2002 Conference Proceedings

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Gaylen Kapperman

Jodi Sticken

Northern Illinois University
Department of Teaching and Learning
DeKalb, IL 60115
Fax: 815-753-8594

The Problem

For individuals who cannot read print symbols, the study of mathematics poses an extreme challenge. In order for a person who reads braille to succeed in the study of mathematics, a necessary condition is mastery of the Nemeth Code, a complex braille code used to display braille equivalents of print math symbols found in all fields of mathematics. Unfortunately, many teachers of students with visual disabilities are ill prepared to provide effective instruction in this braille code. Therefore, legions of academically able blind students cannot read or write the Nemeth Code, and are forced to listen to the contents of math instructional materials and attempt to carry out mathematical operations mentally. It is virtually impossible to achieve mathematical literacy through this ill-advised approach.

The inability to master the concepts underpinning the study of mathematics is a decades-long stumbling block which will constrain the individual in many aspects of life, limiting educational and vocational choices, as well as potential earning capacity. To rectify this untenable situation, the staff of Research and Development Institute is engaged in the development of a tutorial which will provide an effective, independent method for blind students to study the Nemeth Code. This groundbreaking effort, never before attempted by any other group, holds the promise of providing a solution to the intractable problem of mathematical illiteracy among blind students.

The Braille Lite

The interactive Nemeth Code Tutorial has been designed to be used with the Braille Lite, a hand-held computer specifically designed for use by blind persons which combines synthetic speech and a 20 or 40 cell electronic refreshable braille display. The device is small and lightweight, and operates on standard household current or a rechargeable nickel-cadmium battery which provides thirty hours of operation between charges. The braille display is designed to show braille symbols in a series of cells. Each cell is composed of eight tiny pins, housed in small holes, which "pop up" when stimulated electronically. As the Braille Lite sends signals to each cell, the appropriate pins move up slightly out of their holes, tactually perceivable by the braille reader. To move to the next set of braille symbols after reading a line of braille cells, a key is pressed and the next set of braille symbols appears instantaneously. Following this procedure, the reader can move forward and backward through a file. The Braille Lite also has speech capability, enabling the user to simultaneously listen to information and read braille. This marriage of synthetic speech and refreshable braille is the most expeditious combination for a tactile reader to learn the code of braille mathematics.

The Tutorial

Special delimiters have been programmed into the software to cause the Braille Lite to speak Nemeth Code correctly, distinguishing mathematical notation from the code used in literary braille. This is the capability of the software which makes it extraordinarily valuable to the learner. No other device exists that speaks braille mathematics correctly, enabling the learner to compare spoken Nemeth Code symbols to their display on the electronic braille array. This makes learning to read and write the symbols remarkably efficient.

The tutorial content is divided into lessons which include basic concepts initially, and progressively more sophisticated notation in successive lessons. The scope of the notation includes that which is found in all mathematics courses up to and including calculus. Lesson material can be heard by the learner as well as read on the braille display. Each lesson contains explanatory material describing the rules governing various topics within the Nemeth Code and examples of Nemeth Code expressions. Following the explanatory section of each lesson, three sets of interactive exercises are presented to the learner, providing immediate feedback; this is a major strength of this tutorial. In the first exercise set, the learner is presented with spoken mathematics notation which is to be brailled. After the "judge" command is invoked, the Braille Lite announces the number of errors, and marks the first error by raising two pins below it on the braille display. The learner is then given limitless opportunities to correct those errors. There is also a command which can be used to toggle between the incorrect and the correct answer, providing the opportunity for direct comparison.

The second set of exercises emphasizes reading of Nemeth Code symbols. The learner is instructed to read braille shown on the display. The "judge" command causes the Braille Lite to speak the displayed symbols, either one symbol at a time or one line at a time, enabling the learner to compare the correct spoken equivalent to his or her answer.

Proofreading exercises are presented in the third set, where correct spoken symbols are supplied along with a display of braille symbols which contain errors. The learner is instructed to find and correct the errors. The 'judge" command can be invoked to indicate errors. A "show answer" function enables the learner to toggle the braille display between the correct answer and the answer which contains errors.

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