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Abstract

Abstract

The grammar and vocabulary of higher mathematics are different from the grammar and vocabulary of conversational English and conversational American Sign Language (ASL). Consequently, mathematical language presents interpreters with a unique set of challenges. This article characterizes those aspects of mathematical grammar that are peculiar to the subject. (A discussion of mathematical vocabulary and its expression in ASL can be found elsewhere (Tabak, 2014).) An increased awareness of the grammar of mathematical language will prove useful to those interpreters for the deaf and deaf mathematics professionals seeking to express higher mathematics in ASL.

In this article one will, for the first time, find a model of mathematical language created for interpreters that identifies those aspects of the language that must be retained in any accurate interpretation. In particular, the article identifies the characteristic properties of propositions and propositional functions that must be preserved by the interpreter when propositions and propositional functions are expressed in ASL. It identifies the characteristic properties of mathematical language used in the definition of sets and in the statement of theorems that must be preserved by the interpreter when (mathematical) definitions and theorems are expressed in ASL. In addition, the article includes a method of symbolically representing mathematical language which is useful for analysis. The method enables the user to break down complicated-looking mathematical sentences into their simpler constituent parts in order to simplify the problem of interpretation. Numerous examples of mathematical language are included as are examples of how the diagramming technique can be used to clarify the structure of mathematical definitions and theorems.

The method by which this model of mathematical language should be implemented is left to groups of expert practitioners, deaf and hearing.

 

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