Authority and Mathematical Argumentation 1 Running head: AUTHORITY AND MATHEMATICAL ARGUMENTS The Effect of Authority on the Persuasiveness of Mathematical Arguments

Three experiments are reported which investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the author is anonymous. We develop a model which accounts for these data by suggesting that, for both students and researchers, an authority figure only plays a role when there is already some uncertainty about the argument’s mathematical status. Implications for pedagogy, and for future research, are discussed. Authority and Mathematical Argumentation 3 The Effect of Authority on the Persuasiveness of Mathematical Arguments It is widely argued that mathematical argumentation and proof should be central to the practice of learning mathematics at both the school and university levels (e.g. Hanna, 2007; National Council of Teachers of Mathematics [NCTM], 2000; Quality Assurance Agency, 2002; Schoenfeld, 1994). Consequently, students’ conceptions of argumentation and proof have been extensively studied by education researchers. Harel and Sowder (1998), for example, introduced the influential proof schemes framework, a classification of how students gain conviction in mathematical statements. Noting that many different proof schemes have been observed in use by students, Harel emphasized that students should be encouraged to evaluate mathematical arguments by using similar criteria to those deployed by professional research-active mathematicians: “The goal of instruction must be unambiguous; namely, to gradually refine current students’ proof schemes toward the proof scheme shared and practiced by the mathematicians of today.” (Harel, 2001, p.188). Other researchers have shared this view, emphasizing that expert mathematical practice is relevant for the design of pedagogy at both the school and university levels (Brousseau, 1997; Stylianou, 2002). As a consequence of similar views to this, Harel, Selden and Selden (2006) called for further research on expert and novice mathematical behavior, arguing that such research would lead to pedagogical insights. The goal of this paper is to explore the behavior of expert mathematicians and advanced mathematics students with respect to one specific factor that may influence the level of persuasion that they invest in a mathematical argument: the authority of the argument’s author. We first situate this work within the broader educational literature on mathematical argumentation and proof. Authority and Mathematical Argumentation 4