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General Description of MathSpeak™_

Access to Math and Science information is a real problem for students with print disabilities (disabilities that prevent them from normal reading of the printed page). Students with print disabilities have a very hard time understanding the complex math equations that typically occur in Math and Science textbooks by just listening to someone read the math to them. This is mainly because of the lack of a standard for spoken mathematics, and also the traditional problems associated with reliance on a human assistant. This is a problem that can affect the ability of students from grade school through graduate school to learn. The gh MathSpeak™ technology solves this problem by combining a solid standard for spoken mathematics with high-quality computer synthesized speech. This allows the student to work by themselves at their own pace and retain ownership of the ideas learned. The two facets of the gh MathSpeak™ solution are the standard itself, and the computer synthesis for the production of audio renderings.

The MathSpeak™ Standard_

The MathSpeak™ standard itself is very powerful since it is based on the fundamental principles of the Nemeth Braille Code for the Mathematics and Sciences, the current standard for encoding mathematics into Braille. This code, developed by Dr. Abraham Nemeth, a gh employee, allows a student superior access to mathematics by conveying the information unambiguously and concisely using a special grammar and lexicon unique to mathematics. Dr. Nemeth has mapped the advantages of the Braille code over into a special spoken language for mathematics called MathSpeak. It is this language that gh is currently developing from theory to practice.

The power of the MathSpeak standard can best be understood by a simple example of the root problem. Consider the following simple mathematical equation as it would likely be read by a human reader (click the link to listen to an audio file):

x equals a over B plus 1.

Listen to this equation in MathSpeak (wav format)   Listen to this equation in MathSpeak (ogg format)   Listen to this equation in MathSpeak (mp3 format)  

When visualizing this equation, there are actually two possible meanings (or visual renderings) for this one voicing, as shown below:

  • Rendering A: The equation: x equals a over B plus 1 where plus 1 is outside of the fraction.
  • Rendering B: The equation: x equals a over B plus 1 where plus 1 is part of the denominator.

Which is the correct version? For a print-disabled student taking a test, the answer is crucial. Unfortunately, current techniques for the human production of audio for math are rife with these kinds of ambiguities, in addition to being of inconsistent quality, expensive, and time-consuming to make. The reality of everyday life as a print-disabled Math and Science students is that most materials are not available in alternative format and hence human assistants must be constantly employed, which creates a drain on both time and money for both the student and the school.

MathSpeak offers a precise, perfectly consistent version of the above equation each and every time the student listens to it (click the link to listen to an audio file):

x equals BEGIN FRACTION a OVER CAPITAL b END FRACTION plus 1.

Listen to this equation in MathSpeak (wav format)   Listen to this equation in MathSpeak (ogg format)   Listen to this equation in MathSpeak (mp3 format)  

The words in red are special reserved words in MathSpeak that are used to indicate to the listener what the actual semantic meaning of the equation is meant to be. The above MathSpeak snippet can be interpreted (or visually rendered) in only one, unambiguous way:

  • Rendering A: The equation: x equals a over B plus 1 where 1 is outside of the fraction.

Note that both the proper contents of the fraction and the fact that the denominator is a capital (as opposed to lowercase) variable are indicated by the use of MathSpeak. This is but one of the many advantages to the use of an automatically generated, systematic standard.

Another example of the power of MathSpeak comes from the fact that the grammatical system that it uses provides immediate feedback as to the current location of the listener in a complex equation. This means that a listener can actually follow along as a long string of math is read without getting "lost". Although the theory of this delves into some of the very research gh is seeking to do in combination with Purdue, a simple example helps to explain the problem. Consider the following equation:

Equation as described in the content.

In MathSpeak, this would be spoken as follows (click the link to listen to an audio file):

y equals x SUBSCRIPT j SUPERSCRIPT 2e SUPER-SUPERSCRIPT minus i SUPER-SUPER-SUBSCRIPT n SUPER-SUPERSCRIPT pi BASE.

Listen to this equation in MathSpeak (wav format)   Listen to this equation in MathSpeak (ogg format)   Listen to this equation in MathSpeak (mp3 format)  

Although this equation is complex and difficult to listen to regardless of the circumstances, MathSpeak represents the best available method of conveying the information at hand. During any part of the equation, the listener can deduce exactly what level of super- or sub-script that they are currently hearing without having to wait for more context cues. Hence, the subscript of "n" for the variable "i" in the second-level superscript can be properly identified as SUPERSCRIPT SUPER-SUPER-SUBSCRIPT or "go up, up again, and then down".

Although some of the initial groundwork for MathSpeak has been done by Dr. Nemeth and gh, much remains to do in order for a complete and consistent system to emerge. The initial work of Dr. Nemeth represented techniques to convey only the most common mathematical situations (such as fractions, radicals, super- and sub-scripts) and does not account for more advanced constructs. This extension of lexicon must be completed. This lexicon must be studied as to the effectiveness with the computer-generated speech currently used by gh, especially for issues such as pronunciation, clarity, and discriminability. In addition, some linguistic analysis is needed to ground the specification in a solid theoretical framework, including the precise definition of the grammatical rules to be used. All of the above work must be encompassed in an XML framework in order to allow automatic generation of the audio and in order to fit into gh's standard production processes. Finally, extensive testing and user feedback is the only true method to measure the efficacy and utility of the product.



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