Disciplinary authorities or fellow educators? Exploring positionings of mathematicians when interacting with secondary teachers

The communication between mathematicians and secondary mathematics teachers have long been recognized as a critical issue in mathematics education. Yet, such communication remains fraught and limited, in part due to profound communal differences and issues of power and authority. This study is part of long-term research project that investigates how communal differences may be
leveraged as a valuable resource in cross-community interactions in mathematics education. In this paper, we draw on Positioning Theory to analyse the positioning acts of mathematicians and teachers as they discuss and evaluate instructional moves of a teacher presenting a proof in a videotaped secondary lesson. Our analysis distinct sets of acts suggesting that a positional shift occurred when the mathematicians were situated as fellow educators rather than disciplinary authorities or pedagogical critics. We discuss the potential affordances of different positionings.