The NCTM's Professional Standards for Teaching Mathematics (1991) has directed attention to “discourse” in the mathematics classroom. This document recommends that mathematics instruction should promote students' discourse by orchestrating situations in which each individual's thinking is challenged and by asking students to clarify and justify ideas. “Discourse,” as described by the Standards document, highlights the way in which knowledge is constructed and exchanged in the classroom (Ball 1992). Teaching mathematics from the perspective of developing mathematical discourse requires building a new vision for mathematics classrooms and poses a major challenge for mathematics teachers at all levels. This challenge was recognized by D'Ambrosio (1995). She identified the need to build environments in which students construct a “personal relationship” with mathematics as one of the most important requirements for promoting and sustaining the type of discourse envisioned by the reform movement. In such environments, students engage in authentic mathematical inquiry; act like mathematicians as they explore ideas and concepts; and negotiate the meanings of, and the connections among, those ideas with others in class (D'Ambrosio 1995).
Azita Manouchehri areas of research include problem-based mathematics learning and teaching and mathematics teacher preparation.
Mary Enderson research interests include mathematics teacher preparation and authentic assessment of mathematics in the classroom. The authors extend their thanks to the Missouri Middle School Mathematics Project teacher participants, funded by NSF grant no. ESI9453932, for opening their classrooms during the data-collection phase of this article and for generously offering their personal time for interviews.