were simply not compatible. Late that spring a plane geometry aptitude test was given, and to everyone's surprise I earned a nearly perfect score. I believe that score accounted for the circle around my 65. My other grades were high enough to keep me out of trouble and not so high as to call attention to myself. My heart and head were into more important things than school -- including electrical circuits, simple radios, and a fascination with schematic diagrams of vacuum tube amplifiers, oscillators, and rectifiers. I never understood what Ohm's Law had to do with anything, but the layout diagrams spoke to me loudly and clearly. The symmetry of a push-pull amplifier circuit and the phase inverter or splitter to drive its two halves were aesthetically pleasing pictures. This was my circumstance when an unexpected accident left me suddenly and totally blind.
(2) After an absence from school for a year, I had recovered from all my injuries except for the loss of my vision. I had acquired blindness skills as they were then known: i.e. reading and writing Braille with slate and stylus, rudimentary typing skills, traveling with the aid of a sighted guide, using Talking Books, playing Braille cards and checkers, and mastering the layout of the radio dial. The family radio had a short wave band, and amateur radio had just been restored to service after the end of the war. Conversations between Ham Radio operators became an important link to my earlier interests. However, it was time to consider what to do about school.
With the encouragement of our local school officials, it was decided I would return to the regular public high school a year behind my former classmates and resume my education there. The alternative was to attend a residential school for the blind located several hundred miles from my home. The enabling factor in this plan was the existence of a small public fund to pay readers for blind students, and the willingness of several of my high school teachers to perform that service for me. By far the most important of these "teacher/readers" was Mr. James Stiles, who taught my senior chemistry course, but who before then saw me through a mathematics curriculum that included plane geometry, solid geometry, trigonometry, intermediate algebra, and advanced algebra. With Mr. Stiles' help, I connected algebra to geometry and understood how important Ohm's Law was in electronics. Not only my high school, but my college and subsequent performance in mathematics and science had their roots in this critical period. It is therefore important to ask about the adaptive techniques that made these achievements possible.
(3) The most indispensable technique in my mathematics education as a blind student was the gift of language. I do not refer to my own language, but to that of my teachers. I have come to greatly appreciate the habit of accompanying visual displays with their simultaneous rendering in language. Nothing is more discouraging to a blind student than the presenter whose words consist only of such unenlightening strings as "So moving this over to here, and eliminating this and this, this is clearly equal to that."
Upon first returning to school as a blind student, I was fortunate that Mrs. Elizabeth Ham comfortably supplemented her chalkboard sketches with reasonable verbal facsimiles. Mr. Stiles quickly resolved any remaining unclear concepts in our "reading" sessions three evenings per week. I am equally grateful to my calculus instructor Martin Bates at Union College, who later did the same thing in the realm of derivatives, integrals, limits, and the enlarged vocabulary of Greek and Hebrew alphabets; and to Professor Frank Berratone at Western Reserve University whose mathematical statistics course, The Advanced Design of Experiments, was perhaps the highlight of my graduate education. But what about the technology?
(4) During the late 1940's there were few technologies to aid the blind in math and science education. Braille was useful, but to the technically minded there was very little worth reading published in that medium. Before the important work of Professors Abraham Nemeth, Thomas Benham, and others, Braille was not well adapted to technical and mathematical notation. For example, I earned an amateur radio license in 1947 by joining a three person study group consisting of myself, another high school student, and a returned veteran with Army Signal Corps training. The others were not visually impaired. My Braille skills were irrelevant because there was nothing for me to read. We studied for our Federal license examinations together, and eventually all three passed -- I on my first attempt (W2TYE), and the others on their second (W2VCY and W2VDX). Without this essentially social solution I probably would not have had access to the necessary materials. The human reader was the primary assistive technology of the day.
(5) My first break-through in Braille came with the publication in 1949 of The Braille Technical Press, edited by Robert Gunderson, a blind radio amateur (W2JIO) and instructor at the New York Institute for the Education of the Blind. For the next quarter of a century, I eagerly awaited each new issue and carefully accumulated a valuable library of them. In this publication contributors provided careful verbal descriptions of schematic diagrams of electronic circuits. There was no attempt to make a graphic representation in Braille of the pictorial print diagram, but the language equivalent was provided instead. This was an extraordinary resource, and could potentially be extended to mathematics and science more generally. It was a primary source for original circuit designs for auditory electronic test equipment, to which I occasionally made a contribution.
(6) The next important break-through came in the 1950's with the widespread availability of tape recorders as general purpose aids for the blind, and with the publication on tape of Science Recorded by Professor Thomas Benham of Haverford College. Professor Benham was a blind teacher of physics with a keen interest in electronics during the early Sputnik era. He had also developed a specialized Braille notation for his own use in preparing lectures and research notes on mathematical, engineering, and scientific topics. The Benham notation never became widely adopted, but greatly influenced my own individual style of notetaking.
(7) Other technological aids that emerged, enjoyed periods of popularity, and then fell into disuse, included:
(a) raised line drawing materials using cellophane sheets, special styli, and rubber lined clipboards;
(b) tiles, boards, and Braille cubes for arithmetic, such as the Taylor Slate and the Cubarithm;
(c) the abacus, which became very popular among blind persons and especially at rehabilitation centers;
(d) circular slide rules with Braille notation along the perimeter;
(e) the Marchant desk calculator modified to include Braille numbers on its display wheels;
(f) the Thermoform machine, which permitted hand transcribed Braille to be duplicated onto plastic pages;
(g) the Optacon (Optical to Tactile Converter) by which the blind could "feel" the shapes of symbols on the printed page;
(h) the Speech Plus and several other talking calculators that followed each other in rapid succession;
(i) the personal computer.
With the Thermoform machine, blind mathematicians and scientists finally began to have relatively easy access to each others' material. The Nemeth code became the de facto standard. By the 1960's The Braille Book Bank and Recording For The Blind became very valuable resources for Braille and tape materials, and by the 1970's high tech was coming to the aid of the blind in the form of the Optacon, the personal computer, and other devices. Transistorization and miniaturization produced cassette tape recorders that were cheap, small, and powerful enough to accompany blind students to class and capture the audible proceedings relatively unobtrusively.
(8) It is apparent from this sketchy history that major technological aids available today were not available to me when I needed them. I took only a few sketchy notes in classes, preferring to concentrate on following the material, and relying on later reconstructions, "after the fact" notes, generated as soon after class as possible. Forming diads or triads with other students provided reality checks on comprehension of the material, and generally benefited all participants. I have observed that the very act of taking notes serves to consolidate learning, irrespective of whether those notes are ever again referenced. The same cannot be said of the act of taping a lecture.
In high school I usually took examinations orally, with my teacher acting as reader and as scribe. In college and graduate school I was more often given access to an office and a typewriter at the same time my classmates were taking their examinations elsewhere. I would often have to prepare my own Braille copy of test questions with the assistance of a reader, a secretary, a teaching assistant, or the instructor. The time required to do this would come out of my available examination time, although I was never refused extra time if needed to complete an examination. My preferred method was the take-home exam. Modern typewriters are rapidly giving way to the office PC equipped with word processor and attached printer.
My experience was not unique; many of my contemporaries were also busily mastering mathematics and science in the days before the golden age of technology we enjoy today. One is drawn inevitably to the conclusion that technology, while nice, is not strictly necessary for the acquisition of skills. The essential ingredients for me were:
(a) my own motivation and aptitude;
(b) exposure to verbal descriptions that are reasonably equivalent to the graphical materials often used; and
(c) timely access to expert assistance from a teacher, from knowledgeable peers, or from an experienced reader.
(9) My activities as a blind teacher have varied as a function of subject matter, class size, and level of expertise of students. While I have not taught formal mathematics, I have taught computer programming courses at all levels, and mathematically intensive topics in cognitive science, such as artificial neural networks and mathematical modeling.
I have found that from time to time I need feedback from students in classroom situations, and that this feedback is difficult to obtain in large classes. An easy way for me has been the judicious use of humor, the response to which (or lack of response to which) can be quite informative. My lectures are most successful when I follow my Braille lecture notes fairly closely. Printed handouts outlining key points are appreciated by students. I have not made effective use of the chalkboard in large classroom situations. In smaller classes it has been more important for me to be mobile in the classroom, and to use the chalkboard, if only to enumerate and outline the progress of my own arguments. My own Braille notes and prepared handouts continue to be important, but humor has played no role as a communication aid. I encourage more direct feedback in small classes in the form of questions or comments. My best experiences in most recent years have been in advanced seminars on technical topics where in-the-classroom demonstrations on a computer have played a central role. In such cases the computer was speech equipped for my own use, and of course also equipped with a video display for the class. Classes would often end with participants rushing to the PC, rather than to the teacher, with diskettes on which to get copies of the source code of the day's material.
(10) My final generalization is that the abundance of assistance currently available for the blind is not always a blessing. One hears stories all too frequently of disabled student services, such as those at my own university, providing blind students with "note takers" to accompany them to their classes to pay attention for them and take their notes. Worse, one also hears of blind students demanding such care. State services for the blind all too often exercise bad judgment in the allocation of assistive technology for blind students. I have known an instance in Kansas where a blind student was required to demonstrate proficiency in the use of a personal computer by successfully completing a college course in computer programming, as a pre-condition for his being allocated a PC for academic use.
There have also been instances in which lavishly equipped systems were provided to poorly prepared students with no provision for training in their use. A very recent instance has occurred in which a counselor of dubious skill purchased a system containing incompatible components from a supplier of dubious ethics who filled the order. The supplier then offered to solve the compatibility problems after delivering the system for a consultation fee of $750 per day. The student in the meantime has $8,000 worth of unusable computer equipment at her home while her semester marches toward its climax. Has this student or has she not been assisted by our current level of technology?
My conclusion is therefore a two-fold one. Technology is neither necessary nor sufficient for blind persons to perform effectively in the mathematics or science environments. The requirements for such success are more familiar human requirements, including motivation, aptitude, communication skills, networking abilities, and a little ingenuity. To the extent that technology can enhance these more primary qualities, it is an effective aid. When it is used to substitute for them, it is a formula for disaster.
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