Abstract
Student creation of nonstandard units of measurement, and symbols for such units, is a pedagogical technique intended in part to promote students' understanding of mathematics as communication (NCTM, 1989). This paper examines a conflict that arose during such an activity in a sixth-grade classroom. In our view, the students' disagreement reflects the tension among several conflicting requirements of language and symbol use in mathematical communication. Iconic, transparent symbols exist alongside those that are arbitrary and opaque. Technical terms depart from their everyday linguistic counterpart in unpredictable ways. Most importantly, students must recognize and honor conventional, historically grounded uses of expressions and symbols, while also using and actively interpreting innovative and contextually determined uses. We explore the implications of these complexities for student learning and teaching.
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