Abstract
This chapter reviews two strands of identity-based research in mathematics education related to Black children, exemplified by Martin (2000) and Nasir (2002). Identity-based research in mathematics education is a burgeoning field that is disrupting narratives around the meanings of mathematical competence and brilliance. We argue that the identities of Black children as doers and knowers of mathematics are often confused (or mistaken) with stereotypical images of various social identities, as well as wrongly confiscated (or mis-taken), in order to perpetuate persistent narratives of inferiority, criminality, and general ineducability of these children. We use Black children as a particular example within the mathematics education research literature and argue that children within a so-called “collective Black” are subject to the same racial scripts that organize mathematics teaching and learning. While we acknowledge that important lines of identity-based research have emerged to reclaim the rightful identities of Black children and those within the collective Black, we conclude with a critique of this recent literature in which we note the troubling exclusion of girls and young children.
I know this girl don’t got nobody and I couldn’t believe this was happening. I had never seen nothing like that in my life, a man use that much force on a little girl. A big man, like three hundred pounds full of muscle. I was like “no way.” You can’t do nothing like that to a little girl. They didn’t read my any rights. They arrested me after sitting in the office for a couple of minutes. They handcuffed me. It cut my wrist, and really hurt sitting on my hands behind my back. They were like, “So you tried to make a bomb?” I told them no, I was trying to make a clock. He said, “It looks like a movie bomb to me.”
The Troubling Truth of (Mis)Taken Identities
Ahmed Mohamed, Kiera Wilmot, Niya Kenny, and her unnamed peer are examples of children who have suffered from (mis)taken identities within the domains of science and mathematics. Each of these children was arrested—one charged with a felony—in their science and mathematics classrooms. The disciplinary identities of these children were mistaken with stereotypes of being a Black girl or a Muslim boy and, consequently, wrongly taken (i.e., mis-taken), in one case, quite violently. Mistaken identification is not merely a matter of sensational media headlines but has carceral implications. That is, children, like Ahmed, Kiera, Niya, and the unnamed young Black girl, are not only denied labels, such as mathematics doers, tinkerers, knowers, and legitimate observers, but inherit labels of academic disidentification (Osborne & Jones, 2011), such as troublemaker, criminal, and terrorist that serve to naturalize their trajectory out of mathematics and science and into the school-to-prison pipeline. Much has been said about the school-to-prison pipeline (Duncan, 2000; Fasching-Varner, Mitchell, Martin, & Bennett-Haron, 2014; McGrew, 2008; Meiners, 2010; Noguera, 2003; Winn & Behizadeh, 2011), but few have suggested the infrastructure that supports and maintains the school-to-prison pipeline is in fact the discipline of mathematics. For example, ninth-grade algebra courses have been described as a primary indicator, if not driver, of high school dropout rates (Helfand, 2006; Rickels et al., 2016), which necessarily increase the likelihood for incarceration (Levin, Belfield, Muennig, & Rouse, 2007; Sum, Khatiwada, McLaughlin, & Palma, 2009). Furthermore, Algebra I course-taking have been shown to correlate more directly with incarceration rates, than future successes (Tate, 2016). Certainly, mathematics has been described as a “gatekeeper” (Moses & Cobb, 2001; Stinson, 2004), but this term understates the pernicious discursive and structural machinations by which mathematics classrooms actively exclude particular groups of children, who some have referred to as part of the collective Black (cf. Bonilla-Silva, 2002; Martin, 2015).
Collectives, Racial Scripts, and (in Our Case) the Necessity of Black Specificity
The collective Black has included African American, Latin@, Indigenous, Vietnamese, Hmong, Laotian, West Indian and African immigrant children, and extended to Muslim and poor children, as social groups whose status has been racialized, Blackened, or, more pointedly, positioned as inferior (see Bonilla-Silva, 2004). We note that children within this racialized collective are subject to their identities being confused or confiscated within mathematical contexts in order to perpetuate persistent narratives of criminality or general ineducability and, concomitantly, sustain the prestige of mathematical knowledge. Through racial listing and ordering, hierarchies are formed and maintained, such as the racial hierarchy of mathematics ability (Martin, 2009). These hierarchies are predictable organizing principles that provide shortcuts in thinking about mathematics achievement and participation in racial (and gendered) terms—placing Whites and certain Asian groups at the top and Blacks, Latin@, and Native Americans at the bottom.
Our reference to the collective Black is not to suggest that children within this collective experience marginalization or success in similar ways, but to acknowledge that children within the collective are subject to the same racial scripts. According to Molina (2014), racial scripts “highlight the ways in which the lives of racialized groups are linked across time and space and thereby affect one another, even when they do not directly cross paths” (p. 6). Because the shared processes of racialization among different groups often go unrecognized, our theorization strives toward understanding racial scripts. However, our review of the empirical literature of human experience is necessarily specific to the processes of identification and identity development of African American children in mathematics. Such specificity of African American Blackness is not designed to erase or consume individual racialized groups, rather to avoid a collapsing of the collective Black into an indistinguishable multicultural identity. Nevertheless, there are many reasons to engage in the specificity of Blackness within identity-based research literature—three of which we outline here. First, we view the African American experience as a fulcrum for racialized constructions within the U.S. context (Nakagawa, 2012 as cited by Dumas, 2016), insofar as the African American experience provides particular leverage within racial politics. Second, and important, the preponderance of identity-based studies includes or centers African American learners. Third, as African Americans, we have particular familiarity with the African American counterscripts that alter or challenge dominant racial scripts (Molina, 2014). On a similar note, our theorization of racial scripts is also applicable to the arena of science education—a close cousin to mathematics, but certainly a different family. We again do not wish to collapse our analysis of mathematics into science. However, as the introduction makes clear, we recognize similar processes of misidentification and identity development are at play within these domains.
Racial Scripting of Personhood Through Mathematics
Misidentification in any context can be disconcerting, but the implications in mathematics are particularly dire. Recent work details how the cultural and discursive construction of mathematics, as high status knowledge (Apple, 2004), is enabled by the exclusion of particular social groups (Hottinger, 2016; Shah, 2013). For example, Shah (2013) convincingly argues that both race and mathematics rely on similar foundational conceptions of hierarchy, intelligence, and innateness, which create an inextricable and problematic relationship for classroom learning: For many students, learning math is about solving equations and graphing parabolas—it is just another course requirement. However, for students from persistently marginalized racial backgrounds, the stakes are much higher. Certainly, mathematics can act as a material gatekeeper, obstructing access to future economic opportunities and full civic participation (Moses & Cobb, 2001). But learning mathematics can also be about identity and personhood. Living in a world where intelligence has become the primary marker of personhood, and where for five hundred years certain racial groups have been considered under evolved and intellectually deficient, mathematics can represent an opportunity for a student to reclaim cognitive status by showing that she or he is “smart” and can think complex thoughts. Mathematics offers a chance to show the social world that you are a full human being. (Shah, 2013, pp. 30–31)
In short, personhood in the U.S. context is granted—at least in part—through mathematical knowing and doing. (We would be remiss here to fail to mention that Black literacy was criminalized in and during the pre-bellum South [Williams, 2009] to further inscribe Black bodies as subhuman.) It is then no surprise that normative mathematical subjectivity in the U.S. context is constructed as White, male, and upper class (Ernest, 1992; Hottinger, 2016; Stinson, 2013).
Now consider, the project for subjugating and criminalizing Black bodies (figuratively and literally) has been at play far longer and with greater force (Muhammad, 2010; Roberts, 1997), than any project for developing mathematicians and scientists from the collective Black. So, if African American children, for example, can be more readily recognized as deviants or criminals to be subdued and constrained versus as mathematicians or scientists to create, invent, and challenge mathematically based ideas, what does this mean for their educational pursuits within the domains of mathematics and science, for their access to citizenship and democratic representation, or for their hopes for personhood in a 21st century that demands mathematical knowledge? Beyond the moral implications, this grim question speaks to the variety of nonmonetary costs incurred (by both the individual and society) due to the misidentification and underutilization of human potential of African Americans—the dampening of intergenerational effects for social mobility, the criminalization of excess labor, the decline in adaptability to technology, and the potential eclipsing of aspirational sentimentality (Freeman, 2005). The denial of mathematical identities also entails material (i.e., monetary) costs and constitutes a theft, that is, a disinvestment in the opportunity for African American children and a possessive investment in White educational opportunity in mathematics (Battey, 2013). For example, Battey (2013) has shown that earning differentials attributable to mathematics education course-taking favors Whites in the hundreds of billions of dollars over other racial groups. Battey describes mathematics education as a system used to stratify society through the availability of advanced courses, tracking systems, and a regime of guidance counselors who refer children within the collective Black to less rigorous coursework (p. 340). Furthermore, to the extent that children within the collective Black are taught mathematics, the pedagogy is lacking in rigor and breadth—narrowed to assessment practices for increasing standardized test scores (Davis & Martin, 2008). Given mathematics content knowledge provides access to elite colleges and higher paying careers, the misidentification of mathematics knowers and doers is also a matter of lifelong earning potential and material well-being. It is no wonder then that the mathematics education of children within the collective Black has been likened to “sharecropping”—as “sharecropper math” (Moses & Cobb, 2001), that is, a menial mathematics in which children have little to no ownership.
Naming and Claiming: Black Pain and Suffering in Mathematics
We mean not to pivot here to a pithy question that demands a solution (Martin, 2009) and releases ourselves (and the reader) from the gravity of this social and moral problem. Dumas (2014) reminded us that schools and schooling are a site of Black suffering—not merely suffering, but suffering nonetheless. Black, Mendick, Rodd, Solomon, and Brown (2009) have been astute in naming the pain, pleasure, and power located in mathematics. We pause for a moment on the pain and encourage the mathematics education community (i.e., researchers, teachers, policymakers, etc.) to pause with us, acknowledging our role in this suffering and accepting that school mathematics is also a site of Black suffering. Given this sad state of affairs, we endeavor with Dumas (2014), who referenced Tuck (2009), to envision our work in part as an epistemology of mourning that inquires: How do subjects understand their own loss? In what ways might they still be grasping to articulate it? How do we as researchers know this loss in our bodies and express it in our words? Following from this, it becomes important for us to create research designs that allow space for participants to reflect on their own suffering, in ways that are safe, and in ways that allow them to remain protagonists of their own narrative and survivors rather than damaged victims. (Tuck, 2009, p. 26)
We revise their questions in relation to (mis)taken identities in mathematics education: How do children and learners within the collective Black author themselves into the narrative of mathematics? How do children and learners within the collective Black claim or reclaim practices, tools, and meanings about mathematics within their local contexts? In what ways have we developed research designs that allow space for participants to reflect on their own mathematical suffering, pleasure, and power in ways that are safe, and in ways that allow them to remain protagonists of their own narrative and brilliant rather than illiterate? We believe extant identity-based research as exemplified by Danny Martin (2000) and Na’ilah Nasir (2002) provide a way forward for authoring narratives and reclaiming–claiming practices in mathematics. Recent identity-based models and frameworks also hold potential for research designs that capture the experiential complexity of learners within (and outside of) the collective Black. The promise of this work inspires us to explore its origins, findings, and possible futures for liberatory projects designed specifically for Black children and, more broadly, within the collective Black.
Identity as a Site for Disruption
We believe identity-based research in mathematics to be a key site of disruption, even in light of the overwhelming macro-structural forces that organize children’s learning within the collective Black, such as residential segregation, school funding, and tracking policies. For example, consider that children’s lives have been extinguished within micro-scales of time based on readings of an identity, like “Black boy.” Think Tamir Rice and Trayvon Martin, two Black boys gunned down due to the perception of their personhood as thugs, predators, and criminals. These are just two recent and tragic examples. In this sense, identities serve as the organizing link between macro-structural forces and the face-to-face moments in which we all live. Identities—really our consumption of children’s identities—can be extraordinarily powerful in a child’s life trajectory. Our read and interpretation of who children are, what they are doing, and who they are becoming set into motion a constellation of constraints or affordances—at the interpersonal level—that structure interactions, activities, and, ultimately, life opportunities.
Overview of the Chapter
In this chapter, we provide a selective review of the K–12 mathematics education research literature in two parts. The first part is chronology of salient moments for understanding Black mathematics learners. This historical rendering traces the emergence of identity-based research with and about African American children. The second part is a typology that distinguishes between two prominent strands of the identity-based research, exemplified by Martin (2000) and Nasir (2002), respectively. By combining the historical and typological review, we provide an account of how this burgeoning field of identity-research came into being and in what manner it went about disrupting narratives and meanings of mathematical competence and brilliance for African American learners (cf. Leonard & Martin, 2013). Finally, we conclude with our concerns with the paucity of identity research on girls and young children.
The Emergence of Mathematics Identity–Based Research for Black Children
Within identity-based research, children and adolescents’ subjectivities are at the root of knowledge production. Children’s subjectivities and intersubjectivities with their teacher and classmates are described in detail to make sense of the variance in student learning, participation, and achievement. Subjectivities are the idiosyncratic ways in which individuals make meaning of their contexts in space and time. While subjectivity is critical to identity-related research, studies on identity requires more than attention to subjectivity. Identity-based research also involves the interrogation of processes of becoming, as well as the formation and dissolution of relationships between other children, teachers, the content, practices, discourses and tools as a function of context (Sfard, 1998). In the following section, we recount the emergence of identity-based research in mathematics education pointed to understand the experiences of Black children.
Moments in Mathematics Education Research for Black Children
We use a “methodology of moments” (cf. Stinson & Bullock, 2012a) to trace the position of the Black child in mathematics education research. Differences in achievement and participation of Black children tend to be framed in three ways—deficit-based, strength-based, and frames of rejection (Delpit, 2012; Stinson, 2006; Valencia, 2010). Strength-based frames focus on assets in children and their context; whereas deficit frames, while often sympathetic, rather explicitly or implicitly purport that children, their families, or communities are lacking the cognitive, cultural, or structural resources that facilitate learning, well-being, and success. Frames of rejection posit that children and their families are not necessarily lacking resources but seeking coping strategies to maintain cultural and personal autonomy by rejecting the dominant culture or features of their own culture (Stinson, 2006, p. 482). In Figure 1, we juxtapose several decades of mathematics education research with frames of learners to construct a constellation of studies about or critical to the learning of children in the collective Black. By doing so, we find three salient phases for children in the collective Black—individual-in-cognition, individual-in-context, and structure + agency. Like others who have constructed and named moments (Stinson & Bullock, 2012a), we do not suggest that these periods of research are linear or particularly well defined. To be clear, cognitive-oriented research as we describe below is still the predominant paradigm through mathematics learning and knowledge is understood and validated (Silver & Kilpatrick, 1994). These periods represent shifts, surges, and new ways of imagining children and context of the collective Black. Additionally, the dates on which we rely are those of publication and do not accurately represent a true beginning of ideas and conceptions of learners in the collective Black but serve as a markers and guides. To manage the scope of the history, we highlight some of the research that served as a clear antecedent to the identity-based research of Martin (2000) and Nasir (2002), as well as studies that established discourses, like “oppositional identity theory” (Fordham & Ogbu, 1986), to which identity-based research was poised to respond.
Timeline of Moments in Mathematics Education Research to Frames of Learners
Individual-in-Cognition: Can the Black Child Learn?
The individual-in-cognition period serves as the starting point in our timeline and marked a contested space for African American learners in which their intellectual competence was being empirically questioned and justified. For example, “Jensen (1969) proposed that lower-class children and Blacks in particular suffer from an inability to engage in ‘conceptual learning,’ which involves cognitive activity mediating between stimulus and response, and that this deficit is the result of genetic inheritance” (Ginsburg & Allardice, 1984, pp. 197–198). Herbert Ginsburg, along with others, conducted clinical research that refuted claims of cognitive deficiencies and positioned poor and Black learners as cognitively competent (Cole & Bruner, 1971; Ginsburg, 1972). Ginsburg and Allardice (1984) describe poor and Black children’s mathematics learning and development this way: Of course, we do not argue that such an environment, specifically lower-class poverty, is beneficial for those growing up in it, nor that it exerts no effects on psychological functioning. Rather, the study demonstrated that basic mathematical thought develops in a robust manner among lower-and middle-class children, black and white. School failure cannot be explained by initial deficit in basic cognitive skills, specifically System 1 [i.e., intuitive mathematical concepts] and 2 [i.e., counting] mathematical skills. Instead, poor children display important cognitive strengths, developed spontaneously before the onset of formal schooling. These strengths should provide a sufficient foundation for later understanding of school mathematics. (p. 203)
This cognitive period coincided with researchers attempts to correlate student behaviors to achievement primarily through quantitative statistical inference (Stinson & Bullock, 2012a).
Individual-in-Context: Under What Conditions Does the Black Child Learn?
In the next period, the individual-in-context, studies were focused on cultural manifestations of learning at the classroom level. This was the longest period in our schema, spanning at least three decades, and includes a variety of research studies. The individual-in-context period was ushered by a methodological shift toward qualitative studies in the late 1970s. Within this methodological and theoretical turn, Lagemann (2000) notes that anthropologists began investigating schools, schooling, and classroom practices, including discourse. However, along with anthropological methods came anthropological explanations for various social differences. In particular, Oscar Lewis’s (1966) theory of the culture of poverty found traction within educational discourse and was redefined as “cultural deprivation” (Valencia, 2010). While cultural deprivation theories gained traction, there seemed to be little empirical work in mathematics education research to verify such claims with the exception of one study by Kirk, Hunt, and Volkmark (1975), which supported no racial differences between Black and White children (Ginsburg & Allardice, 1984). The culture problem thesis was critiqued by many educational theorists, including John Ogbu—also an anthropologist but in education. Ogbu (1978) put forth his own theory cultural–ecological theory or caste theory, which argued that based on the numerical or the sociohistorical migratory status (i.e., forced or voluntary) of their racial group, children may resist or capitulate to assimilatory practices in school. For example, African American, Native American, and Hawaiian American children, whose historical communities were enslaved, conquered, or colonialized, resist assimilation into schools as a means to maintain their cultural authenticity and autonomy. Cultural–ecological theory led to the acting White hypothesis that suggested Black children construct school success as a White cultural norm (Fordham & Ogbu, 1986). Ogbu’s work importantly introduced theorizing about race through various ecological contexts foregrounding the sociohistorical. This work uses a frame of rejection to refute clams of cultural deprivation (Stinson, 2006). Within this period, mathematics education studies about the collective Black leveraged individual-in-context explanations, such as “acting White,” which attempted to connect children’s everyday decisions within a cultural–historical framework. It is also around this time that Alan Bishop (1988), using anthropological methods, also introduced mathematics as a form of cultural induction or socialization.
The individual-in-context period extended into the mid-1980s. This was a pivotal time in which mathematics learning was considered “products of social activity” and “goes beyond the [cognitivist] ideas that social interactions provide the spark that generates or stimulates an individual’s internal meaning-making activity” (Lerman, 2000, p. 23). In other words, while previous moments in mathematics education had included the social activity, the social was subjugated to individual cognitive processes instead of as a phenomenon of interest that requires a telescopic lens for zooming in and out (Stinson & Bullock, 2012a). It was during this time that Vygotsky’s work was being utilized by Cole, Engestrom, and Lave to understand mathematics practices. Perhaps the social turn is best represented through the study of child candy sellers in Brazil (Carraher, Carraher, & Schliemann, 1985; Saxe, 1988). For example, Carraher et al. (1985) found that while some children had difficulty solving routine school mathematics problems, they were quite proficient in conducting complex calculations outside of school as candy sellers. Of course, this work does not address the marginalized children within the United States, but exemplifies the affordances of foregrounding social context in mathematics learning, as well specifying, a particularized social group of learners (which in this case comprised Brazilian children candy sellers).
Other studies within the individual-in-context period took an institutional approach. Fueling the mathematics education reform movement, these studies focused on instructional programs, that is, a collection of curricular materials, professional development, and instructional techniques, in mathematics education. Perhaps most notably among this research were the quasar studies, which showed the feasibility of broad scale, high-quality mathematics instructional programs in economically disadvantaged and minoritized communities (Silver, Smith, Nelson, 1995). Furthermore, Silver et al. (1995) note, A fundamental premise of the project was that low levels of participation and performance in mathematics by females, ethnic minorities, and the poor were not due primarily to a lack of ability and potential but rather to educational practices that denied access to meaningful, high-quality experiences with mathematics learning. (p. 10)
The quasar work was a continuation of strength-based approach, yet unique in its scale. This work broadened the field’s imagination for national reform for marginalized children in the collective Black.
Still within the individual-in-context period, Malloy and Malloy (1998) proposed that African American children had different learning preferences that should be honored and leveraged in mathematics learning. Malloy and Jones (1998) conducted clinical interviews with 24 African American eighth-grade children. Their findings describe the African American children as showing characteristics endemic to good problem solvers and “exhibit[ing] other positive characteristics usually not credited to African American students” (Malloy & Jones, 1998, p. 161). Additionally, Malloy and Jones (1998) found that the African American children frequently used holistic reasoning, a stance in which you view the world and problems in their totality. Carol Malloy’s work was groundbreaking insofar as little attention until this time had been given to the study of African American learners as a group of learners onto themselves. That is, African American children were generally studied in comparison to White children (McLoyd, 1991).
Of course, this period also marked the introduction of “stereotype threat” (Steele, 1997), as a dampening psychological response to performance within a domain of high salience for fear of enforcing stereotypical images of one’s racial group. Steele’s work is also situated along the frames of rejection band, because his explanatory model ultimately suggests that the “abiding effect [of stereotype threat] on school achievement” leads to academic disidentification (Stinson, 2006, p. 489).
At this point, we note three things about studies within individual(s)-in-context moment: First, mathematics education studies were providing descriptive accounts of student learning at various scales of time and over various levels of analysis. Second, many of those studies focused on students’ individual strengths and competence in their contexts, but these studies failed to provide accounts for the variance of student success or failure. Third, education researchers in anthropology and social psychology were providing explanatory theories of school failure or disengagement, based on frames of rejection of the dominant culture, which in many ways problematically reified deficit notions about Black families, communities, and culture.
Structure + Agency Dialectic: Why Does the Black Child Learn That Way?
In response to the above issues, the structure + agency period unfolds via identity-based research. This body of research directed at the collective Black reconceptualized learning by contemplating the discursive construction of context, accounting for individual difference vis-à-vis agency, and disrupting deficit and rejection-oriented frames of learners. Within the structure + agency period, the notion of context is troubled via “sociocultural, sociohistorical, and sociopolitical assumptions, conditions, and power relations,” and the individual is reinscribed as an agent left to marshal and “resist the surveilling and disciplining gazes of normalization (cf. Focault, 1977/1995)” (Stinson & Bullock, 2012b, p. 1165). Varelas, Settlage, and Mensah (2015), in science education, describe it this way: Structures are considered to be the cultural rules, or schemas, that shape and are shaped by social practices in a domain, and are in a dialectical relationship with resources, the sources of power with the domain and its social interactions (Sewell, 1992). Agency is seen as a person’s capacity to engage with cultural schemas and mobilize resources in ways that did not exist before, creating new contexts and practices. (p. 439)
Therefore, the structure + agency period rejects the notion of a benign, apolitical, and inanimate context preferring an animated, political, and potentially hazardous or radicalized landscape for learning. Similarly, the individual is reenvisioned as an agent that does not merely respond to a radicalized context, but shapes the very nature of this context in light of their access and utilization of various structures, which Varelas et al. (2015) delineate as “physical, material, symbolic, discursive, social, curricular, etc.” (p. 439). Accordingly, the push to grapple with an individual’s subjectivities in mathematical contexts made it necessary to reckon with and about the performed practices, meanings, dispositions, values, social positions, and histories—namely, their identity. There have been several theories regarding the mathematics identity of learners (Anderson, 2007; Boaler & Greeno, 2000; Cobb, Gresalfi, & Hodge, 2009; Martin, 2000; Nasir, 2002), although different emphases are placed on students’ histories, practices, positions, orientations, statuses, and roles. The emergence of identity-based research about and with Black children was by no means natural or the self-evident “next step.” Studying the Black child in this way qualified as a political move to, first, reckon with children’s subjectivities, second, capture the sociohistorical and sociocultural discourses that pulse through concentric contexts, such as classrooms, schools, school districts, communities, and the broader society (Stinson & Bullock, 2012b), and, last, provide some theoretical explanation that maintained the humanity, dignity, and educability of children within the collective Black.
Summary of Mathematical Moments of the Black Child’s Learning
One simple way to read the three periods in mathematics education research is through three questions: (a) whether children in the collective Black can learn mathematics (individual-in-cognition), (b) how (under what conditions and through what modes) do the children in the collective Black learn mathematics (individual-in-context), and (c) why do children in the collective Black learn mathematics the way that they do (structure + agency; cf. Stinson & Bullock, 2012a)? The exploration of this latter question, to which identity-based research responds, has been the subject of debate in the field, insofar as this question is deemed as mathematically dubious because it does not attend to “the nature of quantitative relationships, the meanings of symbolic representations [in math], conceptions underlying advanced mathematical conceptions, and the meaning of arithmetical expressions” (Heid, 2010, p. 103). (For full context of this debate, see also, Battista, 2010; Confrey, 2010; Harel, 2010; Martin, Gholson, & Leonard, 2010.) However, critiques emanating from this stance construe context as domesticated (vs. radicalized) being more or less fixed and extricable from the domain of mathematics, instead of imbricated by a radicalized context. The question of why is imbued with political tensions that “seek not just to better understand mathematics education and all of its social forms but transform mathematics education in ways that privilege more socially just practices” (Gutierrez, 2010, p. 40).
The Contributions of Martin and Nasir
Of course, all identity-based research is not necessarily political in its orientation (e.g., Cobb et al., 2009) and tend to push and pull with varying force on the structure/agency dialectic. However, for Black children, identity researchers took care to grapple with conceptions regarding what it means to be a math person or doer, along with how holding or enacting a racialized identity constrains or affords the identification in and with mathematics. Two lines of inquiry in mathematics identity research exemplify this work—Martin (2000) and Nasir (2002). At this point, we provide a brief overview of Martin and Nasir’s identity-based research in mathematics.
Martin’s seminal study explored mathematical success and failure among African Americans. This interdisciplinary work built on a variety of strength-based studies, such as Bishop’s work on mathematical enculturation, and responded to studies that used frames of rejection, such as Ogbu’s cultural ecological theory. In Martin’s study, he conducted interviews with parents, community members, teachers, and African American children (Grades 7 through 9), as well as conducted observations at the children’s junior high school. One of the greatest contributions of Martin’s work is his multilevel framework. This framework includes several ecological contexts—sociohistorical, community, and school contexts—in which an individual is socialized. The resultant of mathematics socialization is a mathematics identity, which was defined as beliefs about (a) their ability to perform in mathematical contexts, (b) the instrumental importance of mathematical knowledge, (c) constraints and opportunities in mathematical contexts, and (d) the resulting motivations and strategies used to obtain mathematics knowledge. (Martin, 2000, p. 19)
Martin (2000), along with Moody (2000), was among the first to give voice to African American parents and children about their experiences learning mathematics. Through the voices of African American children and parents, learning could no longer be conceptualized in terms of mere transmission and reception, but a swirl of multilevel forces, such as the expectations and beliefs of the community members and teachers, that enable mathematics identities.
Nasir’s (2002) seminal work builds on the sociocultural studies of mathematics learning in context, similar to the candy sellers’ studies by Carraher et al. (1985) and Saxe (1988), and also responds to cultural ecological theory proposed by Ogbu. She conducted two studies that examined the mathematical practices of African American children playing dominoes and basketball, respectively. In the first study, Nasir observed and interviewed African American children at two age levels, elementary and high school. In the second study, Nasir observed and interviewed middle and high school African American, male basketball players. Using two cultural practices (dominoes and basketball), Nasir constructs a mathematics identity-in-practice for African American children. She showed as African American players of dominoes and basketball became more engaged in the practice, they developed goals and identities that were associated with changes in mathematical learning. Nasir (2002) describes it this way: In dominoes, players shifted from basic matching numbers and addition at the elementary school level to complex inferences of probability and logical (if-then) thinking at the high school level. In basketball, players’ mathematical goals shifted from understanding basic statistics involving counts in middle school to calculating relatively complex statistics with percentages and averages in high school. (p. 237)
While the players in Nasir’s study experienced an inbound trajectory within the practices of dominoes and basketball, she notes that many African American children experience a trajectory that is different in school mathematics. Nasir argues that the ways children engage, align, and imagine themselves to the mathematical goals and activities in the mathematics classroom influences their learning trajectories.
The studies conducted by Martin and Nasir are quite different in their orientations and offer different explanatory models for African American children’s learning and participation in mathematics. However, Nasir and Martin share equally disruptive approaches to the study of African American children, specifically, that allow children within the collective Black to reclaim identities of competence and brilliance. To understand the unique contributions of Martin and Nasir, we situate their seminal studies within the body of identity-based research broadly, leaning on recent analyses of this emergent field.
A Typological Rendering of Martin and Nasir
There has been an explosion of identity-based research in mathematics education (Darragh, 2016). In light of this explosive growth, one can barely imagine the breadth of scholarly interpretations of the seemingly self-evident and colloquial term—identity. The body of identity-based research is broad indeed and imagines children’s subjectivities in different scales of time-space (Lemke, 2000); through different disciplinary orientations, such as, sociological, anthropological, and psychological (Varelas et al., 2015); as well as various theoretical approaches, including psychoanalytic, performative, participative, positioning, narrative, and poststructural (Darragh, 2016; Langer-Osuna & Esmonde, in press). Accordingly, one of the challenges facing identity-based research is reigning in the “proliferation of definitions and stances towards the concept of identity” (Edwards, Esmonde, & Wagner, 2011, p. 68). Recent efforts by Darragh (2016) and Langer-Osuna and Esmonde (in press) unpack the multiplicity of theoretical orientations and conceptions of identity, as well as explore the affordances that different methodological approaches entail. We do not endeavor to replicate this work here, but attend to a very specific task of situating the two strands of mathematics identity research, exemplified by Martin and Nasir, within different categories.
Identity-Based Research in Space and Time
We begin with Lemke’s (2000) question: “How do moments add up to lives?” (italics in original, p. 273). This is a question of identities in time but also space. Lemke lobbies for a dynamical view, wherein identity is described over time as a process, that extends beyond confines of mere spatial analysis. That is, Lemke—following Cole (1996)—suggests analysis across multiple scales of time, “from the microgenetic (event scale), meso-genetic (extended activity or project scale), and ontogenetic (developmental-biographical scale) to the historical and evolutionary scales” (p. 287). According to Edwards et al. (2011), Nasir’s study includes both microgenetic and mesogenetic scales of time and local contexts through the consideration of “both moment-to-moment shifting of identity (sometimes called positioning; Davies & Harré, 1999; Holland, Lachicotte, Skinner, & Cain, 2001) and longer term trajectories of identity as a relatively stable sense of self (Erikson, 1968),” whereas Martin’s study goes “beyond local contexts or practices to develop in a relative enduring fashion over the life span” (p. 66), that is, ontogenetic scale.
Identity-Based Research in the Disciplines
In addition to scales of time, Darragh (2016) draws our attention to the different disciplinary perspectives that imagine identity as an entity we possess (i.e., acquisition) or an action that we enact as a role. Darragh describes the possession of an identity as a psychological Eriksonian conception (1968) and the enacting of a role as a sociological Meadian (1913/2011) conception. We nuance the latter category of action to include identities formed through goal-directed activity stemming from anthropological perspectives, including Michael Cole (1996), Yrjo Engestrom (1999), and James Wertsch (1991). Nasir’s early work is firmly situated within this anthropological space. However, Martin pulls from both psychological and anthropological spaces (and some may include sociological). Darragh (2016, p. 27) describes Martin’s work as “bridg[ing] the acquisition-action divide, defining identity as a set of beliefs (something that can be acquired) and also looking at identity in using mathematics to change the conditions of one’s life (an action).”
Theoretical Orientations to Identity-Based Research
Of course, the differences in disciplinary perspectives influence the theoretical orientations of both Martin and Nasir. Darragh (2016) and Langer-Osuna and Esmonde (in press) offer a relatively unified set of categories for the sorting identity–based research: psychoanalytic, narrative, poststructural, positioning, participative, and performative. As shown in Figure 2, while these categories are defined separately, studies of mathematics learning and participation often employ multiple definitions and orientations to identity (at times problematically; Darragh, 2016). Beginning with Nasir (2002), this line of inquiry relies on a participative orientation to identity. This work envisions identity as a social construction achieved through the participation in a social group or community and the use of specific cultural practices. Nasir’s work also uses positioning to describe the interactional negotiation of identities in real time. The other line of inquiry, exemplified by Martin (2000), relies on participative, narrative, and psychoanalytic definitions of identity. Similar to Nasir, Martin sees identity as part of participation or socialization into a classroom community; however, Martin also included children’s (and their parents’) narratives to understand how Black learners author themselves in the contexts of mathematics. Martin’s first study also goes about teasing apart different beliefs, values, and motivations that children held in his study. Langer-Osuna and Esmonde (in press) emphasize the importance of this psychoanalytic orientation insofar as it outlines the psychic reality in which children live, as well as holds up the “mirror” through which children perceive themselves. (It is worth noting that some do not distinguish between the work of authoring and the perceptions we hold about ourselves, i.e., the stories we tell are our identities; Sfard & Prusak, 2005.)
Theoretical Connections of Two Lines of Inquiry Related to African American Children, According to Categories of Identity-Based Research in Mathematics Education
Treatment of Racialized Identities
Within mathematics identity research of Black children, there are two types of social identities—racial and ethnic. “Racial identity,” according to Helms (1996), “may be broadly defined as psychological or internalized consequences of being socialized in a racially oppressive environment and the characteristics of self that develop in response to or in synchrony with either benefitting from or suffering under such oppression” (p. 147); while ethnic identity is one’s familiarity with and competence in the meanings, values, and artifacts of a culture. An important distinction that Helms (1996) draws between racial and ethnic identity is the locus of inquiry for identity processes. The intrapsychic processes tend to be emphasized by racial identity theorists, like Martin; contrastively, interpersonal processes, such as social role fulfillment, tend to be emphasized by ethnic identity theorist, such as Nasir. This does not suggest that race as a construct only operates intrapsychically or ethnicity does not make its way into the psyche.
Nevertheless, the bifurcation of the mathematics identity research for the collective Black falls along these distinct treatments of one’s racialized social identity—as fundamentally ethnic or racial. Finally, acknowledging that a mathematics and a racialized identity are quite different, we note that the complexity in methodology extends to similar categories of: psychoanalytic, narrative, poststructural, positioning, participative, and performative. The racialized identities used by mathematics education research maintain some of its ties to psychology, but also rely generally on racialized signs, significations, and narrations.
Nasir’s Identities-in-Practice
When African American children and adolescents were studied in their own community contexts, researchers found that they exhibited mathematical competencies and abilities, which were not reflected in school contexts (Nasir, 2002). Ecologically, this work focuses on proximal processes, that is, people and objects within the child’s immediate setting. These studies debunked claims of environmental deprivation attributed to the African American mathematics learner. To the contrary, identities-in-practice studies revealed that African American children and adolescents in their everyday contexts show proficiency in carrying out a variety of mathematical tasks. These studies emphasize the cultural aspects of learning, that is, the use of artifacts, symbols, and meanings, like cultural practice of dominoes, basketball, or purchases at a local store, and conceptualize children’s social identities as ethnicity (Nasir, 2002; Taylor, 2009). For example, Edd Taylor’s (2009) study, titled, “The Purchasing Practice of Low-Income Students: The Relationship to Mathematical Development,” focuses on the practice of African American children’s engagement in shopping at liquor stores—a practice typical among some children in low-income, urban communities. Taylor discusses the sociohistorical origins of the liquor store, an edifice born out of structural flight of large supermarkets to “safer” and “more profitable” areas. Taylor (2009) notes, “[A]lthough the term liquor store is descriptive of the role these stores serve in selling alcoholic beverages the stores serve as small markets or convenience stores in these communities” (p. 373). Through this study, Taylor was able to “highlight the distributed nature of students’ purchasing practice, the role of whole number understanding (as a form of prior understanding) in purchasing, and multiple levels of students’ mathematical engagement during the purchasing practice” (p. 406).
Features of Identities-in-Practice
In these studies, the extent of students’ participation within their local communities of practice serves as an indicator of student learning (Lave & Wenger, 1991). Children and adolescents’ ability or inability to carry out mathematics tasks in the classroom is considered a function of their cultural relevance and continuity between home-community and school contexts. Restated in terms of identity, African American children and adolescents’ ethnic (i.e., home-based) and academic (i.e., school-based) identities are considered to be in tension (Nasir & Saxe, 2003). Within this thread, tensions that students experience between their ethnic and academic identities is negotiated and resolved to some end within social space. Potential drawbacks of identities-in-practice studies include that power, ideology, and racism are not explicitly addressed. However, to this critique, we note (as a rebuttal of sorts) that the cultural practices are necessarily shaped by sociohistorical forces. For example, the examination of purchasing practices at liquor stores does account for the effects of structural racism and the allocation of resources in majority-Black, low-income, urban communities. Similarly, the playing of dominoes does index the working-class or poor African American communities and marks historical shifts in cultural capital and meanings of agency as individuals take up this practice (Nasir & Saxe, 2003). Consider that dominoes were a game whose history traces back to ancient China and was played by the elite and, at the turn of the century, a game played by the English in pubs. The decision to play dominoes in contemporary United States, however, signals an entirely different affiliation and way of being. Of course, by drawing on practices seemingly endemic to racialized groups may serve to perpetuate stereotypes, if larger structural forces are not considered as part of the analysis and all members of a racialized group are assumed to participate in the practice in the same way. While there may be implications for teachers and teaching, these implications are constrained to local communities and are not portable. Yet, this line of work presents concrete actions for teachers to employ in the curriculum and in practice. Another potential drawback, if you will, is identities-in-practice studies do not define a mathematics identity (i.e., commitments to the discipline writ large as a subject matter), only specific practices within the discipline of mathematics. In this sense, identities-in-practice are particularized, pragmatic, and potentially disconnected from mathematics as an intellectual activity, that is, to the extent it can be considered well-defined (cf. Resnick, 1989). The identities-in-practice work, in fact, helps reenvision meanings of what mathematics is and can be in different cultural communities. Said differently, identities-in-practice studies do well to challenge the epistemic value of school mathematics.
There are few studies within the identities-in-practice strand. This work is methodologically complex—requiring ethnographic collection methods and micro-analytical methods of student interactions. The affordances of Nasir’s and Taylor’s ethnographic work is the approximation of learning in real time. Unfortunately, there are few studies in mathematics education identity–based research that take up this approach for the collective Black. The predominant approach has been Martin’s focus on racial identity and socialization. We assume this is in part due to the reduced methodological demands—primarily interviews—and the benefits of the direct confrontation of issues of race and racism to which identities-in-practice only allude.
Martin’s Racial Identity and Mathematics Socialization
While race and racism are not typically addressed by identities-in-practice studies, this is the explicit focus of empirical work concerning racial identity and mathematics socialization. These studies draw from African American learners’ narratives about their mathematical experiences in the classroom and seek to understand how African American learners negotiate racial messages in the context of their mathematics learning. On the one hand, findings from these studies recount African American learners’ experiences with racism, negative stereotypes, and lowered expectations; and, on the other hand, these studies provide descriptions of African American student characteristics, relationships, supports, interactions, and management techniques that facilitate success in mathematics learning (Berry, 2008; Martin, 2006; McGee & Martin, 2011; Stinson, 2008). Given the focus on race and racism, studies from this thread consider a broader social and political context and, thus, ecologically, shift between historical, community, school, and home contexts, but primarily distal processes. The two identities under inspection for the African American learner in these studies are racial identity and mathematics identity. For these studies, tension between one’s racial and mathematics identity is negotiated intrapsychically manifesting as narrations of experience. Student learning processes are not generally the focus of these studies. However, students’ internalization of bias—as expressed through one’s racial identity—can be an impediment to learning, that is, most notably through stereotype threat (Steele, 1997).
For brevity’s sake, we discuss three studies, but there are many studies that follow in this tradition. We begin with Robert Berry’s (2008) work with successful middle school, African American boys in mathematics. Berry, through interviews with eight African American boys, found that early educational experiences, support systems, positive attributions of self as a mathematics doer, and supportive alternative identities facilitated the success of these boys. David Stinson’s (2008) study also helps construct the meanings of being an African American, male mathematics doer. In addition to critical race theory as employed by Berry, Stinson uses poststructural and critical theory to analyze four, African American men in their 20s reflecting on their K–12 academic and mathematical experiences. Stinson (2008) found four themes of mathematical success: (a) Observing or knowing family or community members who had benefited from formal education by achieving financial and societal success; (b) experiencing encouraging and forceful family and community members who made the expectations of academic, and mathematics, success explicit; (c) encountering caring and committed teachers and school personnel who established high academic expectations for students and developed relationships with students that reached beyond the school and academics; and (d) associating with high-achieving peer-group members who had similar goals and interests. (p. 1002)
In the third and final study that we review in this strand, we focus on Traci English-Clarke, Slaughter-Defoe, and Martin’s (2012) article titled, “What Does Race Have to do with Math? Relationships between Racial-Mathematical Socialization, Mathematical Identity, and Racial Identity.” Clarke developed a series of survey instruments to identify the socialization experiences of African American children in mathematics. Among the many findings of her study, we focus on racial–mathematical stories and messages that the 168 ninth- and tenth-grade Black youth reported. Three kinds of stories and messages were reported by one third of the Black youth. Approximately 45% of those stories and messages related to racism and racial discrimination in mathematics, 18% of the stories and messages focused on persistence in mathematics classes despite being one of the few, and 27% were related to the message that Asian Americans are good at math. As shown in Figure 2, each of these studies rely on narratives, but take up different theoretical conceptualizations of identity.
Features of Racial Identity and Mathematics Socialization
As for potential drawbacks, racial identity and mathematics socialization studies do not explicitly consider interactive performances of identity. These studies tend to emphasize society’s influence on the individual via socialization processes and, while the agency of African American learners is shown as possible, this agency is not usually described at the interactional order. In other words, while racial identity and mathematics socialization studies make available student agency, rarely do these studies exhibit how that agency is exercised and negotiated in real-time in the context of mathematics learning. As such, the implications for teachers and teaching is less direct and is situated as knowledge to have and values to possess versus actions teachers can actively take. On the one hand, these studies make clear claims to an identity connected to the discipline of mathematics—a mathematics identity. On the other hand, this leaves mathematics as a subject matter intact and unchallenged. Racism and all of its manifestations structurally and symbolically, however, are clearly brought into focus and challenged with this work.
Challenges Within the Extant Identity-Based Research
Identity-based research is not without its challenges. While this work has been critical to disrupting discourses of the collective Black in mathematics education, the disruption has not been equally distributed among subgroups. Particular attention has been paid to Black boys in middle school and beyond in mathematics (e.g., as previously discussed, Berry, 2008; Nasir, 2002; Stinson, 2008). The plight of Black girls and young children (who are occasionally described as not developmentally able to have identities) has received less focus by the field, although there are exceptions at this intersection (Gholson & Martin, 2014; Jones, 2003). The extant mathematics identity–based research is a masculinized narrative of Black adolescence. This raises particular questions about a treatment of race and gender that does not confront the performativity of Blackness and masculinity in the learning of mathematics. That is, how does the performativity of Blackness and femininity by Black girls or boys manifest in mathematics contexts? In the case of Black girls, Dotson (2014), as a philosopher, reminds us that we need epistemological, theoretical, and empirical resources to make Black girls knowable to broader community. Similarly, we need to only look across the disciplinary divide into science education research to see the possibilities of making young Black children’s identities knowable (Kane, 2012; Varelas et al., 2011). For example, Kane (2012) has found children as young as 7 to 9 years (and perhaps younger) are quite capable of identifying with the discipline of science—through both narration and performance. This example serves as a particular warning to this burgeoning field within mathematics education research to create space and take care not to re-instantiate existing patterns of patriarchy and developmental bias that are dampening our capacity to understand teaching and learning in mathematics.
Final Notes on Reclaiming Identities
The emergence of identity-based research allowed the mathematics education research community to contemplate the Black child in mathematics in a radically new way. For example, Martin’s insistence on highlighting Black mathematical success refocused our empirical attention on Black children’s competence, capability, and perseverance. Martin’s work also helped anchor our understanding of mathematics as a racialized experience, which shifted the empirical gaze away from the child—just enough to begin seeing the waves of race pulsing through mathematics classrooms. Nasir’s work was instrumental in naming Black contexts as mathematical, a designation that had not been applied to these cultural spaces. Both Martin and Nasir, in their own rigorous way, reclaimed Black children’s identities in mathematics and asserted Black children’s humanity and competence in mathematical spaces, which had far too long been confused or denied. Given the power of mathematics to confer economic viability on the one hand, and intelligence and personhood on the other, this reclamation of identity is a tremendous disruption to inequalities within mathematics education and beyond.
In this chapter, we have engaged in an exercise of Black specificity out of the necessity to share a particular story—or script if you will—within mathematics education research. However, this script is not unique. It repeats itself among other racialized groups. The script within mathematics education research begins, as all Blackened groups do, with an assertion and then refutation of inferiority followed by an accounting (often quantitative) of the seemingly intractable conditions and outcomes that naturalize hierarchies of mathematics ability. For Black children, Martin and Nasir have played a pivotal role in rewriting these racial scripts. Parallel scripts are in play for racialized groups, but manifest in relation to various identity markers, like language. The history of mathematics education we told and the strands of identity-based research we reviewed are necessarily specific—not to cloak an array of racialized groups of children, but to highlight the structures that enable one to mis(take) Black children and provide fodder for relational (not merely comparative) analysis, among various racialized groups of children (cf. Molina, 2014). Our goal was to call out and name the process of (mis)taking a child’s mathematical identity and to provide at least two powerful ways forward in identifying children within the so-called “collective Black.” Now that we can see the children, we shall call them mathematician, scientist, and scholar—their rightful names.