# Exploring how mathematical authorial identity emerges

## Abstract

The recent mathematics curriculum reforms in the United States resulted in various classroom initiatives and research on cultivating students’ mathematical identity. Among many dimensions of mathematical identity (Fellus, 2019), mathematical authorial identity is connected to how students leverage the interactional space and communicate their ideas about mathematical concepts while invoking authority, especially during students’ peer discussion in mathematics classrooms (Povey & Burton, 2003; Schoenfeld & Sloan, 2016). Despite the emerging importance of students’ mathematical authorial identity, most research on authorship and authority in mathematics classrooms has focused on the relationship between teachers and students, and not on the relationships of students with one another in small groups (Amid & Fried, 2005; Cobb et al., 2009; Wagner & Herbel-Eisenmann, 2014). More attention is needed to understand how the notions of authorship and authority work in students’ interactions with others, and what interactional patterns occur as students construct mathematical authorial identity through classroom discourses (Langer-Osuna, 2016, 2017, 2018; Langer-Osuna et al., 2020). The current study used an applied conversation analysis to investigate students’ interactional patterns of seven small group discussions. These students met virtually four times over one school year to exchange feedback on each other’s mathematical arguments. After transcribing students’ small group discussions, I focused on the occurrences of accounts, which are statements “made by a social actor to explain unanticipated or untoward behavior” (Scott & Lyman, 1968, p. 46). They are typically used by interactants when they offer additional explanation or elaboration in situations when they are accomplishing a dispreferred action. The results indicate that mathematical authorial identity was manifested in three different types of account turns. The first type of account turns was ‘missing accounts,’ which were expected to occur but were missing due to students accomplishing other interactional work. Students deployed this type of accounts as they accomplished various forms of disagreement. The second type of account turns invoked external authority. Students typically deployed this type of account turns towards the end of a sequence, and they were likely to use strong expressions of disagreement. The third type was account turns that invoked shared/internal authority. These account turns usually occurred at the beginning of a new sequence and when students expressed weaker disagreement. The various types of account turns and interactional environments suggest that students actively conceptualize and manage interactional work, such as facework and preference organization, when navigating mathematics classroom discourse. Based on the findings, this dissertation offers pedagogical implications for mathematics educators to actively cultivate group norms that could occasion more interactional affordances for students and be aware of interactional features and sequences that foster students’ construction of mathematical authorial identity.