The social construction of authorities: An interactional ethnographic examination of positional legitimacy

•As a field of mathematics education, we have routinely envisioned a space for students to share authority in their pursuits to construct, understand, and do mathematics. This study fills a much-needed gap in literature, by exploring how young students begin to position each other and the ways they construct and navigate authority relationships to gain legitimacy during collaborative endeavors.•Ritual legitimacy captures the ways students used the rituals and norms of the classroom to gain a position of authority.•Mathematical legitimacy details the ways students used mathematical procedures or perceived correctness to gain a position of authority.•Students intercontextually positioned each other, specifically those who had not attended kindergarten in person versus those who attended face-to-face.•We must critically examine, over long periods of time, how authority is constructed between students first. It is not enough to share authority with students, we must also understand the different sources of authority to ensure that each student has an equitable opportunity to share authority and become a doer of mathematics.