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Handbook for Spoken Mathematics

Introduction

The content of this portion of the site was adapted from Lawrence Chang’s Handbook for Spoken Mathematics: Larry’s Speakeasy (1983). All sections of his original work are included except the section entitled, Diagrams and Graphs. That chapter contains extraordinarily complex graphics which would be impossible to display in such a fashion that it would be accessible to those who are blind or severely visually impaired.

The focus of Chang’s work is to provide the wherewithal by which sighted individuals can read mathematics to persons who are blind. He describes in words each symbol in the major branches of mathematics, from the simplest to the most complex. In essence, Chang’s work represents the spoken vocabulary of mathematics. Thus, one use to which this work can be put is to assist persons who are blind in training sighted readers to accurately read mathematics.

We have added to the reservoir of information in several ways. First, for each symbol, we have included an extended description in which the print symbol is described in words which a person who is blind can appreciate. Secondly, we have included graphic representations of the Nemeth Code equivalents of all of the symbols. The dot configurations are listed in the extended descriptions which accompany the graphic displays. Thirdly, for the Greek Alphabet and Basic Symbols sections, we have included the capability of downloading tactile images of the symbols along with their Nemeth Code equivalents. These images can be sent to an embosser to reproduce them in tactually perceivable form. Thus, tactual readers of mathematics need not depend solely on our verbal descriptions of the print symbols or their Nemeth Code equivalents.

It is our intention to enhance communication in the language of mathematics between and among sighted persons and persons who are blind. In using this work, sighted readers will have the advantage of having a standard vocabulary which they can use to read mathematics aloud. Blind persons will have the capability of examining the symbols tactually as well as linking the verbal description of the print symbols and their Nemeth Code equivalents.

For the Greek Alphabet and Basic Symbols sections, individual symbols and their Nemeth Code equivalents can be selected for downloading or the entire set can be downloaded in one large file. In these sections, a link entitled “download a tactile example of [example name]” will be presented with each symbol. Activating this link will allow the reader to download a Duxbury file containing information related to that specific symbol. Following are instructions for downloading the tactile examples from any page on the website.

First, locate and activate the link labeled “Handbook for Spoken Mathematics.” Next, locate the link labeled “Greek Alphabet” or “Basic Symbols” and activate the chosen link.

Both the “Greek Alphabet” and “Basic Symbols” sections have multiple pages. Use the next page and previous page links to move between pages in a section. On each page, there are links to the tactile examples that can be downloaded. Once the desired page is located using the steps above, the links to the tactile examples can be accessed simply by pressing the tab key until the desired link is located. The link to download the tactile graphic file will be labeled: “download a tactile example of [example name].”

Activating the link to download the tactile graphic file will open a dialog that will prompt the user to open or save the file. Choose save and note the location where the file is downloaded. When the download is complete, the tactile graphic file can be opened using the Duxbury Braille Translator.

If the reader would prefer to download a single file containing all the tactile examples for a given section, they are directed to the download page. Specific instructions on how to download these files are provided in the help section.

This work is not intended to be a tutorial on the rules for brailling the Nemeth Code. There are several excellent sources of information upon which the reader may draw. Thus, it is not our intention to duplicate that work here.