The relationality in/of teacher–student communication

摘要

In mathematics education, student–teacher communication is recognized to constitute an important dimension in/of mathematical learning. Significant effort has been made in recent decades to depart from a focus on the individual in which teachers and student simply use communication to express, to and for others, their private knowledge or thinking. In this paper, we continue this departure taking as a starting point the observation that (mathematical) communication is possible only when there is a relation with others: Communication is the relation with others. That is, we present a way of thinking about student–teacher communication in which geometrical being-in-the-know is conversationally produced. Using fragments of elementary classroom conversations involving three-dimensional geometry as a tool to flesh out this theoretical study, we illustrate (a) how being-in-the-knowwith can be recognized in asking and responding to questions involving mathematical concepts and (b) how conversations are then the fine-tuning of being-in-the-know relations in which mathematical ideas can come forth even in those instances where not-being-in-the-know is asserted.