Opportunities for togethering within a “salon-like” model of collaborative mathematical activity: a case study of math teachers’ circles

Collaboration is generally recognized as important for mathematics learning, though a theory of individual knowledge construction and ownership may be limiting its potential for pursuing collective liberty and democratic renewal. To investigate, scholars have proposed the concept of togethering to describe the mutual care and concern participants show for one another while navigating knowledge asymmetries during collaborative mathematical activity. In this paper, we use activity theory and togethering to analyze the mathematical activity observed within gatherings of Math Teachers’ Circles (MTC), groups of teachers who meet regularly to do mathematics for pleasure. Most MTC groups we study exhibit a practice field approach with participants facilitated through collaborative problem solving toward a predetermined answer. The activity of one group, however, is less formal and raises questions about how the collaborative mathematical activity is structured and how knowledge asymmetry is navigated. To address these questions, we first show how participants within the focal MTC group pursued problems to which no one knew the answer and, in the absence of facilitation, had to attune to one another to organize their activity and fulfill their aims. We then examine a brief episode where participants made a piece of mathematics visible to one another to consider togethering in unfacilitated collaborative activity. From these analyses, we propose that the informality of the group’s approach—likened here to coffeehouse salons—may afford opportunities for togethering, which are essential for democratic societies. Implications for reimagining collaborative mathematical experiences are discussed.