Studies of Identity

• In Event: Approaches to Fostering Young People’s Mathematical Identities: Theory, Design, and Student Uptake

Abstract

This session will consider the methodological issues researchers face when measuring identity in classrooms. This is an important topic, as when students learn mathematics in classrooms, they are not just learning knowledge, they are developing different ways to relate to knowledge and different forms of expertise (Hatano & Oura, 2003). These disciplinary relationships help students form identities as learners and people. Like Wenger (2008), we regard all knowledge development as a process of becoming, and of changing how we relate to the world, which helps form our identities. This focus on identity, belonging, and relationship means that researchers can also consider the ways race, gender, social class, and other categories factor into mathematical participation and opportunities to achieve (Gutierrez, 2011; Esmonde & Langer-Osuna, 2018).
In multiple studies with students across the 11-18 age range, we have compared the identities available to students when they experience mathematics approaches that center collaboration, reasoning, and connection making, with approaches that are focused upon individualized work and the reproduction of isolated procedures, focusing upon gender and racial equity. Different scholars have highlighted the importance of agency and authority within identity development (Holland, 2001; Cobb, Gresalfi, & Hodge, 2009). In studying agency we question the extent to which students are invited to share their own thinking, drawing from classroom observations and student interviews. Our considerations of authority also draw from classroom observations but they are supplemented with specific interview questions that probe students’ sense of authority, such as: What would you do if you did not know how to solve a math question?
Hatano and Oura describe routine experts as those who are able to solve routine procedures, and adaptive experts as those who understand why procedures work, and are able to adapt, apply, or invent new procedures (Hatano & Oura, 2003). These different forms of expertise seem important to students’ developing identities and we have studied them by watching students’ approach to mathematics problems in class, and by giving students problems to work on in assessments.
Each of the methods we have chosen - including classroom observations, student interviews, and mathematics assessments - offer different insights into student identity and expertise, and each offer a range of constraints and affordances. These qualitative methods allow for in depth focus, and fine grained analysis, but they are often limited by the need to draw conclusions from moments in time. This is a serious constraint when student identity is an evolving construct that is always developing and changing. In this session we will consider the different methods that have been used in a range of identity studies and the challenges and opportunities provided by each. We will also consider what is at stake when we do not consider student identity and the need to conduct classroom observations that include a focus on students’ ways of engaging with mathematics, with a particular lens on issues of race, gender and social class.

Authors

• Jo Boaler, Stanford University

• Kyalamboka Brown, Stanford University