African American Mathematics Teachers as Agents in Their African American Students’ Mathematics Identity Formation
by Lawrence M. Clark, Eden M. Badertscher & Carolina Napp - 2013
Background/Context: Recent research in mathematics education has employed sociocultural and historical lenses to better understand how students experience school mathematics and come to see themselves as capable mathematics learners. This work has identified mathematics classrooms as places where power struggles related to students’ identities occur, struggles that often involve students’ affiliations with racial, ethnic, and gender categories and the mathematics teacher as a critical agent in students’ mathematics identity development. Frameworks for identifying resources that mathematics teachers draw on to teach are evolving, and emerging dimensions of teachers’ knowledge, namely knowledge of students’ lived experiences and histories, as well as teachers’ experiences and identities, are increasingly being considered alongside more traditional dimensions of the knowledge teachers draw on in their practice.
Purpose: The purpose of this article is to explore the perspectives and practices of two African American mathematics teachers, Madison Morgan and Floyd Lee, as they support their African American students’ mathematics identity formation and development.
Participants: At the time of the study, Morgan and Lee were high school mathematics teachers in a large urban school district. Both participants were selected for this analysis because of considerable differences in their life histories, pedagogical approaches, and perspectives.
Research Design: Each teacher was observed approximately 25 times and interviewed 9–10 times. The primary data for this analysis consist of a subset of observations and interviews for the purposes of conducting a qualitative cross-case analysis that examines themes, similarities, and differences in Morgan’s and Lee’s approaches to supporting their students’ mathematics identity development.
Findings: Morgan’s and Lee’s experiences, perspectives, and practices characterize two very different perspectives of what constitutes a positive mathematics identity, while both maintain connections to race and racial identities. In both cases, there exists a subtle paradox in the underlying motivations that the teachers communicated in their interviews related to socializing their African American students and the practices they actually employ in their classrooms. Furthermore, both teachers made use of their capacity to serve as models and motivators for students’ current and future success in mathematics.
Conclusions/Recommendations: If equitable high-quality mathematics instruction is a sincere goal of the mathematics education community, we strongly recommend that researchers further explore the ways that teacher identity, including those dimensions associated with race, class, and gender, serves as an instructional and motivational resource as teachers work to create productive and meaningful learning environments for their students.
There is a movement under way that seeks to better understand the mathematics schooling experiences of students by examining these experiences through sociocultural and historical perspectives (Atweh, Forgasz, & Nebres, 2001; Boaler, 2000; Martin, 2000; Nasir & Cobb, 2007; Secada, Fennema, & Adajian, 1995; Stinson, 2006). A guiding tenet of this movement is the acknowledgment that the learning and teaching of mathematics is not culture-free; students at specific intersections of societal communities (racial, ethnic, economic, language, geographical) experience mathematics differently than students positioned in other communities, and these differential experiences potentially contribute to differences in performance on measures of mathematics achievement and competence (Stigler & Hiebert, 1999). A thread of this work focuses on examining U.S. teachers mathematics instructional practice from sociocultural perspectives (Franke, Kazemi, & Battey, 2007) and conceptualizing mathematics learning environments that are equitable and responsive to the needs and experiences of all learners, but particularly U.S. mathematics learners from historically marginalized groups. This work is daunting in that it must consider and respond to group differences and characteristics along racial, ethnic, and class lines (e.g., achievement patterns, learning styles, home and community environments), yet avoid the promotion of policies and practices (academic profiling, tracking, ability grouping, and so on) that, despite best intentions, further marginalize the groups they were designed to support (Oakes, 2008). This work must be responsive to an evident phenomenonunderperformance and underparticipation of African American and Latino students in school mathematics and mathematics-related professionsyet not feed stereotypes of African American and Latino students as inherently deficient by birth into their respective ethnic groups, nor pathologize students parents, homes, and communities. Despite these challenges, a few researchers are forging ahead into this space.
If the relationships between teacher knowledge, mathematics instructional practice, and students mathematics achievement are viewed through a sociocultural lens, nonmathematical dimensions of teachers knowledge, namely knowledge of students lived experiences and histories, as well as teachers experiences and identities, must be examined side by side with more traditional dimensions of the knowledge that teachers draw on to teach mathematics. The small body of literature describing the particular knowledge, skills, dispositions, and insights that African American teachers bring to their instructional practices (see Clark, Jones, & Davis, 2013, this issue) exemplifies the ways in which teachers knowledge of students lived experiences and histories, as well as teachers personal experiences as members of a historically marginalized racial group in the United States, explicitly or implicitly shapes their instructional decisions. Furthermore, recent research on the work and role of African American teachers has pushed beyond viewing the African American teacher as simply serving in a role model capacity (Irvine, 1989). New directions are considering the culturally relevant (Foster, 1997; Irvine, 2002) and political pedagogies of African American teachers (Beauboeuf-LaFontant, 1999; Dixson, 2003) and closely examining the work of African American male teachers (Brown, 2009a, 2009b; Lynn, 2002). This body of literature, however, has not historically been subject centered; the existing literature tends to background the specific academic discipline to make room for more comprehensive discussions of how African American teachers knowledge, experiences, and insights influence their general approaches to instruction. A primary goal of this article, therefore, is to explore the work of two African American mathematics teachers, Madison Morgan and Floyd Lee, for the purpose of gaining a better understanding of their interactions with their African American students. Through the use of theoretical frameworks emerging in the mathematics education literature, namely students mathematics identity and socialization, this article aims to explore two research questions:
What perspectives do these teachers hold of their students mathematics identity and their role in its development?
What practices do these teachers engage in their efforts to socialize their students toward seeing themselves as doers of mathematics?
We begin with a brief discussion of the importance of considering students identity development and teachers socialization practices when exploring teacher and student interactions in mathematics classrooms. Utilizing existing frameworks of students mathematics identity development and teachers socialization practices (Anderson, 2007; Cobb, Gresalfi, & Hodge, 2009; Martin, 2000), we then present an analysis of data collected in Morgans and Lees classrooms. We conclude with a discussion of the ways these two African American mathematics teachers, and perhaps many others like them, engage in the work of socializing their students toward seeing themselves as competent, capable mathematics learners. Furthermore, we discuss how this analysis and similar work present implications for broadening teacher knowledge frameworks in mathematics education to include categories related to teachers knowledge of students mathematical experiences and dispositions (Clark, 2012).
IDENTITY AND SOCIALIZATION IN THE MATHEMATICS CLASSROOM
One promising approach to exploring interactions between mathematics teachers and their students is to examine the role that mathematics teachers presence and instructional practices play in their students identity development as mathematics learners. Some theoretical approaches to defining identity development describe it as the process of becoming a member of a community of practice (Wenger, 1998). The growing interest in incorporating identity and community of practice constructs in mathematics education literature is motivated, in part, by the opportunities these constructs provide for analyzing and explaining affective aspects of mathematics learning such as motivation, engagement, interest, anxiety, and participation (Cobb & Hodge, 2007).
Researchers have illustrated the ways that mathematics classrooms are sites for power struggles that are often related to [students] social identities (Esmonde, Brodie, Dookie, & Takeuchi, 2009, p. 39), identities including, but not limited to, racial, ethnic, or gender categories. The link between identity development and learning is further described by Nasir (2007):
The development of identity, or the process of identification, is linked to learning, in that learning is about becoming as well as knowing. It is my view that this issue of how learning settings afford ways of becoming or not becoming something or someone is central to understanding culture, race, and learning, particularly given the multiple ways that race (as well as social class) can influence both the kinds of practices within which one can become, as well as the trajectories available in those practices. (p. 135)
In the school setting, therefore, learning mathematics is far more complex than coming to know mathematics concepts that were once unknown. It is doing what mathematics learners do, being treated the way they are treated, forming the community they form, and giving personal meaning to the category of mathematics learner (Lampert, 2003). Furthermore, from an identity development perspective, mathematics instruction consists of both socializing students into the norms and discourse practices of the mathematics classroom (Yackel & Cobb, 1996), and influencing students perceptions of themselves as members of a community of mathematics learners or doers of mathematics (Boaler, 1999, 2000). According to this literature, successful doers of mathematics have well-developed mathematical identities (Cobb et al., 2009; Lampert, 2003, Martin, 2000, 2007). A synthesis of existing mathematics identity frameworks (Anderson, 2007; Cobb et al., 2009; Martin, 2000) suggests that a students mathematics identity is, in part, perceptions based, consisting of a combination of perceptions by others and perceptions of self related to a set of interdependent features. These features include: (1) students perceptions of their mathematics ability and the ways these perceptions influence their mathematics performance and achievement; (2) students perceptions of the importance of mathematics inside and beyond their current experiences in the mathematics classroom; (3) students perceptions of the engagement in and exposure to particular forms of mathematical activity, and the ways these engagements influence students seeing themselves as mathematics learners; and (4) motivations that a student possesses in his or her efforts to perform at a high level and attributions about their success or failure in mathematical contexts. Mathematics socialization (Martin, 2000, 2007), therefore, describes the processes and experiences by which individual and collective mathematical identities are shaped in sociohistorical, community, school, and intrapersonal contexts, and is an integral part of the work of the mathematics teacher (Lampert, 2003).
If, then, students at the intersections of two important realms of experience, being African American and becoming doers of mathematics (Martin, 2007, p. 147), are in the process of structuring identities in practice (Nasir, 2007), how do their African American mathematics teachers attempt to influence this process? The following examination of Floyd Lees and Madison Morgans perspectives and practices related to their role in their students mathematics identity development and formation seeks to help us better understand this work.
DATA AND METHODS
SELECTION OF CASES
Madison Morgan and Floyd Lee were purposefully selected for this analysis because of considerable differences in their life histories, pedagogical approaches, and perspectives on mathematics teaching and learning. Each teacher was observed roughly 25 times and interviewed 910 times over the course of a year. The primary data for this analysis consist of a subset of observations and interviews (Leesix interviews and eight classroom observations; Morgansix interviews and seven classroom observations).
DATA ANALYSIS AND PRESENTATION
The complexity of identity constructs creates considerable challenges when one wants to use identity as an analytic tool in education research (Gee, 2000). In an effort to make the analysis manageable, we developed a short set of codes representing dimensions of the synthesis of mathematics identity frameworks. An initial round of coding of interviews focused on Morgans and Lees perspectives, resulting in a conceptually clustered matrix (Miles & Huberman, 1994) organized by the four dimensions of students mathematics identity. A second cycle of coding of both interviews and classroom observations was conducted to identify examples of Morgans and Lees socialization actions and practices that appeared to support their students mathematics identity formation. A guiding perspective of this study is that the classroom actions and practices of participating teachers are not only efforts to impact their students mathematical understanding and proficiency but also efforts to influence positively students perceptions of themselves as capable, competent doers of mathematics (Cobb et al., 2009). This widening of the lens through which we observed mathematics practice provided us with opportunities to acknowledge, consider, and code teacherstudent interactions that may serve as implicit supports for students mathematics learning, yet may resist classification when viewed through existing mathematics best practice instructional frameworks (Interstate Teacher Assessment and Support Consortium, 2011; National Council of Teachers of Mathematics [NCTM], 1991). As a result, events such as Lees speeches on seemingly nonmathematical topics (see Johnson, Nyamekye, Chazan, & Rosenthal, 2013, this issue) could be viewed as potentially having an impact on students perceptions of self and, through that, as a potentially powerful student motivator to engage in and learn mathematical content.
It should be noted that, as analysis and interpretation of data proceeded, it became evident that Lees and Morgans socialization practices did not map neatly on to one dimension of mathematics identity or another; socialization practices appeared to touch on multiple dimensions of students mathematics identity simultaneously. In fact, in many instances, it appeared that Lees or Morgans intent was to illustrate the interdependence and connectedness of students perceptions of their mathematics ability, the importance of mathematics, the nature of mathematical activity, and their motivations and attributions. Despite the resistance of Morgans and Lees socialization practices to map neatly onto individual dimensions, we present examples of socialization practices that appeared to be most highly associated with individual dimensions in an effort to illustrate the ways that a particular practice might be employed to support students mathematics identity formation.
The analysis of the data is presented in two parts. The first part consists of brief biographical sketches of Morgan and Lee. The second part consists of a description of Morgans and Lees perspectives on each of the four dimensions of students mathematics identity, and examples of socialization actions and practices that Lee and Morgan claim or appear to engage in that are associated with each of the four dimensions.
Madison Morgan is an enthusiastic and optimistic 43-year-old African American teacher who had been teaching in the same high school for over 10 years. She had not originally planned on becoming a teacher; she completed a bachelors degree in landscape architecture and practiced in that field for a few years before returning to school and pursuing her mathematics teacher certification. Throughout her teaching career, she sought out opportunities to further her professional preparation, including receiving National Board certification the year of data collection.
Morgan was born and grew up in an urban northeastern city with a large African American population and attended predominantly African American schools during her entire K12 experience. She recalled arriving at college unaware that she was unprepared for college-level mathematics, an experience that left her feeling confused. She stated,
As a student in high school, mathematics was very easy. It was not challenging. It was very skill oriented, balancing equations, you know, uh, it didnt seem as if it required a lot of thought . . . . and like I said, in high school mathematics was really easy. However, it did not prepare me for the mathematics in college. Although, I [had] taken what I had thought were the high-order math courses, I still ended up having to start over in Algebra 1 or Remedial Algebra . . . the school system did not adequately prepare me.
Throughout our interactions with Morgan, it was evident that her perspectives and pedagogical practices were influenced by her perception that she experienced poor preparation in mathematics during her schooling experiences. She stated, As an African American teacher, I know where the school system has failed me, and its my passion to help and make sure that I dont fail my African American students the way Ive been failed. Furthermore, Morgan did not recall having an African American teacher during her entire high school experience.
Floyd Lee, a 25-year-old African American male teacher, grew up in the same community and school district in which he was teaching when we observed him. He described the community in which he grew up as African American, middle class, and blue collar. In our interaction with Lee, he consistently indicated that he was by no means a mathematics expert, or fanatically devoted to the field. He stated,
I think people see you [when you are a math major] as like this really super-smart person. I never really thought I was like super-smart. I thought I was like an average guy who just was able to pick up some things.
He felt that he was a decent mathematics student in high school and college and succeeded in his courses, yet he felt that his success in mathematics was primarily due to high expectations others placed on him and his understanding that successful completion of his mathematics courses was necessary to achieving a greater goalcompletion of high school and college. During his experiences as a student in mathematics classrooms, Lee was admittedly less interested in conceptual understanding and development of his reasoning skills; he appeared to be far more interested in getting the mathematical job in front of him done for the purposes of completing requirements.
Lee recalled having no African American mathematics teachers in high school or college and recognized that his professional path is an uncommon one for African American males. He stated,
You know, being Black, you know, being a man, you know, and being younger too . . . thats a different look all in and of itself . . . you know what I mean? But at the same token [italics added], I do understand mathematics and Ive been teaching mathematics, you know, or working with people in mathematics for a while now.
Lee attended a historically Black college in his home state and chose to teach in the district where he attended school and lives, out of his concern that the students in his community are underserved and in need. He stated,
I think it just kind of happened that way, that I ended up coming back to work with the people who helped me to get to where I am and to service the community that I grew up in . . . I didnt really want to go to the other ones [districts] because I felt like they had, they were already, at least from the perception that they were already excelling. . . . In [his school district], we still need some help, you know, we need some work, so I wanted to come where, I didnt want to come to a place where it was already kind of established, I wanted to go some place where it was, okay, we need to do, we need to do a little work, you know, its not all the way where it needs to be.
Lee views his youth as both an advantage and disadvantage when working with his students. He feels connected to their perspectives and experiences, yet feels that the number of life experiences he has accumulated so far limits the extent to which he feels he can serve as an influence on his students. When discussing whether he sees himself as a role model for his students, he stated,
Uhm, I guess Ill say I do try to model, you know at least, if nothing else that, you [his students] can get through this high school thing, and, you know and start to develop your life. Cause thats really about as far as I could tell you. Cause thats about as far as I [have] gotten. Ive gotten through high school; Ive gotten through college. And Im working on establishing my career. Thats about as much as I can show you.
In summary, Morgans and Lees life histories are different and position them differently with respect to the students they teach. The following section presents Morgans and Lees perspectives on the four dimensions of students mathematics identityability, importance, nature of mathematical activity, and motivations and attributionsand highlights examples of socialization practices that appear to support each of the four dimensions.
MORGAN AND LEES PERSPECTIVES AND SOCIALIZATION PRACTICES
In an effort to articulate Morgans and Lees perspectives on their work and role in supporting their students mathematics identity development, we utilize the four dimensions of students mathematics identity mentioned previously as an organizing framework.
DIMENSION 1: MATHEMATICS ABILITY
Of the many potential roles that mathematics teachers play in their students lives, it could be argued that the mathematics teacher is a central figure in students constructions of self-perceptions of intellect and intelligence. The mathematics classroom is where many students first feel intellectually powerful or inadequate; students receive messages early in their schooling experiences that tell them that their mathematical proficiency is associated with the extent to which they are smart or bright. Furthermore, popular U.S. culture often positions mathematical ability as a proxy for intelligencethe nerd or geek, a common image of the brilliant student, is consistently portrayed as particularly talented in mathematics, science, and technology (Kendall, 1999). The mathematics teacher, therefore, is intimately involved in assisting students in constructing and managing messages of who is and gets to be smart, as well as communicating to students the advantages of being identified as intellectually powerful.
This relationship functions within a social milieu that has historically cast the African American intellect as inferior to the intellectual capacities of almost every other racial and ethnic group in the United States, but particularly inferior to the White intellect. The practice of comparing the intellectual capacity of racial groups has a long history in the United States, dating back to the mid-19th century (Gould, 1996). Over the decades, factors associated with the intelligence gap (and its contemporary counterpart, the achievement gap) have shifted from a focus on genetic, heritable factors between racial groups to a focus on social and environmental factors, like schooling, wealth, and access to power (Berends, Lucas, Sullivan, & Briggs, 2005). Reconceptualizing factors and causes of the intelligence/ability/achievement gap phenomena, however, does not necessarily mitigate its effectsone effect being that African American students are perceived to underachieve chronically in academics relative to other subgroups of the U.S. population. At the end of the day, school administrators, teachers, parents, and students must make sense of and respond to images and messages of the racial hierarchy of mathematics ability (Martin, 2007) that proliferates in the U.S. psyche. Within this historical and contemporary context, it is reasonable to imagine that some mathematics teachers engage in practices and structure classroom discourse in ways that are an attempt to undermine and dismantle the racial hierarchy of mathematics ability in their classrooms and schools. Furthermore, much of this work may be tacit and interwoven into daily interactions with students.
Morgans And Lees Perspectives Related To Their Students Ability
Both Morgan and Lee were well aware of historical and contemporary portrayals of African Americans as less able in mathematics and the ways these portrayals appear to influence students participation and performance. Morgan stated, They make it seem like African American students are dumb and cant do math. Of primary concern to both Morgan and Lee was the ways these perceptions of ability (by others and by self) appear to silence and isolate students, particularly African American male students. Lee stated,
If you have a Black male who doesnt necessarily understand whats going on, he may not ask for help. He may just kind of sit kind of to himself or kind of try to be in the group but not really in the group.
Lee in particular indicated that, from his perspective, the link between students mathematical ability and their mathematics achievement was very weak. He maintained throughout the interviews and observations that two factors separate his students identified as less able from those as more able: (1) low-performing students unwillingness to vocalize that they do not understand and need assistance, and (2) high-performing students perception that their success in mathematics is linked to the quality of their future lives.
In responses to questions related to African American students portrayal as less able, both quickly moved into identifying a multitude of factors they felt were associated with African American underachievement, factors commonly found in achievement gap discourse (Barton, 2003), such as incongruence between home and school cultures, negative peer influences, tracking, and self-fulfilling effects of disproportionate identification of African American males as special education or special needs. They both felt that most of their African American students were aware of portrayals of African Americans as having low ability in mathematics, yet also felt that some of their students consciously resisted being portrayed in this light. From both of their perspectives, the group of students who resisted this portrayal tended to be African American students in the higher math tracks or advanced mathematics courses; both stated that African American students in lower math tracks and remedial courses did not vocalize or exhibit awareness of this portrayal (or if they were aware, they did not care). Lee, in particular, felt that the sources his African American students drew on to resist this portrayal consisted mainly of persons in his students spheres of influence who communicated explicit countermessages. Lee stated,
I think theres a group of students, you know, kids who are trying to . . . Id say live above that stereotype . . . but I think a lot of that has to do with . . . who influences that. You know, your parents and you know people who . . . are in your sphere of influence . . . you know portraying that you can learn and want you to excel and you know, things like that . . . but I dont know if everybodys getting that sameeverybodys not hearing the same . . . message.
Both Lee and Morgan felt that they serve as an influence on their students perceptions of their mathematics ability and are deliberate in their attempts to influence these perceptions. Lee stated,
I think theyre getting it [message about their mathematics ability] from their teachers, home, family, parents, friends, classmates, but I think especially the messages they get from the teacher that can make or break someone . . . if they dont feel like you like them or you dont respect them, . . . you know they feel like they cant participate, they feel like theyre not able, they dont feel comfortable enough to participate, you know in the class discussion and that sort of thing . . . and theyll just kind of shut down.
From Morgans perspective, the mathematical tasks themselves carry strong messages to students and influence their perceptions of their ability, and it is her role to ensure that they are exposed to challenging mathematical tasks. She believes that students who hold negative perceptions of their mathematical ability may maintain these negative perceptions if they only engage in mathematical tasks that the students identify as remediation, regardless of whether the remediation tasks are intended to fill gaps and prepare students for more challenging mathematics tasks.
Socialization Practices Shaping Students Perceptions Of Their Ability
Both Morgan and Lee continually send messages to their students that the mathematics that may appear to be foreign and difficult to them is, in fact, quite manageable. They communicate to students that the mathematics either already resides within them or is familiar to them.
For example, Morgan communicates to students that they have been engaged in algebraic reasoning since they were born. In a classroom exchange, she stated,
How many people believe that you get algebra in kindergarten? Okay does anyone believe that you did algebra after kindergarten? Anybody believe you did algebra before kindergarten? Okay. Anybody believe you did algebra when you was a baby? Check this out check this out check this out. Think about this. Algebra based on definition, algebra is looking at patterns. And based on patterns you make predictions. . . .Francis if a baby cries and every time a baby cries, you pick it up, what do you think the babys going to do when they want you to pick it up? Its gonna cry. Because they know that every time, every time when they cried they either got picked up or they got fed. . . . If a baby realizes that every time they cry, that theyre gonna get fed or picked up, dont they realize dont you realize at that age, or dont they realize at that age that thats some sort of pattern? . . . So I was saying that . . . you learn algebra or you exhibit algebraic knowledge when youre babies.
Lee engages in similar exchanges with his students, however, his practices appear to seek to accomplish two goals. The first is to break the connection between students perceptions of their mathematics ability and their capacity to perform at an acceptable level in his classroom. He often tells his lower performing classes that they differ from his high-performing class in only two waysfocus and effort. Lees socialization practices also appear to be aimed at helping his students manage the fear and anxiety they possess that are related to mathematics. In an exchange with students, Lee stated,
Like you say fractions [and] some people start trembling . . . but a fraction . .. its not even a person . . . but you give it human emotions . . . extracts human emotions and feelings out of you . . . theyre numbers . . . they cant do anything to you . . . numbers making people scared? . . . its a number . . . on a piece of paper . . .in a book . . . whats it going to do?
Lee continually expresses to students that it is more than likely that they have seen the mathematical content and material in prior classes and that they simply need to remember or be attentive as he explains it a different way.
DIMENSION 2: THE IMPORTANCE OF MATHEMATICS
The general perception of mathematics as an important discipline is often due to its practical utility and cultural value (Gowers, 2002). Mathematics undergirds a multitude of disciplines, including engineering, physics, and computer sciencesdisciplines central to technological innovation and economic progress. In recent years, the importance of improving mathematics performance of U.S. students has been the focus of federal legislation (U.S. Congress, 2001) and deliberations of high-profile panels (Committee on Prospering in the Global Economy of the 21st Century, 2007; Kelly, 2008). This focus is largely driven by the ongoing analysis of globalization trends that suggests that countries that develop large populations of well-educated citizens prepared to pursue technologically oriented professions will rise in the ranks of world wealth and power (Friedman, 2005); those countries that lag behind in the development of this human capital will suffer. Given that most U.S. citizens develop their mathematical proficiency in public schools, the mathematical performance of U.S. students is central to the economic and technological competitiveness of the United States (Committee on Prospering in the Global Economy of the 21st Century, 2007). As the language of globalization continues to dominate political and economic discourses, and international comparisons of mathematics performance continue to consistently suggest that U.S. students underperform relative to many other countries (National Center for Education Statistics, 2006), the importance of U.S. school mathematics will only increase.
Marginalized citizens in the United States, particularly African Americans, have historically viewed educational access and the mastery of academic knowledge as keys to progress, with higher paying jobs and better living conditions seen as the payoff. The importance of mathematics in the African American community is less clear, partly because mathematics, apart from most other academic disciplines, has historically been viewed in the United States as the intellectual domain of White males (Campbell, Denes, & Morrison, 2000) and less accessible than other academic disciplines. Martins (2000) analysis of the beliefs of a small set of African American parents and community members provides some insight into the ways in which these parents and community members come to weigh the importance of mathematics in their lives and the lives of their children. Martins findings indicate that parents and community members perceptions of the importance of mathematics are influenced by many complex factors, including their beliefs about African American status, differential treatment in educational and socioeconomic contexts, relationships with school officials and teachers, and perceived minimal opportunities to use mathematics in out-of-school contexts (such as the professions that were available to them). Although no uniform finding emerged related to parents and community members perceptions of the importance of mathematics, there was considerable rhetorical support for their students success in mathematics.
Morgans And Lees Perspectives Related To The Importance Of Mathematics To Their Students.
Considering their professions, it is not surprising that both Morgan and Lee both view mathematics as extremely important to their students lives. Their comments focus mainly on the role that mathematics will play in their students future academic and professional pursuits. More specifically, both view students basic understanding of algebra as extremely important. Morgan stated,
Mathematics, especially, algebra. Algebra is like the threshold to thinking, high-order thinking, and its the threshold to engineering, architecture, landscape architecture, doctors, lawyers, logic, business. You know, it opens the door to a lot of white-collar positions. It opens the door to a better life.
When prompted to discuss the importance of mathematics in the lives of their African American children, their views, however, were somewhat split. Morgan viewed mathematics as particularly important for her African American students in its potential as a mechanism through which her students might view their world, their conditions, and the inequities they experience as African Americans (Gutstein, 2006). Lee, however, did not view mathematics as any more important for African American students than any other group, nor did he mention its power as an analytical tool through which his students might view the world. Lee primarily spoke of the importance of mathematics and the benefits of mathematical proficiency in terms of his students short-term academic successperforming successfully on the high school graduation examination, graduating from high school, and completing college. He acknowledged that engagement in mathematical activity teaches you how to think, that solving algebraic equations opens up your mind, and that mathematics is one of the more useful things in your life . . . and without it youd be in trouble. Yet he primarily views the learning of mathematics as a means to a narrow yet very important end: obtaining a passing score on the mathematics portion of the high school graduation examination. At one point in the interview, Lee stated his views on the mathematics his students were learning:
To me its [math] so insignificant. Granted, it is important. Dont get me wrong. I dont want to say, you know, Im notIm a math teacher so I have to. But to me, its soin the broad scheme of your life, wherelike, granted, mathematics is a part of your entire life, but as far as actually applying some of the things that we do in the classroom and the broad scheme of your life, probably not gonna take place. . . . So when kids ask you questions, like, At what point am I gonna be doing this? . . . I do have to say probably never. When are you gonna need to know how to factor aside from right now? Probably never.
Yet when discussing the graduation assessment, he stated,
I think we have some children like that who dont think that the fight is as big as it really is. So thats why theyre not taking the time to really get ready for it [the graduation test]. But theyre gonna get knocked out in a minute, and then theyll be mad, wondering What happened? Well, thats because you thought that it wasnt that serious and it was a joke. Its not gonna be a joke when youre on your behind looking up at the stars or looking up at everybody else walking across that stage getting their diploma, cause you thought the fight wasnt as big.
Morgan and Lee were asked directly if they felt their students viewed their success in mathematics as a contribution to the African American community. Neither felt that their African American students connected their mathematics success to improving conditions in the African American community. Morgan stated, Theyre seeing it as an individual. . . . How its going to help them individually, but not how it can benefit, how they use their mathematics to benefit the conditions of the African American culture.
Lee made a similar comment when asked if he felt that his students viewed their success in mathematics as a contribution to the African American community. He stated,
Tell you the truth, I think they only see it as getting something for themselves. I dont think they really look at it as, you know, Oh, Im helping the community. . . I think a lot of times they just looking at, you know, trying to get mine.. . . Now Im not saying thats everybody, . . . but I think they just trying to think about, you know, Im just trying to get mine so I can have, you know, my stuff.
Although both made reference to the potential influence of students perception that their mathematics success could be a positive contribution to their personal growth and success and to the greater African American community, neither teacher felt that he or she was in a position to guide his or her students explicitly in this direction. Beyond preparation for the graduation assessment, it appears that neither Lee nor Morgan felt prepared or empowered to push students to see their mathematical performance and success beyond mostly short-term, individualistic attainment. Furthermore, their statements indicate that their current students, although willing to identify themselves as Black or African American, did not consistently reference themselves as part of a larger African American community and did not associate their mathematical success with being an asset or contribution to the larger African American community.
Socialization Practices Shaping Students Perception Of The Importance Of Mathematics.
As stated previously in this article and in additional analysis of her practice (see Birky, Chazan, & Farlow Morris, 2013, this issue), Morgan focuses almost exclusively on engaging students in tasks she believes are meaningful and that will, indirectly, shape her students perspectives of themselves as mathematics learners and of the role mathematics plays in their lives and the world around them. The socialization practices we observed her employ, therefore, were less explicit, yet no less important. Lee, however, employs a wide range of colorful, powerful analogies during discussions with his students about the importance of performing well in mathematics. However, his messages related to the importance of mathematics were typically connected to students performance on the mathematics portion of the high school graduation examination. A most vivid analogy was his comparison of his students preparation and effort to those of a boxer. He often referred to the high school graduation assessment as the opponent, himself the trainer, and his students the fighters. In an exchange early in the school year, Lee presented this analogy to his students:
How many watch boxing? Anybody watch boxing? Anybody ever seen a fight before? Anybody ever been in a fight before?
Been in a fight.
Been in a fight.
But anyway, if you seen a fight or youve been in a fight . . . we have a fight on our hands. Our opponent is the High School Assessment. Thats our- that is what were fighting to get. Thats what were trying to conquer. Were not fighting each other. Were fighting the test. Our goal is to whoop the test. Now are you following me? Our goal is to whoop the test. Now in order to whoop the test you have to be what? Hello?
You have to study. And be prepared, right? You cant just go in there, you cant just go into this fight and not know your opponent, right? Cant just step in there and be like, Okay . . . I aint study, I aint do nothing all school year. Im just gonna go take the test. It doesnt work like that. Cause whats gonna happen if youre not prepared? (pause) Hello?
Youre gonna fail. Translation using fight terms, whats gonna happen?
You gonna lose.
You gonna lose! Youre gonna get your . . . whooped. Am I right?
Morgan typically communicated the importance of mathematics through showing students that mathematics is all around them in their everyday lives.
DIMENSION 3: THE NATURE OF CLASSROOM MATHEMATICAL ACTIVITY
Contemporary perspectives of mathematics learning and teaching encourage teachers of mathematics to engage students in activities that build childrens mathematical proficiency far beyond ways in which it has been traditionally perceived (Kilpatrick, Swafford, & Findell, 2001; NCTM, 2000), that is, mastery of a narrow range of mathematical concepts and skills focused mainly on number sense and computational fluency. Proponents of the contemporary perspective suggest an expansion of mathematics content that children are traditionally exposed to at all grade levels, including algebra, geometry, measurement, probability, and statistics. Furthermore, this perspective emphasizes specific mathematical processes that children are expected to apply and utilize as they experience mathematical content in their classrooms, including reasoning, communicating, higher order problem solving, meaning making, and developing an inquisitive mathematical disposition (Kilpatrick et al., 2001).
In recent years, researchers have conducted large-scale studies documenting mathematics instructional practices in U.S. classrooms (Stigler & Hiebert, 1999; Weiss, Banilower, McMahon, & Smith, 2001; Weiss, Pasley, Smith, Banilower, & Heck, 2003). Findings indicate that despite considerable investment by school districts to bring contemporary visions of math teaching and learning to their classrooms, mathematics instructional practices in the United States are typically highly teacher centered and directed, focused on basic skills acquisition, and provide limited opportunities for students to engage in reasoning and problem solving, particularly as students advance through grade levels. It is evident that on average, mathematics instructional practices in the United States are not focused on deliberately and strategically positioning opportunities for students to engage in cognitively demanding mathematics tasks or to develop an inquisitive stance toward mathematics (Weiss et al., 2003). In short, mathematics instructional practices in the United States are stubbornly stable and difficult to influence once established within the school culture (Stigler & Hiebert, 1999).
If mathematics instructional practices across the United States are cast as traditional (i.e., predominantly teacher centered and skills based), mathematics instruction in urban schools serving low income, high-minority communities tends to be perceived as chronically traditional (if not debilitating) and is particularly targeted for transformation (Haberman, 1991; Knapp, 1995). There has been considerable investment in professional development and resources related to mathematics instruction in urban districts over the past two decades (i.e., NSF Systemic Initiatives); however, direct observations of mathematics instructional practices across the United States indicate that there appears to be persistent patterns of differential quality of instruction across types of communities (urban, rural, suburban), in classes with varying proportions of minority students, and in classes of varying ability levels (Weiss et al., 2003). Of importance here is the extent to which groups of students see themselves as competent, powerful mathematics learners as a function of the nature of the mathematical activity they experience in the classroom. As schools and teachers are increasingly held accountable for student performance on mandated assessments, low-performing urban schools are increasingly incorporating pacing guides to provide students with opportunities to be exposed to appropriate content; however, some teachers find pacing guides constraining and feel that they must move through content prematurely despite inclinations to broaden the nature of mathematical activity (Marsh et al., 2005).
Morgans And Lees Perspectives Related To The Nature Of Classroom Mathematical Activity.
It is evident that Morgan and Lee both want their students to be successful in mathematics; however, the nature of mathematical activity in their classrooms is starkly different. The nature of mathematical activity in Morgans class could be characterized as a quest for mathematical coherence and meaning (Birky et al., 2013, this issue). To this end, Morgan regularly edits, modifies, and reorganizes the activities in the course curriculum guides developed by the district to create units and lessons that she described as holistic. Of interest here is why she would engage in this practice, particularly when the activities and contents set forth in the curriculum guides are designed to ensure adequate coverage of content prior to testing. It appears that the most influential factor in her decisions is her experience as a mathematically underprepared college student despite having been successful in her mathematics courses in high school. Morgan stated,
I want them to feel secure in their mathematical understanding. I want them to be able to go onto college and show somebody. Oh, well here. Let me help you do this. Or, when the [college] professor is going up there and teaching something in their teacher-centered classroom and talking above folks heads. My kid can or my children, my students can say, Oh, I remember Ms. Morgan broke it down to me. And they can connect it to something that theyve already seen. And then, help them to connect onto what the professor may be saying, you know.
Morgan held strong views related to her concerns that low-performing students experience repeated content year after year and that this repetition erodes their mathematics disposition and enjoyment of mathematics. She stated,
[Students say/think about traditional classrooms] Your class is boring. Youre teaching me stuff that I have seen how many times? . . . How to freakin divide decimals? How to multiply decimals? Ive learned this in fourth grade, Ive learned this is fifth grade, Ive learned this in sixth grade! Come on now!
Lee, however, views the repetition of mathematics content from year to year as an opportunity to reinforce known skills and learn skills and concepts that students may be missing. Furthermore, Lee sees repeated exposure to content as useful in the service of preparing students for the graduation test.
As mentioned earlier, Lee feels that his primary responsibility is to provide his students the opportunity to acquire the mathematical knowledge they will need for the state assessment. He senses the pressures from the district to prepare his students for the assessment, and the nature of mathematical activity in his classroom reflects this awareness. Lee stated,
I told my students that you dont have to be a math genius to pass that one [math portion of the state graduation examination]. You just have to be able to read, comprehend it a little bit, and notice certain wordsyou do have to have a little vocabulary. But essentially thats really all youre doing.
Lee feels that he would do things differently if he did not feel the pressures to follow the curriculum guide closely; however, the changes he feels he would make are not related to altering the nature of mathematical activity in his class. As he explained, the shift would consist of taking the time to establish deeper relationships with his students:
So without the [state assessment], I would do things differently . . . I would have class sessions, but I dont think they all be related to math per se. Because one of the things I think I would try to infuse in my classes is that, yes, this is important, and you need to know the math, but you have to understand that there is a life outside of [the school] that we have to deal with too. And Im nobodys parent or anybodys counselor, but at the same token, I feel that its part of my responsibility to help prepare you for not just how to pass my class, but how to be successful outside of my class . . . because sometimes they feel like adults dont really try to understand what they are going through . . . some of us [adults] are so far removed that we cant be touched anymore. But I dont feel like Im in a position where I cant be touched.
In summary, both Morgan and Lee hold the perspective that the nature of mathematical activity their students engage in shapes their students perceptions of themselves as mathematics learners. Lee is interested in diminishing students perceptions that the mathematics at hand is difficult, whereas Morgan wants her students to perceive the mathematics at hand as challenging and believes that holding this perception of the nature of the mathematical activity as challenging is a motivator for her students engagement.
Socialization Practices Shaping Students Perception Of The Nature Of Mathematical Activity.
Both Morgan and Lee draw on their intimate understanding of their students surroundings and social contexts in their practice. Lee, in particular, makes use of his knowledge of African American youth culture in his classroom, and his oratorical flair serves him well in the service of contextualizing explanations of mathematical concepts in language and referents that are relevant and familiar to his students. Examples of this can be found in his explanation of domain and range, in which he made connections to this concept and the geography of the neighborhoods and state in which his students live, as well as a very lively and entertaining explanation of a mathematical function in which he brought a group of girls and boys to the front of the room. Taking advantage of the excitement, humor, and playful discomfort students experience when paired as fictive boy-girl romantic couples, he identified the group of girls as the range and the boys as the domain. He went on to explain that for a relation to be a function, each boy can only have one girlfriend (each X in the domain can only map to one Y in the range). Through use of terms often heard in the language of African American youth culture, he went on to very comically describe different configurations of relationships and asked the class if the different configurations represented a mathematical function:
Alright now, heres the thing. Remember, lets try to use our maturity here. Okay? This may become a little comical, but try to keep it withinokay? Can we do that? Im just speaking generally, but to some of you, cause you know you all like to take stuff and run with it. Alright, now this group is still intact. Right? However, what Ileana does not know is that Shamar only talks to her like through the end of this period cause after the end of this period, they dont really see each other no more, you know, for the rest of the day. So Shamar feels like, you know, I need somebody else, you know, what Im saying, help me out, get through third, fourth period. You know, what Im saying, the afternoon hours. So he goes and talks to Dana. Nice quiet, you know, real cool people. You know what Im saying? So, thats what happens. But Ileana doesnt know that though. Shamarso to the end of this period, Shamar talks to Ileana, but after the periods over, blam, third and fourth period, he needs somebody else, you know what Im saying, get him to the end of the day. Cant, you know, she be on him too much. You know what Im saying. Its okay through the lunch periods, but then third and fourth period needs somebody else. Right Dana?
Youre not agreeing with me. Dont worry about it. Alright, so Shamar is not only paired with Ileana, but hes also paired with who?
Dana, correct? Now, based on what we said about a function, would this be a function?
No, why not?
Whereas Lee tended to contextualize explanations of concepts through the use of referents that were familiar to students, Morgan regularly modified mathematical tasks in ways that demanded that students collect data about themselves and their surroundings (see Birky et al., 2013, this issue).
DIMENSION 4: MOTIVATIONS AND ATTRIBUTIONS
Students are motivated to engage in or disengage from mathematical activity because of a host of factors. Studies of student motivation in mathematical contexts have identified intrinsic (deep interest, joy, or pleasure in engaging in mathematics) and extrinsic (grades, approval by others, avoidance of punishment) motivators that appear to influence student performance (Middleton & Spanias, 1999). Furthermore, studies have identified factors to which students attribute their mathematical success or failure, including ability, effort, task difficulty, luck, and classroom context (Yailagh, Lloyd, & Walsh, 2009). Students motivations to engage and their attributions for their performance are part of a complicated system, however, there is consistent evidence that students motivations and attributions develop early, are stable over time, and are influenced by teacher actions and attitudes (Middleton & Spanias, 1999). Last, it is important to note that decades of analyses of school achievement, course-taking patterns, and standardized-test data reveal prevalent patterns of inequity in students access to significant mathematical ideas (Nasir & Cobb, 2007, p.1). As a result, it is well evidenced that U.S. minority students, language-minority students, poor students, and, to some extent, girls underperform mathematically relative to U.S. middle-class White students. Yet what is unclear are the ways that patterns of performance, success, and failure between subgroups are shaped, in part, by subgroup collective motivations and attributions.
Morgans And Lees Perspectives On Their Students Motivations And Attributions
Both Morgan and Lee felt that they taught some very highly motivated students yet were concerned that too many of their students were not motivated to do what was necessary to perform at a high level in their classes. Lee felt that his highly motivated students had both appropriate supports and influences (parents, peers, and so on) and that they connected success in his mathematics classroom with larger goals and aspirations. He felt that his less motivated students were quite capable of doing well in his class but did not have a support and accountability system in place to keep them motivated. In reference to a conversation he had with his class, he stated,
I told them in there I said you know, I was able to do what I did because somebody always had their foot in my behind. . . thats why youre [his students] not motivated because nobody has their foot in your behind telling you this is what you need to be doing. The best you might get is the 90 minutes here with me.
Furthermore, Lee felt that the primary motivator to do well in his class should not necessarily be the desire to gain a deep mathematical understanding; students should simply want to be good, solid students. He believes that for most of his students, motivation to perform well in his class emanates from a mindset of striving to be a good student and seeing the rewards of being a good student. From his perspective, unmotivated students, despite external appearances, are not confident in their abilities and dont have a sense of a future self. He stated, I guess some would say they [unmotivated students] dont want it. I dont know that its they dont want it more so than they dont believe that they can get it. Lee sees his primary role as helping his students develop the mindset of the good student and use a vision of themselves beyond high school as a motivator to do well in mathematics.
Morgan believes that motivation is a function of the extent to which students perceive mathematics as fun, exciting, connected to their lives, and meaningful. She believes that students are motivated to engage and succeed when the tasks at hand are accessible yet challenging. She stated,
If theyve not been successful in the past with mathematics, then they come in already with a defeated outlook . . . you just [have] to do stuff, hands-on stuff just to break that ice and talk about it and get the opportunity to talk about their understanding that will help alleviate that. And often times, you hear kids say oh, I used to hate math, but you make it fun. I think that when you make it fun, you make it more tangible to the kids. Then, the anxiety level had a tendency of subsiding.
Both Morgan and Lee hold perceptions of what motivates students and the attributions students make for failure and disengagement. Lee holds the perception that students motivations and attributions are linked to students larger academic identity and perception of their future self. Morgan, however, views her students motivations and attributions as functions of the mathematical tasks they have access to.
Socialization Practice Shaping Students Motivations And Attributions
Both Morgan and Lee consistently employ the use of personal story and history in an effort to provide their students with windows into their experience as mathematics learners. Their use of personal history, however, differs. Morgan indicated in her interviews that she uses her personal story to motivate students through communicating to them that the challenging work in which they are engaged in her class was not available to her when she was their age. From her perspective, her story is valuable in that it sends the message, I deliberately push you, challenge you, and demand that you think because I dont want you to have the same experience that I did. Lee also made many references to using his personal story; however, unlike Morgan, it appeared that he used his story as a potential model trajectory for his students. He stated,
Because Im not that far removed from college, we talk about college a lot because a lot of them have college questions. We talk about how you interact with your parents, talking to your parents, and things like thatyou know, about adults and our expectations of young people. . . . And they ask me questions about college and what its like . . . and I tell them, Its nothing like this, but if you wanna get there, heres what you need to do.
Both Morgan and Lee communicate to their students that success in the mathematics classroom is critical to their future success in mathematics classrooms and other numerous endeavors. Lee, however, provides an additional motivation for them to perform well in future mathematics classes: Their mathematical performance is a direct representation of him and his teaching capacity, and he will not allow them to tarnish his reputation by leaving his classroom unprepared for their future math courses. In an exchange with his students, he stated,
They [students future math teachers] gonna see what I did as a teacher, they gonna see what you did as a student. Cause you all represent me. You represent me. Somebody not knowing how good of a teacher I am or how well I teach, you all are a representation of what Im doing. Which is fine. Thats alright. Cause I know that you all are going to represent yourselves well and I know that you represent me.
Lee continuously communicated that if they heed his guidance and instruction, they will be identified with him, and it will be evident to all that he was their teacher and that they were his pupils.
It is evident that Morgan and Lee have much in common. They are both African American mathematics teachers, well respected by their school communities. Furthermore, this analysis suggests that Morgan and Lee hold perspectives and engage in practices that tacitly or explicitly aim to cultivate in their students positive, healthy mathematics identities. The data reveal a complex relationship between Morgans and Lees perspectives on race, their personal experiences as African American mathematical learners, and their perceived role as a mathematics teacher of African American students.
Three important themes emerged from the analysis. First, despite these commonalities, Morgans and Lees experiences, perspectives, and practices differ in ways that reveal two very different visions of what might be considered a positive mathematics identity, and yet both visions maintain connections to race and students racial identities. Second, we found that a subtle paradox exists between the driving passions and motivations that both teachers communicated in their interviews related to their teaching of African American students, and the practices they employ in their classrooms. And third, both teachers tapped into the power of representation as a motivator for students current and future success in mathematics.
DIFFERING VISIONS OF A STRONG MATHEMATICS IDENTITY
Morgan attempts to help her students see mathematics as a powerful tool to unlock and understand complicated phenomena, as a resource that students can use in investigations of everyday occurrences, and as a window through which students might see their worlds. The mathematics identity it appears she is attempting to cultivate in her students is characterized by students seeing themselves as mathematically inquisitive and able; seeing mathematics as important for the purposes of inquiry and understanding their world; and seeing mathematical activity as rich, problem-based experiences reliant on multiple interconnected mathematics concepts. In many ways, Morgans vision of a strong mathematics identity is well aligned to what Kilpatrick et al. (2001) defined as a productive mathematical disposition, particularly in regard to the importance of students seeing themselves as being on a quest to see sense in mathematics.
The data also revealed the ways that Morgans view of a positive mathematics identity is connected to her personal story, her racialized experience, and her students racial identity. Morgan sees herself as an African American female poorly prepared in mathematics and initially prepared for a different profession. Over time, it appears that Morgan has negotiated these experiences in ways that serve as instructional resources she draws on in her mathematics pedagogy. Her pedagogical approach is in part motivated by her desire that her students avoid her experience. Furthermore, discourse in Morgans classroom is almost exclusively mathematical in nature; she rarely engages in conversations related to life lessons or the responsibilities of students to the extent that Lee does.
Lee too is attempting to build strong mathematical identities in his students, yet his vision of a strong mathematics identity is constructed somewhat differently than Morgans. Lee, through his speeches (see Johnson et al., 2013, this issue) and socialization practices, is attempting to cultivate a mathematics identity in his students that is more tightly tied to their broader academic identity and their capacity to successfully navigate high school and college. He is less concerned that his students see sense in mathematics and more concerned that students see sense and importance in doing well in mathematics by way of examinations and grades. His vision of a strong mathematics identity, therefore, consists of one in which students focus less on perceptions of their mathematical abilities and more on their effort and perseverance; locating the importance of mathematics in its immediate role in their lives (success on the mathematics portion of the high school graduation examination); and viewing mathematical activity as ordered, structured, and uncomplicated. Lee continually encourages his students to take the stance that unlimited doors will be opened to them if they view their engagement and effort in his class as a means to a very important endhigh school graduation.
Like Morgan, it appears that his vision of a strong mathematics identity is in part motivated by personal experience. As both peer and authority to his students, Lees mathematics pedagogy is in part motivated by his experiences as a young African American male recent college graduate. He feels that his expertise lies in understanding how to navigate the terrain of the college-bound African American male youth, and he invests heavily in helping students realize that their attention to the necessary responsibilities is associated with that trajectory. He feels that assisting them along this trajectory is his primary role. Lee is focused on helping students understand the importance of consistent school attendance, completion of homework, structure, appropriate effort, and the power of peer influences. He encourages his African American students to live above the stereotype and advises them to take a stance that they need not fundamentally change who they are to be successful in his classroom or school; they simply need to recognize the importance and ramifications of their decisions, their focus, and their effort. Mathematics is seen as an academic context that he uses to instruct them in these larger life lessons.
PARADOXICAL NATURE OF PERSPECTIVE AND PRACTICE
Our analysis of the data also reveals a subtle yet striking paradox. In interviews, Morgan spoke explicitly of her interest in ensuring that her African American students in particular experience high-quality mathematics instruction. She expresses deep passion in teaching her African American students. When asked how her classroom might be different if she taught exclusively non-African American students, she stated,
I still would teach with passion and I still would stress that they understand, but the spice would be missing. You know, how that you make a dish and you have just about all the ingredients, but that thing that gives it that kick? That special ingredient that gives it that kick. I think that special ingredient wouldnt be there. You know, and although I would try and want it to be there, you know, it would be hard for me to put that in because the plight isnt there. Not the plight that I see. You know what Im saying? The plight. The plights that my children experience are not the same plights in a nonAfrican American class and because I know their plight, I can put that special ingredient into it.
Lee, on the other hand, although cognizant of the particular needs of his African American students, did not view his passion for teaching his African American students and his interest in ensuring their success as in any way different from his passion for teaching, and interest for, all his students. Yet, when observing Lee, he, much more so than Morgan, consistently utilized African American and youth culture referents in his classroom and employed African American verbal language patterns. Furthermore, his messages to students consistently conveyed themes of the importance of resisting stereotypes, resilience, and overcoming obstaclesthemes common to research focused on the intersection of African American students racial and academic identities (Nasir, McLaughlin, & Jones, 2009). Of importance to consider here is, why would Lee view his perspectives and practices as marginally motivated by his concerns that his African American students need particular and focused supports, yet when observing his classroom and interactions with his African American students, it appears that he is highly motivated by his concerns related to the particular challenges that African American youth experience in school and society? Furthermore, how is it that Morgan can speak of being highly motivated to meet the needs of her African American students, yet rarely engage with her students in the ways that Lee does? We conjecture that this paradox may partially be explained by Morgans perception that her African American students mathematical empowerment and sophistication are their best defense against the future challenges they may face. We further conjecture that despite classroom interactions that suggest otherwise, Lee does not view his practices as motivated by a focused interest on African American students in part because of his age (25). His young age directs him to draw on youth culture in ways that are perhaps somewhat unconscious to him. In other words, his use of language, his interaction style with his students, and cultural referents are not scripted and deliberate; they closely resemble the ways he socializes with his personal peer group. Yet, whereas his youth may partially explain his use of youth culture as an instructional resource, it does not explain his focus on encouraging students to live above stereotypes, on resilience, and on overcoming obstacles. We feel that there is much more to be explored about Lee, as well as other young teachers of color, in regard to the complexities that emerge when considering their knowledge of youth culture, their own identities, and their motivations to support students within their reach who share their racial or ethnic background.
THE ROLE OF REPRESENTATION
We believe that this exploration provides an illustration of Wengers (1998) position that teachers are far more than representatives of the institution and upholders of curricular demands (p. 276); they are doorways into the adult world. Throughout the interviews, it was evident that in their efforts to construct their own healthy mathematical identities, Morgan and Lee consistently engage in the act of reconciliationfinding ways of making their various forms coexist. Our analysis reveals that in their efforts to influence their African American students mathematics identities, they serve as successful models of this reconciliation. As Wenger (1998) stated,
Teachers need to represent [emphasis added] their communities of practice in educational settings. This type of lived authenticity brings into the subject matter the concerns, sense of purpose, identification, and emotion of participation . . . what students need in developing their own identities is contact with a variety of adults who are willing to invite them into their adulthood. (p. 276)
Ironically, as can be seen in Lees use of the term, represent is commonly used in the African American communitys lexicon to refer to the act of doing an outstanding job that reflects well on ones community, family, and support system. Irizarry (2009) stated, Representin . . . refers to actions carried out by individuals with knowledge and pride in the fact that they reflect the various socially constructed communities of which they might be members (p. 494). As our analysis reveals, Morgan and Lee represent themselves and their communities in their classrooms in many implicit and explicit ways. It is our belief that their position at the intersection of two important realms of experience: being African American and becoming doers of mathematics (Martin, 2006, p. 147) assists them in their efforts to navigate the same experience with their African American students.
Yet the role of representation, for both Lee and Morgan, takes on an additional function. Both acknowledge that their presence and experience represent a community that they want their students to see and have access toAfrican American doers of mathematics. Yet Lee and Morgan also want their students, in current and future mathematical experiences, to represent respectfully the classroom community from which they are emerging. Lee explicitly sends the message to his students that they are representations of him personally; Morgan implicitly sends the message that her students will represent the exposure to the mathematically challenging tasks they experienced in her classroom.
It is important to note, as other researchers have, that teachers of varied races and ethnicities bring with them valuable cultural experiences and perspectives, can engage in practices that support academic success of their African American students, and have expressed and maintained very high expectations for their African American students (Ladson-Billings, 1994). Furthermore, the perspectives and practices of Morgan and Lee are not common to all African American teachers, nor are they exclusive to a subset of African American teachers. This analysis, however, can serve as further evidence that all teachers draw on a host of resources when making pedagogical decisions and rely on much more than their knowledge of content and pedagogy in their interactions with their students. Like Morgan and Lee, it is likely that teachers hold a variety of visions of a strong mathematics identity and believe that these different visions serve students academic and professional trajectories in different ways. This analysis also encourages the mathematics education field, particularly in the areas of teacher education and professional development, to reconsider the emphasis on teachers mathematical and pedagogical knowledge (albeit critical resources on which teachers must possess and rely) and consider additional domains of mathematics teacher knowledge, namely teachers knowledge and understanding of students mathematics identity formation and development (Clark, 2012).
It should also be noted that through the utilization of identity and socialization frameworks, findings of this study build on and extend existing pedagogical frameworks identified in the culturally relevant and culturally responsive teaching literature. Although it has been written that culturally responsive teaching is validating, comprehensive, multidimensional, empowering, transformative, and emancipatory for students (Gay, 2000), this study points to the potential factors that teachers, particularly African American mathematics teachers, identify as conscious or unconscious rationales for engaging in such progressive pedagogies. The contribution of this study to this body of literature, therefore, is two foldthe presentation of instances of what teachers of African American students do in their efforts to positively influence their students performance and the exploration of motivations that teachers identify in their efforts to create learning environments reflective of these progressive pedagogies.
The overarching purpose of this exploration was to provide an account of how two African American teachers perspectives and experiences inform their efforts in assisting their African American students in developing healthy mathematics identities. In an era of sorting and categorizing students by mathematical performance and achievement, it can be argued that one influence on Lees and Morgans practice is their drive to assist in the dismantling of racialized hierarchies of mathematical ability (Martin, 2000). The findings from this exploration encourage further study and raise important questions, as do the results of much of the work in this space. As an emphasis on high performance of U.S. students in mathematics increases because of globalization trends, how will teachers of color, particularly African American mathematics teachers, be viewed as a resource to support African American students performance and success? How can a deeper understanding of their perspectives and experiences be of use to all mathematics educators? If high-quality mathematics instruction is a sincere goal of the mathematics education community, we encourage researchers interested in these and related questions to explore the ways that teacher identity, including those dimensions associated with race, class, and gender, serves as an instructional and motivational resource for teachers in their efforts to create meaningful learning environments for their students.
This work was developed through the support of a grant from the National Science Foundation, Grant No. DRL 0426253. Any opinions, findings, and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the view of the National Science Foundation.
Anderson, R. (2007). Being a mathematics learner: four faces of identity. Mathematics Educator, 17(1), 714.
Atweh, B., Forgasz, H., & Nebres, B. (2001). Sociocultural research on mathematics education: An international perspective. Mahwah, NJ: Erlbaum.
Barton, P. E. (2003). Parsing the achievement gap: Baselines for tracking progress: Policy information report. Retrieved from http://www.ets.org/Media/Research/pdf/PICPARSING.pdf
Beauboeuf-LaFontant, T. (1999). A movement against and beyond boundaries: Politically relevant teaching among African American teachers. Teachers College Record, 100(4), 702723.
Berends, M., Lucas, S., Sullivan, T., & Briggs, R. J. (2005). Examining gaps in mathematics achievement among racial-ethnic groups, 19721992. Arlington, VA: Rand.
Birky, G. D., Chazan, D., & Farlow Morris, K. (2013). In search of coherence and meaning: Madison Morgans experiences and motivations as an African American learner and teacher. Teachers College Record, 115(2).
Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40(3), 259281.
Boaler, J. (2000). Exploring situated insights into research and learning. Journal for Research in Mathematics Education, 31(1), 113123.
Brown, A. L. (2009a). O brotha where art thou? Examining the ideological discourses of African American male teachers working with African American male students. Race, Ethnicity and Education, 12(4), 473493.
Brown, A. L. (2009b). Brothers gonna work it out: Understanding the pedagogic performance of African American male teachers working with African American male students. Urban Review, 41(5), 416435.
Campbell, G., Denes, R., & Morrison, C. (2000). Access denied: Race, ethnicity, and the scientific enterprise. New York, NY: Oxford University Press.
Clark, L. (2011). Conceptualizing teachers knowledge of students mathematics identity formation. Manuscript submitted for publication.
Clark, L. M., Jones, T., & Davis, J. (2013). Conceptualizing the African American mathematics teacher as a key figure in the African American education historical narrative. Teachers College Record, 115(2).
Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 40(1), 4068.
Cobb, P., & Hodge, L. L. (2007). Culture, identity, and equity in the mathematics classroom. In N. S. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas (pp. 159171). New York, NY: Teachers College Press.
Committee on Prospering in the Global Economy of the 21st Century. (2007). Rising above the gathering storm: Energizing and employing America for a brighter economic future. Washington, DC: National Academies Press.
Dixson, A. D. (2003). Lets do this! Urban Education, 38(2), 217235.
Esmonde, I., Brodie, K., Dookie, L., & Takeuchi, M. (2009). Social identities and opportunities to learn: Student perspectives on group work in an urban mathematics classroom. Journal of Urban Mathematics Education, 2(2), 1845.
Foster, M. (1997). Black teachers on teaching. New York, NY: New Press.
Franke, M. L., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practices in mathematics. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225256). Charlotte, NC: Information Age.
Friedman, T. L. (2005). The world is flat: A brief history of the twenty-first century. New York, NY: Picador/Farrar, Straus and Giroux.
Gay, G. (2000). Culturally responsive teaching: Theory, research, and practice. New York, NY: Teachers College Press.
Gee, J. P. (2000). Identity as an analytic lens for research in education. Review of Research in Education, 25(1), 99125.
Gould, S. J. (1996). The mismeasure of man. New York, NY: Norton.
Gowers, T. (2002). The importance of mathematics. New York, NY: Springer.
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York, NY: Routledge.
Haberman, M. (1991). The pedagogy of poverty versus good teaching. Phi Delta Kappan, 73(4), 290294.
Interstate Teacher Assessment and Support Consortium. (2011). InTASC model core teaching standards. Retrieved from http://www.ccsso.org/Resources/Publications/InTASC_Model_Core_Teaching_Standards_A_Resource_for_State_Dialogue_(April_2011).html
Irizarry, J. G. (2009). Representin. Education and Urban Society, 41(4), 489515.
Irvine, J. J. (1989). Beyond role models: An examination of cultural influences on the pedagogical perspectives of Black teachers. Peabody Journal of Education, 66(4), 5163.
Irvine, J. J. (2002). In search of wholeness: African American teachers and their culturally specific classroom practices. New York, NY: Palgrave Macmillan.
Johnson, W., Nyamekye, F., Chazan, D., & Rosenthal, B. (2013). Teaching with speeches: A Black teacher who uses the mathematics classroom to prepare students for life. Teachers College Record, 115(2).
Kelly, A. E. (2008). Reflections on the National Mathematics Advisory Panel Final Report. Educational Researcher, 37(9), 561564.
Kendall, L. (1999). Nerd nation: Images of nerds in U.S. popular culture. International Journal of Cultural Studies, 2(2), 260283.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Knapp, M. S. (1995). Teaching for meaning in high-poverty classrooms. New York, NY: Teachers College Press.
Ladson-Billings, G. (1994). The dreamkeepers: Successful teachers of African American children. San Francisco, CA: Jossey-Bass.
Lampert, M. (2003). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
Lynn, M. (2002). Critical race theory and the perspectives of Black men teachers in the Los Angeles public schools. Equity & Excellence in Education, 35(2), 119130.
Marsh, J., Kerr, K., Ikemoto, G., Darilek, H., Suttorp, M. Zimmer, M., & Barney H. (2005). The role of districts in fostering instructional improvement: Lessons from three urban districts partnered with the institute for learning. Arlington, VA: Rand.
Martin, D. B. (2000). Mathematics success and failure among African American youth. Mahwah, NJ: Erlbaum.
Martin, D. (2006). Mathematics learning and participation in African American context: The Co-construction of identity in two Intersecting realms of experience. In N. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas (pp. 146158). New York, NY: Teachers College Press.
Martin, D. B. (2007). Beyond missionaries or cannibals: Who should teach mathematics to African American children? High School Journal, 91(1), 628.
Middleton, J. A., & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 6588.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.
Nasir, N. S. (2007). Identity, goals, and learning: The case of basketball mathematics. In N. S. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas (pp. 130143). New York, NY: Teachers College Press.
Nasir, N. S., & Cobb, P. (2007). Improving access to mathematics: Diversity and equity in the classroom. New York, NY: Teachers College Press.
Nasir, N. S., McLaughlin, M. W., & Jones, A. (2009). What does it mean to be African American? Constructions of race and academic identity in an urban public high school. American Educational Research Journal, 46(1), 73114.
National Center for Education Statistics. (2006). Comparing mathematics content in the national assessment of educational progress (NEAP), trends in international mathematics and science study (TIMSS), and program for international student assessment (PISA) 2003 assessments. Washington, DC: United States Department of Education, National Center for Education Statistics, Institute of Education Sciences.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Oakes, J. ( 2008). Keeping track: Structuring equality and inequality in an era of accountability. Teachers College Record, 110(3), 700712.
Secada, W., Fennema, E., & Adajian, L. (Eds.). (1995). New directions for equity in mathematics education. New York, NY: Cambridge University Press.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the worlds teachers for improving education in the classroom. New York, NY: Free Press.
Stinson, D. W. (2006). African American male adolescents, schooling (and mathematics): Deficiency, rejection, and achievement. Review of Educational Research, 76(4), 477506.
United States Congress. (2001). Public law: 107-110: No Child Left Behind Act of 2001. Washington, DC: Congressional Record.
Weiss, I. R., Banilower, E. R., McMahon, K. C., & Smith, P. S. (2001). Report of the 2000 national survey of science and mathematics education. Chapel Hill, NC: Horizon Research.
Weiss, I. R., Pasley, J. D., Smith, S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom: A study of K12 mathematics and science education in the United States. Chapel Hill, NC: Horizon Research.
Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York, NY: Cambridge University Press.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458467.
Yailagh, M. S., Lloyd, J., & Walsh, J. (2009). The causal relationships between attribution styles, mathematics self-efficacy beliefs, gender differences, goal setting, and math achievement of school children. Journal of Education & Psychology, 3(2), 95114.