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Access to math for blind computer users - An overview

Author: Thomas Kahlisch
Address: DRESDEN UNIVERSITY of TECHNOLOGY | Department of Computerscience | Institut of Information Systems| 01062 Dresden | Germany
Phone: +49 351 463 8410
Fax: +49 351 463 8491
E-Mail: kahlisch@inf.tu-dresden.de
WWW: http://elvis.inf.tu-dresden.de/~kahlisch

Overview

  1. Basic problems

  2. Pros and Cons of different math notations

  3. Software

  4. Conclusion


1 Basic problems

How to describe two dimensional objects?

Two dimensional objects can be described in a presentational or a semantical way.
Example:
Semantic oriented descriptions are:
X squared or
X index 2
A presentation oriented description is:
x superscript 2

How to describe relationships between these objects?

Relationships between mathematical objects are described by using brackets, parentheses or other delimiters. These elements are necessary to design the hierarchy or structure of an expression. In a complex equation, they increase the number of characters, which have to be read by the blind user, dramatically.

Are 6 dots not enough?

The traditional 6 dots braille notation does not fit with codes used on computers. Examples are the different presentation of capital letters or numbers.

2 Pros and cons of different math notations

6 dot math notations:

  • International Math Notation (Marburg Code)

  • Nemeth Code

  • and many more...

Advantages:

  • compact and semantic oriented description of mathematical expressions

  • closely related to literary braille

  • 6 dots are easy for children to read


Disadvantages:

  • inappropriate to do Math on the computer

  • difficult for sighted people to read

  • the notation is not expandable


8 dot math notations:

  • Stuttgart Math Notation (SMSB)

  • Gardner/Salinas Code (GS)

  • ASCII Mathematical Notation (AMS)


Advantages:

  • very compact description of mathematical expressions

  • moves traditional 6 dot Braille description methods into the world of computers


Disadvantages:

  • SMSB and GS are special Braille fonts

  • no international standard

  • requires special software (editors, reading systems and printer drivers)


The AMS notation is system independent and can be used in an easy way on every computer. The description of mathematical expressions by using ASCII-charcters, causes long chunks of information and a large number of parentheses to provide the structure of the equation.
Math notations used in electronic publishing and the WWW:

  • LaTeX

  • SGML/XML

LaTex is a popular document description language which is commonly used by the Internet community. The system provides a powerful set of instructions to describe mathematical expressions. The software is free and easily accessible and can be used on any kind of computer platform. LaTeX can be used by blind people to write mathematical equations and to print information in a high quality layout. The notation is not very useful for blind people when using it for calculations or solving mathematical problems on the computer.

SGML or, the easier to use subset of this document architecture, XML, is a concept to define structured markup languages. The most popular SGML notation is HTML, which is the current formatting language in the WWW. MathML is a XML format which provides sets of semantic and presentation oriented markup instructions to describe mathematical expressions for the WWW. This notation can be used as a intermedia format which can be translated into different accessible formats: large print, Braille or speech output.

3 Software

ASTER: Audio access to LaTeX-Documents
URL: http://www.cs.cornell/edu/Info/People/raman/aster/
MATHS workstation: SGML-Editor for doing Math by blind users
URL: http://www.grif.fr/fr/grifwork/tide.html
TRIANGLE: A MS-DOS Mathematics scratch pad for the blind
URL: http://dots.physics.orst.edu/triangle.html
LABRADOR: program to translate LaTex into Marburg Code
URL: ftp://www.mvblind.uni-linz.ac.at/pub/tex-cd

4 Conclusion

  • There is no easy solution!

  • Use an intermedia format for providing access to the structure!

  • Use an intermedia format for translation into different notations!