This symposium addresses the topic of equity by presenting three complementary research views about student participation in learning mathematics. Conceptualizing equity in this way, in terms of opportunities for participation in classroom mathematical activity, attends specifically to learning in relationship to broader issues of race, power and identity. The presentations focus on the participation of racialized students in mathematics, in various ways, at different levels of scale. Author 1 examines how various opportunities provide students with different opportunities to learn mathematics. Author 2 analyzes racialized power dynamics within middle school cooperative learning groups. Author 3 focuses on individual trajectories of participation of high school students in and beyond their mathematics class.

1) Teaching with High “Participation Differential” in Urban High Schools

     This study reports findings from a project organized around professional development and culturally relevant mathematics pedagogy (CureMap): 1) teaching mathematics for understanding (Hiebert & Carpenter, 1992);  2) “centering” (Tate, 2005) instruction on students; and 3) developing students’ critical consciousness about (Skovsmose, 1994) and with (Gutstein, 2004) mathematics. Student participation in learning mathematics is an essential theme that undergirds CureMap. Teaching for understanding implies that students learn by engaging in sense-making of problematic situations. Similarly, while “centering” is often taken to mean using familiar contexts in instruction, an additional interpretation is the creation of classroom participation structures so that students can be central participants.
    Six mathematics teachers at two high schools in low-income, urban communities were observed over two years, for a total of 106 lessons. The cognitive demand of each lesson’s mathematical task was categorized (Henningsen & Stein, 1997); the type and duration of classroom participation structures was qualified (Weiss, Pasley, Smith, Banilower, & Heck, 2003), and student engagement was rated (Kitchen, DePree, Celedón-Pattichis & Brinkerhoff, 2007). Our analysis focuses on each lesson’s “participation differential,” which we define to be the signed arithmetic difference between the lesson’s student-centered proportion and the teacher-centered proportion. We highlight the case of the teacher with the most consistently high participation differential and examine relationships with cognitive demand and student engagement. We connect these quantitative findings with the orienting framework of CureMap, making specific recommendations about implications for teacher education.

2) Power and Positioning: Examining the racialized dynamics of cooperative learning
    As students interact in classroom practices, their social identities and interactions serve to position them as certain kinds of people (Gee, 2000). These positions construct power hierarchies that can lead to marginalization during cooperative learning. Because mathematics learning is a racialized experience (Martin, 2006), it is important to question how such positioning is related to race (Esmonde, 2009a). In this paper, we examine power dynamics in cooperative learning and how they impact learning in the context of reform-oriented instruction by constraining student participation.

     Drawing on videotape data from a series of classroom observations, we analyzed the power dynamics of cooperative learning during two different Grade 7 lessons. We analyzed the activity structure, the work practices students developed to accomplish mathematical tasks (Esmonde, 2009b), and the positions that students took up or contested. Work practices and positioning influenced the students’ opportunities to learn (Nasir & Hand, 2008). Finally, we considered students’ racialized identities and identified patterns in the way students were positioned. Findings demonstrate the dialogical nature of positioning and the ways in which racialized students were marginalized by other students. Despite this power dynamic, we found that marginalized students found particular moments to engage in agentic ways (Lewis & Moje, 2003). We conclude with a discussion about whether and how the observed positioning and marginalization were related to race and raise questions for future analysis.

3) Analyzing Practice-Linked Identities: Trajectories of participation within and across the mathematics classroom

     Students negotiate trajectories of participation (Drier, 1999) within the mathematics classroom, and across school and other contexts. These trajectories represent different timescales of activity (Lemke, 2000), which offer multiple lenses on who a learner is becoming with respect to the various practices in which they engage. Analyses of student participation in mathematics classrooms have led to important insights into how learners come to exercise agency around mathematical sense-making, yet have not necessarily illuminated whether they also develop practice-linked identities (Nasir & Hand, 2008). A practice-linked identity means that a learner views her participation in a practice (learning mathematics) as consistent with the kind of person she is becoming. We have found it productive to capture participation across contexts to analyze students’ practice–linked identities.
    This paper reports on an investigation of the trajectories of participation of two racialized high school students within and across their mathematics classrooms. These students entered their mathematics classrooms with weak identities as mathematics learners but came to engage powerfully in the mathematical activity. The findings illustrate how structures in mathematics classrooms provided opportunities for students to leverage aspects of their participation from activities outside of the classroom to more fully participate in their classroom learning.  

    All three papers offer new ways to extend previous analyses of student participation in mathematics (Boaler & Greeno, 2000), with a focus on racialized students. This session will be of interest in that the broader theme of equity is addressed here in new and exciting ways. The session will be organized to maximize session participants’ opportunities to interact with each other about these ideas. We will have a comment board, on which participants can write comments or questions that emerge during the session. The final 30 minutes of the session will be dedicated to discussion with the session participants, around any themes that emerge on the board, as well as on these central questions:

1)     How do these presentations spark different conceptualizations of equitable participation?

2)     What do these findings suggest about equitable mathematics teaching or pedagogy?

3)     How do session participants approach analysis of student participation and classroom participation structures?