by Alfred P. Maneki and Alysha Jeans
From the Editor: Blind students in mathematics, science, and engineering courses encounter serious challenges as they attempt to translate complex equations from print to Braille and from Braille to print. In the following article mathematician Al Maneki and Alysha Jeans, an electrical engineer working in Virginia, draw upon their experiences as blind professionals to describe a solution that has exciting possibilities. This is what they say:
Blind and visually impaired students in the fields of mathematics, science, and engineering often encounter difficulties when they need to present mathematical material to sighted instructors and classmates. Fortunately advances in digital technology offer interesting possibilities. Technology may provide new ways for blind students to solve problems and communicate their solutions to the sighted world in written form.
In most classrooms teaching mathematics, the physical sciences, and engineering relies heavily on visual representations. However, comprehension of the subject matter and contributing to the advancement of knowledge in these areas are not restricted to sighted people. Throughout history blind people have made significant contributions to these fields of study. In this article we examine a promising development that can help blind people prepare technical documents. It has the potential to permit blind persons greater entry into the hard sciences.
LaTeX, (pronounced lay-tech) or, alternatively, la (as in lava) and tech (as in technology), was initially invented as a typesetting language for mathematical notation. It is text based and nongraphical in nature. By typing standard text on a keyboard, one can represent all of the mathematical symbols, from the most elementary to the most advanced. LaTeX can even be used to draw diagrams.
A number of common items are difficult or impossible to type on a keyboard but are simple to produce using LaTeX. These include fractions, subscripts, superscripts, matrices, partial derivatives, and integrals. LaTeX gives the user extremely good control over the formatting of documents. Once a student masters the code, it can be much easier to work with than a mainstream word processor when complicated formatting is necessary. LaTeX code is typed into a text file. The LaTeX software, computer, and printer do all the work to produce a polished document containing readable mathematical notation. Although LaTeX was not created with this purpose in mind, it opens up possibilities for blind students and professionals in the STEM (science, technology, engineering, and mathematics) fields.
The LaTeX language can be learned by anyone, blind or sighted. To submit a math assignment in print, the blind student types LaTeX code into a file and uses the LaTeX software to compile that file into a visually appealing document with standard mathematical notation. LaTeX can convert text-based code into a PDF file for the student to print or email to a teacher or professor.
Recent developments have made LaTeX especially user-friendly for blind people. The MathType software from Design Science, the DBT software from Duxbury Systems, Tiger Software Suite from ViewPlus, and various screen readers have been designed to work together so that blind users can obtain either print or Nemeth Braille from a Microsoft Word file. When MathType is installed, it can interface with Microsoft Word and either DBT or Tiger Software Suite. The blind user types LaTeX code into a Word document (this works with Word 2010 and all other versions of Word of which we are aware). When the document is completed, the user simply hits "Select All" and Alt plus Backslash. The LaTeX code is then automatically converted into mathematical symbols and notations, just as a sighted person would write them. At this point a blind user can print the math document or send it by email. The same document can be embossed in Braille using either DBT or Tiger Software Suite. Screen readers will not properly read the equations in the math document, but they will definitely read the LaTeX code. The user can "Select All" and hit Alt plus Backslash again to convert equations back to LaTeX. If the LaTeX file is written correctly, the blind user can safely assume that the converted math file will also be correct. Both DBT and Tiger Software Suite will either translate the LaTeX file into computer Braille or translate the math file into Nemeth Braille.
One problem with using LaTeX and MathType in this way is that currently there is no way to debug LaTeX code using Microsoft Word. Writing in LaTeX is akin to computer programming; strict rules must be followed about how equations are represented. If the user breaks one of these rules when typing a LaTeX equation, the process of converting the code to readable equations will be derailed. With luck, only the incorrectly written equation will be affected. However, a single error may affect the conversion of the entire document. MathType gives no indication of where or what the error is. The user can avoid such frustrations by creating the entire document in the LaTeX Editor (such as the free open source TeXnicCenter) and using it to compile the document into a PDF file. The LaTeX Editor will point to error locations and indicate what the errors are. This information allows the user to debug the LaTeX document. Using MathType and Word has the advantage of being easier to learn initially, since it requires less knowledge of general LaTeX. However, dealing with errors in the LaTeX code is a serious drawback.
LaTeX allows the blind user to access some mainstream mathematical resources on the web. Some websites have LaTeX tags for their equations. A major example is Wikipedia. Refer to Wikipedia's article on the quadratic equation at <http://en.wikipedia.org/wiki/Quadratic_equation>. If a blind person reads the formulas on this page with a screen reader, she or he will hear their LaTeX representations.
LaTeX was very helpful to Alysha in school. It allowed her to gain access to homework assignments and lecture notes without having to use a reader or ask for the documents to be converted into Braille. Professors often create materials using LaTeX, so it was simple for them to send their LaTeX files instead of the inaccessible PDF files the rest of the class was using. Sometimes reading LaTeX can be tedious, because it isn't really intended for that purpose. LaTeX is no substitute for Braille. However, knowing LaTeX was beneficial to Alysha, because it gave her immediate access to these documents.
If you are overwhelmed by this discussion of LaTeX, be assured that we are here to help you. Before getting into specific details about this help, we want to point out that compiling a LaTeX document or converting it into Microsoft Word with MathType may not be necessary if the intended reader of the document is also familiar with LaTeX. If a blind student's algebra teacher knows LaTeX, she or he may be willing to read an assignment or test in LaTeX code. At the level of secondary school mathematics, LaTeX is not difficult to read and can generally be comprehended from the context.
According to its mission statement, the NFB's website <www.blindscience.org> has been designed to serve as a "national clearinghouse of resources and expertise related to nonvisual scientific exploration." With the cooperation of this website's managers and the NFB Jernigan Institute, we are preparing some simple instructional materials on the use of LaTeX. In fact the first part of our LaTeX tutorial may already be posted on blindscience.org by the time this article is published. The initial part of the tutorial will include the following:
No first draft of a tutorial is ever written perfectly. We hope that many teachers and students will use this material and send us their questions, comments, and suggestions. If there is sufficient demand, we will develop a more complete LaTeX tutorial that will include more example files and a list of LaTeX mathematical notations, together with their equivalents in Nemeth Braille and spoken math.
In our experience many college instructors, students, and researchers are familiar with LaTeX. Therefore, teaching LaTeX to blind students is highly advantageous for preparing them to enter the mainstream scientific world. As is true with the Nemeth Code for Braille Mathematics, students learn bits and pieces of LaTeX as they need them. For example, during algebra courses they will learn LaTeX only for such notions as powers and roots. In calculus they will learn the LaTeX codes for integrals and derivatives. In this way they achieve mastery of LaTeX as they advance in mathematical and other scientific training. The highly consistent and logical nature of the LaTeX syntax is similar to the structure of other programming languages and therefore provides students an excellent introduction to the general theory of computer programming.
We hope that this article has raised more questions about LaTeX than it has answered. We also hope that it will stimulate discussion in the blind community about the wise use of technology to help blind people learn mathematical subjects. If you have further questions or wish to add to this discussion, contact us by email: Al Maneki, <[email protected]> or Alysha Jeans, <[email protected]>.