Victoria Hand

Exploring Sociocultural Perspectives on Race, Culture, and Learning

This article explores the potential uses and extensions of sociocultural theoretical perspectives for integrating and further developing research on race, culture, and learning. Two bodies of literature are discussed and synthesized: (1) sociocultural theory and (2) studies on race, culture, and learning. The article proposes how a sociocultural lens might provide insight and suggests new lines of research on issues of race, culture, and learning. The authors argue for the extension of each of four lines of research in the sociocultural tradition: a concern with multiple levels of analysis, cultural practices as a unit of analysis, tools and artifacts as mediating action, and learning as shifts in social relations. In doing so, the authors raise critical questions for the field of education to consider.

Culture and Mathematics in School: Boundaries Between “Cultural” and “Domain” Knowledge in the Mathematics Classroom and Beyond

principles and procedures in mathematics. The research on the implementation of social justice tasks in the mathematics classroom has also prompted questions about the difficulty of balancing discussions of complex social issues with the mathematics. For example, Bartell (2006) reports that teachers in her professional development course on social justice in mathematics found it challenging to move flexibly between the mathematics content and conversations about social injustice. Gutstein (2006) also admits that in his class, he had to occasionally forgo opportunities to pursue mathematical investigations to deepen the conversations about social issues. Because students often hold strong perspectives about social injustice and these can trigger emotional responses, it is clearly important for teachers to be able to adeptly and sensitively guide students back to the mathematics at hand. We wonder, then, if teachers are being prepared and have bargained for doing this multifaceted work. Also, can social justice activities stemming from students’ social realities sufficiently drive students’ development of sophisticated mathematics knowing across an extended period of time? Or should they mainly serve as supplemental materials to the existing mathematics curriculum, used to convince students that learning mathematics is relevant and even critical to improving their lives and the lives of others? A second challenge is in thinking about how one might apply these approaches in racially or ethnically heterogeneous classrooms. This is an especially salient issue for Funds of Knowledge and the Algebra Project, as to some degree, these approaches assume a degree of coherence within the communities that are being served. How might these approaches be adapted in classrooms where students are from multiple communities? What might it mean to draw on students’ experiences in such multicultural classrooms? This may be less of an issue with social justice approaches, but it still leaves more to be negotiated with and between students in classrooms where there is a wide range of race, class, or socioeconomic groups represented. How are teachers to deal with kids from communities that do not share a social justice perspective or see social justice in terms of their own philanthropy? Would such students (not from working-class families) buy into the basic premises of this approach? What additional support might they need to do so? Another critical issue with social justice approaches is that the time spent on social justice issues is potentially time not spent on math. What about the middle-class and upper-class parents who are unwilling to sacrifice time for “basic math” and relegate these approaches as appropriate only for those from nondominant groups? Similarly, in considering heterogeneity and culturally relevant pedagogy, it may be more difficult in heterogeneous classrooms and communities to have a sense of the community that students come from; there may be greater differences in achievement and histories with school among the students as well as variety in issues of identity that may need to be attended to. A third challenge involves the constraints imposed by the racial and gender makeup of the teaching force in this country and the structure of the profession. 222 Review of Research in Education, 32 The vast majority of teachers in the United States are White, middle-class women (Howard, 1999; Nieto, 2004). This is potentially a population of teachers for whom the approaches we describe may be particularly difficult, as they likely have the most to learn about their students’ communities. Although mathematics teachers are often marginalized within the broader mathematics community, they may not share the same level of marginalization with their nondominant students. Furthermore, teaching is a profession that is largely underpaid and overworked (Darling-Hammond, 1997). Most teachers, given the structure of the school day and demands on their time, have little time to conduct the kind of in-depth investigations of their students and their communities these approaches suggest. Even more important, in the broader context of increased reliance on standardized testing with high stakes for teachers and schools, these approaches that require more of teachers may be unrealistic. Any approach that argues for particular teaching strategies must take into account these very real constraints. However, despite these challenges, we see great promise in the work of the aforementioned approaches, and we offer these critiques as a way to continue to make progress on ways to support increased equity in math classrooms. It is important to note that these approaches highlight the critical role of teachers in reproducing patterns of inequity. In the next section, we focus on the implications our review may have for the knowledge teachers need to have to best support equity and begin to “blur the lines” between cultural and domain knowledge and work simultaneously at all three levels of our model. Because of space, we do not undertake a full review of the vast literature on teacher professional development that includes a cultural or equity lens (see Sowder, 2007; Wilson & Berne, 1999). Rather, we reflect on the implications for teacher training of the research we have reviewed in this chapter, drawing on some of the relevant work in teacher professional development. Toward this end, we briefly consider two questions. What knowledge do teachers need to know, and what professional development models might prove productive possibilities for sharing that knowledge with teachers? Implications for Teacher Knowledge The work of teachers has grown considerably more complex in the past 10 years (Ball & Cohen, 1999; Cochran-Smith & Lytle, 1999; Cochran-Smith & Zeichner, 2005; Lampert & Ball, 1998; Putnam & Borko, 2000). Standards-based instructional practices require that teachers develop a specialized form of mathematics knowledge for teaching (MKT; Ball, 2005; Hill, Schilling, & Ball, 2004; Hill, Sleep, Lewis, & Ball, 2007) that reflects a particular blend of connected domain understanding with techniques and strategies to facilitate productive classroom interactions. Although the details of MKT are currently being worked out, the domain understanding required for eliciting, evaluating, and building (Carpenter, Fennema & Franke, 1996; Lampert, 1990, 2001; Schifter, 2001) on students’ mathematical ideas reflects a facility with and deep understanding of mathematical concepts and procedures across the terrain of K–12 mathematics (Greeno, 1991; Ma, 1999; NCTM, 1991, 2000). Teachers need to have Nasir et al.: Culture and Mathematics in School 223 the opportunity to develop mathematics knowing in practice through ongoing reflection in the classroom and with their peers through the use of records of practice, video, and other learning materials (Kazemi & Franke, 2004; Lampert & Ball, 1998). As Rochelle Gutiérrez (2002b) argues, however, knowledge of dominant mathematics must also be balanced with knowledge of how to enable students to critique the role of mathematics in society and to “contribute toward a positive relationship between mathematics, people, and society in ways that erase inequities on this planet” (p. 172). Delineating a set of teaching practices that encompasses both dominant and critical perspectives on mathematics is complicated by the fact that some classrooms are becoming increasingly diverse while others slip into hypersegregation (Orfield, Frankenberg, & Lee, 2003). Students themselves are also quite complex, as they negotiate hybrid practices, identities, and time scales through new global technologies that transcend traditional racial, social, and linguistic boundaries (Barab, Hay, Barnett, & Squire, 2001; Delpit, 2002; Gergen, 1991; Moje, Ciechanowski, Ellis, Carrillo, & Collazo, 2004). Thus, as we noted, in this chapter we do not presume to be able to comprehensively outline the knowledge teachers need to teach mathematics effectively and fairly. Instead, we juxtapose recent theoretical shifts that blur the boundaries between mathematics and cultural knowledge, with the implications of the various programs we reviewed above to propose ideas about effective mathematics teaching in classrooms with diverse populations of students. First, the Funds of Knowledge approach would suggest that an important aspect of teacher preparation would support teachers in viewing their students as whole people with rich social and intellectual lives outside of the classroom. Activities for prospective teachers might include spending time with students and families outside of school (Civil, 2002; Foote, 2006) and bringing families into schools to better understand students’ interests and skills outside of the classroom and those that exist as funds of knowledge in their communities. Additionally, professional development activities might include a study of modules developed with students’ and families’ funds of knowledge at the center and might offer models for alternative ways to incorporate family and community members into classroom activities. An important aspect of this work would be to support prospective or current teachers in understanding the value (both for students’ learning and for social justice) of shifting the traditional power relations between families and schools and of opening communication channels. Similarly, the activities of the Algebra Project would also suggest that supporting teachers in understanding the importance of and offering suggestions for how to better get to know the young people they are teaching is a critical focus for teacher preparation. The Algebra Project might also share an orientation for teachers that views math teaching as political activity and sees subverting current patterns of unequal access to higher mathematics as an immediate concern. Moses and Cobb (2001) argue that students need to be taught to

The Co-Construction of Opposition in a Low-Track Mathematics Classroom:

Student opposition in school is traditionally cast in terms of individual dispositions, whereby particular students or groups of students are said to “resist” or “oppose” school structures and identities aligned with the dominant cultural group. The author examined instead how the teacher and students in a low-track mathematics classroom jointly constructed opposition through their classroom interactions. Analysis of the classroom interaction revealed the emergence and escalation of a number of classroom practices that became oppositional. These practices were related to the nature of the mathematical activity, the framing and positioning of student participation in this activity, and multiple interpretations of student competence in and out of the classroom. The author found that classroom opposition is fostered by weak opportunities for meaningful mathematical engagement and the transformation of a polarized participation structure into an oppositional one.

(Re)Framing Educational Possibility: Attending to Power and Equity in Shaping Access to and within Learning Opportunities

Accounts of how culture constitutes the learning activities we accomplish with others are flourishing. These accounts illustrate how participants draw upon, adapt, and contest historically situated social practices, tools, and relations to accomplish their learning goals [Vygotsky: Cambridge, Harvard University Press, 1978]. Yet, they often lack attention to the ways that these social features reify and are reified by broader power structures and hierarchies. One way that power plays out in everyday social interaction is through the stories, narratives and ideologies that serve as resources for interpreting and organizing ongoing activity. Individuals become attuned to, coordinate and mobilize around these broader narratives through the frames they engage in moments of interaction. We offer frame analysis as a means of investigating both access to learning environments and opportunities to learn within them. To situate learning opportunities within and across different components of multilevel systems, a distinction is proposed between framing within a classroom or learning environment and framing access to educational processes and institutions. This paper recommends that researchers analyze, and design for, framing that disrupts predominant power structures and expands the possibilities for learning within more equitable social practices.

Operationalizing Culture and Identity in Ways to Capture the Negotiation of Participation across Communities

The ways that people participate (or resist participation) across geographically and culturally diverse communities and in doing so develop new ways of being and perceiving themselves in the world is necessarily nuanced and multifaceted. Scaling the side of a house to show proper deference in entering a kitchen [Holland et al., 1998], rejecting schooling as a symbol of ‘acting white’ [Fordham & Ogbu, 1986], or attending medical school despite criticism from family and community as described in this issue are complex behaviors individuals enact in the context of perceived social and cultural constraints and opportunities they negotiate in their daily lives. This process of negotiation occurs at both local (microgenetic) and global (sociogenetic) levels, as incremental shifts in individual participation reverberate across

The Joint Accomplishment of Identity

Identity has become a central concept in the analysis of learning from social perspectives. In this article, we draw on a situative perspective to conceptualize identity as a joint accomplishment between individuals and their interactions with norms, practices, cultural tools, relationships, and institutional and cultural contexts. Employing vignettes from our prior research, we examine the joint accomplishment of identity with respect to different levels of activity, including how identity develops in relation to the practices of a particular activity, how identity shifts over time across activities, and how more enduring communities and practices frame the ways that identity develops within and across activities. We illustrate, in particular, how a situative perspective on identity enables researchers to capture the dynamic interplay of individuals and resources, thus accounting for aspects of structure and agency in all social interactions.

Making Visible the Relationship Between Teachers’ Noticing for Equity and Equitable Teaching Practice

This study examines mathematics teachers’ noticing for equity. Noticing for equity is a critically important practice given research that documents how particular groups of students feel more or less empowered to take up ambitious mathematics practices. We conducted classroom observations and a series of noticing interviews with four secondary mathematics teachers nominated as exceptional equitable mathematics teachers. Using qualitative methods, we conducted a cross-case analysis to identify common instructional practices these teachers enacted to close participation gaps in their classrooms, as well as the associated ways of noticing during instruction. These findings document the intricate relationship between what teachers committed to equitable mathematics instruction attend to, how they reason about observed phenomena, and how they use this information to make instructional decisions.

Conflicting narratives of success in mathematics and science education: challenging the achievement-motivation master narrative

Abstract A prominent feature of education in the United States is the widespread endorsement of an achievement narrative, which links individual motivation and effort to academic achievement. In mathematics and science domains, this narrative is often coupled with one that special intelligence is required for people to do math and science. We argue that such narrative are especially problematic for students from non-dominant backgrounds, since de-racialized, ready-made narratives such as these obscure how broader sociopolitical structures shape individual and racial group success in school, and normalize the experiences of white children. We analyzed the negotiation of such master-narratives by students from less dominant backgrounds as they figured themselves and others in the world of school achievement, and learning mathematics. Our analysis demonstrates the importance of initiating and orchestrating conversations that support students in explicitly grappling with these master-narratives in order to confront and change the power they hold.

Status and Competence as Entry Points into Discussions of Equity in Mathematics Classrooms

Students do not all benefit equally from participation in collaborative discussions. Issues of equity can be seen in mathematical group work in a variety of ways if equity is defined as a fair distribution of opportunities to learn (Esmonde, 2009). Studies investigating how equity issues arise have typically focused on whether students have access to correct mathematical explanations.