chapter  14
21 Pages

A design research perspective on the identities that students are developing in mathematics classrooms

ByPAUL COBB , MELISSA GRESALFI AND LYNN LIAO HODGE

Our goal in this chapter is to present an interpretive scheme for documenting the identities that students are developing as they engage in (or resist) activities in particular mathematics classrooms. In the approach that we propose, the identities that students are developing can be made tractable for empirical analysis by documenting students’ understandings and valuations of their classroom obligations. As is the case with any perspective on identity, this approach reflects a particular set of research concerns and interests. We clarify that the approach that we propose is grounded in the context of conducting design research at the classroom level. One of our primary concerns is therefore that analyses developed by using the interpretive scheme will feed back to inform the ongoing instructional design effort. An explicit focus on the identities that students are developing as doers of mathematics broadens the scope of classroom design research beyond analyses of students’ mathematical reasoning by also considering the ways that students are coming to think about themselves in relation to mathematics, and the extent to which they are developing a commitment to and are coming to see value in mathematics as it is realized in the classroom. The notion of identity is pragmatically significant because it encompasses a range of issues that are typically subsumed under the heading of affective factors, including students’ persistence, interest in and motivation to learn mathematics. As a first step in clarifying what we mean by identity, we draw on the colloquial meaning of identifying: to associate or affiliate oneself closely with a person or group. Our concern is with both how students come to understand1 what it means to do mathematics as it is realized in the classroom and whether and to what extent they come to identify with that activity. Analyses reported in the mathematics-education literature allow us to differentiate between three distinct cases: those in which students identify with classroom mathematical activity, merely cooperate with the teacher, or resist engaging in classroom mathematical activity, in the process developing oppositional identities (Boaler & Greeno 2000; Gutstein 2002, in press; Martin 2000). Prior investigations document that the extent to which students identify, merely cooperate, or resist can differ significantly from one classroom to another (Boaler 2000; Boaler & Greeno 2000; D’Amato 1992; Erickson 1992; Gutiérrez, Baquedano-Lopez & Tejeda 1999; Mehan, Hubbard & Villanueva 1994). These findings indicate the potential value

of an interpretive scheme that enables us to analyze the relations between the microcultures established in particular classrooms and the identities that students are developing in those classrooms. To be useful, an interpretive approach should therefore attend to four interrelated issues: the nature of mathematical activity as it is realized in the classroom, what students make of that activity and both whether and why they come to identify with, merely comply with or resist engaging in that activity. As we will illustrate, the analytic scheme that we proposed in this chapter satisfies these requirements, thereby making the notion of identity as it relates to design at the classroom level both tractable and relatively concrete. In the following paragraphs, we first outline the basic tenets of the classroom design experiment methodology and consider how the methodology might be elaborated when the intent is to support and understand students’ identification with classroom mathematical activity as well as their development of significant mathematical ideas. We then present the interpretive scheme and clarify its key constructs. Finally, we place the interpretive scheme in a broader theoretical context by discussing its relation to alternative approaches that analyze the identities that students are developing across longer timescales, in the process taking account of issues of race, ethnicity and culture.