The co-development and interrelation of proof and authority: The case of Yana and Ronit

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a 'web of authority' ever present in mathematics classrooms. In past work, it has been shown how those relations of authority may sometimes interfere with students' reflecting on mathematical ideas. However, "...by shifting the emphasis from domination and obedience to negotiation and consent..." (Amit & Fried, 2005, p.164) it has also been stressed that these relations are fluid and are, in fact, a sine qua non in the process of students' defining their place in a mathematical community. But can these fluid relations be operative also in the formation of specific mathematical ideas? It is my contention that they may at least coincide with students' thinking about one significant mathematical idea, namely, the idea of proof. In this talk, I shall discuss both the general question of authority in the mathematics classroom and its specific connection with students' thinking about proof in the context of work done in two 84th grade classrooms.