Valuing the Process: Working With Teachers Around

Chapter

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Valuing the Process: Working With Teachers Around Mathematics for Social Justice Lidia Gonzalez

W

henever I am asked the question Why mathematics for social justice?, my responses are always embedded in my experiences as a high school mathematics teacher in an “underperforming” New York City public school. It was during those experiences that I consistently saw the promise of education smack up against the social, economic, and emotional realities of the urban youth I taught. Though education was consistently held up as the “way out” of such realities, the education these students were receiving was not positioning them to be leaders—in their communities or in society at large—but instead, too often, it was limiting their opportunities to learn while at the same time blaming them for their lack of academic success. Shuffled into remedial classes, labeled as unable to succeed and often treated as such, many of these students succeeded in “living up” to the low expectations placed on them. Those who did graduate too often left with an educational preparation well below that of their peers in more affluent schools. As a high school mathematics teacher, I wrestled with the fact that the system seemed to consistently fail these students and that school mathematics often played a significant role in that failure. As the “gatekeeping” status of school mathematics became disturbing clear, I longed for an equitable mathematics pedagogy that addressed the needs of students from culturally, racially, linguistically, and economically diverse backgrounds (Wager 2008), but I found myself unsure of where to start. Worse yet, I found myself telling students that “hard work” would lead them to success, while increasingly not believing this to be true. My belief in the American meritocracy, the idea that everyone in this country has equal opportunity to succeed if they work hard enough, was quickly fading and being replaced with the troubling belief that my school, and the larger system, served to reproduce the stratified and unjust society in which we live, teaching “conformity to the social, cultural and occupational hierarchy” (Aronowitz 2004, p. 3).

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Interested in equity issues, I entered the doctoral program in urban education at the Graduate Center of the City University of New York. There, my teaching experiences were validated through readings by Anyon (1997) and Kozol (1991), two education scholars who highlight in vivid detail the inequitable and unjust teaching and learning conditions often found in urban schools. Coupled with these readings were insights by mathematics education scholars and activists. For example, D’Ambrosio (1990; see also D’Ambrosio, this volume) describes mathematics as the “imprint of modern society” (p. 20), suggesting that knowledge of mathematics is often a prerequisite for full and successful participation in society. Similarly, Moses and Cobb (2001) compare the struggle for access to algebra for marginalized students to the struggle for voting rights of African Americans during the Civil Rights movement. I was struck by the work of these scholars and others (see, e.g., Frankenstein 1983; Gutstein 2006; Skovsmose 1994; see also Frankenstein, Gutstein, Skovsmose, this volume) who positioned teaching mathematics for social justice (TMfSJ)— or more generally, critical mathematics—as a viable way to address social injustice through the meaningful study of mathematics. Increasingly invested in the empowering possibilities of TMfSJ for students and teachers alike, I began to view school mathematics not as an instrument for social stratification but rather as an instrument for student (and teacher) empowerment (Stinson 2004). No longer a mathematics classroom teacher, but now a mathematics teacher educator, I continue to seek ways to bring my ever-evolving understandings of TMfSJ to other mathematics teachers and teachers educators. My initial attempt to do so was to create and facilitate an extended professional development opportunity with a group of New York City high school mathematics teachers that had a specific focus on learning to teach mathematics for social justice. Basing my work on research derived from this group (see Gonzalez 2008, 2009), I begin this chapter by arguing for an emphasis on “process” when planning to teach others how to teach mathematics for social justice. I then describe characteristics of the TMfSJ group and our work together, highlighting my attempts at valuing teachers’ “voices,” my struggles in gaining legitimacy in the group, and my efforts of fostering teachers’ engagement. After that, I discuss specific successes and present new challenges derived from my ongoing reflections of my work with the TMfSJ group. I conclude with a cautioning about an unintended consequence for those who wish to assist others in learning how to teach mathematics for social justice.

Process vs. Product: What TMfSJ Means to Me In many ways, my understanding of TMfSJ is built upon the work of pioneers in the field such as those whose work appears in this volume. Drawing from these mathematics education scholars and others, I see TMfSJ as consisting of four components. Briefly, the first component is access to high-level quality mathematics instruction for all students, what Gutiérrez (2007) calls dominant mathematics:

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Mathematics that reflects the status quo in society, that gets valued in high-stakes testing and credentialing, that privileges a static formalism in mathematics, and that is involved in making sense of a world that favors the views of a relatively elite group (p. 39).

The second component is the recentering of the curriculum around the experiences of students from marginalized communities, as supported by research that posits a connection to students’ experiences as a necessary condition of successful teaching and learning (DarlingHammond, French, and García-Lopez 2002; Leonard 2007; Tate 1995). Third is the use of mathematics as a critical tool for understanding social life and injustices within it; this is often referred to as critical mathematics: Mathematics that squarely acknowledges the positioning of students as members of a society rife with issues of power and domination…[and] takes students’ cultural identities and builds mathematics around them in ways that address social and political issues in society, especially highlighting the perspectives of marginalized groups (Gutiérrez 2007, p. 40).

And the final, fourth component is using mathematics to actively advocate for social change towards a more equitable society. (For a full discussion of these four components see Gonzalez 2009.) In short, TMfSJ involves engaging students in the exploration of social justice issues that matter to them through mathematics. Herein lies the reason for the title of this chapter. One can find a growing number of TMfSJ resources, including readings, lessons, problem sets and activities (see table 9.1). However, TMfSJ is more than a collection of resources; it is a process that begins with students and ends with advocacy for change. In many ways, the title of this chapter refers to my shifting, ever-evolving perception about the nature of TMfSJ as a process and to my work with the teachers in the TMfSJ professional development group. During the group (described later in the chapter), the teachers and I developed a unit of study addressing a social issue through mathematics. While we valued the unit we developed, looking back on it now I believe that the process we undertook—reading about what social justice in mathematics might mean, identifying a social justice issue that might hold students’ interest, determining relevant standards-based mathematics concepts to explore the issue, and then crafting mathematics lessons that combined the two and advocated for change—was, in the end, perhaps even more valuable than the actual unit we created. Now I wish I had stressed the importance of the process more during our work together. It is this view of TMfSJ as a process that makes work with teachers (and their work with students) challenging (see, e.g., Gutstein, this volume). It would be much easier to present a collection of prepackaged lessons (though these do have their place) and instruct teachers to use these with—or perhaps, impose them on—their students. Instead, I began with the belief that part of our work about learning to teach mathematics for social justice should begin with modeling the very process of an education for justice and participation.

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Table 9.1 Resources for Teaching Mathematics for Social Justice Author/Editor/ Organization Eric Gutstein and Bob Peterson (2005)

Rethinking Schools

Title

Rethinking Mathematics: Teaching Social Justice by the Numbers

www.rethinkingschools.org

Type of Resource

Relevant Materials Contained

book

• Theoretical and practical articles about teaching mathematics for social justice • Sample lessons • Teaching ideas • List of resources

website

• Online magazine containing theoretical and practical articles about teaching for social justice • Links to other online resources • Lesson plans

Radical Math

www.radicalmath.org

website

• Theoretical and practical articles about teaching mathematics for social justice • Data sets • Charts and graphs • List of other resources

Jonathan Osler

The Algebra Project

A Guide for Integrating Issues of Social and Economic Justice Into Mathematics Curriculum. Available at: http://www. radicalmath.org/main. php?id=SocialJusticeMath

www.thealgebraproject.org

online guide

• Practical advice on how to weave social justice into mathematics lessons • Sample lessons • Theory regarding teaching mathematics for social justice

website

• Sample pages from a forthcoming mathematics for social justice textbook • Links to other online resources

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Our TMfSJ Group While working as a doctoral fellow on an unrelated study, I found myself in a large, comprehensive urban high school in New York City—the racial and SES demographics for its students were 55 percent Black, 41 percent Latina/o, and approximately 75 percent low SES. I contacted the assistant principal of Urban HS (a pseudonym, as are the teachers’ names), indicating my interest in working with mathematics teachers around issues of TMfSJ. With her approval, I contacted (through email) the roughly twenty-five teachers in the mathematics department, and I explained the TMfSJ professional development opportunity and participation requirements for the related study (see Gonzales 2008). Seven teachers, all women, chose to participate in the TMfSJ group. While all had worked at Urban HS, two had moved to more affluent schools by the time the group meetings began; they participated nevertheless. Considering the self-selective nature of the group, the teachers evidently were drawn to the ideas of TMfSJ and shared a somewhat similar vision regarding social change and the injustices faced by their students. The teachers, however, were not representative racially and culturally of those in their department, school, or the New York City school system as a whole. Six of the seven were women of color, while less than a third of the teachers at Urban HS self-identified as such. Moreover, although it has been documented that teachers in urban settings tend to differ from their students with respect to characteristics such as race/ethnicity, family background, and SES (Darling-Hammond, et al. 2002; Florio-Ruane 2001), the TMfSJ teachers were from somewhat similar cultural backgrounds as their students. Six of the women reported growing up in low-SES communities, four reported that their family had been on public assistance, and two had even graduated from Urban HS. The seven teachers and I met almost weekly at Urban HS for a total of ten two-hour group sessions over the span of several months. Sessions one through five consisted primarily of discussions guided by overarching questions based on readings we had done about TMfSJ. Beginning with the sixth session, our work turned to the development of a TMfSJ unit of study aimed at teaching high school level, standards-based mathematics while focusing on a social justice issue of importance to the teachers (and we hoped to their students). Many of the TMfSJ lessons and activities that we explored and discussed were derived from the text Rethinking Mathematics: Teaching Social Justice by the Numbers (Gutstein and Peterson 2005) and the website Radical Math (www.radicalmath.org). For an outline of our sessions, see the “Sample TMfSJ Program” on page XX.

Valuing Teacher Voices One of my goals as group facilitator of the TMfSJ group was to value teachers’ histories, experiences, and understandings in the same way that proponents of TMfSJ argue teachers should value the wealth of experiences and understandings students bring to class. Therefore, our first six sessions contained guiding questions meant to spark discussion and reflection while highlighting teachers’ “voices” and ideas. Additionally, the first session started with the question: What is a socially just society and how might we recognize one if we saw it? A heated, though respectful, debate ensued. Some teachers defined socially just societies as offering

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equal opportunities to all, while others indicated that everyone’s needs would be met, though perhaps through unequal treatment. Most teachers felt a need to work toward an equitable and just society while acknowledging that such a “utopia” might be an unreachable goal. In many ways, the teachers’ positions reflected those found in the literature (see, e.g., Rawls 2001; Young 1994). To have these positions put forth by the teachers, however, positioned their knowledge as valued and mirrored what the teachers might be expected to do when working with their own students. Rather than positioning herself or himself as the “expert” on a particular issue, the teacher steps back—while simultaneously leading—and listens to the experts (i.e., the students) within her or his own classroom (Freire 1970/1993). In other words, it is not possible to craft mathematics around the histories and experiences of urban youth if the teacher does not listen to and learn from these youth first.

Struggling for Legitimacy Comfortable with one another after working together over the past two to four years, the teachers sometimes contradicted each other, pushed one another through questioning, and doubted the position of others. As Vanessa explained, “There was never a time when people were not comfortable enough to express their own feelings and their own beliefs and even if people didn’t agree.” I, however, initially felt uncomfortable. Partly this was a result of my outsider status, but it was also because I came to TMfSJ after having been a high school mathematics teacher and so was advocating that the teachers implement a pedagogical approach I had not used myself. Though I actively worked doing so, I sometimes found myself hiding behind the words of the scholars we were reading, afraid to acknowledge my lack of experience as a classroom teacher who actually taught mathematics for social justice. This was especially true in the initial sessions. My perceived lack of legitimacy was compounded by the fact that I was privileged in ways that most of the participants and certainly their students (as well as my former high school students) had not been, and there was a good deal of guilt associated with this privilege. Though marginalized in other aspects of my life, I didn’t originally feel comfortable sharing those experiences. I underwent a struggle to reconcile my feelings as someone from a more privileged background, similar to what Howard (1999) describes in his book You Can’t Teach What You Don’t Know: White Teachers, Multiracial Schools. Nonetheless, becoming more comfortable with the teachers through time led me to admit my insecurities about my own teaching, specifically my lack of experience in TMfSJ. Being honest and open, however, was initially quite difficult. During one session, some teachers shared their opinion that students from marginalized communities need to be pushed academically more than their mainstream peers to gain equal footing among their more privileged counterparts. I acknowledged that at times I often pushed some students less, viewing it as an indication of my understanding of the difficulties a particular student might be facing outside of school. Jenna, one of the teachers from our TMfSJ group, commented that she knew many teachers who did the same because their realities differed from that of their students, and she stressed the importance of recognizing the problem and working to change it. Later, Jenna referred

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to me as a bridge person—a person whose history differs from that of her or his students but who attempts to understand students’ realities and work with students toward changing those realities into more ethical and just possibilities. At that moment, my place in the TMfSJ group felt legitimate. Interestingly, this did not occur when I was spouting academic jargon or facilitating a TMfSJ activity but rather after the humbling acknowledgement that I too had failed some of my own students.

Fostering Teachers’ Engagement I had intended from the start of my work with the teachers to share responsibility with them for how the group might run and what we might do during sessions. I asked the teachers several times if they had a reading, activity, or anything else that could be substituted for what I had originally planned. None did. At times, I set out options for how we might proceed, yet for the first five sessions the teachers deferred to me. In retrospect, I could have tried many things in these sessions to encourage the teachers to be more involved in the group’s development. The teachers, in turn, could have led our discussion of a particular text or facilitated an activity. I could have asked them to research TMfSJ and to bring in resources they found particularly valuable. Although the teachers were very active in the group sessions—sharing ideas and opinions, critiquing the assigned readings, and engaging in the mathematics activities—they did not take ownership of the structure of the workshop as I had initially envisioned until the sessions in which we were developing the mathematics unit: sessions 6–10. In these sessions, teachers did take control, selecting the social issue to be addressed—How well does Urban HS prepare (or not) its students for the future?—and the manner in which to address it. The teachers decided to divide up the work in co-developing the mathematics unit, thus most of our time in these sessions was spent in small groups planning lessons and activities. During these sessions, I worked within one of the groups just like everyone else. The teachers took ownership of both the unit and these sessions. Monica explained: Everyone was interested in it, and we got to pick out our own topic rather than you giving us one. So I think that motivated everybody to say, “Okay, I want to do this, so I’m going to take this part of the project and run with it.”

In earlier sessions, I brought in materials for us to use, but in these later sessions it was the teachers who brought in materials, including data, activities, articles, and other information they found useful for the unit. I recall walking into the room where we met prior to session 7. Vanessa and Reina were engaged in a heated discussion of some statistics they had found online comparing Urban HS to a specialized New York City school in terms of students’ plans after graduation. Vanessa was livid at the fact that few students had listed college, and even fewer a four-year college, as their future plans, and that well over 50 percent had selected “I don’t know.” In a raised voice Vanessa said, “Can you believe this? Can you?” She pleaded with the others, “We have to do something about this.” Her findings were contrasted with those brought in by Reina, where over 95 percent of students in a specialized high school had chosen going to four-year college as their future plans. Vanessa and Reina’s tones of voice, facial expressions, gestures, and words made clear the emotional impact of these statistics had on them, and highlighted the passion that

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teachers brought to the development of the unit. They were genuinely angered and appalled by what they had found, and they vowed to change this particularly troubling statistic. Reflecting later on the roles each of us took over the course of the group, I noticed that the later sessions in which we worked on the unit were not rigidly planned ahead of time and that the “scheduled” activity for those days was simply “work on project.” This openness of scheduled activity, I believe, accounts for why the teachers were eager to take responsibility for these sessions. The lack of a rigid plan in these later sessions implicitly (if not explicitly) suggested that I intended to draw upon the collective histories, experiences, and understandings of the teachers not only to determine what the mathematics unit might be but also to organize how it would be developed. In many ways, for the teachers to take responsibility in earlier sessions would have meant disrupting the “plan” I had conceived, and thus the balance of perceived power in the group. I continue to struggle with finding the right balance between developing a plan to introduce teachers to unfamiliar material and establishing an openness, with teachers, of that very plan.

Unit of study As noted before, the teachers’ concerns about the educational opportunities afforded their students, coupled with their desire to create a relevant mathematics unit of study that students could be on the same side of, led them to ask: How well does Urban HS prepare its students for the future? This question became the overarching issue to explore through mathematics in the unit of study, as the teachers believed that improving the future possibilities of success for Urban HS graduates was an attainable goal their students would be eager to pursue. Reina noted, “I loved the unit we decided upon because it is something practical, that [students] . . . could DO something about.” Drawing on a database from the New York City Department of Education (http://schools. nyc.gov) Vanessa, Reina, and I developed lessons and problem sets that compared Urban HS to two similar open admissions, comprehensive high schools as well as with one specialized high school; we used statistics such as graduation rates, standardized test scores, incidences of violence, and the number of advanced placement courses. Taking up Freire’s (1970/1993) concept of critical knowledge, we explored “not merely how statistics are non-neutral, but why, and in whose interest” (Frankenstein 1983, p. 324), as we highlighted misleading statistics, determined what could and could not be answered by the available data, and outlined whose interests might be served by the data. Nyo and Monica worked on developing lessons and activities that explored how an Urban HS graduate might fare when applying to various types of colleges and how prepared she or he would be to pursue various majors (mathematics, the sciences, liberal and performance arts, etc.). Melissa and Jenna developed mathematics lessons about financial preparation, based on the belief that Urban HS was not preparing students to be financially aware and secure in the future. The teachers felt students could share their findings with other students, parents, administrators, teachers, and other community stakeholders in order to demonstrate Urban HS’s ability to prepare students for the future while advocating for changes to improve that preparation.

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Therefore, Ellen developed a daylong program of activities, billed as a forum for change called Success Day, and envisioned developing opportunities for the school community to work together to arrive at and implement solutions for improving the future possibilities of success for Urban HS graduates.

Where’s the math? An oft-repeated critique of TMfSJ is Where’s the math? In this case, the teachers did not raise this critique as a concern, and the unit we created relied on mathematical content (e.g., statistics and finance) that is often found in many of the materials available for TMfSJ. The group’s focus on these content areas might have resulted from a reliance on statistical and financial activities during our group sessions. Had we a more varied collection of lessons as examples, perhaps we would have focused on different, more rigorous, content. The issue of mathematical rigor in TMfSJ lessons has been discussed by Brantlinger and colleagues (2007), who not only question whether TMfSJ can be taught using advanced mathematics but also whether it might further marginalize some students by creating a “separate” curriculum for those already on the margins. As a rebuttal, advocates of TMfSJ point to the ever-increasing number of TMfSJ materials that rely on upper-level mathematics (see, e.g., McCoy 2008; Gutstein, this volume). Additionally, Wamsted and G. Powell (this volume) challenge the idea that rigorous mathematics and TMfSJ are incompatible through their work with high school and college students, respectively. (For examples of TMfSJ in the younger grades, see Peterson and Stocker, this volume.)

Successes and Challenges In the discussion that follows, I intertwine some of the successes I believe were achieved within the TMfSJ group as well as the challenges present to mathematics teacher educators who might undergo similar work. It is important to note, however, that the discussion is not intended to be the basis of some prescriptive, pedagogical methodology for all others to follow, but rather as a demonstration of my ongoing critical reflections as I continue to explore with mathematics teachers the empowering possibilities of TMfSJ.

Teachers’ Support for and Developing Understanding of TMfSJ Our TMfSJ group was somewhat unusual in that the teachers in it were acutely aware from the beginning of the injustices that their students faced as a result of having, in most cases, faced them themselves. Many saw themselves as successful, despite a lack of equal opportunity, because of their reliance on education, though they were cynical about the education that their students received. For instance, Melissa, in her initial interview, stated: I believe that sometimes the curriculum is set up towards the government. Obviously, if they’re picking the curriculum, they’re picking what they want you to learn. They want to shape you in the way they want to shape you. [Urban HS] is just that—we just want to produce servants. We just want to produce someone who will be the serving class. It was not geared toward producing these high-level, educated, intelligent individuals.

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Overall, the teachers believed that their students were not being adequately served by a system in which the teachers were a part. In the end, this struggle led two of the teachers to leave Urban HS, adamant about the lack of opportunity to learn (and teach) at Urban HS. Despite their beliefs about Urban HS (and similar such schools) the teachers’ initial view about social injustice was that it could be addressed through school better than in school. Nevertheless, as they were introduced to TMfSJ and the idea that teaching mathematics is a political act, this view began to change. They began to see mathematics as non-neutral and as a tool for furthering particular positions: “I feel [TMfSJ] would look more like a way to use math to make arguments about our point of view” (Reina). Eventually, the teachers came to define TMfSJ, in part, as “using various mathematical topics to further gain knowledge and understanding of the world around [us]” (Jenna). The concept that mathematics could serve as a tool for understanding social life was a key element in the teachers’ developing definitions of TMfSJ. Melissa explained that TMfSJ is “using math to show the injustice in the world and how things—how mathematically you can view some of the things that go on, some of the negative things that go on . . . that you are so upset about.” The teachers also understood the value of being able to understand these injustices and talk about them in the socially and politically valued language of mathematics. Collectively, the teachers’ comments illustrated a belief that engaging students in TMfSJ lessons would result in increased awareness and social change, though at times limiting change within the school or neighboring community. The teachers, to varying degrees, also began to see student empowerment as a goal. As Monica noted during her exit interview, “[TMfSJ not only shows] things aren’t right in the world [but also] what [students] can do to make it better using math.”

Teachers’ Evolving Identities Initially, the teachers described their roles narrowly as teachers of what Nyo called straight mathematics (i.e., dominant mathematics). Nyo, for example, took a very “traditional” approach to teaching mathematics, initially calling the incorporation of social issues as a distraction. With time, however, teachers’ views began to shift: I think [participation in the group] changed definitely how I see myself as a teacher in that . . . it’s broadened what I thought teaching was from a very narrow field . . . I really just thought it was you have to do A, B, C for the test, and that’s it, and that’s your job. (Reina)

Throughout our work together, most of the teachers began to express a desire to affect change in the broader society through mathematics, noting they did not initially realize the power teachers have to do so.

Teachers Viewing Social Justice as a “Hook” Though most of the teachers felt that TMfSJ had the possible benefit of increasing students’ engagement in learning mathematics, Nyo sometimes described this possibility of increased engagement as TMfSJ’s most valuable characteristic: “I loved the use of the cartoons that illustrated political issues and how it tied into the data that was later handed out [see, e.g., Frankenstein 2010]. Great introduction to the hardcore math topics.” That Nyo saw TMfSJ as something of

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a “hook” to gain students attention so that they could later learn real mathematics leads me to question her perceptions of TMfSJ as not “hardcore” mathematical learning, an issue we should have addressed more directly in our group. Though none of the teachers responded exclusively to TMfSJ in this way, that Nyo did so sporadically reflects how “traditional” notions of what mathematics is are engrained in many teachers’ beliefs. As teacher educators, working through these traditional beliefs with teachers should be a vital component of our work.

Teachers Questioning Paralysis vs. Empowerment Some teachers feared that examining social issues would serve not to empower students but to paralyze them into inaction, though with time, these fears began to subside: I often worried that making students aware of the injustices they are faced with would cause them to throw in the towel or take on an attitude of self-defeat. But after watching the video [about the school to prison pipeline] [the New York Civil Liberties Union, see http://www.nyclu. org/schooltoprison], I realize that students are fully aware of the injustices they face each day, and all they need is some empowerment, backing and the means to have their issues addressed. (Ellen)

I believe the teachers’ initial fears about paralyzing students and their focus on raising awareness more than on social change stemmed from the fact that while we spoke about how students might advocate for change following certain activities, we ourselves did not do so. In the process of modeling TMfSJ, I failed to model a vital component: advocacy for change. Gutstein (2006) notes, “A crucial aspect of mathematics for social justice is what students do with the mathematics” and that education is about engaging students in “struggles for their own emancipation” (p. 14). The teachers discussed but never experienced the advocacy component of TMfSJ, an important distinction highlighted by Reina’s feedback provided in her exit interview; she argued that sessions could have been improved with a focus “more on how we could address the inequities once we do a lesson.”

Teachers Implementing TMfSJ While seeing added value in TMfSJ, the teachers simultaneously felt tied to the mandated curriculum and pacing guide they were instructed to follow. The teachers therefore indicated they could only implement TMfSJ activities sparingly, using them to supplement the curriculum if “there was extra time [to do so]” (Monica). Of greater concern was the fear that the administration, and in particular the parents, would not be supportive of TMfSJ. Melissa, in her exit interview, explained: “The drawback is: Is it on my pacing guide? Does it relate to what I am supposed to do?” Jenna added, “Some things you don’t want your kids going home and saying,” noting a fear of “having a parent that is against that.” All group members with the exception of Nyo (who was tenured and the most experienced) stated that a lack of support would limit their use of TMfSJ. Vanessa, with less than two years of teaching experience, said in her initial interview that she didn’t want to “get too politicized” in her teaching, “especially when I don’t have tenure.” Such concerns point to the reality that “the capacity for pedagogic ‘dissent’ will depend upon [one’s] school context” (Noyes 2007, p. 126) and that buy-in from the school administration

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should be sought out, especially when working with untenured teachers. With buy-in, teachers would feel supported in their efforts to incorporate TMfSJ, as evidenced by the increasing number of social justice–themed schools where students are regularly engaged in such work. Citing a (perceived) lack of basic mathematical skills of their students, some of the teachers felt students might not be ready for TMfSJ activities, and they saw TMfSJ activities as opportunities for students to apply the mathematics they had already learned as opposed to opportunities for learning new mathematical content. Gau (2005) also found that teachers often believed that students needed to first learn or “know” the mathematics before they used mathematics to learn about or analyze a social issue. The pervasiveness of this belief indicates that teacher educators need to explicitly deal with the issue by providing examples of and developing TMfSJ lessons with teachers that introduce new mathematical content to students. It is important to demonstrate that TMfSJ can be used not only for the reinforcement and application of previously learned content but also for learning new content. Finally, the teachers in general were drawn to those TMfSJ activities that they believed all students could be on the same side of, expressing concern about bringing controversial topics up in their classrooms. “I would love to do that in one of my classes,” Vanessa said of one of the social justice activities; however, showing her hesitation, she added, “but you have to deal with the discussion that comes out of that.” All of the teachers, to varying degrees, expressed concern about discussions that may arise when certain controversial topics, particularly race and racism, are brought into the classroom. Critical mathematics may engender emotional discussions where strong feelings are put forth. As a teacher, preparing for such discussions is important, and so preparing teachers to deal with controversial classroom discussions is a vital component of the work of teacher educators who wish to teach others how to teach mathematics for social justice.

A Concluding Cautioning: The Unintended Consequence of Reina Upon learning about the possibilities of TMfSJ, Reina felt a growing responsibility to her students: So this group kind of made me … more aware that I need to be more socially active, that, you know, I need to be part of effecting change … I have more of a sense of like the same thing I was saying about the kids, like ownership, like I have control over what could happen, you know, but I’m choosing not to exert that control and that power. So these sessions kind of made me like, no, I have to. I have to, because I have that responsibility as someone who knows.

Yet the responsibility placed upon her became too heavy to carry: To make math relevant, to create students who are socially active in what occurs in their lives feels like a huge responsibility. I have always done what was required because it was required. To create for my students something I never needed for myself seems like too much of a stretch on top of everything else that is expected of a teacher.

While all but one of the teachers actively struggled with the promise of TMfSJ clashing with the realities of their school setting, Reina was most affected. She explained, following one session, that

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she could not reconcile her position as a member of the system that was failing her students. She recognized the power of TMfSJ to change student realities and yet felt unable to implement it given the curriculum and other constraints. Close to tears, she explained that she was considering leaving teaching all together as she could not teach mathematics in a relevant, meaningful way as with TMfSJ. My feelings of defeat paralleled those Reina had just shared. I began the group excited to share TMfSJ with teachers who could act on these ideas with students working towards social change. It was supposed to be empowering and transformative. It certainly was not supposed to drive a dynamic educator away from teaching because of the pressure to teach in ways she began to see as relevant and necessary but felt she could not put into practice. Reina’s experience paralleled that which the teachers feared would occur in their students. Instead of empowerment, they worried that students would be paralyzed by the injustices being explored. Just as student paralysis can be challenged through the creation of opportunities for action and empowerment, so too can teacher paralysis be challenged in this same way. This challenge goes back to the fourth component of TMfSJ: action towards change. While Reina saw the promise of TMfSJ, she was unable to envision this pedagogy as viable in her school context. Why should she? After all, she had not witnessed its success within her classroom, in part, because she was not supported through implementation. I take responsibility for not going into these teachers’ classrooms to provide the support necessary to implement what for them was a new and radical pedagogy. In the end, thankfully, Reina decided not to leave teaching. Instead, she moved to a middle school where she expected to have more freedom to address issues that her students are facing through mathematics.

REFERENCES Anyon. Jean. Ghetto Schooling: A Political Economy of Urban Educational Reform. New York: Teachers College Press, 1997. Aronowitz, Stanley. “Against Schooling: Education and Social Class.” Social Text 22, no. 2 [79] (2004): 13–35. Brantlinger, Andrew, Eric Gutstein, Patricia Buenrostro, and Swapna Mukhopadhyay. Teaching Mathematics for Social Justice: Is There Math There? (2007). Paper presented at the annual meeting of the National Council of Teachers of Mathematics, Atlanta, Ga. D’Ambrosio, Ubiritan. “The Role of Mathematics in Building a Democratic and Just Society.” For the Learning of Mathematics 10, no. 3 (1990): 20–23. Darling-Hammond, Linda, Jennifer French, and Silvia García-Lopez (eds.). Learning to Teach for Social Justice. New York: Teachers College Press, 2002. Florio-Ruane, Susan. Teacher Education and the Cultural Imagination: Autobiography, Conversation, and Narrative. Mahwah, N.J.: Lawrence Erlbaum Associates, 2001. Frankenstein, Marilyn. “Critical Mathematics Education: An Application of Paulo Freire’s Epistemology.” Journal of Education 165, no. 4 (1983): 315–39. Frankenstein, Marilyn. Learning Activities Using “The Yes Men Fix the World” (2010). Retrieved from http:// theyesmenfixtheworld.com/guide/Main_Page. Freire, Paulo. Pedagogy of the Oppressed, trans. by Myra Bergman Ramos. New York: Continuum, 1993. (Original work published 1970) Gau, Tonya Rae. Learning to Teach Mathematics for Social Justice. Doctoral dissertation, University of Wisconsin–Madison, 2005. Retrieved from ProQuest Dissertations & Theses http://gradworks.umi. com/31/86/3186083.html. (AAT 3186083)

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Gonzalez, Lidia. Mathematics Teachers as Agents of Change: Exploring Teacher Identity and Social Justice through a Community of Practice. Doctoral dissertation, City University of New York, 2008. Retrieved from ProQuest Dissertations & Theses http://gradworks.umi.com/33/25/3325435.html. (AAT 3325435). Gonzalez, Lidia. “Teaching Mathematics for Social Justice: Reflections on a Community of Practice for Urban High School Mathematics Teachers.” Journal of Urban Mathematics Education 2, no. 1 (2009): 22–51. Retrieved from http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/32/13. Gutiérrez, Rochelle. “(Re)Defining Equity: The Importance of a Critical Perspective.” In Improving Access to Mathematics: Diversity and Equity in the Classroom, edited by Na’ilah S. Nasir and Paul Cobb, pp. 37–50. New York: Teachers College Press, 2007. Gutstein, Eric. Reading and Writing the World with Mathematics: Toward a Pedagogy for Social Justice. New York: Routledge, 2006. Gutstein, Eric, and Bob Peterson (eds.) Rethinking Mathematics: Teaching Social Justice by the Numbers. Milwaukee, Wis.: Rethinking Schools, 2005. Howard, Gary R. We Can’t Teach What We Don’t Know: White Teachers, Multiracial Schools. New York: Teachers College Press, 1999. Kozol, Jonathan. Savage Inequalities: Children in America’s Schools. New York: HarperPerennial, 1992. Leonard, Jacqueline. Culturally Specific Pedagogy in the Mathematics Classroom: Strategies for Teachers and Students. New York: Routledge, 2008. McCoy, Leah. “Poverty: Teaching Mathematics and Social Justice.” Mathematics Teacher 101, no. 6 (2008): 456–61. Moses, Robert P., and Charles E. Cobb, Jr. Radical Equations: Math Literacy and the Civil Rights Movement. Boston, Mass.: Beacon Press, 2001. National Center for Educational Statistics. School and Staffing Survey (SASS) (no date). Retrieved from http:// nces.ed.gov/surveys/sass. New York City Department of Education. Homepage (no date). Retrieved from http://schools.nyc.gov. New York Civil Liberties Union. School to Prison Pipeline campaign (no date). Retrieved from http://www. nyclu.org/schooltoprison. Noyes, Andrew. Rethinking School Mathematics. London, United Kingdom: Sage, 2007. Rawls, John B. A Theory of Justice. Cambridge, Mass.: Harvard University Press, 1971. Skovsmose, Ole. Towards a Philosophy of Critical Mathematical Education. Dordrecht, The Netherlands: Kluwer, 1994. Stinson, David W. “Mathematics as ‘Gate-Keeper’?: Three Theoretical Perspectives that Aim Toward Empowering All Children with a Key to the Gate.” The Mathematics Educator 14, no. 1 (2004): 8–18. Tate, William F. “Returning to the Root: A Culturally Relevant Approach to Mathematics Pedagogy.” Theory Into Practice 34 (1995): 166–73. Tate, William F. “Race, Retrenchment, and the Reform of School Mathematics.” In Rethinking Mathematics: Teaching Social Justice by the Numbers, edited by Eric Gutstein and Bob Peterson, pp. 31–40. Milwaukee, Wis.: Rethinking Schools, 2005. Wager, Anita Andrews. Developing Equitable Mathematics Pedagogy. Doctoral dissertation, University of Wisconsin–Madison, 2008. Retrieved from ProQuest Dissertations & Theses http://gradworks.umi. com/33/27/3327857.html. (AAT 3327857) Young, H. Peyton. Equity in Theory and Practice. Princeton, N.J.: Princeton University Press, 1994.

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APPENDIX: SAMPLE TMfSJ PROGRAM Summary of Group Sessions NOTE: Sessions will include a discussion of readings for that day. (The sessions may be modified as needed to incorporate participants’ ideas and suggestions.) Each session will also include one or more activities and/or lessons that combine social justice and mathematics.

PRE-SESSION (READINGS) 1. Tate, William F. “Race, Retrenchment, and the Reform of School Mathematics.” In Rethinking Mathematics: Teaching Social Justice by the Numbers, edited by Eric Gutstein and Bob Peterson, pp. 31–40. Milwaukee, Wis.: Rethinking Schools, 2005. 2. Gutstein, Eric, and Bob Peterson. “Introduction.” In Rethinking Mathematics: Teaching Social Justice by the Numbers, edited by Eric Gutstein and Bob Peterson, pp. 1–6. Milwaukee, Wis.: Rethinking Schools, 2005.

SESSION 1 Leading Questions: What does teaching mathematics for social justice (TMfSJ) mean in the research literature and for us as a group? Summary of Session: Introductions; discussion of what mathematics for social justice means to the participants and in the research literature; explore how these definitions of mathematics for social justice affect or should affect our roles as teachers; exploration of group and participants’ goals and their participation Activities: Explore political cartoons through a mathematics for social justice lens* and problem on systems of equations** Homework: Due session 2: 1. Martin, Danny Bernard. “Hidden Assumptions and Unaddressed Questions in the Mathematics for All Rhetoric.” The Mathematics Educator 13, no. 2 (2003): 7–21.

SESSION 2 Leading Questions: How do our identities, histories, and privilege affect how we teach? Summary of Session: Discussion about our own identities and beliefs; exploration of our own assumptions (sharing key moments) through the reading of scenarios, participation in activities, and questioning one’s assumptions Activities: World Wealth Simulation & Ten Chairs of Inequality** Homework: Due session 3: 1. Rethinking Schools Editors. “Still Rethinking Our Classrooms: Creating Classrooms for Equity and Justice.” Rethinking Schools 21, no. 3 (2007): 10–12. 2. Gutstein, Eric. Reading and Writing the World with Mathematics: Toward a Pedagogy for Social Justice, pp. 1–19. New York: Routledge, 2006.

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SESSION 3 Leading Questions: What are/should be our roles as teachers? How can we focus our teaching on the experiences of students while respecting and valuing their backgrounds? Summary of Session: Discussion will center on our roles as teachers; how we have envisioned them and how this does or does not vary from what we do and what the research suggests for us to do Activities: Activities from Geometries of Inequality & Racial Profiling Unit* Homework: Due session 4: 1. Turner, Erin E., and Beatriz Font Strawhun. “With Math, It’s Like You Have More Defense.” In Rethinking Mathematics: Teaching Social Justice by the Numbers, edited by Eric Gutstein and Bob Peterson, pp. 81–87. Milwaukee, Wis.: Rethinking Schools, 2005.

SESSION 4 Leading Questions: What does TMfSJ look like? Summary of Session: A look at practical ideas and suggestions for TMfSJ Activities: Who does the lottery benefit?** Homework: Due session 5 1. Dean, Jana. “The Future of Driving: 8th Grade Algebra Meets Rising Gas Prices and Peak Oil.” Rethinking Schools 21, no. 2 (2006/2007): 40–46.

SESSION 5 Leading Questions: What beliefs do we hold about our students? What topics/issues do they face which we might structure our unit around? Summary of Session: Exploring teacher beliefs about students, their abilities, likes, dislikes, backgrounds, and how these can affect pedagogy Activities: Home Buying while Black or Brown and Study of Unemployment Rates* Homework: Due session 6 1. Find and bring in materials and data that might aid in our unit development 2. Osler, Jonathan. A Guide for Integrating Issues of Social, Political, and Economic Justice into Mathematics Curriculum. Retrieved from http://www.radicalmath.org/main. php?id=SocialJusticeMath.

SESSION 6 Leading Questions: How can we prepare to develop a unit of study? Summary of Session: Brainstorming and deciding on a topic for our unit of study; outline key ideas and characteristics of the unit of study. Activities: Integrals and Equity* Homework: Due session 7: 1. Work on unit of study

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SESSION 7 Summary of Session: Work on the unit of study Activities: Health Trends and Patterns in New York** Homework: Due session 8: 1. Work on unit of study 2. Gutstein, Eric. Reading and Writing the World with Mathematics: Toward a Pedagogy for Social Justice, pp. 129–64. New York: Routledge, 2006.

SESSION 8 Summary of Session: Work on the unit of study Homework: Due session 9: 1. Brantlinger, Andrew. “The Geometry of Inequality.” In Rethinking Mathematics: Teaching Social Justice by the Numbers, edited by Eric Gutstein and Bob Peterson, pp. 97–100. Milwaukee, Wis.: Rethinking Schools, 2005.

SESSION 9 Leading Questions: What are some issues we might face in trying to implement our unit of study? Summary of Session: Discussion about student resistance, school structures and other factors that may impact the implementation of the unit; course evaluations; final thoughts regarding group

SESSION 10 Final Thoughts and Next Steps Summary of Session: Take turns presenting pieces of the mathematics unit. Discussion about what we have learned from the group sessions and how we might be able to continue to support the members of our community of practice. Brainstorming ideas for how we might be able to share what we have learned with others at the school.

*These activities are from: Gutstein, Eric, and Bob Peterson (eds.) Rethinking Mathematics: Teaching Social Justice by the Numbers. Milwaukee, Wis.: Rethinking Schools, 2005. **These activities are from: Radical Math. (n.d.). Homepage. Retrieved from http://www.radicalmath.org/main.php?id=about.