# The Variables of a Blind Person's Math Experience

#### The following is a keynote address given by Cary Supalo:

I am currently a fifth year graduate student at the Pennsylvania State University working on my Ph.D. in chemistry education. I recently received a National Science Foundation research in disabilities education grant to work on a project titled "Techniques and Tools to Enhance Blind and Visually Impaired Students' Participation in High School Level and General Chemistry Laboratory Classes." We are developing a suite of tools with Vernier Software and Technology Company that can be used in chemistry lab classes across the country. This project will use JAWS scripts to make the screen reader speak in real time the data being collected by these probes. We are also modifying the high school curriculum at the Indiana School for the Blind, where we will be field testing these techniques along with developing other hand-held data-acquisition tools for the blind students to obtain their observational data more independently. We hope this project will open doors of opportunity for blind students to pursue science, technology, engineering, and math careers.

I was asked to comment on my experiences with mathematics as a blind person and the way I got to where I am today. It all started when I was in seventh grade. The end of the school year was quickly approaching. I was enrolled in the remedial math class, scoring top marks on every homework and class assignment. I was under the impression that math involved only addition, subtraction, multiplication, division, percentages, fractions, and the ever-dreaded story problems. Each year I seemed to learn a new area in math. One year it was decimals; another it was the concept of negative numbers. However, as you can see, there was never any progression.

When it was suggested in my individualized education program (IEP) meeting that year that I make the jump into algebra, I remember my teacher pulling me out of class to go to meet with my IEP team for the first time. I had never seen this group before or even known that they existed. They explained to me that I was doing so well in math that they felt it was in my best interests to progress to algebra and bypass the pre-algebra class. My first thought was, what is algebra? I thought this was a big decision for me, but it was one that I wanted to make. I believed I could do well, but I understood that bypassing pre-algebra was not the traditional way it was done.

The next year, I started eighth grade and algebra class. I had to learn an entirely new terminology of math as well as the more advanced Nemeth Braille code. I was given a textbook in Braille, fortunately. Even so I had the difficult challenge of taking notes in class. My tape-recording method didn't seem to work since my teacher said many times, "This times this equals this interesting result." I tried raising my hand to ask what he was talking about, but I was shy and didn't like interrupting.

My parents, itinerant teacher, and I had a special meeting with my algebra teacher some time after the first exam, in which I hadn't performed very well, to discuss what was happening. I explained my problem with note taking when he did not speak all of the variables. He agreed to be more precise in his speaking, and I was allowed to use a Braillewriter in the classroom to take notes. I performed all of my algebraic work on a Perkins Brailler. I then read my work back to someone, usually one of my parents, who transcribed it into print. This method worked quite well, and I successfully completed algebra.

I then moved on to high school and the honors geometry class. I viewed this as even a bigger challenge than algebra because until at least November I would not have a textbook. Those in authority decided that the transcriber should prepare the part of the book to be used second semester, and first semester I would work with hand-transcribed pages prepared by our local transcriber using a hot glue gun to make tactile drawings. This was very difficult for me, and I fell behind in part because I did not receive any part of the book in Braille until the end of October. In the mean time I was asked to try and get as much out of the lectures as possible. As you can imagine, this was difficult. We were discussing concepts like "all vertical angles are congruent" and "side-side-side" and "angle-side-angle" theorems for congruent triangles. I didn't really understand what they were talking about, but I was at least learning some of the terminology so that, when I finally did receive my Braille materials, I could understand what the words meant.

In an attempt to help me catch up, the school district provided a tutor to help me in the evenings. The goal was to get me up to speed so that I could take my first semester final exam on time. In our school, exams were administered the third week after Christmas break. I worked with my tutor over the break, and eventually I did successfully take my first semester final exam at the same time as the rest of my class, although achieving this goal was quite a struggle.

The second semester was easier than the first because I finally had my book. I eventually progressed through algebra 2 and precalculus using these same methods. In these classes I learned about things like imaginary numbers, parabolas and other types of graphs, the importance of the unit circle in converting degrees to radians, etc. Some concepts such as the X=Y values for the common angles on the unit circle I memorized in an attempt to solve problems relating to trigonometry more quickly. I also spent time memorizing other important values like the square root of 2 and the value of pi (3.14214). These skills later paid dividends on advanced placement exams in college as well as on the ACT and GRE exams.

When I wanted to take calculus my senior year, my itinerant teacher informed me, my guidance counselor, and others that no blind person had ever taken calculus before and I wasn't going to be the first. I was upset, but I reluctantly accepted this pronouncement as my fate. So senior year I took a business math class in which we learned to count change, determine percentages, and other everyday tasks. I could of course do these calculations in my head in a matter of seconds. I could complete the homework before arriving at my next class. It got to the point where the teacher did not even require me to turn in my homework because, having been my algebra 2 teacher, he knew I could do the work. I was required to look at the exercises, perform the tasks mentally, and nothing more. I did fulfill all of the class requirements for this course, allowing me to complete the math requirement to graduate from high school.

After graduation I went on to college. Because of this business math class and the encouragement from my guidance counselor I decided to major in business management and minor in psychology--In other words, a non-STEM [science, technology, engineering, and math] career path.

In 1993, the summer before I began college, I was fortunate enough to learn about the National Federation of the Blind's national convention in Dallas, Texas. I had never been to such a meeting before and did not know what it was all about. My dad and I decided to go to the convention. I saw hundreds of blind people traveling independently and doing pretty much whatever they wanted to do. There I met a blind high school calculus teacher. I also met a blind electrical engineer, among numerous other mentors. From this experience I learned the importance of having a network of blind people with whom to meet and share ideas. I also adopted the Federation's positive attitude about blindness so that I no longer let my blindness limit what I thought I was able to achieve. This was a refreshing experience after the business math class.

I spent my first year at Northern Illinois University. I quickly learned Northern was not the place for me since its disabled student services office provided extremely custodial services to the blind students. These services were designed to take care of the blind students rather than to encourage their independence. I also changed my major to electrical engineering. I had an uncle who was a EE, and I had always wanted to be an EE. I soon realized my degree path was limited at Northern and decided to attend a school with a more established engineering and science program. So I transferred to Purdue University, where I enrolled in the engineering calculus class. I requested a Braille textbook and was promptly informed that Purdue did not have to provide me with a Braille textbook. I did not know better, so I was content to try the class with a book on tape.

This was difficult because I ended up spending over twenty hours a week on Braille transcription before I even started the homework or my work for other classes. I eventually had to drop this class. I enrolled in the class the next semester and had similar difficulties.

After not getting through the class, I eventually changed my major. I wanted to be a scientist or engineer but could not do so without this calculus course. I changed my major a number of times, at last settling on communications. I then discovered that, since I had withdrawn from the calculus course first semester with an incomplete because of medical problems, my grade would be entered as an F if I did not finish the class requirements.

About this time I attended a National Association of Blind Students Seminar, where a lawyer from the Department of Justice was speaking. I asked him about the Braille book requirement. He informed me that post-secondary institutions receiving federal monies were required to provide the book in Braille unless they could demonstrate that doing so would be a financial burden on the university. I brought this point to the attention of university officials and made the request again. They then agreed to provide the book in Braille.

I worked out an arrangement with the School of Science at Purdue for an extension on the incomplete so that whatever grade I now earned would replace the incomplete, so I enrolled in the calculus class that fall. Having the text in Braille with diagrams made all the difference. It was still a challenge, but with the access issue solved the challenge of the material actually made it enjoyable. I viewed this class as a gateway to all other technical majors. Because I passed this class, I changed my major and declared it as chemistry. I then took the subsequent calculus classes and successfully passed them all.

Having declared a chemistry major, I was required to take additional classes in the areas of statistics and quantum mechanics. I learned how to do 1-tailed or 2-tailed t-tests, how to calculate standard deviations, and how to calculate probability statistics. This led me into both mechanics and electricity and magnetism physics classes, which climaxed when I reached the dreaded physical chemistry classes, consisting of the study of thermodynamics and quantum mechanics.

These classes required the highest level of Nemeth code knowledge I ever needed. I was fortunate that Purdue provided these documents and their tactile graphics. They were produced by the Taevis Lab. The acronym stands for Tactile Access to Education for Visually Impaired Students. I had to obtain these textbooks on audio tape and use the tapes to follow along with the Braille in order to learn the Nemeth code symbols that were being used, but this method worked quite well. I was able to use the symbols I learned this way on all homework assignments, quizzes, and exams. Once I had passed these two senior-level chemistry courses, I graduated from Purdue with my bachelor of science degree in chemistry.

From there I entered graduate school at Penn State, where I am pursuing my doctorate in chemistry. I was required to take a series of graduate-level chemistry courses in the areas of surface science, polymer chemistry, mass spectrometry, chemical kinetics, quantum mechanics, and organic chemistry. Almost all of these classes required some form of the Nemeth code. Chemical kinetics and quantum mechanics used a large number of the advanced Nemeth code symbols that I had learned my senior year at Purdue. Using the same techniques of working on homework sets with a Braillewriter, taking exams with Braille documents, and responding to conceptual questions on my portable notetaker or a PC, I was able to fulfill these requirements. Using tactile drawings and the Braille Nemeth code has assisted me in every phase of my graduate career. I used them extensively in the defense of my master's degree in December 2004. Without tactile drawings produced on a tactile-graphics-capable Braille embosser and the refreshable Braille display on my portable notetaker, I couldn't have completed this degree. These skills will assist me in almost all future presentations and other defenses that I will find myself involved in over the next few years.

In sum, for me, having access to Braille and tactile drawings was the key to my success with mathematics. At that point having computers with speech to read math was only a thing for the science fiction fans.

Because of my experiences with math, I was able to get to where I am today, but there are many blind children who will not want to deal with the access challenges in math. Many perceived obstacles face blind students. For example, there may be problems with accessibility, such as the ones I experienced. However, students may also encounter improperly trained teachers and negative attitudes towards blind students' mathematical abilities. These factors may prohibit a blind child from studying advanced math such as algebra 2, pre-calculus, and more advanced calculus classes, but this is not an indicator for accurately measuring a blind students mental capability to perform math related tasks.

I also acknowledge that the needs of blind and visually impaired students are variable based on background, visual acuity, and mental capacity. Therefore the ways I have described for myself are not the only ways blind people can learn math. I simply offer my experiences to you today as one illustration of what a blind person had to go through in order to achieve a level of proficiency that allowed him to pursue a STEM career. I think this is one of the major goals for which we have all gathered here today. Once we have set our goal to achieve math accessibility by means of legislative initiatives, technological developments, and other access information resources, we can eliminate these barriers, and more blind and visually impaired persons will want to pursue STEM careers.

I would like to thank the NFB Jernigan Institute and the coordinators of the GAMA [Goals for Achieving Math Accessibility] summit for allowing me to address you all this morning. Thank you very much.