Personal Perspectives on Unified English Braille for Mathematics

[摘要] Being a mathematician, I utilize Unified English Braille formathematics on a regular basis. This paper represents my personal perspectiveson Unified English Braille for mathematics and its advantages.I am a mathematician. I read and wrote mathematical materialas a sighted person until Valentine`s Day of 2002 when I was in the eighthgrade. As the result of a shooting accident, I became completely blind. Thus, Ineeded to learn another way in which to read and write mathematics.I learned English Braille American Edition, the Nemeth Codefor Mathematics and Science Notation (Nemeth Code), and Computer Braille Code.I even taught myself the Music Braille Code, the Braille Code for ChemicalNotation, and grade three braille. I recall one German homework assignment Ihad in high school where I wrote the date using Nemeth Code. A brailletranscriber assigned to me told me to use Nemeth Code only for mathematics. Iwondered why there were multiple braille codes, for when I could see, I did notneed to use different print codes to write material in different subject areas.However, I thought nothing of it because I did not want to question establishedpractices after being blind for only a year or two. Accordingly, I used NemethCode only for mathematics.I used Nemeth Code for mathematics until my second year(2014) as a graduate student at Texas Tech University (TTU). During my secondyear (2007) at the University of Maine at Farmington, where I spent my firsttwo years of college, I met a blind student who told me about a new braille code.That is when I discovered that the Braille Authority of North America (BANA)was researching this uniform braille code, but I did not learn it then becausethe United States had not yet adopted the new code. Then, in 2013, I read anannouncement that said the Braille Authority of North America had adoptedUnified English Braille (UEB), so I researched and downloaded The Rules ofUnified English Braille (2013) and Guidelines for Technical Material (2008).For a little over a year I studied these two books using my refreshable brailledisplay. At first, it seemed strange that mathematics in UEB was representeddifferently than mathematics in Nemeth Code was, but after I became used to howUEB mathematical symbols were written, they made sense. It was easy to readboth text and mathematics because I could do so without constantly having toswitch between codes. Then, at the beginning of my second year as a mathematicsgraduate student at TTU, I did all of my work using only UEB. The first monthor two I read a bit more slowly, but after I practiced consistently, readingbecame easier. The process was much like when I first learned braille in 2002.I studied algebra, number theory, statistics, and topologyat a graduate level using UEB. Whenever I encountered a symbol I did notrecall, I referred to the International Council on English Braille`s tworulebooks, mainly Guidelines for Technical Material. After using these booksfrequently, I did not need to refer to the rulebooks much at all. Just likeNemeth Code, a user does not need to memorize the whole rulebook before usingUEB for mathematics; it just takes practice.Regarding reading speed for mathematics, Paul Halmos (1960)writes in Naive Set Theory: "He should not be discouraged if he finds thathis reading rate is considerably slower than normal." In other words,studying mathematics is about understanding mathematical concepts, not speedreading through mathematical symbols. Indeed, mathematical documents do notcontain just a list of equations with no English content. Mathematicians alsouse narrative dialog to explain mathematical concepts. Typically, amathematical textbook contains axioms, definitions, and theorems such that theproof of a theorem guides a reader narratively through a mathematician`sreasoning process. For example, Euclid`s Elements has very few mathematicalsymbols, but guides the reader through a proposition in unsophisticatedlanguage using definitions, postulates, and common notions explainedbeforehand. In fact, all the graphics in Euclid`s Elements were added later on.I am employed as a teaching assistant at TTU. I am alsobecoming certified as a braille transcriber, and I intend to transcribemathematical documents after I earn transcriber certification. This is becauseone issue blind college students face is simply accessing higher educationmathematics via braille. In fact, I had to purchase braille transcribingservices for three mathematical textbooks with no help from my university`sDisabled Student Services office. When a professor wrote to the DisabledStudent Services office requesting that six documents be transcribed intobraille so that I could analyze graphical data, they replied, "We do nottranscribe documents into braille any longer as it is not the most effectivealternative to [sic] making a document accessible" (L. Phillippe, personalcommunication, December 2, 2015). I therefore plan to earn a Doctor ofPhilosophy degree in mathematics and research and develop reasonableaccommodations for blind students enrolled in higher education mathematicscoursework. Use of UEB should help facilitate such accommodations.LaTeX is a powerful program for processing mathematics whichprofessors of mathematics use all the time. I use LaTeX myself to writemathematics; after writing a mathematical document via UEB directly on myrefreshable braille display, I translate each mathematical symbol into LaTeXcoding and then transfer the result to my computer so that I can format it viaLaTeX. If there is one braille code for both text and mathematics, then apackage for LaTeX can be created such that LaTeX can either output a UEBbraille file or create a document that can be translated by a brailletranslation program. A professor at TTU told me that if he got a grant and wasable to learn UEB, he would look into creating a package for LaTeX; the packagewould allow LaTeX either to be processed directly into braille or to betranslated into braille using a braille translation program.I end where I began: I am a mathematician who successfullyutilizes UEB for all mathematical material and am excited that I can!

[学科分类] 眼科学

[关键词] simple game;power indices;influence relation;power relation;performance relation