The Algebra of identity : Toward a new framework for understanding the co-construction of identity and engagement in mathematics classrooms.

This dissertation presents a framework to understand students' co-construction of identity and engagement in mathematics classrooms.

The framework interprets classrooms as figured worlds in which students' out-of-school lives and classroom activity structures emerge as a hybrid mix of resources.

The framework captures how students, in individual ways, draw on these resources to engage in collaborative tasks and to position themselves and others as kinds of people, leading to varied learning opportunities.

The framework was applied to analyze students in a small group in an applied, project-based Algebra class.

Primary data sources include: (a) 23.25 hours of three videotaped group projects, (b) 12 student interviews, and (c) 30.75 hours of field-notes.

Analyses corroborated the utility of the framework. The project-based classroom emerged as a figured world in which students were treated as if they were respectful professionals with agency over their activities and ideas, both by the teacher and one another.

Further, this agency allowed students to draw on resources from their out-of-school lives (e.g., neighborhood experiences) in addition to those the classroom provided (e.g., student roles).

Through two case studies, analyses show how students' use of these hybrid resources mediated trajectories of identity and engagement, both enabling and constraining learning opportunities.

Results highlight the benefits and challenges of affording students' use of hybrid resources.

A comparative case of two students who served in group leader roles (a classroom resource) showed that their group members interpreted their respective project-related directives differently.

Gendered interpretations of leaders' directives ultimately marginalized the female group leader and privileged the male group leader, leading to differential learning opportunities.

A second case highlighted how one tough disengaged student increasingly engaged with group projects across the year.

The classroom figured world supported his use of out-of-school experiences to serve as helpful resources that he used to reconcile his classroom and personal identities.

The emergence of positional identities and patterns of engagement have been studied separately in extant research.

The present framework shows promise for illuminating the interplay between these constructs and how they contribute to emergent learning opportunities in the complex worlds of classrooms.