Teachers facilitate math talk in the classroom, but introducing a structured discussion format called the talking circle can influence opportunities for equitable student participation. Drawing on my reflections over the 2013–14 academic year and reviewing my detailed teaching notes and lesson plans, I take a close look at the structure of the talking circle and compare it with that of two other discussion formats that I commonly use in my classroom—traditional whole-class discussions and small-group discussions. I explore a mechanism that can potentially disrupt patterns of stratified classroom talk, with tradeoffs between frequency and spontaneity of student contributions. I hope teachers can use this information to begin experimenting with talking circles in their classrooms, finding versions that fit their school culture, and to reflect critically on the issue of promoting equitable classroom discourse. Education scholars increasingly embrace the definition of equity as the equal or fair distribution of opportunities to learn (e.g., Esmonde 2009). Adhering to this definition, I focus on equitable classroom discourse that involves equal access to participation for all students across all public conversation formats. Suppose that only the same three or four students contribute regularly to traditional whole-class oral discussions, a format in which the teacher organizes participation in large part by calling on students. The teacher’s facilitation, combined with the students’ automatic behaviors, may unwittingly result in a type of stratified classroom talk (more on this later) that constrains opportunities for all students to experience themselves as full participants in the mathematical discourse and reifies status hierarchies. Stratified classroom talk is the conversational pattern whereby, over time, certain students contribute more frequently than all other students to public discussions. I do not intend to place a value judgment on this classroom phenomenon per se. However, I consider it not optimal for learning for all students because of its tendency to reproduce social-status hierarchies and its effect on student identity—that is, how students see themselves as doers of mathematics. In my classroom community, students who identify strongly as mathematically competent tend to volunteer and contribute most frequently to whole-class discussions. These same students also demonstrate higher achievement on assessments and classwork throughout the school year. Conversely, students who do not perceive themselves as doers of mathematics—according to their journals, written surveys that I conduct throughout the year, and my ongoing personal conversations with students—tend to contribute less frequently during whole-class discussions, if at all. There are one or two exceptions to this trend, but it generally holds true. When I consider the class as a whole, my underlying assumption is this: Students’ self-perceptions, patterns of participation in whole-class discussions, and achievement and learning outcomes are linked and influence one another in important ways (see fig. 1). Further, minimizing stratified classroom talk disrupts status hierarchies and alters negative patterns of participation and achievement. The goal of this article is to present the talking circle as a format that helps minimize stratified talk. Before describing the talking circle and the mechanisms for implementing it in a math classroom, let me first provide a brief sketch of how my school’s broader vision of social justice and culture inspired the evolution of the talking circle, from an informal community-building measure to a pedagogical tool used for supporting the development of mathematical discourse. SOCIAL JUSTICE THROUGH CLASSROOM CULTURE June Jordan School for Equity is a small public high school located in a large, diverse urban district in the San Francisco Bay Area. More than 90 percent of the students are Latino, African American, and recent immigrant students—all from the working-class and low-income neighborhoods surrounding the school. June Jordan School for Equity is becoming increasingly well known for its value system—embodied in our slogan, “Get RICH!” (Respect, Integrity, Courage, Humility)—as well as our advanced framework for social justice pedagogy. The teachers share a vision of this framework and try to foster a process of “restorative justice” through our individual and collective practices. In addition, all the math teachers at June Jordan share the explicit goal of realizing the school’s vision of restorative justice by means of mathematics pedagogy specifically: We believe that our students’ success in school math influences and is influenced by broader sociopolitical narratives of power, oppression, and liberation of students of color from marginalized communities. Central to our school’s restorative-justice approach is a set of nonacademic rituals that are practiced by all teachers in their classrooms. One such ritual is the talking circle, in which the students’ desks are moved to form a circle and a speaker’s instrument (in my room we use a calculator) is passed around the circle and symbolizes the student’s right to speak publicly and freely. Passed along from student to student, the speaker’s instrument allows only the student holding it to speak and therefore provides equal opportunity for all students’ voices to be heard. Typically, there are two rounds of share-outs. On the first round, we ask students to respond to an initial prompt; on the second round, we ask students to either respond specifically to something that was said in the first round of share-outs or add something new to the discussion. In this way, the talking circle operates as an informal therapeutic practice that is carried out in a highly structured and mediated discussion format. At June Jordan School for Equity, we believe that providing a space for students to heal from trauma and harm that occurs within our community is an integral part of our work, and the talking circle is but one tool that we use in that effort. Before the 2013–14 school year, I had viewed talking circles as an important feature of the school culture. However, as a discussion format, it remained separate from the mathematical discourse. I occasionally put the talking circle on the agenda as a response to conflict, but at other times I used the talking circle as a positive check-in—an opportunity for students to voice their concerns and appreciations about the emerging culture of our particular classroom community. Students also suggested that we form talking circles in response to issues that come up in the moment. During one such impromptu, student-initiated talking circle, the idea of using this format for math was first introduced—by a student. At the end of this particular talking circle, as students rearranged their desks back to small groups, one student said to me enthusiastically, “We should have math class like this. Everyone can see everyone else.” I implemented the first mathematical talking circle the following day and began using it regularly as part of my routine teaching practice. Next I compare talking circles with traditional whole-class discussions and small-group discussions in terms of their structure, typical share-out patterns, and how the discourse produced within each format tends to either reproduce or disrupt existing status hierarchies in class. FORMATS FOR PARTICIPATION Various discussion formats in a mathematics classroom either enable or constrain certain patterns of participation. Looking at the formats that I routinely use, I found that in traditional whole-class discussions, the mathematically confident and high-status students offer limited share-outs. Small-group discussions tend to yield increased share-outs, yet again only by mathematically confident and high-status students. Talking circles, however, increase share-outs across all students and thus destratify classroom talk. Figure 2 presents schematic profiles of the three formats as well as an adaptation of the talking circle, unmediated, that I am working on to successfully implement in my classroom. In a mathematics talking circle, share-outs are students’ verbal contributions to public mathematical discourse. They vary in complexity, from “As the number of side increases, the area goes to pi . . . or 3.14” to merely a compliant statement such as “I agree with her comment about the area and sides.” Prompts may be direct or open-ended. A direct prompt is intended to draw out student responses to known-answer questions—for example, “Is this reflected image correct?” An open-ended prompt is intended to bring about student reflection and mathematical debate—for example, “Do you notice anything interesting about this triangle tiling pattern?” The following questions combine direct and open-ended prompting strategies: • “What did you notice about the tiling pattern?” • “What about this intersection here?” • “What about the fact that the sum of these six angles has to equal 360 degrees—what does that tell us about our original triangle?” Note that the different types of prompts—direct, open-ended, and a combination of the two—can be used in all formats. I do not believe there is one best type of prompt for use in the talking circle; teachers may consider and adapt them as needed for particular lessons. That said, I use open-ended prompts more frequently than any other kind of prompt in any format. Traditional whole-class discussions involve the teacher at the front of the class, prompting students with questions and fielding their responses. I use this format at least once during every class session to discuss warm-up problems, solutions to group tasks, and so forth. Although this format is useful for eliciting student ideas and generating strategies, I have noticed that the same three or four students tend to drive the conversation; and these are the very students regarded by their peers as the most mathematically capable (as indicated by their responses to “math sociogram” surveys that I conduct throughout the year). The traditional whole-class format typically yields limited individual share-outs by mostly the mathematically confident and high-status students. Small-group discussion and collaboration constitute the bulk of my lesson plans. Here, my main instructional strategy is to visit with each group to ask and respond to questions. I have noticed that this format typically yields increased individual share-outs (as compared with format A), yet still by mostly mathematically confident and high-status students in relation to other members in their group. Reflecting on my experiences and reviewing my notes, I conclude that formats A and B, combined, often result in classroom mathematical talk that is socially stratified. When I first began experimenting with the talking circle, I noticed that it led to an increase in the number of individual share-outs by all students, across all student cohorts, thus disrupting existing patterns of stratified classroom talk. When the talking circle was applied in a mathematics context, use of the speaker’s instrument increased and equalized student voice. The highly structured and mediated nature of the talking circle enabled all students to make a unique contribution to the whole-class discussion or agree to something that was already said. This approach has important implications for equity because equal opportunity for all students to contribute to the discussion is built into the format. Students do, in fact, have the option to pass on their turn in the circle, yet classmates discourage their peers from passing and encourage one another to participate, sometimes even calling out one another, stating that a student’s action is or is not “RICH!” Looking closely at the talking circle’s structure reveals a tradeoff between frequency and spontaneity of students’ share-outs, both of which are factors in equitable discourse. On the one hand, as mentioned earlier, the inherent structure of the talking circle provides equal opportunities to contribute to the classroom discussion. That is, putting aside the underlying quality of individual mathematical reasoning and looking only at the frequency of share-outs, I find that the talking circle supports equitable participation for all students because it destratifies classroom talk. On the other hand, given the highly mediated structure of the talking circle, this format decreases spontaneity—in some instances, it virtually eliminates it—and increases repetitiveness in share-outs. This structure also slows down the process of building ideas, at times reducing student motivation to become or stay invested in the task. This tradeoff has compelled me to focus on issues of equitable classroom discourse across the different formats that I use in my classroom. ADAPTATIONS AND FURTHER POTENTIAL Moving forward, I am challenging myself to find different adaptations of the talking circle that maintain its capacity to equalize student voice while at the same time increasing the spontaneity and complexity of share-outs by all students. For example, one adaptation I have been experimenting with involves modifying the rules of the speaker’s instrument to include a number of “speaker’s options,” such as requiring the choice to allow interjections or questions from classmates or the direction to whom the instrument goes to next. Another worthy target I have been pursuing, but finding quite challenging, is gradually eliminating the use of the speaker’s instrument and speaker’s options, with the goal of students becoming more familiar and comfortable with naturalistic forms of mathematical engagement and debate (i.e., an unmediated talking circle; see format D in fig. 2). I have also tried different adaptations of just the speaker’s instrument. For instance, sometimes I introduce the speaker’s instrument into both whole-class and small-group discussions to explore whether it can help destratify the mathematical talk in these setting. The structured discussion format of the talking circle harbors the potential for supporting mathematical debate that is accessible to all students. In this context, equity in mathematics education can be defined as unpredictable patterns of share-outs during any whole-class discussion (cf. Gutiérrez’s  and Esmonde’s  definitions of equity). I do not mean to suggest that teachers use talking circles instead of all other formats. Rather, they are one more tool to add to the teacher’s tool kit of discourse techniques for supporting equitable discourse in a mathematical classroom. Last, whereas most of this article focuses on the mechanisms and implications of the talking circle, I do not want to lose sight of the fact that general classroom culture plays a critical role in whether or not this format is successfully introduced into the classroom. I leave it to readers to explore how the talking circle might be best implemented in their classroom community to help minimize stratified talk and support mathematics learning for all students. REFERENCES Esmonde, Indigo. 2009. “Mathematics Learning in Groups: Analyzing Equity in Two Cooperative Activity Structures.” The Journal of the Learning Sciences 18 (2): 247–84. Gutiérrez, Rochelle. 2002. “Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda.” Mathematical Thinking and Learning 4 (2–3): 145–87. MARCUS HUNG, firstname.lastname@example.org, teaches ninth and tenth graders algebra and geometry at June Jordan School for Equity in San Francisco. He is a Math for America Master Teacher Fellow at the University of California Berkeley, and he collaborates with other educators to create and promote equitable practices in the classroom.