| This dissertation examines how aspects of mathematical generalizing are produced through the situated talk and activities of students and their teacher in an eighth grade mathematics classroom. The study investigates generalizing as a social practice—distributed across people, embodied action, and physical representations. To understand how generalizing takes place in practice, I observed a group of students working on two project-based mathematics units over the course of a school year. These projects involve modeling with complex representational systems that allow students to construct and evaluate designs in the contexts of architectural design and population modeling.; The analysis combines video-based ethnography with close studies of talk and interaction to document how students coordinate language, embodied activity, and physical representations to generalize. Building on a grounded theoretical analysis of students' work on the two project-based design units, this study makes two main points. First, it identifies the classroom conditions under which students come to use mathematics as a tool for working on extended design projects. Second, it identifies a set of routine discursive practices that the classroom participants use to generalize. In examining how students and their teacher create and inhabit classroom environments for engaging in meaningful mathematical activities, this study aims to illuminate aspects of the complex relationship between learning mathematics, discourse, and students' experiences in mathematics classrooms. |
