TEACHING MATHEMATICS AS A LANGUAGE The acquisition of language is both unconscious and conscious. As a child, in the unconscious mode, one comprehends the spoken language and visualizes its meaning. Assuming normal physical and mental development, and, when ready, a child enters the conscious mode to speak, read and write the language. My own ignorance about language development became apparent when, in attempting to learn a second language, | discovered that I never knew how I learned the first! In my teaching of mathematics, I had been ignoring the "language" that I was expecting my students to learn. When giving lessons on "word problems," I was expecting my students to read and write before they could comprehend, visualize and speak. The acquisition process had been reversed. And since I cannot remember the last time my students felt "fluent" in mathematics, | assessed this reversal and now offer the following instructional suggestions. Method The teacher could view the student as a beginner to the vocabulary and structure of the language of mathematics and permit a "silent period" to develop listening comprehension and readiness to speak (the unconscious mode). Instruction might point out the vocabulary, parts of speech, symbolism, grammatical rules and sentence- producing skills necessary to speak the language of mathematics. Once in the conscious mode, the student could be encouraged to speak, when ready, and "rewarded" with positive reinforcement. Once the forms and patterns of the language are established orally, the student should be able to begin to read. The student is well into the conscious mode when he/she writes the language—as writing is but a mere record of speech. For example, a lesson on solving linear equations: During the "silent period" it could be suggested that solving an equation is like unwrapping a package—i.e., if the bow was the /ast item on in wrapping, it will be the first item off when unwrapping. The required vocabulary might include: NOUNS - equation, solution, variable ADJECTIVE - linear VERBS - to equal, to solve SYMBOLISM - equal sign, lower case letters for variables, operation signs, grouping symbols RULES - Addition/Multiplication Properties, Distributive Property, Order of Operations The associated application problems could be handled similarly. The instructor must be even more willing to allow the student to linger in the acquisition (unconscious) mode where the necessary visualization and comprehension of abstract concepts takes place. For example: Let your students /rear the language first—speak to your students; read aloud to them. Let your students speak the language—permit thinking aloud or brainstorming in groups as a way to bridge the unconscious and conscious modes. Let your students read the language—help them to make the necessary association between what they have heard and spoken as they begin to read. For example, six more than a number, like Sue is six years older than John, translates as x + 6. Let your students write the language—encourage students to think, say and write anything within reason that lifts the haze of abstraction. Outcomes As instructors of mathematics, we must be as diligent in helping our students acquire second language proficiency as is any other foreign language teacher. When competency in a subject is measured in terms of aural, oral and written capabilities, teaching mathematics as a language is as important as teaching about the subject itself. And as did I, perhaps students will end up learning as much about their first language as they did about the second! Suzanne S. Austin Mathematics Department For further information, contact the author at Miami-Dade Community College, 300 N.E. 2nd Avenue, Miami, FL 33132. Suanne D. Roueche, Editor September 11, 1987, Vol. IX, No. 17 INNOVATION ABSTRACTS Is a publication of the National Institute for Staff and Organizational Development, EDB 348, The University of Texas at Austin, Austin, Texas 78712, (512)471-7545. Subscriptions are available to nonconsortium members for $35 per year. Funding in part by the W. K. Kellogg Foundation and Sid W. Richardson Foundation. Issued weekly when classes are in session during fall and spring terms and once during the summer. “ The University of Texas at Austin, 1987 — Further duplication is permitted only by MEMBER institutions for their own personnel. Issn 0199-106x PAGE IG.