1999 Conference Proceedings

Go to previous article 
Go to next article 
Return to 1999 Conference Table of Contents

The Accessible TRIANGLE Graphing Calculator

Randy Lundquist and John Gardner
Science Access project
Department of Physics
Oregon State University
Corvallis, OR 97331-6507


Graphing calculators have become a standard tool in American classrooms. They are used in math and a number of scientific fields. Lack of an adequate accessible graphing calculator for blind children is often cited as one of the major "missing technologies" affecting education of blind children.

The Science Access project has developed a Windows 95 program that can be used on a small notebook computer as a powerful scientific calculator, including the ability to compute and plot functions y(x). The plot is visible on the screen and can also be "viewed" conveniently in audio. This program will be a part of the Windows 95 TRIANGLE application but is also being made available as a stand-alone TRIANGLE Graphing Calculator application.

TRIANGLE is self-voicing and works with any speech engine that fully conforms to the Microsoft speech interface (SAPI). A blind user can use a Windows 95 screen reader configured to "go to sleep" when opening or switching into TRIANGLE or the TRIANGLE Calculator program. In principle these could also be accessible through an on-line braille display. Even the audio graphing function can be replicated by a moving icon on a braille display. However this possibility cannot easily be incorporated at the present time. When the Microsoft braille interface is finalized and is supported by one or more popular braille displays, we hope to add self-brailling/display capability.

We believe that the TRIANGLE Calculator largely fulfills the need for a graphing calculator usable by blind and dyslexic people. Although a notebook computer is more expensive and bulkier than a standard graphing calculator, any person with print disabilities should, in our opinion, be using a computer for reading and writing anyhow. Even in classroom situations, a print impaired student can access a notebook computer in audio through an inexpensive earphone such that other students are not disturbed. We also anticipate that the TRIANGLE Graphing Calculator may be very useful for many people who are not officially "print-impaired", in particular the large group of "auditory learners" who often have difficulty interpreting visual graphs.

Calculator Functionality

The TRIANGLE Graphing Calculator has an on-screen calculator modeled on the scientific calculator that is bundled with Windows. It can be used by a sighted person with a mouse to click the buttons. Each button has an intuitive keyboard equivalent that permits sighted or print-impaired users to make calculations rapidly using the keyboard only. If self-voicing is enabled, each key function is spoken as it is exercised. It is also possible to tab among all keys and click them with spacebar. A context-sensitive help file gives the keyboard equivalent for each button and explains its function. The latter capability should make the calculator friendly to learn and use.

This calculator has two expression evaluators that permit a user to enter an arbitrary function of x and plot one or both expressions. The audio plot can display either function separately or display their sum or difference. Constants and expressions can be defined and stored for later use.

The Audio Plot

The audio plot displays y vs. x by mapping the x axis to time and the y axis to tone. Preliminary results from [Comparison tests] made by several hundred sighted undergraduate and graduate students have indicated that simple audio graphs of this type are almost as effective in conveying information as visual graphs.

The primary disadvantage of audio graphs relative to visual graphs is difficulty of detecting curvature. For example, student testers could differentiate between the graphs y=x and y=x squared more accurately with visual graphs than with audio tone plots.

When the tone plots were enhanced by adding "tick mark" beats, the differences between these two tone graphs became much more obvious to test subjects. These tick marks have a constant repetition rate if the line is straight but increase in rate if the graph curves up as with the plot of x squared.

Calculator users are provided with several tone plot options including playing of tick marks and suppressing the zero point so that only the shape of the graph is played. The user can step through the graph in either the positive or negative x direction, can search for special points such as maxima, minima, or zeros. The x and y coordinates can be read at any point, or a table of values read in tabular form.

The TRIANGLE Graphing Calculator program is available in beta form and can be downloaded from the SAP web site. We are unable to supply the required SAPI speech engine but can recommend vendors for those that work well. At the time this paper is written, the only popular speech engine that is fully compatible with the MS speech interface, and therefore the only one that works properly with the TRIANGLE Graphing Calculator, is FlexTalk. However, we expect several others to be available in 1999 because of the recent release of much better SAPI interface controls by Microsoft that speech engines can now use as a test of compliance.


This research was supported in part by the National Science Foundation.


Science Access Project URL: http://dots.physics.orst.edu/

A discussion of Microsoft's Speech Application Programmers Interface (SAPI) is available at: http://research.microsoft.com/stg/

[Comparison tests] http://www.physics.orst.edu/~sahyun/survey/

Go to previous article 
Go to next article 
Return to 1999 Conference Table of Contents 
Return to Table of Proceedings

Reprinted with author(s) permission. Author(s) retain copyright.