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Social Identities and Opportunities to Learn: Student Perspectives on Group Work in an Urban Mathematics Classroom

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Journal of Urban Mathematics Education
December 2009, Vol. 2, No. 2, pp. 1845
©JUME. http://education.gsu.edu/JUME
INDIGO ESMONDE is an assistant professor in the Department of Curriculum, Teaching, and
Learning at the Ontario Institute for Studies in Education (OISE) University of Toronto, 252
Bloor St. W., Toronto, ON, Canada, M5S 1V6; email: iesmonde@oise.utoronto.ca. Her research
interests include equity and identity in mathematics education, sociocultural theories of learning,
and teacher education for social justice.
KANAJANA BRODIE is an undergraduate student in the Equity Studies program at the Uni-
versity of Toronto; email: kanjana.brodie@utoronto.ca. Her research interests include minority re-
presentation and educational equity.
LESLEY DOOKIE is a recent M.A. graduate and current research assistant in the Department
of Curriculum, Teaching, and Learning at the Ontario Institute for Studies in Education (OISE)
University of Toronto, 252 Bloor St. W., Toronto, ON, Canada, M5S 1V6; email: ldookie@oise.utoronto.ca.
Her research interests include equity in mathematics education.
MIWA TAKEUCHI is a Ph.D. candidate in the Department of Curriculum, Teaching, and
Learning, at the Ontario Institute for Studies in Education (OISE) University of Toronto, 252
Bloor St. W., Toronto, ON, Canada, M5S 1V6; email: miwa.takeuchi@utoronto.ca. Her research
interests include English language learners‘ opportunity to learn in mathematics classroom.
Social Identities and Opportunities to Learn:
Student Perspectives on Group Work in an
Urban Mathematics Classroom
Indigo Esmonde
University of Toronto
Kanjana Brodie
University of Toronto
Lesley Dookie
University of Toronto
Miwa Takeuchi
University of Toronto
In this article, the authors investigate group work in a heterogeneous urban high
school mathematics classroom. Two questions are explored: How do students de-
scribe cooperative group work in their mathematics class? How do students de-
scribe the way their socially constructed identities influence the nature of their
group interactions in mathematics classrooms? The authors present a case study
of the ways in which race, gender, and other social identities might influence the
nature of group work in reform-oriented high school mathematics classrooms.
The analysis, based on 14 interviews with high school students, focused on stu-
dents’ perceptions of group work and their theories about when cooperative
groups work well and when they do not. Students named interactional style, ma-
thematical understanding, and friendships and relationships as the most influenti-
al factors. Using an analytic lens informed, in part, by critical race theory, the
authors highlight the racialized and gendered nature of these factors.
KEYWORDS: cooperative learning, gender, identity, mathematics education, race
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 19
And then the next statement was, ―I have been attracted to someone
of the same sex,‖ and absolutely everyone in the classroom sat
down except for me. And I was standing there and, so uh. It was
just horrendous. The next 2 weeks were just really painful to go
through, and to have people treating me differently, and girls
kind of like, scooting away whenever I sat near them.
Willow, a 9th-grade, bisexual, biracial girl
Backgrounds, if our backgrounds are too different
we don’t get along. …I don’t know, [the teacher]
always seats me with people she knows
I’m gonna get into it with.
[Who do you get into it with?]
I don’t know…
most of the White people in the class.
Candie, a 10th-grade, lesbian, African American girl
n these two quotes, Willow and Candie tell the interviewer (Indigo Esmonde)
about school experiences in which their socially constructed identities had an
influence on their opportunities to learn. In the first quote, Willow describes an
activity in a social studies class where she outed herself as bisexual, and then
went through a very painful few weeks in which other girls acted uncomfortable
around her. In the second quote, Candie describes her difficulty working with
classmates who have a different background.When asked to elaborate, Candie
describes her difficulties with most of the White students in her class.
In these brief excerpts, the two students describe how some aspects of their
social identities influenced classroom collaboration. (Willow describes the impor-
tance of her gender and sexual orientation, but not race; whereas Candie describes
the importance of her race, but not gender or sexual orientation.) In many mathe-
matics classrooms, students work together with their peers, in whole-class and
small-group discussions. While student interaction has been lauded for its poten-
tial to support critical mathematical thinking and independent problem solving,
educators have also recognized that these interactions have the potential to rein-
force inequity, as highlighted by Willow and Candie‘s comments.
Several scholars have written about curricular and pedagogical strategies to
enhance cooperative learning, and the issues of equity that might arise in coopera-
tive contexts (see, e.g., Bianchini, 1999; Cohen & Lotan, 1997; Webb, Nemer,
Chizhik, & Sugrue, 1998). Throughout this corpus of research, it has become
clear that who students are influences what and how they learn together. In other
words, issues of identity are central to the learning that takes place in cooperative
I
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 20
group work. Nonetheless, there is still little research that explicitly addresses stu-
dent perspectives on their social identities and why or how they matter. In this ar-
ticle, we build on the research about cooperative learning by documenting what
students have to say about group work in mathematics classrooms. Two questions
guided our inquiry:
1. How do students describe cooperative group work in their mathematics class?
2. How do students describe the way their socially constructed identities influence the na-
ture of their group interactions in mathematics classrooms?
Identity and Mathematics Learning
We use the phrase socially constructed identities, or sometimes social iden-
tities, to refer to social categoriesincluding, but not limited to race, ethnic, or
gender categoriesthat are often imposed on people within a particular context.
We use the phrase to refer to identities that are self-imposed as well as those iden-
tities that one imposes on others. We are concerned with both because in everyday
interaction people attend not only to their own identities but also to the identities
of those around them. In this article, our goal is to understand more about which
social identities matter in mathematics classrooms, and how they matter.
Understanding the importance of social identities in structuring opportuni-
ties to learn is especially important for mathematics education because the field
has only recently begun to take equity as a central focus for research (Secada,
1995). A variety of studies have documented the racialized (Martin, 2006, 2007,
2009), gendered (Mendick, 2005), and classed (Lubienski, 2002) nature of ma-
thematics learning in classrooms across the United States. These multiple facets
of social identities operate simultaneously to structure people‘s lived experience.
Therefore, in this article, we take an intersectional approach to analyzing identity
(Crenshaw, 1991), and consider how people‘s multiple forms of identity, some-
times referred to as a ―nexus of multimembership‖ (Wenger, 1998, p. 158), influ-
ence the nature of their experiences in school.
These social categories are complex, even more so when we consider their
intersectional nature. For example, a recent study of racial identity development
in high school focused on two prominent categories for African American youth:
street savvy and school oriented (Nasir, McLaughlin, & Jones, 2009). In this
study, Nasir, McLaughlin, and Jones demonstrated the multiple forms of working-
class African American masculinities and femininities that were at play in the
school. Barnes (2000), in another classroom study, developed an analysis of two
types of middle-class masculinities in the mathematics classroom: one dominant
and one subordinate. Both of these studies highlight the importance of recogniz-
ing the multiple ways that even a single social identity category can be instan-
tiated in the classroom.
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 21
Therefore, the theoretical framework through which we view identity comes
from sociocultural theories of learning in which learners are viewed as people-in-
context and learning as shifts in identity within a particular learning context (Lave
& Wenger, 1991; Rogoff, 2003; Wenger, 1998). As an analytic construct, identity
allows the researcher to focus on individual experiences without losing sight of
larger social contexts in which identities are constructed and made meaningful.
Through participation in various kinds of social practices, individuals construct
identities and have their identities constructed for them by others (Wenger, 1998).
Nasir and Hand (2006) conceptualize identity as when
individuals come to participate in a cultural practice, they negotiate an identity that is
part what they have come to view as consistent about themselves in their lives, part
what they perceive to be available to them in a practice, and part how they are per-
ceived by social others. (p. 467)
In this conceptualization, the self, others, and socially organized practices all play
a part in shaping practice-linked identities. Thus, identities are both enduring and
shifting with each new context and experience.
The strength of the sociocultural approach is to consider identity as prac-
ticeactivity- or community-basedconstantly constructed and reconstructed in
interaction. But the strength of sociocultural theory‘s focus on practice-based
identities can also be construed as a weakness, given that with a few exceptions
(see, e.g., Gutierrez & Rogoff, 2003; Lee, 2007; Nasir & Saxe, 2003; Nasir et al.,
2009), the field has not adequately considered the ways social identities like race,
gender, and class (or socioeconomic status), interact with and inform the con-
struction of practice-based identities. Mainstream sociocultural theories are typi-
cally color-blind, and ignore the ways in which social identities are made part of
the structure of everyday practices (Nasir & Hand, 2006).
The sociocultural approach has primarily been used to focus on how indi-
viduals come to self-identify within a practice, but research has also considered
how identities are imposed by others, and how these imposed identities act to
structure a practice (Rogoff, 2003). In the classroom, how a student identifies oth-
ers can have consequences for that student‘s own learning, as in the case when a
student decides who in the classroom is ―smart‖ and therefore who might provide
her or him assistance in her or his own learning. And how others identify a stu-
dent has consequences as well, because if a student is seen as smart, for example,
they are typically offered more opportunities to engage in meaningful academic
activity (Cohen & Lotan, 1997).
We therefore turn to other theoretical approaches that inform our sociocul-
tural-based analysis of social identities in schools. We provide three examples of
classroom researchinformed by three different theoretical approachesthat
have attended to the influence of social identities in classroom mathematics learn-
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 22
ing. First, we discuss critical race theoretical approaches to study the racial and
mathematical identities of African American learners; next, we discuss research
on stereotype threat theory with respect to race, gender, and mathematics; and
third, we discuss sociological research on expectation states theory, status, and
social interaction.
First, since Ladson-Billings and Tate‘s (1995) introduction of critical race
theory (CRT) into education, researchers have increasingly investigated ways in
which race structures U.S. schools at the macro policy level and the micro interac-
tional level (see, e.g., two edited volumes on CRT and education: Dixson &
Rousseau, 2006b; Parker, Deyhle, & Villenas, 1999). For instance, Anderson and
Powell (2009) used CRT to examine the role of race in constructing the historical
conditions and the contemporary status of education in particular school districts
and schools. Whereas, Martin (2006) used tenets of CRT to explore the racialized
nature of mathematics learning for African American people in the United States.
During Martin‘s interviews with adults, his participants described a number of
ways in which White teachers responded to students‘ racial identities by diminish-
ing the nature of the mathematics education they received. Along with critical
race theorists (see, e.g., Dixson & Rousseau, 2006b), Martin argues that race and
racism are pervasive in the United States, and that it is important to challenge
claims of objectivity and alleged neutrality—often coded as ―colorblindness‖ in
educational settings and in educational research (see also Martin, 2009). Metho-
dologically, Martin uses CRT‘s concept counternarrative, which places an em-
phasis on the voices of people of color to describe the effects of racism in their
everyday experiences, as opposed to dominant narratives that deny the importance
of race.
Second, in a psychology-based theoretical approach, Steele and colleagues
have amassed an impressive body of research documenting the effect of stereo-
type threat on the performance of people from marginalized groups (for a com-
prehensive review of stereotype threat theory, see Steele, Spencer, & Aronson,
2002). Stereotype threat theory describes the threat, in ―real-time,‖ of one‘s per-
formance being judged based on a stereotype. For example, African Americans
can face a stereotype threat based on the stereotype that they cannot succeed aca-
demically, and women face a stereotype threat based on the stereotype that they
are less mathematically capable than men. In some contexts, when (some) mem-
bers of the marginalized group have reason to believe that they will be judged
based on a stereotype, their performance (say, on an academic test) can suffer be-
cause of the anxiety of trying to manage the threatening situation.
Although the majority of stereotype threat research has been conducted us-
ing quasi-experimental methods, recently Nasir and colleagues have used ethno-
graphic methods to explore the theory in classrooms (Nasir et al., 2009). In a
similar ethnographic study (one that did not explicitly take stereotype threat as a
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 23
lens but whose findings nevertheless resonate with it), African American students
in a school with a well-publicized racialized achievement gap reported that their
peers treated them as if they were ignorant and expected them to struggle with
their schoolwork (Rubin, 2003). In this school, even when teachers tried to build
community by creating racially diverse collaborative groups, African American
students were often isolated from their friends and marginalized in academic
work. In diverse classrooms, students may be very aware of the ways that their
teachers and peers view them as members of racialized groups, and may react to
stereotype threats when they expect that others will treat them negatively because
of their racial identities.
Third, we consider research on expectation states theory, a sociological
theory of status that models how individuals construct expectations for one anoth-
er‘s competence in activity (Berger, Cohen, & Zelditch, 1972). This theory states
that in many situations, members of a group will act as if higher status people are
more competent than lower status people, regardless of the demands of the activi-
ty. Status can be conferred based not only on social identity categories like race,
gender, and socioeconomic status but also on other hierarchies such as a person‘s
rank or credentials (e.g., well-educated people have more status; a manager has
more status than the people they supervise). Classroom research has demonstrated
the importance of status, highlighting how high-status students tend to dominate
small-group and whole-class discussions and learn more from these interactions
(Cohen & Lotan, 1997). While Cohen, Lotan, and colleagues have argued that
popularity and perceived ability are the most consequential status characteristics
in classrooms, social identities like race, gender, and socioeconomic status are
likely to contribute to status hierarchies as well (Chizhik, 2001). Although the
theoretical foundation of expectation states theory asserts that one can simply
add up status characteristics, we argue, however, from an intersectional ap-
proach, that multiple status characteristics can qualitatively influence one another.
Race is experienced differently depending on one‘s gender and one‘s socioeco-
nomic status, and vice versa.
These three approaches to understanding the influence of social identities all
point to the importance of not only analyzing how students self-identify in terms
of social identities but also how they are identified by others, and how they identi-
fy others in the group. In other words, one‘s opportunities to learn are not only in-
fluenced by one‘s own identities but also by the identities of others. In short, from
Martin‘s (2006) research and CRT, we emphasize the value of listening to narra-
tives and counternarratives as students describe their experiences; from the re-
search on stereotype threat theory, we consider the various stereotypes that might
be present in the classroom, whether they are explicitly voiced or not; and from
the research on status, we again emphasize the importance of intersectionality be-
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 24
cause of the ways multiple status characteristics might interact in classroom inte-
raction.
This study considers how students‘ identities (their own identities, imposed
identities, and the ways they identify others) are made salient in the narratives
they tell about their mathematics classroom. We analyze a set of interviews con-
ducted with high school students about group work in their mathematics class-
room, and report on the social categories that students used to describe themselves
and their peers. Drawing from CRT, we highlight the stories shared by students of
color and girls, but we also include narratives from students from dominant
groups, expecting that students from various social positions will tell different
kinds of stories about their collaborative experiences. We discuss how various
categories were invoked (or avoided) to explain the success and failure of group
work for mathematics learning. Through this analysis, we contribute to a broader
understanding of how social identities are made salient in mathematics class-
rooms, specifically as students work together in small cooperative groups.
Methods
The analysis used a case study design (Yin, 1989) in an attempt to better un-
derstand the nature of cooperative group work in one particular mathematics
classroom. We were inspired by Willow and Candie‘s remarks on their difficulties
working with peers because of their social identities, and constructed the present
interview study to gain a better sense of the nature of group work in a single ma-
thematics classroom community. (Unfortunately, Willow had left the school
shortly after the interview quoted in the epigraph, in part because of the expe-
riences she described. Candie, however, was still a student at the school at the
time of the follow-up study but she had completed her required mathematics
courses and consequently was not part of the focal classroom.)
Following Yin‘s (1989) recommendations for case study design, we outline
the research questions and the related propositions, the unit of analysis, and then
the research context, data collected, and strategies for interpreting the data. The
research questions were: How do students describe cooperative group work in
their mathematics class? How do students describe the way their socially con-
structed identities influence the nature of their group interactions in mathematics
classrooms? We draw on interview data to describe students‘ perspectives on
group work in a reform-oriented, urban high school mathematics class, and dis-
cuss several ways in which students argue that their socially constructed identities
do (or in some cases, do not) influence their group work. The data for this analy-
sis are taken from a set of 14 interviews that were conducted in the winter and
spring of 2007. The interviews were part of a larger study examining mathemati-
cal thinking and learning at the high school level. The interviews took place at the
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 25
same school, and with many of the classmates of Willow and Candie, who took
part in a related study in 20042005 (Esmonde, 2009b).
Although our approach to understanding identity is informed primarily by
sociocultural theories, we are also informed by CRT‘s emphasis on ―voice‖ in
which the voices of people of color (students, parents, teachers, researchers) are
highlighted as they tell their own stories (Dixson & Rousseau, 2006a). Often these
stories are framed by educational researchers as counternarratives against the do-
minant racial (and racist) narratives of the educational community. Because this
study is not limited to a focus on race, but instead discusses social identities more
broadly, we chose to interview a variety of students. In our analysis, we will fore-
ground counternarratives against a backdrop of the dominant narratives from our
interviews.
Another reason to interview a broad range of students for this study is be-
cause we do not assume that race, gender, or any other a priori set of social cate-
gories are the most prominent ways that students conceptualize identity in the
classroom. We recognize that most social categories are complex and contested,
and that they may be strategically introduced in some contexts, and downplayed
in others (Gee, 2000; Pollock, 2004). In other words, it is of interest to know
whether and when students invoke race, gender, and other social categories in
their narratives about mathematics classroom experiences.
At the outset of the study, we assumed that students would not necessarily
openly discuss social identities that are sometimes taboo topics (e.g., race, socioe-
conomic status), especially if students were from privileged groups, or if they
were hesitant to address these topics with the interviewers. Therefore, we de-
signed the interview to provide opportunities for students to discuss these issues if
they wanted to. By not directly asking about social identities, we could study the
ways in which these categories were independently invoked or omitted by various
students. We anticipated some explicit, and some covert, discussions of social
identities, as well as some avoidance of this topic (Pollock, 2004).
We employed two levels of analysis for the study. The case focuses on a
single classroom because we wanted to capture students‘ practice-linked identities
for a single practice-linked community. However, we also expected that students
with different social identities would have different perspectives on group work in
their classroom; therefore, for our second research question that investigates the
influence of social identities, our unit of analysis was the individual student. Each
student lived at the intersection of multiple forms of identity, and would have a
unique perspective on classroom group work that was shaped by these identities.
Research Context
The school was situated in a small urban city in northern California, USA,
and was a small school program within a larger school. The larger school, Bay
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 26
Area High School (pseudonym, as are all proper names throughout), was the only
high school in the city, and the student body was diverse in terms of race, ethnici-
ty, and socioeconomic status. The small school, Media Academy, was a program
that focused academically on issues of social justice as well as media studies and
media production. Students in the small school applied to be part of the program,
and were admitted, in part, to match the demographics of the broader school
community. The school admitted between 6090 students per year and empha-
sized community building both within and across grade levels.
With respect to social identity categories such as race, gender, socioeconom-
ic status, and sexuality, the Media Academy included an explicit focus on issues
that are often derived from these categories throughout all years of the program.
In the 9th grade, this focus manifested particularly in the core classes of Social
Studies and English in which students learned about systems of oppression and
privilege. Students were encouraged to write about and explore issues of identity
in writing and video assignments. In Willow‘s quote in the epigraph, she de-
scribed an activity at the very beginning of her 9th-grade year in her core class in
which issues of oppression and identity were explicitly discussed. Unfortunately,
as Willow described, these conversations sometimes created unsafe spaces for
some students. Additionally, in the same interview, Willow described her anger at
other White students who did not defend themselves when accused of racism by
students of color.
Despite efforts by teachers to provide an equitable education to all students
in the school, the larger school‘s long-standing racial achievement gap was not
erased in the Media Academy. In fact, during the year of this study, a group of
students and teachers collaborated to educate themselves and the Media Academy
community in general about racialized achievement differences in the school, ad-
vocating for more equitable educational opportunities.
With respect to mathematics, the Media Academy had two mathematics
teachers in the year of this study. Ms. Delack, a White woman with a working-
class background, was in her third year of teaching at Media Academy; she had
taught the students of this study for all 3 years (except for three students, one of
whom was interviewed, who joined the class in 2007). The three mathematics
courses were de-tracked, using the Interactive Mathematics Program (IMP)1 cur-
riculum (i.e., all students experienced somewhat the same ―level‖ of mathematics
instruction). Students, however, had previously been tracked in middle school;
therefore, a given mathematics class might contain students from different grade
levels, depending on whether a particular student had taken Pre-Algebra or Alge-
bra I in the 8th grade, or whether she or he had failed a mathematics course since
1 For information about the Interactive Mathematics Program (IMP) curriculum, see
http://www.mathimp.org/.
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 27
arriving in high school. The class we focus on in the present study was composed
of 30 11th- and 12th-grade students.
Ms. Delack‘s approach to mathematics teaching relied on students‘ colla-
borative work. Students worked in groups on a daily basis and were responsible
for constructing mathematical knowledge together. The IMP textbook did not
contain the usual series of theorems, worked examples, and definitions. Instead,
students were presented with lengthy word problems and were expected to work
as a small group and then as a whole class to construct methods for solving the
problems. Definitions, theorems, and generalizations were usually constructed in
whole-class discussions, and often represented on collaboratively created posters
that would remain displayed around the room.
Ms. Delack employed several techniques to help students work productively
in groups. She generally asked them to ask one another questions first, and to only
approach her if they could not resolve something on their own. She held what she
called ―process quizzes‖ in which groups were responsible for solving problems,
while she assessed the quality of their collaboration. She held whole-class discus-
sions in which students and teacher talked about the value of cooperative group
work and encouraged all students to stay involved. In the latter half of the year,
inspired by research on Complex Instruction (Cohen, Lotan, Scarloss, & Arellano,
1999), Ms. Delack began assigning roles to students (facilitator, reporter, record-
er, process checker) so that each student had a specific task to perform, and
groups reflected on their collaborative process every day.
Interview Participants
For the purpose of this case study, we invited all students in Ms. Delack‘s
class to participate in the proposed study. Out of the 30 students, 14 agreed to par-
ticipate. The demographics of our interview participants are listed in Table 1. All
demographic information is derived from student self-identifications on surveys
or responses provided during the interviews. The table demonstrates that our in-
terview participants included both young men and young women, both grade le-
vels, and almost all the racial/ethnic groups in the classroom. (The one Asian
American-identified student in the class did not participate in an interview.)
Interview Protocol and Analysis
The first author (Indigo Esmonde) and a colleague from Stanford University
conducted the interviews; both are White, middle-class women. Esmonde (the
first author) was well known to the students, having conducted research and vo-
lunteering in their classroom for the past 3 years. The other interviewer (Kathleen
O‘Connor) was unknown to the students prior to the study, and visited the class-
room several times for the sole purpose of conducting interviews.
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 28
Table 1
Names and Demographics of Interview Participants2
Name
Gender
Race
Namaya
W
African American
Tony
M
Latino
Tariq
M
Latino
Giulia
W
White
Haley
W
White
Mike
M
White
Noreen
W
White
Nuncio
M
Multiracial
Dustin
M
White
Chelsea
W
White
Elly
W
Multiracial
Karmina
W
Latina
May
W
Multiracial
Samantha
W
Multiracial
Interviews were semi-structured and focused on student beliefs about the ef-
ficacy of group work, and were designed to elicit stories from students about
group interactions that went well and interactions that didn‘t go well.‖ After
some initial general questions, the interview protocol was subdivided into four
major sections. The first section contained questions that asked students to de-
scribe an incident in a group that didn‘t go well; the second, to describe an inci-
dent in a group that went well; the third, to reflect on how they might design a
mathematics classroom community for effective group work; and the fourth, to
describe their current group. Each major question in the subsections included a
number of prompts to elicit detail from students. (See Appendix A for the full in-
terview protocol, including prompts.)
To address the first research question, all interviews were roughly tran-
scribed and then coded with a series of open codes. All data were coded iterative-
ly, with new codes being added or refined throughout the process. These codes
were used to capture the important factors that influenced the outcome of group
work, according to students. Each of the authors participated in coding. Each of
the codes was developed collaboratively, and refined until we came to agreement
on examples and non-examples for each code. The four basic codes are defined in
2 Although the category multiracial masks quite a bit of diversity, the term is used here because it
is how students self-identified.
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 29
Table 2. (Further examples and explanations of these codes are developed in the
Results section.)
Table 2
Codes for Interview Data
Code
Description
Interactional style
Utterances that describe the kinds of actions or
ways of being that support or detract from group
work
Mathematical understanding
Utterances that describe the ways in which the na-
ture of a person or group‘s mathematical under-
standing supports or detracts from group work
Friendship and relationships
Utterances that describe the ways in which friend-
ship, relationships, and feelings of comfort or safe-
ty (or lack thereof) support or detract from group
work
Social identities
Utterances that explicitly make reference to social-
ly constructed identities, and describe how these
identities support or detract from group work
To address our second research question, we examined the socially con-
structed identities of each interviewee, and the socially constructed identities of
the classmates they mentioned during their interviews. Our goal was to identify
any patterns about how these identities were used or avoided, and to determine
whether and how they influenced the cooperative group work experience. As a
part of this analysis, we examined students‘ descriptions of one another to deter-
mine whether they matched or challenged stereotypes related to social identities
and mathematics learning.
Our analysis of the second question was guided by both the responses pro-
vided during the interviews and the meanings conveyed through the ―subtext‖ of
the transcribed interviews (Banning, 1999). In other words, during the analysis,
we drew on Banning‘s analysis of the internal conflicts and contradictions in a
feminist course at a public university. Banning employed an analysis of the ―text‖
(field-notes, transcribed interviews, etc.) and the subtext (the unspoken assump-
tions and beliefs) for her study. Similarly, in our analysis, we attempted to docu-
ment the subtext of our transcribed interviews. While students did not always
openly discuss socially constructed identities during the interviews, we argue that
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 30
some of their narratives employed covert strategies for discussing race, gender,
and other social categories.
To explore the subtext of the students‘ transcribed interviews, we first iden-
tified (as best we could) the social identitiesrace, gender, and grade levelof
all interview participants. For all participants, we collected narratives from their
interviews in which they described their own interactional styles and the interac-
tional styles of specific peers. We identified the social identities of these named
students as well. (Not all of the students mentioned in this article were partici-
pants in the study, so they do not appear in Table 1.)
From this collection of narratives, we looked for relationships between stu-
dents‘ identities and the descriptions and stories they told and that were told about
them. In our search for these patterns, we were partly guided by familiar stereo-
types based on race, gender, and socioeconomic status, and partly guided by any
new patterns that might emerge from the descriptions and stories provided during
the interviews. This approach is in keeping with grounded theory; in that, we
stayed close to the data and allowed the findings to emerge from constant compar-
ison between the interviews and a gradual elaboration of a set of codes (Glaser &
Strauss, 1967). However, we were also guided by CRT; therefore, we were ex-
pecting that race, gender, and socioeconomic status (among, perhaps, other social
identities) would emerge during the interviews but that these might be hidden. As
Banning (1999) points out, in contexts marked by hierarchies, those with power
tend to use ―power-evasive discourse‖(p. 160) and it would be naïve to expect
them to explicitly highlight the ways in which they maintain their privilege. We
next describe the themes that emerged from this grounded theory approach.
Results
Students’ Perspectives on Successful and Unsuccessful Groups
In the discussion of the findings, we first describe the results of the first re-
search question: How do students describe cooperative group work in their ma-
thematics class? For this investigation, our unit of analysis was the entire class
and we did not distinguish between individual students. The four codes (or
themes) were developed through repeated analyses of the data to describe factors
influencing mathematical group work. We summarize students‘ views on how
these four factorsinteractional style, mathematical understanding, friendship
and relationships, and social identitiesinfluenced success and failure of group
work. In presenting the data, we attempt to maintain the complexity and internal
tensions that students expressed during their interviews. The analysis for this re-
search question might appear unrelated to our earlier comments on the centrality
of social identities in mathematics classrooms. However, we feel it is important to
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 31
describe what students did focus on during their interviews before deconstructing
the more covert messages of the interviews in the later analysis.
Interactional Style
The most common factor that students mentioned during their interviews
was what we called interactional style. This category included descriptions of
student personalities, and different ways of interacting in a group. For example,
the following two statements were coded for interactional style:
I felt like they‘ve been pretty supportive. (Noreen)
When there‘s people that take, I guess a dominant role in a group? And kinda work
through everything themselves and just tell people the answers? Like that doesn‘t
work for me. Just because of the fact that I need to be able to work through it for
myself to really get it. I‘m a very experiential learner. (Karmina)
Both statements describe styles of individual group members or the group as a
whole.
When asked to describe a positive group work experience, all students
agreed that good group work involved a combination of people who could work
well together. Students emphasized the importance of sticking together as a
group, solving problems together, and not leaving any members behind. There
was strong agreement amongst the students in these descriptions of positive group
work.
Despite this near consensus on the characteristics of good group work, there
was additional complexity revealed during the interviews. Students discussed the
constellation of factors that could influence the appropriate interactional style for
a group, and in a related note, discussed the tensions inherent in collaborating in
school when their primary responsibilities were to themselves as individuals, and
not to the group. Furthermore, students differed in their opinions about whether
there was a single best way to interact, or whether different individuals had differ-
ent best interactional styles. We discuss each of these findings in turn.
According to the students‘ responses, interactional style alone could not ac-
count for the success or failure of group work; there was a set of variables at play.
During the interviews, it was rare that a student‘s narrative about group work was
coded only for interactional style. For example, students recognized that interac-
tional styles were often influenced by the context of the group collaborationthe
type of task, their level of mathematical thinking, or their comfort level or friend-
ship with others in the group.
Students also described a tension between trying to do good group work
(i.e., spending as much time as needed so that all group members understood the
material) while also trying to complete their schoolwork correctly and quickly. In
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 32
other words, students were torn between their desire to be inclusive and the pres-
sure to succeed academically. For example, some students told us they (or their
peers) liked to work quickly so they could complete the homework in class and
some students reported that they were reluctant to ask too many questions, be-
cause they did not want to slow down‖ their peers. Noreen, for instance, reported
feeling pressured to say she understood explanations from her peers even when
she did not in order to allow them to move on. Her statement illustrates the di-
lemma faced by many students in which they had to choose between what they
considered good group work, and their personal academic or social goals.
An additional complexity relating to students‘ comments on interactional
style was found when they acknowledged the diversity of learning needs in the
classroom and how it influenced group work. For example, Noreen stated, there
are certain people, with their personalities, [who] are never really going to work
really, really well together, and you can‘t really make them.‖ Karmina reiterated
this point in her earlier quote (in which she identified herself as an ―experiential
learner‖), implying that different students might need different kinds of interac-
tions to support their learning. Thus, what might work for one person might cause
difficulties for another. Several other students echoed this sentiment.
Mathematical Understanding
Students often discussed how different levels of mathematical understand-
ing influenced how well a group worked together. For this code, we focused on
the instances where students described how their own level of mathematical un-
derstanding, as well as their perceptions of the mathematical understanding of
other students, affected the group‘s interactions. For example, the following
statement by Haley is categorized into this code: ―The groups that usually do the
best, [are] where someone‘s really good at math and they‘re someone that‘s like
broadly liked. (Note that Haley discusses mathematical understanding in the con-
text of other personality factors, i.e., ―being broadly liked.)
Generally speaking, our interview participants took one of two differing
views on the optimal mathematical understanding for a group. Some students as-
serted that groups should consist of a heterogeneous mix of people with different
levels of understanding so that those who needed extra help could ask their peers.
Other students, however, argued that they preferred to work in groups where eve-
ryone had similarly high levels of mathematical understanding.
All students who advocated this second position characterized themselves as
high achievers. Giulia stated that she did not like group work because she did not
like being put into groups where people were behind in math and ―don‘t bother‖
to get caught up. She preferred groups where everyone had the same amount of
math and successfully finished their work. Noreen was another high achiever
who felt that some group members with different levels of understanding just
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 33
aren‘t going to work.‖ She described the pressure of being in charge, and said she
never wanted others to feel like she was taking over or being a suck up.
Therefore, she preferred to be in groups where others did not need her help.
Even among students who said they preferred heterogeneous (ability)
groups, we heard many stories about how difficult it was to work in such groups.
High achieving students who held such beliefs often admitted to feeling that their
groups slowed them down and they were not always keen to stop their work to
help out their peers. For example, Dustin reported during his interview that he
preferred to get his work done as early as possible, rather than help out struggling
students. For those who requested help from peers, such behavior was upsetting,
as they felt that they were being ignored. Samantha stated, ―I‘d ask [a student in
the group who was making progress] well, like, do you know what‘s going on and
she would be like, ‗Oh, and it‘s like this‘ and then kind of just ignore it and I‘d get
really frustrated. In contrast to high achievers, students who were positioned as
slower than the rest of the group sometimes felt they slowed down their group‘s
progress. These students reported feeling pressured to say they understood certain
concepts when they did not.
Friendship and Relationships
With the code friendships and relationships, we focused on the parts of the
transcribed interviews where students described whether or not they were friends
with group mates, liked someone, had something in common (e.g., common inter-
ests), got along with people, had prior knowledge of people, and the importance
of building community in the class and in the group. For example, Haley said: ―I
think that with the right people everyone could be working and learning. But I
think that, like, with the wrong people you can really get set back.
Students agreed that friendships had both positive and negative impacts on
group work and explained some associated tensions. While students perceived
good relationships as necessary for successful group work, they also reported that
friendship could add challenges. For example, Tariq claimed, ―some friends will
work good together and some friends just won‘t do anything.‖
Students said they felt pressured to socialize with friends, felt left out when
they were not friends with group members, and also felt that they could not stop
friends in their groups from talking with each other and getting distracted. Stu-
dents pointed out that this social talk usually did not lead to productive mathe-
matical work. Regarding this point, Chelsea stated that friendships can be a
drawback because if we‘re all so close we‘re going to be talking to each other.
Similarly, Dustin said, with friends, ―it‘s a little tempting to like, catch up on stuff
you haven‘t caught up on.‖
The negative effects of friendships could also extend to group members who
were outside of the circle of friendship. When describing one group in which she
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 34
was with two older girls who were good friends, Haley remarked, ―I didn‘t have
really like any sort of authority to get them to start working because she wasn‘t
friends with them. Haley, Tony, Noreen, and several other students argued that
feeling comfortable in a group was an important aspect for the success of group
work. When students felt comfortable in their groups they were able to ask ques-
tions without embarrassment and this supported their mathematical learning.
Social Identities
During the interviews, students rarely discussed socially constructed identi-
ties such as race, gender, or socioeconomic status. In this section, we report on
many of the explicit statements that students made regarding these kinds of identi-
ties and their influences on group work. In our coding of the interview responses
for this category, we searched for any explicit reference to race, gender, socioeco-
nomic status, or other relevant identity markers. In the process of coding, we add-
ed one other type of identity that was frequently mentioned: grade level. We also
coded statements into this category when students mentioned a value for diversi-
ty without specifying what type of diversity they were referring to. We felt that
the word diversity was often a way of talking about race or culture, without expli-
citly mentioning this potentially controversial term (Pollock, 2004).
Grade level. Many students mentioned grade level during their interviews.
Their mathematics class included both juniors and seniors, and this fact influ-
enced students‘ narratives about one another. This social identity may have been
related to friendship and relationships because students tended to know same-
grade peers better.
The implications of this social category on classroom hierarchies were com-
plex. On the one hand, we felt that in this high school, as in many others in the
United States, the seniors were at the top of a social hierarchy, followed by ju-
niors. A remark from Noreen illustrates this hierarchy as she described group dy-
namics. Noreen claimed that Kim was in an older position because she was a
senior in a group of juniors. Because Kim was older, Noreen believed that Kim
would have felt confident that people were not taking over and that she had a
voice. On the other hand, in this particular class, the students who were seniors
had either failed or been tracked into a low-level mathematics course in the
past. Therefore, the juniors in the course were more likely to be positioned as ma-
thematically talented.
Race, gender, and socioeconomic status. Members of marginalized groups
most frequently mentioned social categories. That is, girls were more likely to
mention gender, and students of color were more likely to mention race. Only one
student mentioned socioeconomic status (in an oblique way, by referring to stu-
dents from different neighborhoods in a social context where someone‘s so-
cioeconomic status could be predicted based on the neighborhood they lived in).
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 35
When these categories were explicitly raised, students often described valuing di-
versitythat is, having groups that included students of different racial or ethnic
backgrounds, students from different neighborhoods, or half boys and half girls.
For example, Chelsea, a White girl, described a group that she felt had not worked
well because the group contained four leader-ish girls. She felt that groups
needed people with different personalities, linked personality with gender, and
ended by saying that groups worked better when they consisted of half boys and
half girls.
Although many of the students‘ statements superficially applauded diversity,
several students described diverse groups that were not functional. Specifically,
students from marginalized groups told us they preferred groups that were more
homogeneous. For example, Elly, a multiracial girl of low socioeconomic status
told us that she preferred to work with other girls. Elly went on to tell us that
when she worked in groups she could not help but interpret people‘s individual
behaviors through a social justice lens. She provided, in some detail, a narrative
about being grouped with two White boys and a Latina girl in which the two
White boys dominated every interaction. She then pointed out that sometimes
more homogeneous groups might lessen this type of power struggle.
Another student, Tony, a Latino boy, told us that he preferred to work with
other people of color, and specifically Latino boys, because they socialized out-
side of school and he knew them fairly well. This comment was interesting, be-
cause earlier in the interview Tony had said that it did not matter who you are.
He stated that so long as students stayed focused, group collaboration could go
well. We emphasize that in this remark he does not essentialize students of color
by saying that there is something about these students that makes collaboration
work better. Instead, he told us that his social sphere was mainly composed of
students of color and that their positive social interactions outside of school sup-
ported positive mathematical interactions in class.
Analysis of Subtext of Student Interviews
After we completed the aforementioned analysis on students‘ perspectives
of successful and unsuccessful groups, we developed an interest in uncovering
some of the more subtle ways in which students‘ socially constructed identities
appeared during the interviews. Although students rarely discussed the impor-
tance of social identities for group work explicitly, upon closer examination of
student talk, we anticipated finding implicit messages about race, gender, and so-
cial identities. This section focuses on our second research question: How do stu-
dents describe the way their socially constructed identities influence the nature of
their group interactions in mathematics classrooms?
For the analysis of the second question, we examined the students‘ interview
responses more closely to identify whether and how social identities might have
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 36
been implicated in their descriptions of interactional styles, personalities, and ma-
thematics achievement. By setting individual students as the unit of analysis, we
considered how our interview participants described themselves, and how they
described their peers. In many cases, we had access to students‘ self-
identifications for race and gender, and after researching and volunteering with
these students for 3 years, I (the first author) also had access to the ways in which
students were routinely racialized and gendered by others in the classroom. There-
fore, for each interviewee, we listed all the classmates that they mentioned, the
social identities that were associated with each of these classmates, and then we
considered how interviewees described their classmates. For example, when
Chelsea described being irritated with the way Haley dominated group work, we
noted that both Chelsea and Haley were White girls. Race, gender, and grade level
were the most visible categories to us. We were not, however, aware of all stu-
dents‘ socioeconomic status or other social categories that might have been at
play. We recognize that there is danger in imposing social identities on students.
We risk simplifying multiple layers of students‘ social identities or erasing diver-
sity within one social category. However, we observed that these identities were
routinely imposed on the students every day in the classroom. When we used the
construct of social identity for our analysis, we referred to identities that are self-
imposed, and also to the identities that one imposes on others. In other words, we
were concerned with both self-identification and the identities students imposed
on others. When we looked under the surface of students‘ innocuous discussions
of interactional style, mathematical understanding, and friendship and relation-
ships (or feelings of comfort), we began to make connections between these
themes and students‘ social identities. In particular, we discuss patterns that
emerged in three areas: group leadership and other styles of group interaction, the
ways in which students handled the tension between getting their own work done
and helping others, and student preferences for group mates.
Our analysis of the interview responses revealed a general tendency for
White students to describe themselves as taking on leadership type roles in the
group work and for Latino/a, African American, and multiracial students to de-
scribe themselves as taking on more passive roles. This tendency was the case
even for students of color who described themselves as dominant or leaders
in general. More specifically, Mike (White boy), Haley (White girl), and Giulia
(White girl) described themselves as leaders throughout their interviews whereas
Tony (Latino boy), Karmina (Latina girl), and Namaya (African American girl)
described a general reluctance to take on such a role.
When considering the relationship between gender and roles within group
work a similar pattern emergedboys tended to be group leaders. This pattern
was particularly evident in groups that consisted of all White students, or all stu-
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 37
dents of color (where gender seemed to be the most salient marker of difference
between students). As one example, when Tony (Latino boy) was working with
Tariq (Latino boy), Namaya (African American girl), and May (Multiracial girl),
Tony described that he and Tariq took on the leadership roles and did most of the
work. Tony went on to report that he and Tariq also did the group presentations.
A similar example was noted in the interview with Haley, a White girl. When
working with a group of girls, Haley described herself as being a leader. Howev-
er, when put in a group that included boys, Haley said she took on a more passive
role and described a boy who took on a strong leadership role:
There was this guy and he was really kind of like the leader and he was really, he got
everyone to do their work. Well he just, he dominated every conversation we had,
so then when he decided to do math, which he did, he wanted to do his work, he did
get good grades, so when he decided to do his math, kind of our group did it. And
not to say that I didn‘t have conversations with other people in my group, it‘s just he
was like kind of like a leader and kind of, I don‘t know, I don‘t actually like him that
much but like it‘s just he is good at getting people to do group work. (Haley)
As evident in these examples, students‘ social identities—their own, and the iden-
tities of others in their groupsbecame salient and likely influenced the roles
they took on during group work.
During this second phase of the analysis, we found further examples of the
tension that students described between doing good group work (working collabo-
ratively and helping one another) and getting work done. The analysis of the tran-
scribed interviews revealed that students responded to this tension in various ways,
which led, in several cases, to the exclusion of some students from the group work.
For example, when telling her story of a group that did not work very well togeth-
er, Namaya shared her experience of being excluded that may have contributed to
her frustration and lack of participation in the group:
I was like, ―what‘s going on?‖and they kept telling me like, ―hold on‖ and then they
would just forget that I had even asked them what was going on. I had to beg them to
keep me…to tell me what was going on. …I really needed them to keep me included
so I could understand, but they didn‘t. (Namaya)
Her group members at the time were Chelsea and Chris (two White students) and
Jaime (a Latino boy).
This tension between getting one‘s own work done and helping the group
was reported many times during the interviews. However, students responded to
this tension in different ways. Karmina, a Latina female, tells a story in which she
chose to assist a classmate. Specifically, she recalled an incident working with
Dustin (White boy), Amelia (White girl), and Kayla (African American girl):
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 38
I was in a group with, Amelia and Dustin, and Kayla, I think. Um, and Kayla had
been gone [to a youth leadership program] for a week, so, when she came back, she
had a lot of catching up to do. And Dustin and Amelia are both really dominant
people when it comes to, like, the work, um, so, they were kinda speeding through it,
not really making sure that, we got it, and I was kinda like catching Kayla up. So, it,
it was just, really weird cuz then we would get to these things and we‘d be like I
don‘t get it and then they‘d get kinda frustrated and not wanna tell us, and just kinda
get an attitude. (Karmina)
While Karmina was engaging in what most students would have agreed was good
group work, her two peers were rushing to get the work done, thus leaving her
behind. Good group work, then, does not always benefit all students.
Her peers in the group, both White students, clearly did not make the same
choice. They chose not to slow down to help Kayla. We also interviewed Dustin,
and although he did not specifically discuss this group, he told us that in general,
when he was in heterogeneous groups, I feel like maybe they‘re not getting it as
fast as me, so I feel like I just wanna get it done or go ahead or whatever.These
examples illustrate the impact that this tension had on various students and how,
as a result, students of color were marginalized and excluded. This exclusion is
even more poignant because of the way Namaya and Karmina described them-
selves as strong leaders in other groups, consisting primarily of other students of
color.
We stress, however, that it is important not to see students of color as help-
less victims in groups where they do not take on leadership roles. In Namaya‘s
narrative above, she explained how she repeatedly asked for help from the group,
but the group ignored her. She attempted to be an advocate for herself, but the
other group members still excluded her from their discussions. As critical race
theorists have insisted, Namaya‘s story about her participation in this group pro-
vides a counternarrative to the dominant stories being told about group work in
this classroom. More specifically, these stories contrast with dominant narratives
about students who just ―don‘t care‖ and therefore do not voluntarily participate
in group work (echoed in Giulia‘s previous narrative). Far from not caring, Na-
maya‘s counternarrative illustrates that students can be excluded from groups de-
spite their best efforts to engage. That exclusion can lead to frustration and disen-
gagement, which ironically may then further exclude students from productive
group work.
Perhaps as a result of such clashes, we found that when we examined whom
students named as good group members we noticed that, by and large, students of
color identified other students from marginalized racial groups. For example, To-
ny, a Latino boy, explicitly reported his preference for working with Latino and
African American students. He later explained that he learned better when work-
ing with these students because he felt comfortable to ask questions and to answer
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 39
the questions of his peers. When working with these students, he tried to be as
active‖ as he could in this group.
More evidence came during the interview with Karmina, a Latina girl, when
she described working well with her best friend Samantha, a multiracial girl. Spe-
cifically, she recalled that they helped each other work through problems and built
understanding together. The fact these students are both seniors is also notewor-
thy. Karmina reported, however, not working well with Haley, a White girl, who
was also a junior, as Haley would rush through work and jump in‖ to explain the
answers.
Overall, we found that all of the students of color in our small sample dem-
onstrated a preference for working with other students of color. They were more
likely to be friends with one another, more likely to be in the same grade level,
and to have similar values or interactional styles. The White students that we in-
terviewed named some White students and some students of color as their most
preferred peers to work with. This preference might be because these privileged
students did not have to struggle to create opportunities to learn for themselves.
This pattern of marginalized students preferring to work with other margina-
lized students did not hold out for gender, demonstrating that the way gender op-
erated in the classroom was distinctly different from race. Most boys and girls
displayed a preference for mixed gender groups, although two of the girls (Elly
and Chelsea) mentioned all-girl groups that had worked well. In Chelsea‘s story,
she described being surprised to find that an all-girl group could work well.
Discussion
In this article, we provided an analysis of the texts and subtexts of a group
of high school students‘ narratives about mathematics group work. Based on our
analysis, we have shown that students experience mathematics classrooms as sites
for power struggles that are often related to their social identities, and we have
discussed how these power struggles may affect student opportunities to learn.
We found that within this classroom, White students, especially boys, despite the
best efforts of marginalized students to make their voices heard, often dominated
group discussions.
The major themes that students described in their narrativesinteractional
style, mathematical understanding, and friendships and relationshipsheld covert
racialized, gendered, and classed meanings. Our analysis of the subtext of the
transcribed interviews resonates with other research about the impact of social
identity. In California high schools, mathematics achievement and friendship
groups tend to be highly racialized and gendered, and, perhaps less visibly,
classed (Noguera, 2003; Olsen, 1997; Pollock, 2004; Rubin, 2003). As pointed
out previously, in this school, students recognized racialized and socioeconomic
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 40
patterns of achievement. Students of color were over-represented in lower tracked
mathematics classes while White and Asian students were under-represented. Fur-
thermore, stereotypes about boys‘ superior mathematics skills continued to be a
subject of debate in public forums, and in this particular high school, it was well
known that middle- and upper-class students from the hills tended to be higher
achievers than their working-class or poor counterparts from the flats. Thus,
when students talked about how mathematics achievement influenced the way
groups worked together, and dismissed some students as not caring, or not staying
focused, there may have been an unacknowledged racialized, gendered, or classed
dimension to these assertions.
Friendship patterns also tended to be associated with these social identities.
Although many students had cross-race or cross-gender friendships, and this small
school community had done much work to build community across race, gender,
and socioeconomic status, it was still the case that friendship groups were rela-
tively homogeneous with respect to race and socioeconomic status. Our interview
respondents mentioned that they were friends with people they felt comfortable
with, perhaps indicating some shared experiences, shared language, and shared
understandings of the world that can come from sharing similar social identities.
This study is particularly important for sociocultural theories because the in-
terviews were grounded in a particular practicegroup work in a mathematics
classroomand therefore highlight the interconnections of practice-linked identi-
ties with broader social identities. These practice-linked identities as mathematics
students were shaped by students‘ social identities (as when Tony described his
preference for working with other Latino/a students), and reciprocally, the social
identities were shaped by their mathematics identities (as when some of the ―lead-
er-ish girls‖ decided that this social identity made mathematical collaboration
more difficult). Our analysis therefore provides one possible methodological and
empirical perspective to include these social categories into a sociocultural analy-
sis of learning.
The CRT perspective proved important to our analysis because of the em-
phasis on counternarratives. Although only a small number of students explicitly
discussed social identities during their discussions of group work, we believe it is
no coincidence that the students who did so were those who were in traditionally
marginalized groups. White students did not discuss race, and boys did not dis-
cuss gender, perhaps because their privilege blinded them to these aspects of
classroom life. (Another explanation, of course, is that they were simply reluctant
to discuss these identities during the interviews.) The juxtaposition of these domi-
nant narratives with counternarratives highlights some of the complexity of group
work in mathematics classrooms.
This complexity was represented many times during the student interviews.
Students described not only the multitude of factors that influence group work but
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 41
also the real tensions inherent in trying to accomplish the multiple and sometimes
competing goals of group work. In telling their narratives, students never relied on
just one factor to explain the success or failure of group work. Instead, they de-
scribed how interactional styles, mathematical understanding, friendships and re-
lationships, and (in some cases) social identities all contributed to the process and
outcome of group work.
Group work has been touted as a way to get students from different
groups to respect one another, but researchers have cautioned that teachers must
take an active role in fostering that respect (Aronson &Bridgeman, 1979; Boaler,
2006). In our interviews, boys and girls of color and White girls reported their
marginalization in group work in this classroom. Students seemed to have mixed
feelings about heterogeneous groupings, whether these grouping were heteroge-
neous based on mathematical understanding, friendship, grade level, or social
identities. While students almost universally recommended heterogeneous groups,
they also almost universally described problems that arose in such groups. Va-
luing diversity may be a powerful narrative in current high schools, yet these sto-
ries provide counternarratives that illustrate that in diverse groups the same power
imbalances that characterize social life outside schools might be reinscribed in
collaborative groups.
These heterogeneous groups might actually be supporting privileged
groupsespecially White boysrather than creating spaces with rich opportuni-
ties to learn for students of color and for girls in general. While our analysis is
certainly speculative in some cases, we feel that the stories we were told during
the interviews call into question the role of heterogeneous groups in mathematics
classrooms. Even in a classroom with a teacher who was aware of equity issues,
and in a school where students studied issues of oppression and social justice,
these systems of oppression were at play and influenced students‘ opportunities to
learn mathematics.
Conclusion
As I (the first author) have argued elsewhere (2009a, 2009b), equity issues
in mathematics classrooms are complex and simple solutions may not be enough.
Although in this article we have used student narratives to highlight the ways in
which heterogeneous groups may reinforce pre-existing inequities, we do not
support racialized or gendered forms of grouping or tracking as solutions to this
problem. While in some cases, single-sex or race-based (e.g., Afrocentric) schools
may help some members of marginalized groups to succeed academically, in most
cases the de facto segregation that happens in schools deepens the divide between
groups. We urge the mathematics education community to take this issue on di-
Esmonde et al. Social Identities and Mathematics
Journal of Urban Mathematics Education Vol. 2, No. 2 42
rectly, and to consider ways in which teachers in heterogeneous classrooms can
support all students‘ opportunities to learn rich mathematics.
Acknowledgments
This article is partially based on a presentation given at the Research Presession of the annual
meeting of the National Council of Teachers of Mathematics, Washington, DC, April 2009. This
work was supported, in part, by the National Science Foundation under Grant No. SBE-0354453
to the Learning in Informal and Formal Environments Science of Learning Center, as well as by
the Connaught Fund at the University of Toronto. Any opinions, findings, and conclusions or rec-
ommendations expressed in this material are those of the authors and do not necessarily reflect the
position, policy, or endorsement of the National Science Foundation or the Connaught Fund.
The interview protocols were created as part of a collaborative effort fromBrigid Barron, Nicole
Casillas, Leslie Herrenkohl, Emma Mercier, Veronique Mertl, Na'ilah Nasir, Kathleen O‘Connor,
Roy Pea, Leah Rossman, and Kersti Tyson. Indigo Esmonde and KathleenO‘Connor conducted
the interviews. We would like to thank the students and teacher at Bay Area High School who ge-
nerously donated their time to this project.
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Appendix A
Interview Protocol
1. Tell me about yourself (name, grade level, etc.).
2. How often do you work in groups in your math class? How much of each class period is
spent working in groups?
3. Tell me a story about a time you were in a group that didn‘t work so well.
a. Who were the characters involved?
b. Can you describe what the group was supposed to be doing together? What hap-
pened?
c. How did it work out?
d. What do you think the other people were thinking/feeling in this situation? (Can
probe for a specific person from their story)
e. Why do you think it didn‘t work so well? (What‘s your theory about why this
group didn‘t work so well?)
f. If you were to go back and were in this situation again, what do you think you
might do differently to make this go better? What might others have done to
make this go better?
4. Tell me a story about a time you were in a group that worked well together.
a. Who were the characters involved?
b. Can you describe what the group was supposed to be doing together? What hap-
pened?
c. How did it work out?
d. What do you think the other people were thinking/feeling in this situation? (Can
probe for a specific person from their story)
e. Why do you think it worked so well? (What‘s your theory about why this group
worked so well?)
5. Imagine you (are a teacher, and you) are going to set up a new collaborative unit for your
students. Take us through how you would set it upwhat would you think about, what
would you do to make sure the groups would work well? What resources would you use?
When would you use group work?
(Note: Ask each probe question separately after they have had a chance to answer fully.)
a. What would the physical setup look like?
b. How would you form the groups?
c. What kind of feedback would you give the groups?
d. How would you assess how the groups are doing?
e. What kind of product would you have the groups working on?
f. What kinds of relationships would you want people to have, how would you
support this?
g. What kinds of challenges do you think you would face? How would you address
them?
6. Tell me about the group you‘re in right now. How is the group working together?
a. What is your role within the group?
b. What roles do the other group members take on?
c. Do these roles change for different kinds of activities?
... While it is well-established (Freeman et al., 2014;Springer, Stanne, & Donovan, 1999) that, at the undergraduate level, active learning strategies improve outcomes for students generally over lecture-based instruction, research on how students actually participate and experience their participation in classrooms that have students work in small groups is limited. In particular, most studies that consider the effects of small groups in classrooms have either used only during-instruction data such as observations and assessment scores (Bianchini, 1997;Chiu, 2000a;Sullivan, Ballen, & Cotner, 2018)or post-instruction data such as interviews and surveys (Cooper & Brownell, 2016;Esmonde, Brodie, Dookie, & Takeuchi, 2009;Theobald, Eddy, Grunspan, Wiggins, & Crowe, 2017).This means that while we might have some sense of what happens in the classroom and what students think or feel about what happens in the classroom, we have very little sense about how these are connected. Moreover, existing literature does not consistently explain how issues of identity, such as gender identity and sexual orientation, influence how students work together and experience small group work in the classrooms (Bianchini, 1997;Chiu, 2000a;Cooper & Brownell, 2016;Esmonde et al., 2009;Sullivan et al., 2018). ...
... In particular, most studies that consider the effects of small groups in classrooms have either used only during-instruction data such as observations and assessment scores (Bianchini, 1997;Chiu, 2000a;Sullivan, Ballen, & Cotner, 2018)or post-instruction data such as interviews and surveys (Cooper & Brownell, 2016;Esmonde, Brodie, Dookie, & Takeuchi, 2009;Theobald, Eddy, Grunspan, Wiggins, & Crowe, 2017).This means that while we might have some sense of what happens in the classroom and what students think or feel about what happens in the classroom, we have very little sense about how these are connected. Moreover, existing literature does not consistently explain how issues of identity, such as gender identity and sexual orientation, influence how students work together and experience small group work in the classrooms (Bianchini, 1997;Chiu, 2000a;Cooper & Brownell, 2016;Esmonde et al., 2009;Sullivan et al., 2018). ...
... Interactions between social factors and group work. While past research establishes the effectiveness of having students work in small groups as an instructional strategy, other research establishes ways in which social factors can influence the experience and outcomes of working in groups for students as individuals and as participants in groups (Bianchini, 1997;Chiu, 2000a;Cooper & Brownell, 2016;Esmonde et al., 2009;Heller & Hollabaugh, 1992;Laursen et al., 2014;Sullivan et al., 2018;Theobald et al., 2017). The findings of these studies are not always consistent -particularly in regards to issues of gender and group work -but there are more consistent trends in the literature around friendship and perceived academic ability. ...
Thesis
Full-text available
To address the ongoing labor shortage for jobs in science, technology, engineering, and mathematics (STEM) fields, many different initiatives have been undertaken by practitioners, instructors, and researchers. Two major ones have been efforts to improve undergraduate mathematics instruction and to increase diversity and inclusiveness in STEM fields, including with regards to gender identity and sexual orientation. One major ongoing shift in undergraduate mathematics instruction is a shift to increase active learning, often through tasking students to engage in collaborative problem solving in small groups. It is known that active learning strategies like these improve student outcomes over the use of lecture alone. However, there is much less research considering how the social nature of group work can affect student experience in their undergraduate mathematics classes that use it. Social factors outside of the mathematical content could be expected to play a role when learning through group work, an inherently social activity; moreover, these factors could play a greater role for students who have traditionally been excluded from STEM environments. To better understand how social factors may influence student participation and experience in small group work in undergraduate mathematics classrooms, a study was conducted that incorporated video-taped in-class observations of students working in small groups along with stimulated recall interviews of students individually. A taxonomy by Chiu (2000b) was used to interpret, code, and analyze actions taken by the participants in group work, with interviews coded in terms of what ideas students discussed in response to selected interactions. From analysis of the observations and interviews, three main findings are drawn. First, social unfamiliarity among group members can negatively influence a student’s experience within a group and the group’s overall ability to collaborate. Second, student gender identities and beliefs about how gender and mathematics are related can also play a role, especially when students are unfamiliar with each other, although these data do not suggest exactly when or how this can happen. Third, students may work together ways that are socially productive, but are not mathematically productive. These takeaways broaden our understanding of how groups work in undergraduate mathematics classes while also setting some clear directions for future research on this topic.
... Moreover, their analysis of group observations, student interviews and focus groups revealed a range of other influences on group interaction such as participation, group roles, tasks and cohesion, and conflict avoidance. Esmonde et al. (2009) examine group work in a heterogeneous (based on mathematical understanding, friendship, grade level, or social identities) urban high school mathematics classroom and present a case study of the ways in which race, gender, and other social identities might influence the nature of group work. They use the term 'socially constructed identites' or 'social identites' to refer to social categoriesincluding, but not limited to race, ethnic, or gender categoriesthat are often imposed on people within a particular context. ...
... The present study examines the influence of social categories, which are extensions of social identities that are relevant in face-to-face interactions among students during their group work. The selection of age, gender, nationality, ethnicity, religion, mother tongue, and English language ability as the social categories for this study was informed by studies conducted by Clarke et al. (2007), Esmonde et al. (2009), andItuarte &Davies (2007), and based on the reviews of the concept of social categories in the work of Tajfel (1981Tajfel ( , 1982, Hogg andAbrams (1988, 1993), Jenkins (2008aJenkins ( , 2008b. ...
... However, this specific paper reports on which of the social categories of age, gender, nationality, ethnicity, religion, mother tongue, and English language ability that were identified for study impact on students' preferences in self-selecting groups. The researcher employed the following research questions: Which of the social categories identified for the study, as informed by work by Clarke et al. (2007), Esmonde et al. (2009), andItuarte &Davies (2007), namely those of age, gender, nationality, ethnicity, religion, mother tongue and English language ability impact on the formation of self-selected groups? ...
Article
Full-text available
When students of multi-ethnic and multi-lingual Malaysians and international students from culturally diverse backgrounds work together in group assignments, negotiations on whom to include or exclude would take place during the formation of self-selected groups. Social categories appear to influence students’ choices in group membership during these face-to-face interactions. Set against the backdrop of Intercultural Communication, the objective of this study is to investigate the influence of the specific social categories of age, gender, nationality, ethnicity, religion, mother tongue, and English language ability on self-selected group work formation. Relying on a basic quantitative approach for a case study, a set of questionnaires with a 5-point Likert-type scale was developed. Participants were asked whether or not they prefer to work with other participants from the same or similar social categories. The study found that in the formation of self-selected groups, the social categories of age and English language ability are significantly influential. This study affirms that social categories influence students’ choices in self-selected group work formations.
... The following were the research questions posed about the possible influence of social categories on the group work interactions of the participants in the study: 1. Which of the social categories identified for the study, as informed by the work of Clarke et al. (2007), Esmonde et al. (2009), andItuarte &Davies (2007), namely those of age, gender, nationality, ethnicity, religion, mother tongue and English language ability impact on the formation of self-selected groups? 2. How do these social categories influence interactions during group work? 3. What are the implications of this study, if any, for IC? ...
... These multiple methods served to triangulate the data collected for the study. Holliday (1999) Kramsch (1988, 2012 Communication Gudykunst (1988) Jandt (2010) Group work Clarke et al. (2007) Esmonde et al. (2009) Ituarte & Davies (2007 Language & IC Gudykunst & Kim (1997) Ting-Toomey & Chung (2005) Martin & Nakayama (2013, 2014) Nair-Venugopal (2003, 2015 Piller (2007,2011,2012) Identity Hall, S. (1996) Bucholtz & Hall (2003 Social identity Tajfel (1981Tajfel ( , 1982 Jenkins (2008a) Social categories Hogg & Abrams (1988) Pragmatics Thomas (1995) Yule (1996) Face Goffman (1967) Politeness Theory Brown & Levinson (1987) Rapport Management Spencer-Oatey 2008) Journal of Language and Communication, 8(2),180-205 (2021) The questionnaire was administered to first establish which of the social categories identified for the study had an impact on the formation of self-selected groups. The participants were asked as to respond to a 5-point Likert-type scale on whether or not they preferred to work with other participants from the same or similar social categories of age (Q1), sex/gender (Q2), nationality (Q3), ethnicity (Q4), religion (Q5), mother tongue (Q6), and English language ability (Q7). ...
Article
Full-text available
Intercultural Communication as a subfield, this paper presents the results of examining the influence of the specific social categories of age, gender, nationality, ethnicity, religion, mother tongue, and English language ability on the formation of self-selected groups and group work interactions of students in a private Malaysian university. An interpretive conceptual framework was used to highlight how these social categories influenced the face-work (Goffman 1967) and politeness (Brown & Levinson, 1987) strategies employed to manage rapport (Spencer-Oatey, 2008) in order to achieve successful group work. The study involved a total of 193 culturally diverse students in the Faculty of Management in the private university. Using an ethnographically informed qualitative approach (Hammersley, 2006; Neuman, 2011) the participants were observed during group work sessions and the interactions audio-taped. The data corpus comprised transcripts of audio-taped recordings, close-ended survey questions, self-reports from post-hoc interviews, feedback from expert informants and field-notes from direct participant observations. The study found that age and English language ability are significantly influential in the formation of self-selected groups, while age, gender, mother tongue, and English language ability were salient and influential in face-to-face group work interactions. This study contributes towards an understanding of the influence of social categories in intercultural group work interactions within the context of a Malaysian university.
... [4,7]. Therefore research on mathematical identity has become a research trend over the last ten years [8,9]. This is done because identity research is able to reveal more deeply a person's relationship with mathematics. ...
... Mathematical identity is a context-bound concept. This context allows a person to have many narrative identities connected to a different context or social relationship; for a mathematical identity, the context is related to activities that involve a person with mathematics [5,8]. Therefore it is essential to follow the development of a person's mathematical identity with regard to their interactions and experiences in society in which they have previously participated. ...
... Amongst these barriers, researchers identify low teacher expectation of those in lower groups to engage mathematically (Anthony & Hunter, 2017;Marks, 2014;McGillicuddy & Devine, 2018); the pressure of accountability regimes (Alderton & Gifford, 2018;Bradbury, 2019;McGillicuddy & Devine, 2018) and the need for practice change to be supported by significant professional development (Anthony & Hunter, 2017;Bradbury, 2019). Reluctance to abandon existing ability grouping also reflects concerns expressed by teachers (McGillicuddy & Devine, 2018) and pupils (Esmonde, Brodie, Dookie, & Takeuchi, 2009) that higher attainers will be "held back" by mixed attainment working. Moreover, as Marks (2013) cautions, change to practice must be accompanied by change to thinking; removal of ability grouping structures does not immediately change pre-existing expectations of performance or beliefs about pre-determined ability. ...
... Indeed, data presented here demonstrate the role of the HA pupil in stimulating a conjecture later challenged by the LA pupil, or in beginning a line of thinking subsequently further developed by the LA pupil. However, this paper does argue that the HA pupil's contributions are not the only source of benefit for either pupil; furthermore, data does not support concerns voiced by teachers and pupils (Esmonde et al., 2009;McGillicuddy & Devine, 2018) that HA pupils will be held back by working with LA peers. LA pupils in Tereshchenko et al.'s (2019) study believed that they could contribute to mixed group mathematics working and this paper shows that in the primary classroom, this is indeed the case. ...
Article
Full-text available
Existing research establishes that lower attaining pupils derive mathematical learning benefit from working in mixed attainment groupings. However, gains for lower attaining pupils are seen to derive from the contributions of higher attaining peers; evidence of the contributions that lower attaining pupils make to mixed attainment activity is currently lacking. This study contributes evidence of the merits of mixed attainment working through its focus on the mathematical contributions of lower attaining primary pupils to mixed attainment pair activity. It draws on the construct of mathematical noticing and focuses on the development of pupils’ noticing of mathematical pattern, structure and property. Close video analysis of pupils’ speech and action during paired activity establishes that primary school mixed attainment working can produce bi-directional benefits, with lower attaining pupils making important contributions to task progress and contributing mathematical insights in advance of and beyond those of their higher attaining partners.
... Our findings extend previous research on how mathematics teaching in P-12 settings can perpetuate a culture of exclusion (Louie, 2017) which marginalizes race-and gender-minoritized mathematics learners (e.g., Esmonde et al., 2009;Nasir & Hand, 2008). While research has documented how K-12 mathematics teachers often lack readiness to critically examine issues of race in mathematics teaching (cf., Gutiérrez, 2013), limited research has investigated how such issues arise in undergraduate teaching. ...
Article
Background: Calculus instruction is underexamined as a source of racialized and gendered inequity in higher education, despite research that documents minoritized students’ marginalizing experiences in undergraduate mathematics classes. This study fills this research gap by investigating mathematics faculty’s perceptions of the significance of race and gender to calculus instruction at a large, public, historically white research university. Methods: Theories of colorblind racism (Bonilla-Silva, 2006) and dysconsciousness (King, 1991) guided a critical discourse analysis of seven undergraduate calculus faculty’s perceptions of instructional events. Findings: Our analysis revealed two dominant discourses: (i) Race and gender are insignificant social markers in undergraduate calculus; and (ii) Instructional events can be objectively deemed race- and gender-neutral. We illustrate how calculus faculty varyingly engaged these colorblind discourses and discourses that challenged such conceptions of instruction. We also highlight how faculty dysconsciousness in reports of instructional practices reflect potential operationalization of dominant discourses that reinforce colorblind racism. Contribution: With limited research on faculty perspectives on racial equity in mathematics, our study documents how color-evasive, gender-neutral discourses among mathematics faculty shape orientations to instruction that reinforce the gatekeeping role of calculus in STEM higher education. Implications are provided for race- and gender-conscious undergraduate mathematics instruction and faculty development.
... They concluded that these social boundaries (categorisation) should be challenged in order to promote pro-social learning among students.  Esmonde et al. (2009) found that 'socially constructed identites' or 'social identites ' -including, but not limited to race, ethnic, or gender categorieswere often imposed on people within a particular context. In a classroom setting, these social identities were at play and influenced students' opportunities to learn. ...
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Communicating appropriately in a target language (English language) requires both ESL Malaysian learners and their counterparts Arab EFL learners to develop linguistic and pragmatic awareness in the target language. One aspect of such development is their use of linguistic hedges to modify their speech acts and realize politeness. However, little attention has been given to investigate these learners’ linguistic and pragmatic use of these devices. The purpose of this study is to fill this gap in the literature by conducting a study that examines the use of hedges in relation to politeness between these two groups of learners while exchanging their opinions in focused group discussions created on WhatsApp application. To this end, the current study used a descriptive design that employed quantitative and qualitative methods to identify the types, frequency, and pragmatic functions of hedges in relation to politeness. The sample consisted of four EFL Arab learners and five Malaysian ESL learners who study English in a Malaysian university. The data collected in forms of comments by means of focused group discussions were coded and analyzed based on Fraser’s (2010) Taxonomy of English Hedges. They were then uploaded to Excel to find the frequency and percentages of the types of hedges used. This was followed by a detailed pragmatic analysis based on Brown and Levinson’s (1987) Politeness Theory. The findings showed that both types of learners use hedges in stating their opinions. However, they use different categories and hedges types and realize politeness differently.
... Following this initial assignment, the instructor considered each group individually, making small changes to increase students' comfort level and group functioning. For example, Kelly worked to ensure that there were no groups with only one woman or one student of color (Dasgupta et al., 2015;Esmonde et al., 2009), and that students who were concerned about their anxiety or shyness were grouped with other students who would likely be able to accommodate those concerns. The latter changes were made based on knowledge of student personalities and needs gathered via students' written reports, informal classroom observations, and previous group exam interactions. ...
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... Given the inherently social nature of group work, there are a number of issuesidentity, friendship, perceived academic ability, to name a fewthat could be expected to influence how students interact and their experiences. Indeed, work at the secondary level and in other disciplines suggests as much (Bianchini, 1997;Eddy, Brownell, Thummaphan, Lan, & Wenderoth, 2015;Esmonde, Brodie, Dookie, & Takeuchi, 2009;Theobald, Eddy, Grunspan, Wiggins, & Crowe, 2017). This study explored how these factors might influence students' interactions within groups through observations of small groups solving math problems in the undergraduate math classroom and post-observation interviews with individual students. ...
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This paper discusses the small groups literature on status organizing processes in decision-making groups whose members differ in external status. This literature demonstrates that status characteristics, such as age, sex, and race determine the distribution of participation, influence, and prestige among members of such groups. This effect is independent of any prior cultural belief in the relevance of the status characteristic to the task. To explain this result, we assume that status determines evaluations of, and performance-expectations for group members and hence the distribution of participation, influence, and prestige. We stipulate conditions sufficient to produce this effect. Further, to explain the fact that the effect is independent of prior cultural belief, we assume that a status characteristic becomes relevant in all situations except when it is culturally known to be irrelevant. Direct experiment supports each assumption in this explanation independently of the others. Subsequent work devoted to refining and extending the theory finds among other things that, given two equally relevant status characteristics, individuals combine all inconsistent status information rather than reduce its inconsistency. If this result survives further experiment it extends the theory on a straightforward basis to multi-characteristic status situations.
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This article discusses mathematics education research in relation to equity and current U.S. reforms. Although mathematics education researchers and reformers give attention to equity, work in this area tends to ignore relevant social and cultural issues. I begin by surveying articles on equity published in recent, mainstream education journals, highlighting the lack of attention given to social class and ethnicity. I discuss the implications of this limited research base. Specifically, I argue that current mathematics education reforms have been shaped by good intentions and existing research, neither of which offers adequate guidance to address the complexities of equity in mathematics classrooms today. Drawing from a study of social class differences in students' experiences in one reform-oriented classroom, I discuss the challenges and dilemmas inherent in sociocultural approaches to research in mathematics education and their potential contributions. I call for research from a sociocultural perspective, focusing on ways in which students from underrepresented groups can struggle when encountering particular instructional approaches, and ways in which teachers and students are able to address such struggles.