Negotiating Knowledge Through Mathematical Activities in Classroom Interactions

Abstract

What students are learning in mathematics classrooms can be analysed from a wide range of perspectives, focusing on the mathematical content, the mathematical processes or the mathematical activities. There is also a social dimension intertwined with this cognitive dimension that focuses on what mathematical activities in particular are established as socio-mathematical norms within a classroom. It is through these norms that students learn what it is to both learn mathematics and what it means to do mathematics. In this article I add a further epistemic dimension to illustrate how these socio-mathematical norms are co-constructed through interactions in a dynamic way. The analysis reported in this paper draws on video data of 65 lesson segments where students made their thinking explicit, taken from an original sample of 133 naturally occurring mathematics lessons with 81 teachers identified as including cognitively demanding mathematics. Using ethnomethodological conversation analysis and the epistemic dimensions of interaction initially outlined by Heritage and colleagues, a fine-grained sequential analysis of the interactions including students’ detailed contributions around cognitively demanding activities within these lessons illustrates how epistemic access, primacy and responsibilities are continually negotiated in interaction. Students’ rights to make knowledge claims or obligations to demonstrate their knowledge are negotiated in ways that influence students’ and teachers’ epistemic authority and stance. The analysis shows how the cognitive and social dimensions are intertwined both at an individual level but also at the classroom level that establish and reinforce the norms around the access and primacy of ideas and knowledge in interaction. These epistemic negotiations have consequences on the nature of mathematical activities that students experience and participate in, and subsequently their opportunities to learn mathematics.