PAR FOR THE COURSE: DEVELOPING MATHEMATICAL AUTHORITY Daniel L. Reinholz University of California, Berkeley reinholz@berkeley.edu Perceived mathematical authority plays an important role in how students engage in mathematical interactions, and ultimately how they learn mathematics. This paper elaborates the concept of mathematical authority (Engle, 2011) by introducing two concepts: scope and relationality. This elaborated view is applied to a number of peer-interactions in a specialized peer-assessment context. In this context, self-perceived authority influenced the way feedback was framed (as either questions or assertions). Key words: Authority, Calculus, Classroom Research, Formative Assessment Introduction Individuals who are proficient in mathematics need not rely on an external authority; using the logic of the discipline, mathematicians know when they are right. Helping students become mathematicians requires helping them develop such authority grounded in mathematical reasoning. In this paper I build on the concept of mathematical authority (Engle, 2011) in the context of undergraduate mathematics education. According to Engle (2011) authority begins to develop when students are “authorized” to share what they “really” think, and is solidified when students develop into local “authorities,” based on how students are positioned in the social space of the classroom. Implicit is the idea that authority “belongs” to students, existing beyond the confines of a single classroom situation. In what follows, I address the context-dependent nature of authority, and how it may (or may not) be transferred between contexts. While authority does have some bearing on how one solves problems individually, it becomes most relevant when we think of one’s mathematical interactions with others; mathematical authority is a relational construct. Moreover, as is the case with self-efficacy (Bandura, 1997), it is an individual’s perceived mathematical authority that determines how they engage in mathematical interactions, not their actual ability to make authoritative statements about mathematics. Thus, it is important to consider authority not as a static attribute, but rather as something that depends on how an individual situates oneself (and is situated by others) in a mathematical interaction (Boaler & Greeno, 2000). To extend the notion of mathematical authority, I introduce two concepts: scope and relationality. Perceptions of authority operate at a number of levels, increasing in generality (scope): (1) a specific problem, (2) a topic, (3) a mathematical domain, (4) the domain of mathematics, and perhaps (5) academics in general. Generalized authority is more readily transferable than localized authority, but is also less robust. (While an individual with a PhD in analysis has generalized authority that would extend to all of mathematics, a few failures in abstract algebra would be more detrimental to local self-perceived authority than a few failures in a related area of expertise (e.g., Banach spaces), because of the individual’s topic-specific - and more robust - authority in analysis.) The relational nature of mathematical authority plays out in interactions between multiple individuals (e.g., partner work, small-group work, or a class discussion). Relationally, mathematical authority depends on: (1) one’s self-perception of one’s own authority, and (2)