| Because language is the primary medium through which mathematical understandings are shared, the form of the discourse in mathematics classrooms is significant. For fluid communication, it is necessary for teachers and students to use language as though it accurately represents their mathematical ideas. However, when attention is directed toward language, new possibilities can be opened up for seeing more clearly the nature of the classroom discourse and the nature of mathematics itself.;In this investigation, I use Norman Fairclough's critical discourse analysis to uncover alternative possibilities for participation in mathematics classroom discourse. While co-teaching pure mathematics to a class of thirty-two 15- and 16-year old students, I had an nineteen-week conversation with the students and their regular teacher. As I directed these participants' attention to features of their language practice in the classroom, a student perspective on mathematics learning was drawn out. Together we also discovered a range of possibilities available to mathematics learners and teachers within their classroom discourses. This critical awareness also exposed silences.;While the students in this conversation generally resisted my interest in language by withholding significant participation, the exceptions to this passive resistance were generative. Three streams of the larger conversation exemplify some possibilities associated with attention to language. When I wanted to show students that the voice of their utterances could take on various forms, some of them actively resisted accepting the validity of mathematical statements that suggested human agency. Some students became interested in the ways they looked away from each other during their mathematics communication and looked through symbols to see mathematics. Other students argued about the significance and dangers of using "de-emphasizers" such as just to support minimal articulation.;Silence is a factor in each of these streams of conversation---the silenced person, the evasion of the person's face and the avoidance of explanation. An awareness of the tendency to silence the human agent in mathematics classroom discourse can help teachers attune themselves to this and other silences, and can provide researchers with new insight into the nature of the discipline and students' relation to the discipline. |
